Autonomous path planning for radar and sonar sensing faces significant challenges arising from dynamic targets, obstacle occlusions, and low signal-to-noise (SNR) conditions. We propose a hierarchical sensor scheduling framework that combines a long-horizon strategic planner, based on the Rapidly-exploring Random Tree star (RRT*) algorithm, with a fast-adapting tactical planner. Efficient coordination of the two planners is achieved via a novel message passing mechanism, enabling guidance of the sensor out of complex environments while maintaining effective target tracking. Additionally, we introduce an RRT* rerooting strategy that significantly reduces computation time and so expedites the update of the strategic plan. Extensive simulation results demonstrate that our proposed fusion approach outperforms conventional stand-alone short-term and long-term planners in challenging scenarios and low-SNR regimes,

We present a sensor scheduling algorithm to plan the motion of multiple autonomous platforms for cooperative tracking of targets within a region that contains obstacles and occlusions. The platforms have kinematic constraints and their sensors have restricted field of view and range. The proposed algorithm is a variant of the Rapidly exploring Random Tree star algorithm (RRT*) that has been adapted to the problem of determining paths for multiple independent kinematically constrained platforms to optimise their tracking performance. To guide the scheduling algorithm, we define a tracking cost based on the Posterior Cramér Rao Bound (PCRB) derived from the predicted positions of the platforms and targets. Through simulations of generated paths, we show that the algorithm generates rational plans for tracking targets and that the tracking cost accurately predicts the realised performance of the platforms.

Extensive deployment of wireless infrastructure provides an alrernative ability to locate smart phones in indoor environments by the use of received signal strength (RSS). This low-cost technology is, however, susceptible to environmental distortions, requiring sophisticated signal processing. In this paper, we propose to design a Viterbi algorithm under a double-layer hidden Markov model (DHMM) for reliable smartphone user tracking. Use of a batch processing scheme enables the DHMM Viterbi algorithm to effectively make use of auxiliary information such as room topology and user orientation for estimating the most likely user location sequence (route). Comparisons between the proposed Viterbi algorithm and an existing filtering algorithm from a theoretical perspective are also conducted. Experimental results show that use of the Viterbi algorithm is able to provide more reliable indoor positioning results.

We consider an instance of a radar jamming countermeasure problem, where the radar and the jammer have uncertainty about the radar environment (for instance, about the noise variance and the radar cross section variance), and they have to account for these uncertainties with statistical priors. The radar-jammer interaction is modelled as a two-player zero-sum repeated Bayesian game (also called an incomplete information game). We discuss the computation of the optimal strategies and present numerical results that illustrate the optimal strategies in an example.

Probabilistic logics combine the ability to reason about complex scenes, with a rigorous approach to uncertainty. This paper explores the construction of probabilistic spatial logics through the combination of established qualitative spatial calculi together with Markov logic networks (MLNs). Qualitative spatial calculi provide the basis for automated representation and reasoning with complex spatial scenes; MLNs provide a rigorous basis for handling uncertainty and driving probabilistic inference. Our approach focuses specifically on the combination of an uncertain knowledge base with a certain spatial reasoning rule-base. The experiments explore how uncertain knowledge propagates through certain qualitative spatial inferences, using the specific example of reasoning with cardinal directions. The results provide a template for probabilistic qualitative spatial reasoning more generally, with applications to a wide range of common scenarios for situational awareness and automated reasoning under uncertainty.

Location-based services (LBS) such as LoRa geolocation are important aspects of IoT applications. In this article, we propose a hierarchical clustering-based technique for urban vehicle localization using received signal strength indicator (RSSI) measurements in a public LoRaWan network. The solution relies on a two-layer hierarchy: the first layer consists of a$K$-Means clustering to partition a large urban area into several regions based on geographical coordinates of the datapoints. A coarse localizer utilizes kernel density estimation to model the received signal distribution of each gateway and determine in which the most probable regions of interests the vehicle is located, followed by a finer localization step at the second layer. For each region, reference points are grouped based on the similarity between the gateway coverage vectors. A spatial kernel-based fingerprint method that adopts spatial co-location patterns between neighbors is introduced to provide support for further fine granularity positioning within each region. The Kullback–Leibler divergence is used to measure similarities between observations and fingerprints, and the final position estimation is based on a weighted kernel regression model. The system is evaluated using a publicly available LoRaWan data set collected in large urban areas in the city of Antwerp, Belgium. We are able to achieve a median error of 158.41 m and a mean error of 346.03 m based on the raw LoRa RSSI data, and it is reported as the best accuracy based on the same data set in the literature.

