The detection of an active primary user (PU) by a secondary base station (SBS) is essential for an interweave cognitive radio (CR). This work proposes a Bayesian method for model order selection to the detection problem in a multi-PU single-SBS CR network, where the PUs and the SBS are equipped with multiple antennas. Each PU transmits separate known beacon sequences when they are active but the multiple-input multiple-output (MIMO) channels from the PUs to SBS are not known. We select a Bayesian model among potential models of the received beacon sequences to decide the number of active PUs. It is accomplished by imposing Zellner’sg-prior on the unknown MIMO channels, obtaining the Bayes factor (BF) between an alternative hypothesis and the null hypothesis, and evaluating the posterior probability from the BFs as the test statistic. The resulting BF has an analytical form in terms of the hyperparametergfrom the prior. We develop three methods to address the unknowng. The first method assigns the inverse-gamma hyperprior togand uses the expectation of BF overginstead. The second estimatesglocally which is different for each data model and the third obtains thegestimate globally which is common to all candidate models. We conduct rigorous analysis for the proposed Bayesian selectors and determine the suitable ranges for the shape and scale parameters of theg-prior. In addition, analysis shows that they are consistent in fulfilling the information and model selection criteria. Numerical results reveal that the three proposed selectors have comparable performance and outperform the baselines Akaike information criterion (AIC), Bayesian information criterion (BIC), extended BIC (EBIC), and false discovery rate (FDR) at various settings of the signal-to-noise ratio (SNR), the length of beacon sequences, and the number of SBS antennas.

This paper addresses the multistatic localization problem with the receiving sensors distributed on a rigid body (RB) whose position and orientation are not known. We propose to jointly estimate the unknown object position together with the RB position and orientation, simply called joint object and rigid body localization (JORBL), using time delay (TD) measurements from both the direct-propagation and indirect-reflection paths between the transmitters and sensors. Two scenarios are considered, one with synchronization between the sensors and transmitters and the other without. We begin by investigating the benefits of having the direct-path TD measurements compared to using the indirect-path TDs only for JORBL, in terms of estimation accuracy and minimum number of transmitters and sensors needed, through analyzing the Cramér-Rao lower bound (CRLB). Afterward, in the presence of synchronization, we propose a JORBL method by formulating a non-convex constrained weighted least squares problem and applying semidefinite relaxation to obtain the solution by semidefinite programming. The proposed method is then extended to the case without synchronization. The mean squared error analysis demonstrates that the proposed methods can achieve the CRLB accuracy for small Gaussian noise, which is further confirmed by numerical simulations.

wireless communication environment may not experience direct line-of-sight propagation whereas the number of receivers (Rxs) is often limited. We propose the utilization of only non-line-of-sight (NLoS) received signal strength (RSS) measurements observed at a single Rx to locate a target, via a positioning algorithm accounting for data association ambiguity that may occur in a real-world scenario. Considering the stochastic nature of a network geometry, tractable expressions are derived for the probability of acquiring at leastLNLoS RSS measurements during localization. In light of the computational complexity of our solution, we investigate the minimum number of RSS samples required to meet the specified localization accuracy, thereby guiding system design. Furthermore, the probability distribution of the trace of the Cramér-Rao lower bound is obtained analytically, which offers a comprehensive understanding of the fundamental limits of the single-Rx localization scheme without resorting to intensive simulations.

Moving rigid body localization requires the estimation of not only the position vector and rotation angles but also its translational and angular velocities, which leads to a very challenging problem. This paper demonstrates the feasibility and develops a semidefinite relaxation (SDR) method for locating a moving rigid body with constant translational and angular velocities using time-of-arrival (TOA) measurements only collected at several successive instants over a time period. More specifically, we analyze the localizability and determine the minimum numbers of anchors, sensors, and observation samples required for this particular problem. Afterward, beginning with a proposed model by transforming the TOA relation with the unknowns, we construct a constrained weighted least squares (CWLS) problem by introducing auxiliary variables. The CWLS problem is nonlinear and complicated to tackle owing to the large number of variables and the special orthogonal group constraint on the rotation matrix. To solve this difficult problem, we use SDR and transform it into a convex semidefinite programming problem to obtain a preliminary estimate. Subsequently, a more accurate solution is achieved through orthogonalization and refinement to compensate for the performance loss caused by approximations and relaxation. Theoretical mean square error analysis shows that the proposed method is able to achieve the Cramér-Rao lower bound performance under small Gaussian noise. Simulation results also demonstrate the effectiveness and robustness of the method proposed.

A rigid body receiver (RBR) forms a sub-sensor network that can enhance the measurements and increase the fault tolerance for localization. We address the problem of locating an object using non-cooperative illuminators in the absence of their positions and time stamps, with the time measurements collected by several uncoordinated RBRs at noisy positions without their orientations and synchronizations. This work proposes the use of the modified polar coordinate representation to formulate the problem, which is found to achieve higher noise tolerance than the Cartesian counterpart. We first derive the Maximum Likelihood Estimator (MLE) based on such a formulation, and then investigate a distributed approach that determines the object position local to each RBR and combines the local positions to furnish the global position estimation. The analytical study shows that it yields identical performance to centralized processing when the observations are Gaussian and uncorrelated among the RBRs. Closed-form and generalized trust region subproblem solutions for distributed localization are developed, together with analysis and simulations to support the optimum performance.

When we try to locate an object in a crowded urban area or an obstacle-rich environment, direct line-of-sight (LOS) propagation is usually absent and the Global Navigation Satellite System (GNSS) is often denied. In such a difficult scenario, we employ a moving transceiver that exhibits LOS propagations to connect the object and each sensor to determine its location. On the other hand, the transceiver positions and velocities are not known due to unreliable GNSS signals, which creates an extra level of challenge to the problem. By collecting the time delay and angle-of-arrival (AOA) sensor measurements with the object, two methods are proposed to address this localization problem. The first solution is efficient in computation; it linearizes the measurement model and obtains the transceiver parameters and object position by two linear weighted least squares (LWLS) estimators. The second method is resilient against large measurement noise; it solves the problem using semidefinite programming optimization by applying semidefinite relaxation. Both solutions are suboptimal due to the linearization or relaxation errors and they are refined by a separate LWLS estimator to improve the accuracy. Additionally, the theoretical analyses include the derivation of the Cramér-Rao lower bound, the contribution of AOA to the localization performance, the effect of the number of transceivers on the positioning accuracy, and the optimality of the proposed methods after refinement. The algorithms developed and the analyses performed are supported by simulations.

This paper investigates the joint source and sensor localization (JSSL) problem using hybrid time-difference-of-arrival (TDOA) and angle-of-arrival (AOA) measurements in a multi-source-multi-sensor scenario. Without the knowledge of sensor positions, this problem jointly estimates the relative positions of the sources and sensors together. We first conduct the localizability analysis by examining the rank of the Jacobian matrix, from which we obtain the minimum number of sources and sensors required for TDOA-AOA JSSL and the special configurations where the JSSL problem is not solvable. Next, we construct a novel parametric model by integrating the TDOA and AOA measurements, and use it to formulate a non-convex constrained weighted least squares (CWLS) problem. JSSL is then accomplished by solving the CWLS problem through semidefinite relaxation and semidefinite programming. Finally, theoretical analyses are conducted. It shows that the proposed CWLS solution is able to achieve the Cramér-Rao lower bound performance under small Gaussian noise. Moreover, it reveals that increasing the number of sources or sensors can improve the overall JSSL performance. Simulation results validate the theory and also demonstrate the capability of the proposed method for TDOA-AOA JSSL.

This paper investigates the rigid body localization (RBL) problem in 3-D using hybrid time-of-arrival (TOA) and angle-of-arrival (AOA) measurements without synchronization among the sensors on the rigid body and with the anchors, where relays at unknown positions are exploited to improve the RBL performance by generating additional measurements in the relay propagation paths and enhance the localization geometry by having the relays as pseudo receivers. The large number of unknown parameters in the localization system leads to a very challenging problem. We propose a two-step method that jointly estimates the rotation angles and position of the rigid body, the relay positions, and the synchronization offsets. In the first step, a non-convex constrained least squares problem (CWLS) is formulated based on the transformed measurement models, and it is solved by semidefinite programming (SDP) after semidefinite relaxation (SDR). The CWLS solution is suboptimal due to the loss of useful information incurred by the measurement model transformations. In the second step, a refinement procedure is followed to compensate for the performance loss by solving a linear weighted least squares problem. Apart from the solution method, the performance gain from the relays is confirmed by a theoretical analysis with the Cramér-Rao lower bound (CRLB). Moreover, the mean square error performance of the proposed two-step method is shown to reach the CRLB under the small Gaussian noise condition. Simulation results validate the theoretical studies and demonstrate accurate RBL of the proposed method.

In practical underwater environments, the uncertain and varying propagation speed of an acoustic signal makes time-based localization of an acoustic source challenging. In this paper, we utilize the isogradient sound speed profile (SSP) model with random model parameters to address the underwater source localization problem using time-of-arrival (TOA) measurements. To better reflect the real-world environments, the SSP we used is indeterminate where its model parameters have unknown random deviations from the nominal values. We propose a two-step method for locating an underwater acoustic source for this highly nonlinear challenging problem. In the first step, we propose an approximation to the TOA model that takes the sound speed dependence on the source depth into consideration, and formulate a non-convex constrained weighted least squares (CWLS) problem to obtain an initial source position estimate. In the second step, we expand the original TOA model by the second-order Taylor series at the initial estimate, and then create a different non-convex CWLS problem to obtain a refined solution. Both CWLS problems are solved by applying the semidefinite relaxation technique. Moreover, the proposed method is extended to the case where the source is not time synchronized with the sensors. Furthermore, we derive the Cramér-Rao lower bound (CRLB) for this particular localization problem and show by mean squared error (MSE) analysis that the proposed method is capable of achieving the CRLB performance under small Gaussian errors in the measurements and SSP model parameters. Simulation results confirm the effectiveness of the proposed method in achieving good localization performance.

