This paper studies tracking of an elliptical extended object with unknown but fixed lengths of major and minor axes. In most practical applications (e.g., tracking vehicles or aircraft carriers), the size of the extended object is time invariant, while the orientation and kinematics may change over time. In order to describe this problem accurately and improve tracking performance, we handle the problem by modeling the kinematics and orientation information as a state vector, and estimate it in a Bayesian framework. We model the unknown but fixed lengths of axes of the object as non-random parameters, and estimate them using maximum likelihood estimation (MLE). To evaluate the proposed approach, simulation results of an extended target tracking scenario are presented, which illustrate that the proposed modeling and estimation is effective.

Angle of arrival (AOA) and received signal strength (RSS) measurements have been commonly used in wireless localization due to easy access and simple implementation. In this paper, we investigate source localization using the AOA-only and hybrid RSS/AOA measurements, respectively. In AOA localization, we approximate the angle error using a range-related quantity. Then the optimization problem based on maximum likelihood (ML) is converted to a convex semidefinite programming (SDP) problem. In hybrid AOA/RSS localization, the ML estimator is decomposed into an RSS part and an AOA part. The AOA part follows a similar procedure as in the AOA localization. Taylor series expansion and relaxation are applied in optimizing the RSS part. These two parts are closely related through the range. The proposed methods avoid the nonconvexity in the original ML estimators for both AOA-only and hybrid AOA/RSS localization problems. Numerical examples show good performance of the proposed methods in both AOA and hybrid AOA/RSS localizations. They are close to or better than the LS methods in the literature.

This paper deals with the problem of remote state estimation with limited communication resources. We propose an online data-driven communication scheme based on cumulative innovation and derive the corresponding minimum mean square error (MMSE) estimator. The communication scheme allows to achieve a trade-off between communication costs and estimation performance. The remote estimator can improve the estimation performance based on the fact that no transmission of data indicates a small cumulative innovation. Further, it is proved that the estimator has guaranteed stability-the expected norm of the mean square error (MSE) matrix is bounded and an upper bound is given. We also derive the conditional probability of a future transmission. A simulation example is provided to illustrate the effectiveness of the proposed method.

For automotive radar-based extended object tracking (EOT), measurements are originated from the edges of the object, which usually has a regular shape. To handle this problem, this paper proposes an EOT approach, in which the object is assumed rectangular. Since a rectangular shape can be fully captured by its vertices, modeling and estimation of the extension can be reduced to those of the vertices, which are then included in the object state. Then an object being rectangular can be described as a quadratic equality constraint on the state. A measurement model is proposed with the scattering centers being assumed uniformly distributed over the observable edges of the object. It is further assumed that measurements at each time correspond to at most two adjacent boundary edges. By taking advantage of this, a data association method is proposed, in which the association events are largely eliminated. Given an association, the target state can be estimated in the linear minimum mean-square-error framework with the shape constraint treated as a pseudo-observation. The estimated state is then projected into the constraint space to improve estimation performance. Simulation results of an EOT scenario using automotive radar are given to illustrate the effectiveness of the proposed approach.

This paper studies target classification by using both feature data and kinematic measurements. The problem is tackled in a distributed architecture, where local deciders make decisions based on their local data and the center fuses local decisions, both by a multi-hypothesis sequential test. We adopt the matrix sequential probability ratio test (SPRT) for the local tests and the fusion rule. The centralized fusion and distributed fusion are compared. A lower bound on the overall average sample number of distributed fusion is presented to help determine the thresholds of the local tests to improve the performance of distributed fusion. Numerical results are provided to demonstrate the performance of our algortthm.