Edge computing is an indispensable technology that overcomes delay limitations of cloud computing. In edge computing, computational resources are deployed at the network edge, and computational tasks and data of end terminals can be efficiently processed by edge nodes. Considering the computational resource limitations of edge nodes, collaborative edge computing integrates computational resources of edge nodes and provides more efficient computing services for end terminals. This article considers a computation offloading problem in collaborative edge computing networks, where computation offloading and resource allocation are optimized by means of a collaborative load shedding approach: a terminal can offload a computing task to an edge node, which either can process the task with its computing resource or further offload the task to other edge nodes. Long-term objectives and long-term constraints are considered, and Lyapunov optimization is applied to convert the original nonconvex computation offloading problem into a second problem that approximate the original problem and it is still nonconvex but has a special structure, which gives rise to a new distributed algorithm that optimally solves the second problem. Finally, the performance and provable bound of the distributed algorithm is theoretically analyzed. Numerical results demonstrate that the distributed algorithm can achieve a guaranteed long-term performance, and also demonstrate the improvement in performance achieved over the case of computation offloading without collaborating edge nodes.

This paper optimizes path planning for a trunk-and-branch topology network in an irregular 2-dimensional manifold embedded in 3-dimensional Euclidean space with application to submarine cable network planning. We go beyond our earlier focus on the weighted costs of cables (cable laying cost, resilience, design level and repair rate) to include the cost of branching units (BUs), including material and labor, as well as submarine cable landing stations (CLSs). This optimization also includes choices of locations of BUs and CLSs. These are important issues for the economics of cable laying and significantly change the model and the optimization process. We pose the problem as a variant of the Steiner tree problem, but one in which the Steiner nodes can vary in number, while incurring a penalty. We refer to it as the weighted Steiner node problem. It differs from the Euclidean Steiner tree problem, where Steiner points are forced to have degree three; this is no longer the case, in general, when nodes incur a cost. We are able to prove that our algorithm is applicable to Steiner nodes with degree greater than three, enabling optimization of network costs in this context. The optimal solution is achieved in polynomial-time using dynamic programming.

This paper presents a new joint radar and communication technique based on the classical stepped frequency radar waveform. The randomization in the waveform, which is achieved by using permutations of the sequence of frequency tones, is utilized for data transmission. A new signaling scheme is proposed in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. Considering the optimum maximum likelihood detection, the union bound and the nearest neighbour approximation on the communication block error probability is derived for communication in an additive white Gaussian noise channel. The results are further extended to incorporate the Rician fading channel model, of which the Rayleigh fading channel is presented as a special case. Furthermore, an efficient communication receiver implementation is discussed based on the Hungarian algorithm which achieves optimum performance with much less operational complexity when compared to an exhaustive search. From the radar perspective, two key analytical tools, namely, the ambiguity function and the Fisher information matrix are derived. Furthermore, accurate approximations to the Cramer-Rao lower bounds on the delay and Doppler estimation errors are derived based on which the range and velocity estimation accuracy of the waveform is analysed.

This paper presents a new waveform that is suitable for simultaneous data transmission and radar sensing. The approach considers a classical random stepped frequency radar waveform that is suitable for the emerging automotive radar application. The randomization in the waveform, which is achieved by using permutations of the sequence of frequency tones, is utilized for data transmission. More specifically, we propose a new Lehmer code based signaling model that modulates data based on the selection of the permutation. Considering maximum likelihood detection, the union bound on the communication block error probability is derived for baseband communication both in an additive white Gaussian noise (AWGN) channel and Rayleigh fading channel. Using the Hungarian Algorithm, an efficient implementation method for the communications receiver is also presented. From the radar perspective, we derive the ambiguity function, which is a key analytical tool in radar waveform design, and characterize the behavior of the Lehmer code based random stepped frequency radar waveform. Numerical examples are used to illustrate the performance of the proposed waveform.