This paper addresses the passive source localization problem using hybrid angle-of-arrival (AOA) and time-difference-of-arrival (TDOA) measurements observed by single stationary receiver at several time intervals, when the source is moving with a constant velocity trajectory. We first show that the localization problem cannot be achieved using a sequence of one kind of measurements (i.e., AOAs only or TDOAs only), but can be accomplished by using both AOA and TDOA observations together. Then we develop a parametric model by integrating AOA and TDOA, and then formulate a non-convex constrained weighted least squares (CWLS) problem that is applicable to the 2-D and 3-D scenarios for locating the source. Benefiting from the integrated model, the global solution of the CWLS problem is guaranteed without having local convergence or divergence issues. Furthermore, we conduct the mean square error analysis to validate that the proposed method is able to reach the Cramer-Rao lower bound accuracy under small Gaussian noise for the 2-D and 3-D cases. Simulation results also confirm the good performance of the proposed method.

Multidimensional scaling (MDS) is an attractive method for location-related applications due to its robustness against noise. This paper applies MDS to time difference of arrival (TDOA) localization in the modified polar representation (MPR) for integrating near-field and far-field localizations. The new MDS formulation yields a constrained optimization problem in terms of the source position. We then propose a computationally efficient and noise robust solution to solve this problem. The solution is closed-form and asymptotically unbiased. It can achieve better mean-square error (MSE) in the large noise region and possibly lower bias than the closed-form solutions from the literature, and also has attractive complexity.

We address the unified near-field and far-field time-difference-of-arrival source localization problem, in which the signal propagation speed is unknown, and the prior knowledge that whether the source is in the near-field or far-field is unavailable. Using the unified near-field and far-field model obtained by expressing the source position in the modified polar representation (MPR), two different methods, the semidefinite relaxation (SDR) method that achieves noise resilience and the two-step closed-from solution method that accomplishes low complexity, are proposed to jointly estimate the MPR coordinates and the propagation speed. For the SDR method, we express the propagation speed as the sum of a pre-selected constant and the residual to form a non-convex constrained weighted least squares problem, which is then relaxed into a convex semidefinite program by applying SDR. The two-step method obtains a coarse estimate in Step 1 by solving the quadratic programming problem without considering the relations among the variables, and then refines the coarse estimate in Step 2 by estimating the correction to compensate the error resulting from ignoring the relations. Theoretical mean square error analysis confirms that the proposed methods can reach the Cramer-Rao Lower Bound performance, which is also validated by using both simulated and real data.

This paper addresses the localization problem in unique coordinates of a far-field object. Using moving transceivers as relays for the sensor signals in reaching the object, we utilize the range measurements from the sensors through the transceivers to the object to determine its position. The transceivers have no self-localization capability such that their motion parameters are unknown. Moreover, neither transceiver relay times nor object reflection delay are known, causing additional unknown range offsets. We propose an effective three-step method for this localization problem. The first step eliminates the object position and range offsets by formulating a constrained weighted least squares (CWLS) problem and estimates only the transceiver motion parameters. Using the preliminary estimate of the motion parameters, the second step formulates another CWLS problem to obtain the object position estimate, which is used to determine the range offsets by a linear WLS estimator. Finally, a refinement procedure follows in the third step by formulating a different CWLS problem to compensate for the performance loss. To solve the non-convex CWLS problems, we introduce semidefinite relaxation to transform them into convex semidefinite programs. Both mean square error analysis and simulation results show that the refined CWLS solution is able to achieve the Cramer–Rao lower bound performance when the SNR is not very low.

This paper addresses the rigid body localization (RBL) problem using an unsynchronized sensor network, where clock offsets between sensors and anchors are present. We first investigate RBL using unsynchronized time-of-arrival (TOA) measurements to determine the necessary and sufficient conditions for this problem by analyzing the rank of the Fisher Information Matrix. When the condition is fulfilled, a constrained weighted least squares (CWLS) problem is formulated to jointly estimate the position and rotation angles of the rigid body together with the clock offsets. Besides the non-convex nature, the CWLS problem contains nonlinear constraints resulting from the orthogonality property of the rotation matrix. To solve this difficult problem, we propose to apply semidefinite relaxation (SDR) to relax it as a convex semidefinite program. Furthermore, we investigate the RBL problem using hybrid TOA and angle-of-arrival (AOA) measurements. The Cramer-Rao Lower Bound (CRLB) analysis shows better performance of RBL by hybrid TOA-AOA than by AOA only when more than one anchors are used. The CWLS problem is extended to include the AOAs and the associated SDR method is derived. Finally, mean square error analysis shows that the proposed methods are able to achieve the CRLB performance under small Gaussian noise. Numerical results confirm the theoretical analyses and validate the performance of the proposed methods.

In this paper, we address the multistatic localization problem when the transmitter position is not known and the synchronizations among the receivers and with the transmitter are not available. Aided by a calibration object, the problem is solvable where the unknown object position, the transmitter position and the synchronization errors can be estimated using the time delay measurements from the direct paths between the transmitter and receivers, and the indirect paths reflected by the calibration and unknown objects. To solve this challenging problem, we propose a three-step estimation method that obtains a different unknown in each step. Specifically, the transmitter position is estimated by formulating a constrained weighted least squares (CWLS) problem in the first step, and a linear weighted least squares estimator follows to determine the synchronization errors in the second step. Finally, the object position is estimated by formulating a different CWLS problem in the third step. The solutions are closed-form in all three steps, and thus, the proposed method is computationally efficient. Furthermore, the proposed method is extended to the more practical scenario in which the calibration object position error is present. The mean square error analysis validates that the object position estimate is able to achieve the Cramer-Rao lower bound performance under small Gaussian noise, which is further confirmed by numerical simulations.

Considering all or part of the sensors are at known positions, this paper addresses the problem of locating a 3-D moving object with a linear constant velocity trajectory using angle-of-arrival (AOA) observations. We start by analyzing the minimum number of sensors and show that at least two sensors with known positions are needed for this problem. For the case of all sensors at known positions, we formulate a weighted least squares (WLS) problem with the capability of bias reduction, called the bias-reduced WLS (BR-WLS) problem, to limit the bias caused by the transformation of the measurement models. The BR-WLS problem has a closed-form solution, and thus, solving it is very computationally efficient. For the case where only part of the sensors are at known positions, we first theoretically analyze the performance gain by including the sensors at unknown positions for localization, and then extend the proposed BR-WLS method to jointly estimate the object motion parameters and the unknown sensor positions. For both cases, we show that the localization mean square error (MSE) can reach the Cramér-Rao lower bound (CRLB) when the noise is small and Gaussian distributed. Moreover, we also derive the theoretical expressions of the residual biases for the object position and velocity estimation by the proposed solutions. Simulation results confirm the good performance of the proposed solutions and also validate the theoretical results.

This paper addresses the challenging problem of multistatic localization of a stationary object with a set of synchronized receivers, when the transmitter position is unknown and the synchronization with the transmitter is unavailable. Using the time delay measurements from the direct and indirect paths, we propose to jointly estimate the object and transmitter positions together with the clock offset. To accomplish the joint estimation, we first formulate a non-convex constrained weighted least squares (CWLS) minimization problem, where the approximations involved could introduce a large amount of estimation bias. We then extend the formulation to arrive at a bias-reduced CWLS (BR-CWLS) problem that has the ability of reducing the bias. The BR-CWLS problem, which is non-convex, is handled by applying the semidefinite relaxation technique to reach a convex semidefinite program that can be directly solved by a software package. Simulation results demonstrate the good performance of the proposed method in achieving the Cramer-Rao lower bound performance and reducing the bias.

Recent research has shown that using the 1-D signal arrival angles observed by linear arrays can locate a 3-D source in unique co-ordinates. Current methods to solve this localization problem are based on semidefinite programming (SDP) or gradient-based iteration, which are either computationally demanding or facing divergence or local convergence issues. This paper reformulates the maxi-mum likelihood (ML) estimation of the 3-D localization problem using the factor graph model, where an effective algorithm is designed through message passing. Although iterative, the proposed solution is more robust to measurement noise than the Gauss-Newton (GN) iterative solution, and the complexity is lower than the SDP solution without the need to introduce semidefinite relaxation error. Simulations validate the analytical performance and complexity, and con-firm the superiority on the convergence of the proposed solution.

The signal emitted by an acoustic source may be propagating in an environment in which the speed is not known, such as in solid or ocean. Localization of such a source through observing the signal by a number of sensors requires joint estimation with the propagation speed. This work applies the nullspace projection approach to the pseudo-linear formulation for the localization problem to obtain a closed-form solution, which is refined by error-compensation to reach the final estimation. In contrast to the methods from the literature that are either suboptimal or computationally demanding, the proposed method is both statistically and computationally efficient, and is shown analytically to achieve the Cramér-Rao Lower Bound accuracy.

The presence of radically irregular data points (RIDPs), which are referred to as the subset of measurements that represents no or little information, can significantly degrade the performance of ellipse fitting methods. We develop an ellipse fitting method that is robust to RIDPs based on the maximum correntropy criterion with variable center (MCC-VC), where an adaptable Laplacian kernel is used. For single ellipse fitting, we formulate a non-convex optimization problem and divide it into two subproblems, one to estimate the kernel bandwidth and the other the kernel center. We design sufficiently accurate convex approximation to each subproblem that will lead to computationally efficient closed-form solutions. The two subproblems are solved in an alternate manner until convergence is reached. We also investigate coupled ellipses fitting. While there exist multiple ellipses fitting methods in the literature, we develop a coupled ellipses fitting method by exploiting the underlying special structure, where the associations between the data points and ellipses are absent in the problem. The proposed method first introduces an association vector for each data point and then formulates a non-convex mixed-integer optimization problem to establish the data associations, which is approximately solved by relaxing it into a second-order cone program. Using the estimated data associations, we then extend the proposed single ellipse fitting method to accomplish the final coupled ellipses fitting. The proposed method is shown to perform significantly better than the existing methods using both simulated data and real images.