Most conventional multitarget tracking systems assume that in each scan there is at most one measurement for each target. This assumption is, however, not valid for over-the-horizon radar (OTHR), where a target can generate multiple measurements through different propagation modes. A typical multitarget tracking algorithm may fail in this system. For tracking multiple targets using OTHRs, we propose an approach named the decentralized multipath multiple-hypothesis tracker (DM-MHT), where uncertainties in both measurement origin and measurement mode are handled jointly. In DM-MHT, when forming the global hypotheses, each mode first forms local hypotheses separately, because the measurements generated by the same target through different propagation modes are rather different. This largely simplifies data association, and the best global hypotheses are obtained by solving a constrained integer programming problem. Then the measurements that are associated with the same track through the different propagation modes can be used to obtain the overall estimates. The overall estimates are fed back to the corresponding propagation modes to improve tracking performance. Simulation results demonstrate that the proposed approach is effective, and its computational complexity is greatly reduced compared with the existing multiple-detection MHT.

Evidence combination is typical uncertainty reasoning or information fusion in the theory of belief functions, which combines bodies of evidence stemming from different information sources. In traditional applications of evidence combination (e.g., pattern classification), given a sample, the basic belief assignments (BBAs) of different information sources are generated first, and then they are combined by a rule, e.g., Dempster's rule. In this paper, we propose a new modelized method for evidence combination. By just inputting the sample into the learned model of combination, a “combined” BBA is obtained. That is, it does not need to generate multiple BBAs for each sample for the combination. In our proposed modelized combination, we can generate different combination models with different combination rules. Experimental results and related analyses validate the rationality and efficiency of our proposed method.

This paper presents an approach to joint tracking for capturing and classification (JTCC). Target tracking for capturing requires that the estimates be within a close neighborhood of the estimand rather than have a small average error, as for traditional tracking problems. Target classification determines the class of targets. Tracking for capturing is an estimation problem while classification is a decision problem, and they are highly coupled. So JTCC is a joint decision and estimation (JDE) problem. To solve this problem jointly, we first consider a generalized Bayes risk in a previously-proposed JDE framework. By minimizing this Bayes risk, we obtain the joint solution, and its estimation part simplifies to a generalized maximum a posteriori estimator. The JTCC approach adequately addresses the coupling between decision and estimation and the specifics of tracking for capturing. To evaluate the proposed algorithm jointly, we also give a joint performance measure: joint capturing and correct classification rate. Simulation results show that JTCC outperforms the decision-then-estimation, the separate decision-and-estimation, and the conditional joint decision-and-MMSE-estimation methods in joint performance measure.

In this paper, we propose a new algorithm for a recursive implementation of constrained multiple model (MM) maximum a posteriori (MAP) estimation. The recursive procedure is formulated in a sliding window fashion, where the measurements are processed sequentially. For each recursion, an iterative alternating coordinate-ascent (ACA) maximization process and our previously developed constrained sequential list Viterbi algorithm (CSLVA) are used to find the best constrained solution (mode and state sequence estimates) within the window. Performance results from simulation of two application examples are provided to demonstrate the capabilities of the proposed method.

In this paper we consider the Gauss-Hermit quadrature (GHQ) rule for numerical integration. Since GHQ is exact for any polynomial of up to a certain degree, we propose a method to improve GHQ when the integrand is not close to a polynomial by transforming it to one approximated by a polynomial, which fits GHQ well. The problem of optimizing the GHQ rule through this transformation is formulated and solved as a nonlinear leastsquares problem with linear constraints. The proposed optimized GHQ method is compared with traditional methods for two numerical examples that show its higher accuracy. While our method is applicable in many different areas, in this paper we apply it to nonlinear filtering. A new quadrature Gaussian filter is developed and compared with several popular nonlinear filters through simulation of two nonlinear examples.

This paper studies the problem of distributed filtering for state estimation of a dynamic system by using observations from sensors in a network, and proposes a greedy gossip-based distributed filtering (GG-DF) algorithm. The sensor nodes can make estimation and work collaboratively. The information transmission across the network abides by the asynchronous gossip strategy that only two neighboring nodes are selected to communicate and exchange information with each other in each communication round. First, we propose a cost function of the estimation error of the entire network. Then, we derive our algorithm by making a greedy selection to minimize the cost. Finally, we provide performance and convergence analysis of the proposed algorithm, along with simulation results compared with existing methods.