Hidden Markov Chains (HMCs) and, more recently, Hidden semi-Markov Chains (HsMCs) have been used by several groups of researchers to provide a model for indoor localization. A homogeneous HMC is completely determined by the state initial probability vector and the state transition probability matrix. This is also true for the HsMC provided the state duration probability is given. These parameters are often chosen heuristically but when sufficient measurement training data are available, they can be learned using the well-known Baum-Welch algorithm. Given the model parameters, approaches such as the forward-only algorithm, the forward-backwards algorithm and the Viterbi algorithm can be applied for state sequence inference under the HMC/HsMC framework. In indoor localization applications, there is often insufficient prior information to specify such parameters in advance of the application and they have to be learned from limited amounts of training data. In this paper, we endeavour to evaluate the parameter learning accuracy of the Baum-Welch algorithm using varying amounts of training data, and evaluate the influence of applying inaccurate model parameters on these typical state estimation algorithms under both the HMC and HsMC frameworks. All of the evaluations are based on received signal strength (RSS) for application to indoor localization.

We study a job-assignment problem in a large-scale server farm system with geographically deployed servers as abstracted computer components (e.g., storage, network links, and processors) that are potentially diverse. We aim to maximize the energy efficiency of the entire system by effectively controlling carried load on networked servers. A scalable, near-optimal job-assignment policy is proposed. The optimality is gauged as, roughly speaking, energy cost per job. Our key result is an upper bound on the deviation between the proposed policy and the asymptotically optimal energy efficiency, when job sizes are exponentially distributed and blocking probabilities are positive. Relying on Whittle relaxation and the asymptotic optimality theorem of Weber and Weiss, this bound is shown to decrease exponentially as the number of servers and the arrival rates of jobs increase arbitrarily and in proportion. In consequence, the proposed policy is asymptotically optimal and, more importantly, approaches asymptotic optimality quickly (exponentially). This suggests that the proposed policy is close to optimal even for relatively small systems (and indeed any larger systems), and this is consistent with the results of our simulations. Simulations indicate that the policy is effective, and robust to variations in job-size distributions.

We study the path planning of submarine cable systems with trunk-and-branch tree topology on the surface of the earth. Existing work on path planning represents the earth's surface by triangulated manifolds and takes account of laying cost of the cable including material, labor, alternative protection levels, terrain slope and survivability of the cable. Survivability issues include the risk of future cable break associated with laying the cable through sensitive and risky areas, such as, in particular, earthquake-prone regions. The key novelty of this paper is an examination and solution of the path planning of submarine cable systems with trunk-and-branch tree topology. We formulate the problem as a Steiner minimal tree problem on irregular 2D manifolds in R3. For a given Steiner topology, we propose a polynomial time computational complexity numerical method based on the dynamic programming principle. If the topology is unknown, a branch and bound algorithm is adopted. Simulations are performed on real-world three-dimensional geographical data.

Sonobuoy fields, comprising a network of sonar transmitters and receivers, are used to find and track underwater targets. For a given environment and sonobuoy field layout, the performance of such a field depends on the scheduling, that is, deciding which source should transmit, and which waveform should be transmitted at any given time. In this paper, we explore the choice of cost function used in myopic scheduling and its effect on tracking performance. Specifically, we consider 5 different cost functions derived from the predicted error covariance matrix of the track. Importantly, our cost functions combine both positional and velocity covariance information to allow the scheduler to choose the optimum source-waveform action. Using realistic multistatic sonobuoy simulations, we demonstrate that each cost function results in a different choice of source-waveform actions, which in turn affects the performance of the scheduler. In particular, we show there is a trade-off between position and velocity error performance such that no one cost function is superior in both.

This paper considers the joint recursive estimation of the dynamic state and the time-varying process noise covariance for a linear state space model. The conjugate prior on the process noise covariance, the inverse Wishart distribution, provides a latent variable. A variational Bayesian inference framework is then adopted to iteratively estimate the posterior density functions of the dynamic state, process noise covariance and the introduced latent variable. The performance of the algorithm is demonstrated with simulated data in a target tracking application.

Wireless network slicing is a promising technology for next-generation networks to provide tailored on-demand services to mobile users. We consider a scheduling policy for wireless network slicing with the aim to maximize the energy efficiency of the network defined as the ratio of long-run average throughput of user requests to the long- run average power consumption. This gives rise to a problem of extremely high computational complexity which prevents direct application of conventional optimization techniques. We propose a scalable priority-based policy, referred to as the Most Energy-Efficient Resource First (MEERF). MEERF is proved to be asymptotically optimal in the special case appropriate for a local wireless environment with highly dense user population and exponentially distributed service time requirement. The robustness of MEERF to different service time distributions is demonstrated by extensive simulations. We present numerically the effectiveness of MEERF %balancing the QoS and relevant power consumption by comparing it with benchmark policies in a more general network with potentially geographically distributed users and infrastructures. The results show that MEERF outperforms the benchmark policies in most of our experiments and achieves up to 52% improvement in terms of energy efficiency.