This paper proposes an objective Bayesian detector for the binary hypothesis testing problem in which the observation vectors are IID and follow multivariate Gaussian distribution under both the null and alternative hypotheses. The mean vector and covariance matrix under each hypothesis are not known, they also do not have special structure other than the covariance matrices are partially ordered in the positive definite cone with their difference positive semi-definite. An example of such a problem is the detection of Gaussian random signal in Gaussian noise. Non-informative priors are imposed on the unknown parameters for computing the marginals and evaluating the Bayes factor test statistic, where the prior for the covariance matrix is applied to the Cholesky factorization of the precision matrix. For the null hypothesis, we propose conjugate priors for the unknowns. For the alternative hypothesis, we propose uniform prior on the mean vector, and a class of objective priors that encompasses the Jeffreys, Independence Jeffreys, Geisser and Cornfield, Haar Measure and Reference priors for the precision matrix. The proposed priors enable closed-form expressions for the marginals and lead to an objective Bayes factor having the posteriors mainly governed by the data. The proposed detector is analyzed for justifying the priors used, deriving the theoretical moments, and approximating the false alarm and detection probability densities by the shifted Gamma distributions. The developed detector exhibits improvement in detection performance over the energy detector (ED) and the generalized likelihood ratio test (GLRT).

This paper investigates the elliptic localization for moving object problem from time delay (TD) and Doppler frequency shift (DFS) measurements, where the transmitter position and velocity are unknown. The transmitter is not perfectly time synchronized such that unknown offsets exist in the TD and DFS measurements. We propose to jointly estimate the object and transmitter positions and velocities and the offsets. Using the TD and DFS measurements from both the indirect and direct paths between the transmitter and the receivers, we formulate a non-convex weighted least squares (WLS) problem. Local convergence may occur when solving the non-convex WLS problem, implying that good estimate is not guaranteed. Thus, we relax the non-convex WLS problem into a convex semidefinite program by applying semidefinite relaxation (SDR). Moreover, we theoretically show that the performance can be improved by using multiple transmitters as compared to that using single transmitter, although more unknown parameters are introduced. We then extend the proposed SDR method to handle the multiple transmitters case. Finally, the mean square error analysis is provided to show that the proposed WLS method reaches the Cramer-Rao lower bound accuracy under small Gaussian noise condition. Simulation results validate the theoretical analysis and show the superior performance over the existing methods.

The motion of sensors during the measurement period, if not accounted for, can degrade significantly the localization accuracy. This paper investigates the sensor motion effect for the positioning of an object, using angles of arrival only or together with time of arrival measurements. The biases from the AOA and TOA data models when ignoring the motion effect are examined. Positioning algorithms for AOA localization and mixed AOA-TOA localization that account for the motion effect are developed by the pseudo-linear formulation. The algorithms derived include the computationally attractive closed-form estimators and the noise resilient semidefinite programming solutions. The bias coming from the pseudo-linear formulation is analyzed in detail, and it can be subtracted from the closed-form solution to obtain a bias-suppressed estimate. Simulation validates the effectiveness of the proposed solutions in achieving the CRLB performance under Gaussian noise before the thresholding effect occurs.

This paper addresses the localization of a constant velocity moving object in 3-D using angle-of-arrival (AOA) measurements. Compared with the maximum-likelihood estimator, pseudo-linear approach for AOA localization has a large amount of bias resulting from the model transformation to simplify the solution finding. This work aims at reducing the bias and developing bias-reduced semidefinite relaxation (SDR) methods for estimating the initial position and velocity of the object, in a batch or sequential manner. This is accomplished by first formulating a bias reduced constrained weighted least squares (BR-CWLS) problem from the transformed measurements, through introducing an auxiliary variable and adding a quadratic constraint. Such an intractable non-convex problem is tackled next by applying the SDR technique and relaxing it into a convex semidefinite program (SDP), which is shown to be capable of reaching the solution of the original BR-CWLS problem. For sequential estimation, we formulate a different BR-CWLS problem and utilize SDR for obtaining a sequential estimation method that updates the initial position and velocity estimates at each time step. We conduct the mean square error (MSE) and bias analyses for both estimation methods to assess their expected performance. Simulation results verify the ability of bias reduction and the good performance of the proposed methods.

This paper addresses the multistatic localization of a moving object in position and velocity using time delay (TD) and Doppler frequency shift (DFS) measurements, where the position of the transmitter is unknown and has not yet been synchronized with the receivers. Based on the TD and DFS measurements from the direct and indirect paths, we formulate a non-convex weighted least squares (WLS) minimization problem, and then apply semidefinite relaxation (SDR) to relax the WLS problem into a convex semidefinite program. Simulation results show that the proposed SDR method is able to achieve the Cramer-Rao lower bound accuracy under mild Gaussian noise condition and outperforms the existing method.

Locating a device is a basic element for many Internet of Things (IoT) applications. In particular, it often demands an algorithm having low complexity to limit the energy consumption and most important, sufficient robustness without knowing the device in the near-field for point localization or in the far-field for direction of arrival (DOA) estimation. This article proposes a new localization algorithm that can achieve the two purposes, with the theoretical analysis to validate the optimal accuracy and the real data experiment to support the promising performance. The first objective is achieved by a closed-form solution and the second is accomplished by using the modified polar representation (MPR) of the source position, based on a new formulation for the localization problem. While the MPR localization method has been introduced before, it is not sufficiently robust for IoT application to handle the large equal radius (LER) scenario or the presence of sensor position errors. The proposed algorithm uses a different MPR formulation, which is able to handle the LER scenario, sensor position errors, and has low computational complexity.

This work proposes a method to acquire the geometry of a room in terms of the size and shape by exploiting the signal propagation times of the single bound reflections (SBRs). The information of room geometry is crucial for improving localization and assisting robot navigation under complex indoor environments. The data association problem for the SBR time measurements from the same reflection surface is addressed by the minimal measurement estimator (MME) together with the density-based clustering method. A best linear unbiased estimator (BLUE) is derived to integrate the MMEs of the same surface for the room geometry estimation. Analysis shows and simulation validates that the proposed method achieves the Cramèr-Rao Lower Bound (CRLB) performance for Gaussian data model.

The performance of ellipse fitting may significantly degrade in the presence of outliers, which can be caused by occlusion of the object, mirror reflection or other objects in the process of edge detection. In this paper, we propose an ellipse fitting method that is robust against the outliers, and thus maintaining stable performance when outliers can be present. We formulate an optimization problem for ellipse fitting based on the maximum entropy criterion (MCC), having the Laplacian as the kernel function from the well-known fact that the ℓ1-norm error measure is robust to outliers. The optimization problem is highly nonlinear and non-convex, and thus is very difficult to solve. To handle this difficulty, we divide it into two subproblems and solve the two subproblems in an alternate manner through iterations. The first subproblem has a closed-form solution and the second one is cast as a convex second-order cone program (SOCP) that can reach the global solution. By so doing, the alternate iterations always converge to an optimal solution, although it can be local instead of global. Furthermore, we propose a procedure to identify failed fitting of the algorithm caused by local convergence to a wrong solution, and thus, it reduces the probability of fitting failure by restarting the algorithm at a different initialization. The proposed robust ellipse fitting method is next extended to the coupled ellipses fitting problem. Both simulated and real data verify the superior performance of the proposed ellipse fitting method over the existing methods.

Non-invasive heart rate estimation is of great importance in daily monitoring of cardiovascular diseases. In this paper, a bidirectional long short term memory (bi-LSTM) regression network is developed for non-invasive heart rate estimation from the ballistocardiograms (BCG) signals. The proposed deep regression model provides an effective solution to the existing challenges in BCG heart rate estimation, such as the mismatch between the BCG signals and ground-truth reference, multi-sensor fusion and effective time series feature learning. Allowing label uncertainty in the estimation can reduce the manual cost of data annotation while further improving the heart rate estimation performance. Compared with the state-of-the-art BCG heart rate estimation methods, the strong fitting and generalization ability of the proposed deep regression model maintains better robustness to noise (e.g., sensor noise) and perturbations (e.g., body movements) in the BCG signals and provides a more reliable solution for long term heart rate monitoring.

Elliptic localization where a transmitter actively sending out a signal to locate an object from its echo appears in many practical systems including multiple-input-multiple-output (MIMO) radars and wireless communications. In this article, the elliptic localization problem when the transmitter position is not known is addressed. We propose an effective method for joint estimation of the object and transmitter positions. Using the range measurements from the direct paths between the transmitter and the receivers together with the indirect paths through the object, we formulate a non-convex weighted least squares (WLS) minimization problem. The non-convex nature of this problem makes it difficult for an iterative search algorithm to reach the optimal solution, implying that good estimate is not guaranteed. To handle this difficulty, we propose to solve the formulated WLS localization problem by applying the semidefinite relaxation (SDR) technique, resulting in a convex semidefinite program (SDP). The proposed SDR method is then extended to the more general case when multiple transmitters at unknown positions are used and the receiver positions are subject to errors. Simulation results show that the proposed method can attain the Cramer-Rao lower bound (CRLB) accuracy under Gaussian noise and has superior performance over the existing method.

This paper addresses the rigid body localization problem using angle-of-arrival measurements. We formulate the problem as a constrained weighted least squares (CWLS) minimization problem with the rotation matrix and position vector as variables, which is a challenging non-convex problem. To approximately solve this problem, we first relax it as a convex semidefinite program (SDP), and then tighten the relaxed problem by adding some reasonable second-order cone constraints. Simulations show that the tightened SDP problem is able to reach the performance of the original CWLS problem, making its solution achieve the Cramer-Rao lower bound accuracy, when the noise level is not too high.