Source localization is of great importance for wireless sensor network applications. Locating emission sources using received signal strength (RSS) measurements is investigated in this paper. As RSS localization is a non-convex optimization problem, it is difficult to achieve global optima. Many optimization methods have been proposed to relax it to a convex optimization problem. Unlike these methods, we propose a convex combination scheme. By introducing a highly accurate linear approximation of a logarithmic function, the source location is represented by a convex combination of a set of virtual anchors. Then the original problem is relaxed to be a convex optimization problem of finding the optimal combination coefficients, which can be solved efficiently using constrained least squares. To obtain the virtual nodes, we construct parallel lines and use their intersections to form a convex polygon, which covers the source location with certain probability. The vertices of the polygon are taken as the virtual nodes. Numerical examples verify the performance of the proposed method in both localization accuracy and computational efficiency.

This paper considers state estimation of stochastic systems with outliers in measurements. Traditional filters, which assume Gaussian-distributed measurement noise, may have degraded performance in this case. Recently, filters using heavy-tailed distributions (e.g., Student's t-distribution) to describe measurement noise are gaining momentum. This paper proposes a new model for the state and an auxiliary variable (related to measurement noise) as having a normal-gamma distribution. This modeling has three advantages: first, it can describe heavy-tailed measurement noise since the measurement noise is t-distributed; second, using a joint distribution naturally considers the interdependence between the state and the measurement noise; third, it helps to develop a simple recursive filter. We derive the normal-gamma filter for linear systems. Analysis shows its superiority in robustness to traditional filters. Performance of the proposed filters is evaluated for estimation and tracking problems in two scenarios. Simulation results show the efficiency and effectiveness of the proposed normal-gamma filter compared with traditional filters and other robust filters.

This paper deals with the problem of estimating the state of a discrete-time stochastic linear system based on data collected from multiple sensors with limited communication resources. For the cases of transmitting measurements and local state estimates, respectively, we design data-driven communication schemes based on a normalized innovation vector and corresponding fusion rules in the (approximate) minimum mean square error (MMSE) sense. These communication schemes can achieve a trade-off between communication costs and estimation performance. These fusion rules can allow the estimator to improve its estimate based on the fact that no transmission of data indicates a small innovation. A simulation example is provided to confirm the effectiveness of the proposed strategies.

Our newly proposed approach to extended object tracking (EOT) using extension deformation is simple and effective. This approach assumes that the extension of an object is deformed from an ellipsoidal reference extension, which unfortunately restricts its use for complex extensions. To overcome this weakness, this paper proposes that the current object extension be modeled as deformed from the one at the previous time without using a reference extension. This deformation can be fully described by the evolution of several control points on the extension. Then modeling and estimation of the extension can be reduced to those of the control points, which are treated as the state components of the extension. This new approach fits the reality better than the existing one, so a more complex or time-varying extension can be accurately described and estimated. To evaluate what is proposed, a simulation study of maneuvering EOT is carried out. The results demonstrate the benefits of the proposed approach.

For the over-the-horizon radar (OTHR) based target tracking, the reflecting height of the ionosphere, which reflects radar signals, is important. Existing methods assume that this height is exactly known a priori. In practice, however, we can only determine its range, not its specific value. To circumvent this problem, we propose to use a multiple-model approach in which each model corresponds to a specific height for OTHR tracking. More specifically, first an autonomous multiple-model multipath probabilistic data association (MPDA) tracker is proposed to estimate the target state. To handle the problem that a small fixed model set does not cover a large height range well, an expected-mode augmentation MPDA tracker is proposed, which augments a basic model set by an online expected mode of the height. Considering that the model is a nonlinear function of the height, we also present a best model augmentation MPDA tracker, in which a basic model set is augmented by a best candidate model that minimizes a Kullback-Leiber (K-L) divergence. This algorithm utilizes the nonlinear relationship of the model with the height. Simulation results demonstrate that the proposed algorithms are effective and have better performance than existing MPDA algorithm.