Sonobuoy fields, comprising a network of transmitters and receivers, are commonly deployed to find and track underwater targets. For a given environment and sonobuoy field layout, the performance of such a field depends on the scheduling, that is, deciding which source should transmit, and which from a library of available waveforms should be transmitted at any given time. In this paper, we propose a novel scheduling framework based on multi-objective optimization. Specifically, we pose the two tasks of the sonobuoy field-tracking and searching-as separate, competing, objective functions. Using this framework, we propose a characterization of scheduling based on Pareto optimality. This characterization describes the trade-off between the search-track objectives and is demonstrated on realistic multistatic sonobuoy simulations.

The Chinese Remainder Theorem (CRT) enables phase unwrapping for measurement of a distance using multiple wrapped phases of sinusoidal transmissions, such as in radar, sonar, or wireless geolocation. In the presence of measurement noise, the existing CRT algorithm assumes that the correct number of wrapping wavelengths can be obtained after a round off operation by ignoring the received signal noise. In this paper, additional hypotheses for the output of the round off process are formulated and a modified CRT algorithm for range estimation is proposed. We show that an improved distance reconstruction rate over the existing CRT algorithm is achieved from both analytical calculations and numerical simulations.

As the use of automotive radar increases, performance limitations associated with radar-to-radar interference will become more significant. In this paper, we employ tools from stochastic geometry to characterize the statistics of radar interference. Specifically, using two different models for the spatial distributions of vehicles, namely, a Poisson point process and a Bernoulli lattice process, we calculate for each case the interference statistics and obtain analytical expressions for the probability of successful range estimation. This paper shows that the regularity of the geometrical model appears to have limited effect on the interference statistics, and so it is possible to obtain tractable tight bounds for the worst case performance. A technique is proposed for designing the duty cycle for the random spectrum access, which optimizes the total performance. This analytical framework is verified using Monte Carlo simulations.

Doppler radars are low cost and light weight sensors that have a potential to find wide applications in building a large team of mobile vehicle platforms. Because of the nonlinearity associated with the measurement from Doppler radars, it is both interesting and challenging to extract meaningful information from the low cost sensors. Building upon the authors' previous work on self localization with a feature-based map with known landmark associations using Doppler radars and an Extended Kalman Filter (EKF), this paper investigates the effects of positioning and the number of landmarks in a feature-based map on the accuracy of the position estimation of a robot. The computations of Cramer-Rao Lower Bound (CRLB) at the terminating sample show that the CRLB has a drastic reduction when the number of landmarks is increased from 1 to 2 while the root mean square errors (RMSE) of EKF indicate a gradual error reduction for the first 4 landmarks. The results presented in this paper will provide an essential guideline on the experiment design for feature-based robot self-localization.

This paper describes the implementation of a miniature open-source and cost-effective SLAM-robot, utilizing a novel occupancy-grid SLAM algorithm based on the concept of random-finite-sets (RFS). This robotic platform is remotely controlled to move and scan unknown environments using a differential drive system algorithm, sending instantaneous position feedback to the remote operator. The mobile robot utilizes a LIDAR-Lite 2 laser range finder to map the environment while simultaneously estimating its position and orientation within the map. Even though there are many mobile robots that implement this behavior, the main advantage in this proposed robotic platform is modeling of LIDAR measurements at each scan as a RFS. This model provides robustness against the random count of received returns, due to false and missed detections, allowing the use of an inexpensive LIDAR sensor and commercial off the shelf hardware.

In this paper, we investigate cooperative passive sensor trajectory planning for tracking a target where the tracking error is sensor trajectory dependent. We consider the problem under a scenario of tracking a moving target using two unmanned bearings-only sensors. The basic idea is to maximise the target information acquired from the processing measurements of the two sensors by cooperatively scheduling their future trajectories at which sensor measurements will be taken. In the literature this problem is modeled by a partially observed Markov decision process and optimal action which maximises an expected reward function is sought. Three reward functions, namely, the Expected Reward, the Determinant, and Trace of the associated Fisher Information Matrix (FIM) for the underlying problem are analysed and discussed. These rewards may only be evaluated practically through various approximations. We show that the correlation between two sensor states is weakened significantly for the Expected Reward due to linearisation and thus the closed-form Expected Reward as well as the Trace of FIM are inappropriate for this sensor trajectory scheduling problem. Finally, we present simulation results which are based on the example of a non-cooperative target chasing via two cooperative bearing-only sensors.