This paper develops an objective Bayesian detector for asserting the presence of primary user (PU) signal buried in additive noise/interference using a sequence of complex vector samples from a multi-antenna spectrum sensing system. The PU signal is zero mean Gaussian and the noise/interference is Gaussian with possibly non-zero mean and spatial correlation. No prior knowledge is available except the signal has non-zero power when present. For the noise only hypothesis, we propose a uniform prior for the mean, and a mix of the conjugate and uniform priors for the covariance matrix inverse in terms of the Cholesky factorization. For the signal presence hypothesis, we propose a class of objective priors that includes Jeffreys, independent Jeffreys, left-Haar measure and right-Haar measure priors. The test statistic is derived in closed-form and the setting of hyperparameter is devised to ensure the test is meaningful for the detection problem. Numerical results support the promising performance of the proposed detector over other state-of-the-art methods.

Accurate localization of an autonomous underwater vehicle (AUV) is essential in many applications. The motion of an AUV during the measurement acquisition period can be significant and the localization performance can suffer considerably if it is neglected. A new time delay model that accounts for the motion is proposed for moving AUV localization. The non-recursive form of the proposed model is next derived. An algebraic explicit positioning solution based on the non-recursive model is developed when the measurement noise and transponder location errors are present. Simulation results illustrate the importance of accounting for AUV motion in localization, and validate the theoretical analysis that the proposed solution can reach the Cramér-Rao lower bound (CRLB) accuracy over the small error region under Gaussian noise.

Time difference of arrival (TDOA) point positioning in the Cartesian coordinates is practical for a near-field source, and it will suffer from the thresholding effect when the source is in the far-field where only direction of arrival (DOA) can be obtained. Localization in the modified polar representation (MPR) is able to alleviate this problem, where point positioning and DOA estimation are unified into a single framework. The state-of-the-art literature only has an iterative realization of the maximum likelihood estimator (MLE) for this problem. This paper develops an algebraic closed-form positioning solution for MPR. The proposed algorithm avoids the initialization issue and is much more computationally efficient than the MLE with comparable accuracy. Simulation results validate the advocated performance.

In this paper, we consider the development of algorithms for the automatic detection of buried threats using ground penetrating radar (GPR) measurements. GPR is one of the most studied and successful modalities for automatic buried threat detection (BTD), and a large variety of BTD algorithms have been proposed for it. Despite this, large-scale comparisons of GPR-based BTD algorithms are rare in the literature. In this paper, we report the results of a multi-institutional effort to develop advanced BTD algorithms for a real-world GPR BTD system. The effort involved five institutions with substantial experience with the development of GPR-based BTD algorithms. In this paper, we report the technical details of the advanced algorithms submitted by each institution, representing their latest technical advances, and many state-of-the-art GPR-based BTD algorithms. We also report the results of evaluating the algorithms from each institution on the large experimental data set used for development. The experimental data set comprised 120 000 m2of GPR data using surface area, from 13 different lanes across two U.S. test sites. The data were collected using a vehicle-mounted GPR system, the variants of which have supplied data for numerous publications. Using these results, we identify the most successful and common processing strategies among the submitted algorithms, and make recommendations for GPR-based BTD algorithm design.

Rigid body localization (RBL) extends the traditional point positioning by determining not only the position but also the orientation of the body. This paper considers RBL using the range measurements between the sensors on the body and the outside anchors that have position uncertainties, where a calibration emitter at an inaccurate location is employed to mitigate the anchor position errors. This is a highly nonlinear constrained optimization problem as the rotation matrix defining the orientation must belong to the special orthogonal group. We first propose the use of rotation angles to parameterize the orientation, which enables the reduction of the problem to an unconstrained optimization. It is then sufficient to consider the unconstrained Cramér-Rao Lower Bound (CRLB) for analyzing the effects of anchor position errors and noisy calibration position on the localization performance, and such an analysis is prohibitive when using the constrained CRLB. We next propose and analyze three Maximum Likelihood estimators obtained from the unconstrained formulation that have different levels of approximation and complexity. We also enhance the divide and conquer and the semi-definite programming solution from the literature such that they can work with the presence of a calibration emitter and account for anchor position errors.

This paper addresses the rigid body localization problem using a convex optimization approach. We propose a semi-definite relaxation (SDR) method for locating a stationary rigid body using arrival time measurements, and extend it for moving rigid body using both arrival time and Doppler measurements. Localization of a stationary (moving) rigid body involves not only the position (and velocity) but also the rotation angles (and angular velocity), making it a challenging optimization problem with nonlinear constraints. We approximate the maximum likelihood problem with a constrained weighted least-squares (CWLS) minimization and apply SDR to obtain a coarse estimate. The orthogonalization and refinement procedures are followed next to recover the performance loss caused by relaxation and approximation. It is shown analytically that the CWLS solution can achieve the Cramér–Rao lower bound accuracy for Gaussian noise when the noise level is not significant. The simulations show that the proposed method achieves better accuracy than the previously developed methods.

This paper develops two convex relaxation solutions for the unified localization of a signal source using time difference of arrival measurements, regardless of whether the source is in the near field for coordinate positioning or in the far field for the direction of arrival estimation. The previous study on unified estimation only derived an iterative solution, which is sensitive to initialization. Albeit a coarse initialization was supplied to start the iteration, it may not be sufficient to ensure convergence to the global solution especially when the source is close to the sensors. The proposed solutions come from two novel formulations for optimization, one using the weighted least squares with the modified polar representation of the source position as variable and the other applying fractional programming with the Cartesian coordinate representation instead. Both the optimization problems are solved by first performing semidefinite relaxation and then tightening the relaxed problem by including a set of second-order cone constraints. The two formulations are created from different approaches. Nevertheless, we are able to prove that both the formulations reduce to solving exactly the same mixed semidefinite/second-order cone program and thus establish their equivalence. Furthermore, the proposed solution method is extended to the more practical scenario when sensor position errors are present. The results from both the simulated and real experiments show that the proposed method achieves almost the same performance of the iterative maximum likelihood estimator under ideal initialization.

Angles of Arrival (AOAs) are popular measurements to locate a signal source. They can yield a position if the source is near the sensors or a DOA if it is far away. Point positioning and DOA localization require different estimators and the knowledge if the source is near or far is needed. Nevertheless, such knowledge about the source range is often not available in practice. This paper first analyzes the consequences of point positioning of a distant source and DOA estimation of a near one. It next proposes a unified estimator that provides a position estimate if it is near or a DOA estimate if it is far, without requiring any prior knowledge about the range region of where it lies. The estimator is derived using the Maximum Likelihood criterion with the Gauss Newton implementation, using the modified polar coordinates to represent the source location. A preliminary solution using the semi-definite relaxation is developed to initialize the estimator. Simulations validate the performance of the proposed estimator in reaching the CRLB performance.

In this letter, we propose a method to improve the localization accuracy of a rigid body using the range measurements between the anchors and several sensors mounted on the body. Rigid body localization aims to estimate the rotation matrix and position vector of the sensor array on the body and it is a nonlinear and challenging problem to solve. Through the application of semidefinite relaxation to the original maximum likelihood formulation, we can obtain a coarse estimate of the rotation matrix and position vector that is robust to measurement noise. We next apply orthogonalization and refinement to the estimate and gain back the performance loss from relaxation and approximation. Simulation results show that the proposed method can reach the Cramér–Rao lower bound performance even at high noise levels where existing estimators cannot.

Point positioning of a signal source is feasible if it is not far from the sensors and direction of arrival (DOA) localization is only applicable if it is distant. Point positioning and DOA localization employ different estimation models and prior knowledge about the source range is often not available to decide which model is appropriate. This paper introduces the modified polar representation to unify the localization of a source using angle of arrival (AOA) regardless if it is near or far. From the Gaussian AOA measurements, we utilize the hybrid Bhattacharyya-Barankin (HBB) bound to illustrate it is not possible to obtain the Cartesian coordinates of a distant source when applying the near-field model, and derive the DOA bias of a not so distant source when using the far-field model. An iterative maximum likelihood estimator (MLE) is next derived under the modified polar representation with a single model, where the HBB bound confirms the stable behavior of the estimator regardless it is near or far. The algorithm yields a position if the source is close and a DOA if it is distant. A preliminary solution to initialize the MLE using semidefinite relaxation is also proposed. The HBB bound, the analysis and the algorithm are extended for hybrid AOA-TDOA localization.

This paper proposes a Bayesian detector for spectrum sensing in a multi-antenna cognitive radio (CR) network in which no channel state information (CSI) is available. The Bayesian approach for detection necessitates a prior distribution of the CSI in terms of the spatial covariance matrix, and unfortunately it is often improper and cannot be applied directly. We shall introduce the use of the Fractional Bayes Factor (FBF) approach to handle improper prior, which in turn yields a well-defined Bayes factor as the test statistic for detection. A number of priors of the CSI are examined and a closed-form expression for the test statistics is derived. The developed Bayesian detector is compared with those by using the conjugate priors for both hypotheses and the generalized likelihood ratio test (GLRT), and it yields considerable improvement in detection performance.

Identifying the location of a target is a fundamental application in multistatic sonar. Numerous attempts have been made to improve the accuracy, computational efficiency and robustness of target positioning. Previous studies mostly use time delay and angle measurements for localization, or time delays and Doppler shifts if relative motions exist among the transmitters, target and receivers. This paper considers the joint use of time delay, Doppler shift and angle measurements to locate a moving target. We develop an explicit algebraic solution to the problem, and illustrate the benefit of using all three kinds of measurements. The proposed solution is shown by theoretical performance analysis and confirmed by simulations to be able to reach the Cramer-Rao Bound (CRB) accuracy under Gaussian noise, when the noise level is not significant.