Detection with multiple distributions is considered. Rather than formulating the problem with multiple hypotheses, we formulate the problem in a binary hypothesis testing framework by a multiple model approach. Three classes of the Multi-Model Detection (MMD) problems are considered: simplex, compound, and mixture. Three concepts of optimality are given for these three problems, including Uniformly Most Powerful over Mixtures (UMPM) for the mixture case. The relationships between different optimality are analyzed. A method of designing a UMPM test based on Uniformly Most Powerful (UMP) test is proposed. Several examples of the UMPM test for MMD problems with Gaussian distributions are given. Simulation results are provided that verify the theoretical conclusions.

The Sequential Probability Ratio Test (SPRT) is a classical detector for problems with an unfixed sample size. Though it is optimal under some conditions, SPRT can be directly used only for a binary hypothesis with exactly known distributions. In this paper, sequential detection problem with an uncertain hypothesis distribution is considered, in which the uncertain distribution is formulated in a multi-model form. A combined SPRT algorithm is given based on the multi-model set. The detection performance and model design of the algorithm are analyzed, especially for the Gaussian distribution problem. Simulation results show that the proposed algorithm can handle the uncertain detection problem effectively.

A fault detection, identification, estimation and state estimation (FDIESE) problem involves joint decision and estimation (JDE). Decision contains detection and identification, while estimation is for fault severeness and system state. Both detection and identification are highly coupled with estimation and a fault is identified after detection. To solve this problem, an approach named nested joint FDIESE (NJFDIESE) is proposed. It considers detection and state estimation jointly first, and then does identification and fault severeness estimation jointly given the detection. NJFDIESE addresses adequately the coupling among detection, identification and estimation. Moreover, to estimate the fault severeness, which is modeled as a bounded continuous-valued random variable, a variable-structure interacting multiple-model estimator is proposed in the NJFDIESE framework. To evaluate the proposed algorithm, results of a simulation study of a flight control system with sequential actuator failures are presented. They show that the NJFDIESE outperforms the decision then estimation, the separate estimation and decision, and the existing joint FDIESE methods in joint performance.

This paper proposes a new approach for constrained multiple model (MM) maximum a posteriori (MAP) estimation through the expectation-maximization (EM) method by using our previously developed constrained sequential list Viterbi algorithm (CSLVA). The approach is general and applicable for any type of constraints provided they are verifiable. Specific algorithms for implementation are designed, and the performance of the proposed method is illustrated by simulation.

This paper addresses the shrinkage estimation problem of high-dimensional covariance matrices with low sample size data. A class of structured target matrices that include banding, thresholding, diagonal and block diagonal matrices is proposed, and an optimal oracle shrinkage coefficient is derived. To approximate the oracle estimator, an iterative method is presented and proved to be convergent. Moreover, a closed-form solution of its limit, which is guaranteed to be in the unit interval, is obtained. For the banding and thresholding target matrices with unknown bandwidth and threshold respectively, two adaptive algorithms are presented to estimate the covariance matrix, and some properties on the estimation error are discussed theoretically. Some simulations are given to illustrate the competitive performances of proposed covariance matrix estimators.

For highly nonlinear problems, the linear minimum mean-square error (LMMSE) estimation using a nonlinearly converted measurement can outperform the one using the original measurement. For a function space of measurement conversions, every function in the space can be represented as a linear combination of a basis of the space. Then the LMMSE estimator using a vector with its entries forming a basis of the space is optimal among all the estimators that are linear in the measurement conversions in the space. However, a basis of a space may consist of infinitely many functions and may be hard to determine. To solve this problem, this paper proposes a kernel based filter (KBF), which is equivalent to the LMMSE estimator using the conversion vector but is simpler, more convenient and feasible. Using deterministic sampling and the kernel trick, the KBF can be represented in kernel functions of the sampled and the real measurements provided the space is a reproducing kernel Hilbert space associated with the kernel functions. Because calculating the basis functions directly is avoided by using kernel functions, the computational complexity can be greatly reduced and it is unnecessary to get the basis explicitly. Simulation results show the effectiveness of the proposed filter.

This paper studies and formulates the problem of distributed filtering with a diffusion strategy for state estimation of a dynamic system by using observations from sensors in a network. The sensor-nodes have estimation ability and work in a collaborative manner. The information transmission across the network abides by the diffusion strategy that each node communicates only with its neighbors. First, we propose a cost function for a trade-off between accuracy and consensus. Then, we derive our algorithm based on this cost and analyze its mean-square performance. Illustrative numerical examples are provided to verify the good performance of our method.