This paper addresses the problem of optimizing the information rate of a multiple-input multiple-output (MIMO) secondary user (SU) in an underlay cognitive radio (CR) network when channel state information (CSI) from the SU to the primary user (PU) is inaccurate. Rather than applying the commonly used interference temperature metric, the proposed SU transmit precoder limits the interference leakage rate (LR) to maintain the quality of service (QoS) for the PU. We model the uncertainty in CSI as deterministic with the Schatten norm and apply the worst-case principle to derive a robust solution. Two solution methods are proposed to address the design with the LR metric. The first simplifies the LR metric that is valid under the low interference-to-noise ratio (INR) condition and the second uses an iterative linearization technique. We demonstrate the performance of the proposed solutions by numerical simulations.

A moving target creates the Doppler effect on the transmitted signal, which can be exploited to improve the target localization accuracy in multistatic sonar that normally utilizes differential delay time measurements only. In this letter, we first examine the contribution of Doppler measurements via the Cr$\acute{\text{a}}$mer–Rao lower bound (CRLB) study, and then develop an algebraic closed-form solution for the moving target localization problem. The proposed algorithm is shown in both theory and simulation to be able to reach the CRLB performance under Gaussian noise, when the measurement error is small.

This letter focuses on locating passively a point source in the three-dimensional (3D) space, using the hybrid measurements of time difference of arrival (TDOA) and angle of arrival (AOA) observed at two stations. We propose a simple closed-form solution method by constructing new relationships between the hybrid measurements and the unknown source position. The mean-square error (MSE) matrix of the proposed solution is derived under the small error condition. Theoretical analysis discloses that the performance of the proposed solution can attain the Cramér-Rao bound (CRB) for Gaussian noise over the small error region where the bias compared to variance is small to be ignored. The proposed solution can be extended directly to more than two observing stations with CRB performance maintained theoretically. Simulations validate the performance of the proposed method.

This paper addresses the problem of precoder design that maximizes the throughput of a secondary user (SU) in an underlay multiple-input multiple-output cognitive radio network, where the channel state information (CSI) from the SU to the primary user (PU) is unavailable or inaccurate. The design maintains the quality of service for the PU through an interference amount measure in terms of the interference temperature or the leakage rate. For the case of unknown CSI, we propose an iterative adaptation algorithm by exploiting the side information in the primary communication network. For the case of imperfect CSI, we model the amount of uncertainty to be within a convex set defined by the Schatten norm and apply the maximin optimization to obtain the solution. To complete this paper, we derive the conditions on the CSI uncertainty radius under which the robust design with imperfect CSI would not perform better than the one with unknown CSI, when using the interference temperature metric. The proposed techniques are supported by numerical simulations.

This paper develops an attractive estimator for locating an object using time differences of arrival with inaccurate sensor positions in the large equal radius (LER) scenario. The estimator is developed through a geometric approach without the need of introducing an auxiliary variable. It is shown analytically to be able to reach the Cramer-Rao Lower Bound (CRLB) accuracy under Gaussian noise over the small error region when the LER condition is strong. The estimation bias resulted from the LER modeling in the absence of measurement noise is derived and it can be compensated if it is significant when the LER condition is weak. The proposed estimator is more computationally efficient than the other LER positioning estimators from the literature. To complete the study, a detector for the LER scenario is included.

This paper proposes an estimator for refining the inaccurate positions and clocks of the anchors during the localization and synchronization of a sensor node in a wireless sensor network. It solves the highly nonlinear problem in closed-form through parameter transformation and multi-stage weighted least squares processing. Theoretical analysis and simulation studies show that the proposed estimator is able to provide the CRLB accuracy for both the sensor node and the anchors under reasonable amount of Gaussian errors.

Locating a signal source using angles of arrival (AOAs) in a wireless sensor network is attractive because it does not require synchronization of the distributed receivers as in the time-based localization. A challenge for AOA positioning is that the solution tends to have a large amount of bias compared with the maximum-likelihood estimator when using the computationally attractive pseudolinear formulation. AOA localization has been well studied for the 2-D situation, and relatively few developments are for the more practical 3-D scenario. This paper proposes a closed-form solution for 3-D localization using AOAs that can handle the presence of sensor position errors, achieves asymptotically the CRLB performance, and maintains a bias level close to the maximum-likelihood estimator. Theoretical analysis and simulation studies corroborate the performance of the proposed estimator.

Computationally efficient source location solutions from TOAs or TDOAs require the squaring of the measurements before optimization. The squaring operation changes the characteristics of the measurements and causes degradation in the localization accuracy, unless proper weightings are applied when forming the cost function for minimization. The previously developed weighting values are useful for measurements with accurate sensor positions only. This paper extends the study and derives the weightings when the sensor position uncertainties are present such as in sensor networks. The resultant cost functions for TOA and TDOA positionings are analyzed and the performance accuracy is shown to attain the CRLB asymptotically under Gaussian noise. Simulations validate the performance of the new cost functions and the theoretical investigations.

Voiced speeches have a quasi-periodic nature that allows them to be compactly represented in the cepstral domain. It is a distinctive feature compared with noises. Recently, the temporal cepstrum smoothing (TCS) algorithm was proposed and was shown to be effective for speech enhancement in non-stationary noise environments. However, the missing of an automatic parameter updating mechanism limits its adaptability to noisy speeches with abrupt changes in SNR across time frames or frequency components. In this paper, an improved speech enhancement algorithm based on a novel expectation-maximization (EM) framework is proposed. The new algorithm starts with the traditional TCS method which gives the initial guess of the periodogram of the clean speech. It is then applied to an${L_1}$norm regularizer in the M-step of the EM framework to estimate the true power spectrum of the original speech. It in turn enables the estimation of the a-priori SNR and is used in the E-step, which is indeed a logmmse gain function, to refine the estimation of the clean speech periodogram. The M-step and E-step iterate alternately until converged. A notable improvement of the proposed algorithm over the traditional TCS method is its adaptability to the changes (even abrupt changes) in SNR of the noisy speech. Performance of the proposed algorithm is evaluated using standard measures based on a large set of speech and noise signals. Evaluation results show that a significant improvement is achieved compared to conventional approaches especially in non-stationary noise environment where most conventional algorithms fail to perform.

Modern applications use mobile or randomly deployed sensors whose positions are not precise when locating a signal source. An estimator would require statistical knowledge of the sensor position errors to reach the optimum localization performance. Further accuracy improvement necessitates a calibration emitter whose position is known exactly to correct the sensor positions. Under Gaussian error model, this paper shows that when the covariance matrices of the sensor position errors and the measurement noise satisfy certain relation, taking the sensor position errors into account is not necessary and a simpler estimator that pretends the sensor position uncertainties are absent is sufficient to reach the optimum performance. The performance gain from a calibration emitter depends on where it is placed. We derive the optimum calibration position by improving the Fisher information matrix of the source location estimate. The optimum position is of theoretical interest and may not be practical. A suboptimum criterion for realistic calibration emitter placement is then proposed. We shall use TOA, TDOA, and AOA localizations to illustrate the derived results. Simulations support very much the theoretical developments and performance analysis.

This paper addresses the problem of joint localization and synchronization of multiple sensor nodes simultaneously using the time stamp information from message exchanges between the sensor nodes and beacons and among the sensor nodes. Through parameter transformation and multi-stage processing, two computationally efficient algebraic solutions are developed for this challenging non-linear estimation problem. One is without message exchanges among the sensor nodes and the other is with the exchanges. Theoretical analysis shows that the performance of the proposed solutions is able to reach the CRLB accuracy for the sensor node positions, as well as the clock parameters over the mild error region. Simulation results support very well the theoretical performance of the proposed solutions.

The problem of determining the position of a sound source using mobile devices such as smart phones is considered in this paper. A novel calibration stage is developed to cancel out the time offsets of the time differences of arrival measurements. Two localization algorithms, one closed-form solution and the other iterative approach, are implemented to examine the performance of the proposed sound source localization system. Real-world experiments were conducted for 2-D and 3-D in-door localization. The experimental results validate the proposed localization technique which has acceptable localization bias and mean-square error.

Modern localization systems/platforms such as sensor networks often experience uncertainty in the sensor positions. Improving the sensor positions is necessary in order to achieve better localization performance. This paper proposes a joint estimator for locating multiple unknown sources and refining the sensor positions using TOA measurements. Rather than resorting to the traditional iterative nonlinear least-squares approach that requires careful initializations, the proposed estimator is algebraic and computationally attractive. The small noise analysis shows that the proposed estimator is able to attain the CRLB performance for both the unknown sources and the sensor positions. Simulations support the efficiency of the proposed estimator.

This paper presents Nest, a novel system using wirelessly connected smartphones to localize remote targets based on sound and image inputs. The system has four major components: image-based localization, acoustics-based localization, wireless ad-hoc networking, and middle-ware services for time synchronization and secure communication. Single-image, two-image, and TDOA-acoustics based methods have been developed and a prototype system has been implemented on Google Nexus One smartphones running Android. Experimental results show that the localization accuracies of the single-image-based and two-image-based method are around 94.6% and up to 92.1%, respectively. The localization errors of the acoustics-based method are within 80 centimeters.

The nonlinear nature of the source localization problem creates bias to a location estimate. The bias could play a significant role in limiting the performance of localization and tracking when multiple measurements at different instants are available. This paper performs bias analysis of the source location estimate obtained by the maximum likelihood estimator, where the positioning measurements can be TOA, TDOA, or AOA. The effect of bias to the mean-square localization error is examined and the amounts of bias introduced by the three types of measurements are contrasted.

A reliable estimator for speech presence probability (SPP) can significantly improve the performance of many speech enhancement algorithms. Previous work showed that a good SPP estimator can be obtained by using a smooth a-posteriori signal to noise ratio (SNR) function, which can be achieved by reducing the noise variance when estimating the speech power spectrum. In this paper, a wavelet based denoising algorithm is proposed for such purpose. We first apply the wavelet transform to the periodogram of a noisy speech signal to generate an oracle for indicating the locations of the noise floor in the periodogram. We then make use of that oracle to selectively remove the wavelet coefficients of the noise floor in the log multitaper spectrum (MTS) of the noisy speech. The remaining wavelet coefficients are then used to reconstruct a denoised MTS and in turn generate a smooth a-posteriori SNR function. Simulation results show that the new SPP estimator outperforms the traditional approaches and enables a significantly improvement in the quality and intelligibility of the enhanced speeches.

The fitting of a collection of noisy data points to a circle is a nonlinear and challenging problem, and it plays an important role in many signal processing applications. This paper proposes a semi-definite programming solution for the circle fitting problem based on the semi-definite relaxation technique. The relaxation of the maximum likelihood estimation converts a nonconvex problem to an approximate but convex one that can be solved by using the semi-definite programming method. The performance of the proposed solution is examined via simulations and compared with the K?asa method.

This letter considers the problem of simultaneously locating multiple disjoint sources and refining erroneous sensor positions using TDOA measurements. The previous work by Yang and Hoto solve this problem cannot provide optimum accuracy for the sensor positions. The proposed estimator improves the previous method so that both the source and the sensor position estimates can achieve the Cramer–Rao lower bound (CRLB) accuracy. The theoretical derivation is corroborated by simulations.

Estimating the location of a signal source based on TOA measurements is an important problem in many applications. In the presence of sensor position errors, the accuracy of a source location estimate could be degraded significantly. This paper first derives the CRLB of the source location when sensor position errors are present. It continues to develop the theoretical increase in the mean-square error of a source location estimate when the sensor position errors are ignored. A closed-form solution of the source location that accounts for the sensor position uncertainties is then proposed. Simulations are performed to validate the CRLB performance of the proposed solution when the noise level is small.

This paper proposes a new closed-form solution for the position and velocity of a moving source obtained from the time differences of arrival(TDOAs) and frequency differences of arrival(FDOAs) of its emitted signal arrived at a number of receivers. The method uses weighted least-squares formulation and imposes quadratic constraints among the positioning variables to improve performance. The proposed solution can achieve the Cramer-Rao lower bound(CRLB) accuracy for Gaussian TDOA and FDOA noise with a higher noise threshold than the previous method [7]. Simulations are included to examine the performance of the proposed solution and compare with the previous method.

The use of calibration emitters is known to be able to improve TDOA source localization accuracy when sensor positions are not accurate. This paper derives through CRLB analysis the conditions under which the sensor position errors can be completely eliminated in a source location estimate via deploying multiple calibration emitters whose positions can be erroneous. The implications on the geometric arrangements of calibration emitters to satisfy the conditions are elaborated. In particular, to fully remove the effect of sensor position errors, we need a sufficient number of calibration emitters and they together cannot lie in the same plane with any sensor. The theoretical developments are supported by simulations.

The Matching Pursuits Dissimilarity Measure (MPDM) is an effective way to to compare signals that are sparsely approximated using a Matching Pursuits method. The CAMP algorithm uses an MPDM distance measure in Competitive Agglomeration clustering to model and classify signals. The MPDM approach can only compare signals originating from a single source. Many landmine detection systems use multiple sensors to make simultaneous measurements of the same region of interest. In this paper we propose a Multimodal MPDM that can be used with CAMP to fuse signals from multiple sensors. We demonstrate the effectiveness of the Multimodal MPDM over the single sensor MPDM in improving discrimination of landmines from clutter objects.

The fitting of a number of noisy data points with a circle has found numerous applications in image processing and pattern recognition. This paper examines two methods to estimate the circle parameters: the Maximum Likelihood (ML) method and the Full-Least-Squares (FLS) method. The ML method is based on the noisy model from the data while the FLS method minimizes the geometric distance square. We first provide the iterative solutions of them using Taylor-series linearization approach. We then show analytically that FLS does not yield the ML solution. This is in contrast to previous study that the FLS method gives the same solution as ML. FLS method approximates the ML estimation only if the noise power is much less than the circle radius square. Simulations are included to support the theoretical development.

This paper applies the OWA aggregation operator to hand-held GPR data to improve the detection of landmines. Data from a number of sweeps are collected when the hand-held detector is operating in discrimination mode. The energy density spectra of the GPR signal return from individual sweeps are estimated and two OWA aggregation operations are performed to select the good quality sweeps that will be used for landmine detection. Experimental results using the real data collected from two different test sites show that the OWA operations provide significant performance improvement for landmine detection at high probability of detection.

Free-space propagation with the energy decay factor equal to two is often assumed in energy-based localization algorithms. In practice, non-ideal energy decay factors that are different from two can occur. This paper derives the Cramer-Rao Lower Bound (CRLB) for source localization with non-ideal energy decay factor and performs a sensitivity analysis of the localization algorithm presented in [6] with respect to the energy decay factor. The algorithm in [6] is found to be quite sensitive to the variations in the energy decay factor. This paper then proposes an extended algorithm for [6] that takes the non-ideal energy decay factor into account. Simulations show that the proposed solution reaches the CRLB accuracy for Gaussian noise as the signal-to-noise ratio tends to infinity.

A variety of algorithms are presented and employed in a hierarchical fashion to discriminate both Anti-Tank (AT) and Anti-Personnel (AP) landmines using data collected from Wideband Electro-Magnetic Induction (WEMI) and Ground Penetrating Radar (GPR) sensors mounted on a robotic platform. The two new algorithms for WEMI are based on the In-phase vs. Quadrature plot (the Argand diagram) of the complex measurement obtained at a single spatial location. The Angle Prototype Match method uses the sequence of angles as a feature vector. Prototypes are constructed from these feature vectors and used to assign mine confidence to a test sample. The Angle Model Based KNN method uses a two parameter model; where the parameters are fit to the In-phase and Quadrature data. For the GPR data, the Linear Prediction Processing and Spectral Features are calculated. All four features from WEMI and GPR are used in a Hierarchical Mixture of Experts model to increase the landmine detection rate. The EM algorithm is used to estimate the parameters of the hierarchical mixture. Instead of a two way mine/non-mine decision, the HME structure is trained to make a five way decision which aids in the detection of the low metal anti personnel mines.

Conventional speaker identification and speech recognition algorithms cannot deal with noisy and multiple speaker environments. For example, IBM via Voice has low recognition rates if dictation is done in a noisy environment. In order to achieve high performance in speaker identification and speech recognition, we propose an integrated approach that takes every facet of the process into account. Here we summarize some preliminary results from the application of this integrated approach to robust speaker identification and speech recognition. A real-time stand-alone software prototype has been developed to evaluate the effectiveness of the approach.

Conventional speaker identification and speech recognition algorithms do not perform well if there are multiple speakers in the background. For high performance speaker identification and speech recognition applications in multiple speaker environments, a speech separation stage is essential. Here we summarize the implementation of three speech separation techniques. Advantages and disadvantages of each method are highlighted, as no single method can work under all situations. Stand-alone software prototypes for these methods have been developed and evaluated.

Ground penetrating radar (GPR)-based discrimination of landmines from clutter is known to be challenging due to the wide variability of possible clutter (e.g., rocks, roots, and general soil heterogeneity). This paper discusses the use of GPR frequency-domain spectral features to improve the detection of weak-scattering plastic mines and to reduce the number of false alarms resulting from clutter. The motivation for this approach comes from the fact that landmine targets and clutter objects often have different shapes and/or composition, yielding different energy density spectrum (EDS) that may be exploited for their discrimination (this information is also present in time-domain data, but in the frequency domain we can remove a phase if desired and can reveal better spatial characteristics and therefore often achieve greater robustness). This paper first applies the finite-difference time-domain (FDTD) modeling technique to establish the theoretical foundation. The method to generate EDS from GPR measurements is then described. The consistency of the frequency-domain features is examined through two different GPRs that have different spatial sampling rates and frequency bandwidths. Experimental results from several test sites, based on GPR data collected over buried mines and emplaced buried clutter objects, corroborate the theoretical development and the effectiveness of the proposed spectral feature to increase the accuracy of landmine detection and discrimination.

In this paper, we present an online stochastic approach for landmine detection based on ground penetrating radar (GPR) signals using sequential Monte Carlo (SMC) methods. The processing applies to the two-dimensional B-scans or radargrams of 3-D GPR data measurements. The proposed state-space model is essentially derived from that of Zoubir, which relies on the Kalman filtering approach and a test statistic for landmine detection. In this paper, we propose the use of reversible jump Markov chain Monte Carlo in association with the SMC methods to enhance the efficiency and robustness of landmine detection. The proposed method, while exploring all possible model spaces, only expends expensive computations on those spaces that are more relevant. Computer simulations on real GPR measurements demonstrate the superior performance of the SMC method with our modified model. The proposed algorithm also considerably outperforms the Kalman filtering approach, and it is less sensitive to the common parameters used in both methods, as well as those specific to it.

The Generalized Sidelobe Canceller (GSC) efficiently realizes the optimal Linearly Constrained Minimum Variance (LCMV) beamformer and delivers excellent beamforming results by reducing directional interference and noise. However, when the input signals are contaminated by other type of noises, such as background and diffused noises, the overall performance of GSC can be even worse than the traditional delay-and-sum beamformers. In this paper, we investigate the application of the spatially adaptive multiwavelet (MWT) denoising technique to the GSC in an environment with severe diffused noise. Comparing with the traditional scalar wavelets, the multiwavelets can better characterize the noise information in the signal such that better denoising performance can be achieved. Different approaches for integrating the GSC and the multiwavelet denoiser were studied. It is found that by adding two denoisers, one to the fixed constrained part and another to the final GSC output, an improvement of 2dB in SNR can be achieved as compared with the traditional GSC method.

The localization of an acoustic source can be based on the energy measurements at a number of spatially separated microphones. This is because the amount of source energy attenuation at a microphone is proportional to the square of the distance between the source and the microphone. This paper develops an algebraic closed-form solution for the acoustic source localization problem using energy measurements, under the condition of direct line-of-sight and free space propagation. First-order analysis is applied to the proposed solution to study its performance, where only the linear noise terms are kept in obtaining the mean-square localization error. The first-order analytical results show that the proposed solution reaches the Cramer–Rao lower bound (CRLB) accuracy for Gaussian noise as the signal-to-noise ratio tends to infinity. In addition, the proposed solution provides much better accuracy than other closed-form solutions available in literature. Improvement on the proposed solution that extends its operating range beyond the threshold noise level was made by imposing nonnegative constraints. Simulations are included to corroborate the performance of the proposed method.