Emission source localization and sensor registration using received signal strength (RSS) measurements is investigated. Previous studies for RSS localization assume that the sensors receiving signals are bias free, which is not the case in practice. This issue is taken into consideration in this paper for the localization problem. To avoid non-convexity of the global optimization problem for the traditional maximum likelihood (ML) or least squares (LS) estimation, we present novel semidefinite programming methods, linear least squares (LLS) and constrained LS (CLS) methods by approximating and linearizing the original model. The methods are divided into two types: URSS and DRSS. The former estimates the source location and sensor bias simultaneously while the latter estimates the sensor bias after localizing the source. Numerical examples show that our proposed methods have good performance. Some of them are close to the Cramer-Rao Lower Bound (CRLB).

Evaluating the performance of multi-target tracking with respect to tracks rather than unlabeled estimated points is important and challenging. Existing approaches assume exact knowledge of the ground truth. However, this is far from the reality. This paper proposes a method to deal with the case of unknown ground truth by measuring the difference between mock tracks and the assumed targets in the measurement space. The mock tracks are generated using the tracking results (tracks) of the algorithm. The assumed (true trajectories of) targets are extracted from the observations using the prior knowledge of the target motion. The method assigns the mock tracks to the assumed targets and then calculates the metrics. To solve the important and complex assignment problem, we propose a voting method, in which the assumed targets vote for the mock tracks. The voting rule is designed based on the prior knowledge. Incorporating the prior information and the online measurements, the proposed evaluation method makes good use of the mock data method and a voting strategy. Analysis and simulation demonstrate its effectiveness.

Distributed Kalman filters are often used in multisensor target tracking where the fusion center receives local estimates and fuses them to obtain the global target state estimate. With such a fusion architecture, each local tracker can communicate less frequently with the fusion center than the local filter update rate. The global target state estimate via track fusion is usually less accurate than that of the centralized estimator when local estimation errors are correlated and local trackers communicate to the fusion center with bandwidth constraints lower than the measurement rate. This paper focuses on the tradeoff between bandwidth and tracking accuracy for track fusion with communication constraints. We show that the performance degradation increases for track fusion on demand compared with the centralized estimator as the number of local trackers increases. We relate the steady state analysis of track fusion under bandwidth constraints to noisy Wyner-Ziv source coding problem and compare our results with the theoretical rate distortion curve of the quadratic Gaussian CEO problem. We conclude that track fusion on demand is a side-information unaware strategy while the awareness of the correlated estimation errors at each local tracker can improve the track fusion accuracy significantly.

This paper addresses the problem of designing objective functions for autonomous surveillance-target search & tracking (S&T)-by unmanned aerial vehicles (UAVs). A typical S&T mission inherently includes multiple, most often conflicting, objectives such as detection, survival, and tracking. A common approach to cope with this issue is to optimize a convex combination (weighted sum) of the individual objectives. In practice, determining the weights of a multiobjective combination is, more or less, a guesswork whose success is highly dependant on the designer's assessment and intuition. An optimal (trade- off) point in the performance space is hard to come up with by varying the weights of the individual objectives. In this paper the optimal weights design problem is treated more systematically, in a rigorous multiobjective optimization (MOO) framework. The approach is based on finding a set of optimal points (Pareto front) in the performance space and solving the inverse problem - determine the weights corresponding to a chosen optimal performance (trade-off) point. The implementation is done through the known normal boundary intersection (NBI) numerical method for computing the Pareto front. The use of the proposed methodology is illustrated by several case studies of typical S&T scenarios.

Many problems involve joint decision and estimation, where qualities of decision and estimation affect each other. This paper proposes an integrated approach based on a new Bayes risk, which is a generalization of those for decision and estimation separately. Theoretical results of the optimal joint decision and estimation that minimizes the new Bayes risk are presented. The power of the new approach is illustrated by applications in target tracking and classification.