A variety of algorithms for the detection of landmines and discrimination between landmines and clutter objects have been presented. We discuss four quite different approaches in using data collected by a vehicle-mounted ground-penetrating radar sensor to detect landmines and distinguish them from clutter objects. One uses edge features in a hidden Markov model; the second uses geometric features in a feed-forward order-weighted average network; the third employs spectral features as its basis; and the fourth clusters edge histograms. We present the results of a large-scale cross-validation evaluation that uses a diverse set of data collected over 41 807.57$\hbox{m}^{2}$of ground, including 1593 mine encounters. Finally, we discuss the results of that ranking and what one can conclude concerning the performance of these four algorithms in various settings.

When overlaying spread spectrum (SS) transmission over a narrowband system, the performance of the spread spectrum system will be significantly degraded due to the interference from the narrowband signal. This paper proposes two computationally attractive and efficient adaptive techniques for narrowband interference (NBI) suppression in DS-CDMA system: adaptive linear predictor algorithm and adaptive NBI re-estimation algorithm. Unlike existing techniques in literature which use either estimator/subtracter approach or code-aided approach, the proposed methods combine these two approaches together and show that a much better performance can be achieved. In addition, the proposed algorithms are blind and do not require any training symbols and interference characteristics. The proposed methods not only provide faster convergence speed than the pure code-aided approach (without using a predictor and subtractor), but also give better BER performance

It is well known that sensor location uncertainty can seriously deteriorate the source location accuracy. In this paper, we provide the analysis of how much degradation the source location accuracy is expected to be with respect to the amount of sensor location error. We first derive the source location MSE when the estimator assumes no sensor location error but in fact there is. Then, the CRLB is evaluated and compared with the one without sensor location error. The analytical results allow us to decide whether a new algorithm to account for the sensor location error is necessary to improve the source location accuracy.

Partial adaptation is often used to reduce the computation and improve tracking ability of an adaptive array. In some practical situations, the received signal to be processed contains some interferences whose characteristics are known. The previously proposed partially adaptive concentric ring array is not able to utilize the prior information of known interferences without sacrificing the number of degrees of freedom, which will cause higher steady state error and smaller number of interferences that can be cancelled. We propose in this paper an improved partially adaptive concentric ring array that can utilize the prior knowledge to improve performance and maintain the same number of degrees of freedom. The proposed method designs the non-adaptive weights to remove the known interferences, and is shown to provide much faster convergence speed and lower steady state error than the original method.

Uncertainty in sensor (receiver) locations can seriously deteriorate the source localization accuracy. A localization algorithm needs to take the sensor location errors into account in order to improve source location estimate. This paper considers the localization for the position and velocity of a moving source using the time differences of arrival (TDOAs) and frequency differences of arrival (FDOAs) of a signal received at a number of sensors that have random location errors. The proposed method is based on the Taylor-series method that jointly estimates both the source and sensor locations simultaneously. Simulation results show that with a reasonable initial guess close to the true solution to begin with, the proposed method converges to the true solution and achieves the CRLB accuracy for both near-field and far-field sources.

Traditional design of critically sampled prefilters for discrete multiwavelet transform ignores the preservation of the linear phase property, which is important for many applications, such as image coding and digital communications. Balanced multiwavelets solve this problem but make the filters longer. By using linear phase filter banks, we propose a simple algorithm for the design of orthogonal symmetric prefilter banks that can be used with the discrete multiwavelet transform. The prefilter bank resulted is orthogonal and critically sampled and can preserve the approximation power of the multiwavelet as well as the linear phase property. Experimental results show that the systems using the proposed symmetric prefilter banks give better performance as compared with using nonlinear phase prefilters.

The accuracy of source localization is sensitive to the knowledge of the receiver positions. In the presence of receiver position error, a robust algorithm is necessary to improve performance. This paper presents an iterative algorithm for estimating alternately the location of an emitter and the positions of receivers using time difference of arrival (TDOA) measurements, when the receivers have random position errors. The proposed solution is based on weighted least-squares (WLS) minimization, and does not have convergence problems. The estimated accuracy of emitter and receiver locations are approaching the CRLB under Gaussian noise with small receiver position error. The performance of the proposed algorithm is evaluated through simulations.

When overlaying spread spectrum (SS) transmission over a narrowband system, the performance is significantly degraded by the narrowband signal. The paper presents an adaptive predictor approach for narrowband interference suppression in SS code-division multiple-access (CDMA) systems. Two adaptive methods are derived; one uses a linear predictor and the other a nonlinear predictor. They both use a predictor to estimate the interference which is then subtracted from the received signal to improve performance. The proposed adaptive methods are blind in the sense that they do not require training data. The proposed methods not only provide faster convergence speed than the case without using a predictor, but also give better BER performance. At a BER of 10/sup -4/ and SINR = -20 dB, the proposed methods yield 1.4 dB and 2.4 dB improvement in SNR (E/sub b//N/sub 0/) respectively.

This paper proposes an iterative algorithm for multiuser detection in uncoded synchronous code division multiple access communication systems based upon an approximate maximum a posteriori (MAP) formulation. For symbol estimation in the continuous domain, direct use of the a priori symbol distribution in the estimation process is prohibited because it is not differentiable. The proposed algorithm approximates the discrete finite alphabet symbol distribution by a sum of continuous Gaussian distributions centered at the true values of the symbol constellation. This approximation allows the development of a gradient-based iterative MAP estimator that employs the structure of the particular symbol constellation to improve estimation accuracy. Although iterative, the proposed method does not use a tentative solution from another multiuser detector. Simplifications of the proposed algorithm for constant modulus modulation and its special forms for M-ary phase-shift keying are given. Also, an optimum step size is derived to achieve fast convergence. The performance of the proposed algorithm is shown to outperform other well-known multiuser detectors such as minimum mean square error, the decorrelator, and the multistage hard-decision parallel interference canceller, especially for the near/far scenario.

The paper generalizes our previous work on BPSK (Blunt, S.D. and Ho, K.C., Proc. IEEE ICASSP, p.2313-16, 2002) to multiuser detection for constant modulus constellations in synchronous CDMA communication systems based on maximum a posteriori (MAP) estimation. The known finite alphabet of discrete transmitted symbols is approximated as a stochastic parameter with Gaussian distributions centered at the true values of the symbol constellation. This allows for the development of a MAP estimator that takes a priori knowledge of the symbol constellation into account in order to improve estimation accuracy. We examine the performance of the proposed algorithm for BPSK, QPSK, and 8PSK and compare the results with other well-known multiuser detection techniques.

To minimize the number of birdstrikes, a common method is to use microphone arrays to monitor and identify dangerous birds near the airport or some critical locations in the airspace. However, it was recognized that the range of existing ground-based acoustic monitoring devices is only limited to a few hundred meters. Moreover, the bird classification performance in low signal-to-noise environments such as airports is not very satisfactory. This paper summarizes the development of a high performance bird classification system using a hidden Markov model (HMM) and Gaussian mixture model (GMM). Experimental results verified the classification performance.

The design of an adaptive concentric ring array for broadband beamforming is a challenge due to the large number of adapting coefficients. In this paper, the concept of setting the weights among different rings to enhance the beamformer output is used to design a partial adaptive ring array for applications in nonstationary signal environment. We decompose the weights of the array into two components: the weights for each receiving element within a ring and the weights for each ring. The partial adaptive array is obtained by setting the weight for each receiving element based on a priori knowledge of the direction of arrival (DOA) of the desired signal, and only the weights for each ring are adapted in real-time. The partial array design results in faster convergence rate, better performance and smaller amount of computation compared to a fully adaptive array. Experimental results demonstrate the advantage of the partial adaptive array design.

Landmine detection is an important and yet challenging problem remains to be solved. Ground penetrating radar (GPR) is an effective sensor to detect landmines that are made of plastic or have low metal content. Most GPR signal processing algorithms apply processing in the time (depth) domain. This work proposes to use the frequency domain features from the GPR signal to improve the detection of weak plastic mines and to reduce the number false alarms due to clutter objects. The motivation comes from the fact that the energy density spectrum may be different between mine targets and clutter objects, although both may have strong GPR signal return in the time domain. Experimental results based on clutter lane data collected at a test site corroborate the effectiveness of the proposed spectral features to increase the accuracy for landmine detection.

Signal processing algorithms for hand-held mine detection sensors are described. The goals of the algorithms are to provide alarms to a human operator indicating the likelihood of the presence of a buried mine. Two modes of operations are considered: search mode and discrimination mode. Search mode generates an initial detection at a suspected location and discrimination mode confirms that the suspected location contains a land mine. Search mode requires that the signal processing algorithm generate a detection confidence value immediately at the current sample location and no delay in producing an alarm confidence is tolerable. Search mode detection has a high false-alarm rate. Discrimination mode allows the operator to interrogate the entire suspected location to eliminate false alarms. It does not require that the signal processing algorithm produce an alarm confidence immediately for the current sample location, but rather allows the system to process all the data acquired over the region before producing an alarm. This paper proposes discrimination mode processing algorithms for metal detectors (MDs), or electromagnetic induction sensors (EMIs), ground-penetrating radars (GPRs), and their fusion. The MD discrimination mode algorithm employs a model-based approach and uses the target model parameters to discriminate between mines and clutter objects. The GPR discrimination mode algorithm uses the consistency of detection as well as the shape of the detection peaks over several sweeps to improve the discrimination accuracy. The performances of the proposed algorithms were examined on a dataset collected at a government test site, and performance was compared with baseline techniques. Experimental results showed that the proposed method can reduce the probability of false alarm by as much as 70% at a 100% correct detection rate and performed comparable to the best human operator on a blind test with data collected at approximately 1000 locations.

When there is a relative motion (rm) between a signal source and a receiver, the signal arrives at the receiver with a time-scaling. Under this condition, estimating the time-difference of-arrival (TDOA) of the signal at two receivers will have large errors, if the estimator ignores the effects of the rm. The correct approach estimates both the TDOA and scale-difference-of-arrival (SDOA) between the signals of the two receivers, via the maximization of the cross-ambiguity function (CAF). This paper first derives the bias of TDOA estimation under rm, when neglecting SDOA. It then gives a new, fast method, based on the Newton root finding algorithm, for determining the maximum of the CAF. Simulation results indicate that the TDOA and SDOA mean square errors attain the Cramer Rao lower bound.

The objective of both bearings-only tracking (BOT) and Doppler-bearing tracking (DBT) is to obtain the target trajectory based on bearings, and Doppler and bearing measurements respectively, from an observer to the target. The BOT and DBT problems are nontrivial because the measurement equations are nonlinear. The pseudo linear formulation allows a linear estimator to solve for the solution, but the solution obtained is biased. This paper proposes an estimator based on the pseudo linear equations that produce an unbiased solution. The proposed method applies least-squares minimization on the pseudo linear equations with appropriate constraints on the unknown parameters. Simulations are included to illustrate the performance of the proposed estimator. The proposed estimator achieves the Cramer-Rao lower bound (CRLB) for Gaussian noise around small error region.

In this paper we address the problem of speech acquisition using a concentric circular ring array with omnidirectional microphones. The goal of our design is to achieve a specified sidelobe level in the beam pattern. A previous work by Stearns et al. (1965) proposed a method to achieve low sidelobe level for a continuous concentric ring antenna. The method assumes a narrowband signal and uses continuous ring and therefore is not suitable for speech application. This paper generalizes Stearns' method to broadband signal acquisition in 3D using a discrete ring array. A compound ring structure is employed to reduce the number of rings involved. An example is given to demonstrate our design method. The proposed design method can be used to produce a nonadaptive beamformer with a certain desirable beam pattern, or to generate the weight constraint corresponding to the white-noise beam pattern in an adaptive beamformer.

This paper proposes an iterative algorithm for multiuser detection in synchronous CDMA communication systems based on maximum a posteriori (MAP) estimation. This approach performs better than the maximum likelihood (ML) estimator due to the use of probabilistic knowledge regarding the distribution of the received signal amplitudes. We assume that for every user the PDF of the signal level value in a bit time is the average of two Gaussian distributions centered at plus and minus the mean signal amplitude. The result is a gradient-based algorithm containing a ML term that determines the “direction” of bit estimation convergence, and a prior knowledge term that improves the accuracy of the bit estimate. Due to the prior knowledge term, the algorithm reaches a minimum closer to the true received bit values and therefore realizes more accurate bit estimates and a lower bit error rate (BER) than ML alone.

Land mine detection using ground penetrating radar (GPR) is a difficult task because the background clutter characteristics are nonstationary and the land mine signatures are inconsistent. A particularly difficult scenario is the case for which a GPR is mounted on a hand held device with no position or velocity information available to a signal processing algorithm. This paper proposes the use of linear prediction in the frequency domain for land mine detection in this scenario. A frequency domain clutter vector sample is partitioned into subbands. Each subband is modeled by a linear prediction model; the current vector sample is expressed as a linear combination of the past few vector samples plus random noise. The detector first computes the maximum likelihood estimate of the prediction coefficients, and then uses the generalized likelihood method to determine if a land mine is present. The effect of subband processing on the accuracy of the detector is evaluated. Detection results are presented on data collected from a variety of geographical locations. The data sets contain over 2300 mine encounters of different size, shape and content, and a larger number of measurements from locations with no mines. The proposed detector is compared to the baseline differential energy detector. The proposed algorithm reduces the false alarm rate by 60% for all the targets at 90% probability of detection, and 70% for the deep anti-tank mines at 90% probability of detection.

This paper considers the problem of adaptive identification of a sparse system such as in echo cancellation application. A sparse system has a small number of coefficients that are different from zero. We propose the use of the Haar transform to locate non-zero coefficients such that only the non-zero coefficients will need to be adapted. The consequence is an increase in convergence speed and a decrease in computation. The performance of the proposed algorithm is evaluated through simulations.

Echo return loss and impulse response are important characteristics of an echo path for the design of echo cancellers. This paper presents methodology used to measure the impulse response and the echo return loss of an echo path. The design of the signal is described. We then present the measurement results from over 100 samplings of long distance calls which were made within North America. The measurement results are compared with the study reported by AT&T in 1972.

Two popular digital cellular standards deployed in North America are IS-95 CDMA and GSM. If these two systems are operating within the same geographic area such as a large metropolitan city, their signals can interfere with each other and cause performance degradation. This paper proposes the use of the least-squares technique in the spectral domain to identify the presence of GSM interference in a CDMA signal and to estimate the interference level if it is present. Simulation results show that the proposed method can detect interference with a signal-to-interference ratio up to 14 dB when the observation time is 20 msec and the signal-to-noise ratio is 10 dB.

When the characteristics of a digitally modulated signal are unknown, the estimation of its modulation parameters is indispensable for many digital communication applications. It is therefore very useful to establish a lower bound on the parameter estimation accuracy of a modulated signal. This paper presents the modified Cramer-Rao lower bound (MCRLB) for the modulation parameters of an offset quadrature phase shift keying (OQPSK) signal and that of a minimum shift keying (MSK) signal embedded in additive white Gaussian noise (AWGN). The modulation parameters considered are the carrier frequency f/sub c/, the carrier phase /spl theta//sub c/, the signal amplitude A and the symbol time T/sub s/. The MCRLB is dependent on the observation time, the modulation parameters and the pulse shaping function. The MCRLB is evaluated with the raised cosine and lowpass pulse shaping functions. When the roll-off factor of the raised cosine filter increases, the MCRLBs of the four parameters increase, regardless of whatever the modulation type is. In addition, the MCRLB on the T/sub s/ of a MSK signal is 3 dB lower than that of an OQPSK signal. When the bandwidth of the lowpass filter increases, the MCRLBs on f/sub c/, /spl theta//sub c/ and A of an OQPSK signal increases, but the MCRLB on the T/sub s/ of an OQPSK signal decreases. On the other hand, the MCRLBs on the modulation parameters of the a MSK signal all increase.

Direct computation of the continuous wavelet transform (CWT) using FFT requires O (Nlog/sub 2/N) operations per scale, where N is the data length. The Shensa (1992) algorithm is a fast algorithm to compute the CWT that uses only O(N) operations per scale. The application of the algorithm requires the design of a bandpass and a lowpass filter for a given mother wavelet function. Previous design method involves multi-dimensional numerical search and is computationally intensive. This paper proposes an iterative method to design the optimum filters. It computes in each iteration least-squares solutions only and does not need numerical search. The proposed filter design method is corroborated by simulations.

This paper studies the use of wavelet transform for delay and Doppler estimation between a sensor pair with relative motion between source and/or receivers. In passive sonar or radar estimation, the optimum wavelet is one of the receiver outputs and a method which scales the wavelet in discrete form is proposed. In active estimation, the maximum-likelihood (ML) estimator is shown to be equivalent to performing a wavelet transform of one of the receiving signals followed by a cross-correlation. The optimum wavelet in this case is equal to the weighting in the ML cost function. The wavelet approach combines noise filtering and scaling together, yielding a reduction in complexity. The proposed estimators were shown to approach the Cramer-Rao lower bound for delay and Doppler estimation.

A new approach to the identification of a constant amplitude signal with frequency/phase modulation is investigated. The authors model the incoming signal phase as a linear combination of a set of orthogonal vectors and use the significant coefficients as features for identification. Because of the data compression ability of orthogonal transform, a few coefficients are sufficient for signal representation, thereby reducing the processing time and system complexity. The choices of transforms and feature size are discussed. The performance of the new identifier is studied through simulations.

Closed-form solutions for locating a source based on time differences of arrival (TDOAs') of a signal to a number of spatially separated sensors are developed. The methods require only two least-squares minimization stages and are not iterative. The convergence and large computation problems associated with the conventional linear iterative solution can thus be eliminated. Position covariance matrices are shown to be identical to the Cramer-Rao lower bound when TDOA estimation error is small. Simulations are included to study the algorithms' performance and compare with existing techniques.>

The paper derives a geolocation estimator from range difference and range rate difference measurements collected by orbiting satellites. When the emitter is known to be located on the the Earth's surface, the accuracy in locating the emitter's position is improved by constraining the position estimate. An important factor associated with the constrained problem is the selection of an appropriate model of the Earth. As opposed to a spherical model, which introduces latitude dependent bias, the oblate spheroid closely resembles the Earth. Quadratic constraints formed from an oblate spheroid model of the Earth are applied in constraining the geolocation solution.>

A model to improve the performance of an adaptive tracker for delay estimation in noisy environments is proposed. The system consists of an adaptive filter and a time varying gain control. While the adaptive filter inserts an appropriate time shift to the incoming signal, the gain control will provide a proper scaling to the filter output respective to the additive noise. Both the filter coefficients and the variable gain are adjusted simultaneously by minimizing the output mean-square error according to Widrow's least mean square (LMS) algorithm. This arrangement can decouple the adaptation of time shift and noise statistics, which in turn will give rise to a better convergence characteristics of the delay. Simulation results are included to demonstrate its capability in tracking time shift accurately under noisy environments.>

An adaptive configuration is introduced for time delay estimation whereby two adaptive filters, one giving a time delay and another a time advance of equal amount, are adapted simultaneously to minimize the errors. This configuration gives a fourfold increase in convergence speed compared with the conventional single adaptive filter. Proofs for convergence and speed up are given, together with verification from simulation results.>