Many problems involve both decision and estimation where the performance of decision and estimation affects each other. They are usually solved by a two-stage strategy: decision-then-estimation or estimation-then-decision, which suffers from several serious drawbacks. A more integrated solution is preferred. Such an approach was proposed in [14]. It is based on a new Bayes risk as a generalization of those for decision and estimation, respectively. It is Bayes optimal and can be applied to a wide spectrum of joint decision and estimation (JDE) problems. In this paper, we apply that approach to the important problem of joint tracking and classification of targets, which has received a great deal of attention in recent years. A simple yet representative example is given and the performance of the JDE solution is compared with the traditional methods. Issues with design of parameters needed for the new approach are addressed.

The ability to meaningfully assess performance is crucial for understanding, developing and comparing estimators. The optimality of an estimator relies on estimation criterion and there exists a significant gap between estimation criterion and application requirements, so the estimation criterion is not go for evaluating or comparing algorithms. Different viewpoints for performance comparison can help practitioners gain better insight and choose proper estimators for their applications. In this paper, two classes of relative measures of performance are investigated. First, to characterize the application requirements we propose the use of a desired error PDF. The concentration and deviation measures w.r.t. the desired one are developed to quantify the estimation performance of each algorithm. Second, we examine Pitman’s closeness as an estimation performance measure. We then propose the relative loss and relative gain as performance measures, which utilize the joint information of both estimators in all possible cases. Illustrative examples are given for these measures.

This paper addresses the problem of feature-based estimation of the 3D motion (rotational+translational) and structure of a rigid object from a sequence of 2D monocular images. A rigid object is represented by a set of junctions-groupings of line segments that meet at a single point-which has several advantages over other techniques. An overall scheme for 3D object tracking using enhanced junction detection via a modified Hough transform and state estimation using an un scented Kalman filter was developed in a previous paper. This paper focuses on a crucial part of the overall tracking scheme-the association (matching) of the predicted and observed junctions. The problem is formulated systematically as a general global assignment problem which allows for the treatment of uncertainties such as occlusion and appearance of new features. Appropriate assignment costs are proposed that account for junction topology and geometry. In addition, a general convex programming approach for two and multiple frame junction matching is also proposed. Simulation results illustrating the accuracy of the junction association algorithms as well as the over all object tracking scheme are provided. Overall, the approach demonstrates that well established data association methods developed for "point" multitarget tracking can, after appropriate adaptation, be very useful for tracking rigid objects

For pt.I see ibid., p.Z001330-7 (2006). Many estimators and filters provide assessments of their own estimation error. Are these self-assessments trustable? What is the degree to which they are trustable? This is Part II of a two-part series that provides answers to some of these questions, referred to as the credibility of the estimators. It proposes several tests for credibility and a test-based solution to the problem of comparing estimators' credibility. Numerical examples are provided to illustrate the utility and effectiveness of the proposed tests

Most estimators and filters provide assessments of their own estimation error, often in the form of mean-square error. Are these self- assessments trustable? What is the degree to which they are trustable? This is Part I of a two-part series that provides answers to some of these questions, referred to as the credibility of the estimators. It formulates the concept of credibility, proposes tests for MSE-credibility, and discusses their superiority to the existing test. Numerical examples are provided to illustrate the utility and effectiveness of the proposed tests and the drawbacks of the existing test

Many estimators and filters provide assessments (e.g., MSE matrices) of their own estimation errors. They are, however, obtained based on simplifying assumptions that are not necessarily valid. Then the questions are: Are these self-assessments trustable? How trustable are they? We referred to these problems as the credibility of the estimators/filters. Solid technical answers to the first question are provided in two companion papers for this conference based on statistical hypothesis testing. Complementary to those, we answer the second question in this paper by proposing a family of metrics, called noncredibility indices (NCI) and inclination indicators (I2), that measure how credible various self-assessments are. We show that the NCI and I have many desirable properties and are more appropriate than a bunch of possible alternatives and by far superior to a heuristic measure currently in use explicitly or implicitly. We also provide simple numerical examples to illustrate the application of the metrics proposed