Sonobuoy fields, consisting of many distributed emitter and receiver sonar sensors on buoys, are used to seek and track underwater targets in a defined search area. A sensor scheduling algorithm is required in order to optimise tracking performance by selecting which emitter sonobuoy should transmit in each time interval, and which waveform it should use. In this paper we describe a new long term sensor scheduling algorithm for sonobuoy fields, called the continuous probability states algorithm. This algorithm reduces the scheduling search space by keeping track of the probability that a target is undetected, rather than modelling all possible detection outcomes, which reduces the computation complexity of the algorithm. It is shown that this approach results in high quality tracking for multiple targets in a simulated sonobuoy field.

The Radio Frequency Identification (RFID) is a rapidly developing technology with growing applications in several fields. One of the key applications is the localisation of tagged objects using signal phase difference information via dual-frequency technology. In this application, unwrapping signal phases to acquire the range between the reader and RFID tag is the major issue that has typically been addressed in the literature using either the Chinese Remainder Theorem or Lattice Theory. In this paper, a lattice-based method robust to phase measurement noise is presented to resolve the wrapped range. The proposed algorithm is shown to be more robust and efficient than existing approaches in terms of the reconstruction probability. Simulations are presented to illustrate the performance of the proposed algorithm.

Stepped frequency radar technology, where the transmit waveform consists of a sequence of tones, has long been suggested for cost-effective and high-resolution applications. One recent use of this technology is in automotive application where, in addition to cost-effectiveness, a random stepped frequency (RSF) waveform can significantly reduce the interference between vehicles. In this paper we provide a generic framework for the range and Doppler measurements for multiple targets. We further suggest two possible methods for reducing the computational complexity of RSF waveforms processing, which is important for future automotive applications.

The Chinese remainder theorem (CRT) is often used to find unwrap signal phase over multiple wavelengths as a means of estimating total travel time of a signal. Existing approaches, implemented efficiently in closed form using either standard CRT or methods derived from lattice theory, require the wavelengths involved to be coprime. This can be a limiting factor in real applications, especially where the available signal bandwidth is limited. In this letter, we derive a new algorithm to extend the closed-form lattice algorithm to accommodate non-coprime wavelengths. The benefit of this development is demonstrated with a Wi-Fi wireless device localization example.

Optimal determination of a UAV using a vision-based system to match images against a database is an important problem. It can be reformulated to the problem of using multiregion scene registration to match areas of a noisy and distorted image to a geo-referenced image. Under the assumptions that the mapping between sensed and geo-referenced images preserves gradients of straight lines cross mapping points on images and registration errors are all Gaussian distributed, we derive a two-stage weighted linear least square algorithm which localises the UAV optimally. Performance of the proposed algorithm is demonstrated via Monte Carlo multiple runs along with those available in literature.

We formulate the target tracking problem for radar in a multipath environment where significant uncertainty on the locations of the multipath causing obstacles (walls) is present. Most of the recent efforts towards investigating target tracking in multipath environments assume knowledge of these wall locations. Relaxing this assumption makes the tracking problem very challenging. We propose a statistical filter (tracker) and a data association method based on importance sampling to address these challenges.

Use of the phase of a signal to measure distance carries an inherent ambiguity. The problem is typically addressed by the use of several different frequencies and the Chinese Remainder Theorem or lattice methods, but these methods result in computational complexity issues. The difficulties are increased by the presence of noise. This paper presents a lattice-based algorithm to resolve phase ambiguity more efficiently and under more relaxed constraints than existing approaches. Simulations are presented to illustrate the performance of the proposed algorithm and compared with existing methods.

We study the problem of job assignment in a large-scale realistically dimensioned server farm comprising multiple processor-sharing servers with different service rates, energy consumption rates, and buffer sizes. Our aim is to optimize the energy efficiency of such a server farm by effectively controlling carried load on networked servers. To this end, we propose a job assignment policy, called Most energy-efficient available server first Accounting for Idle Power (MAIP), which is both scalable and near optimal. MAIP focuses on reducing the productive power used to support the processing service rate. Using the framework of semi-Markov decision process, we show that, with exponentially distributed job sizes, MAIP is equivalent to the well-known Whittle's index policy. This equivalence and the methodology of Weber and Weiss enable us to prove that, in server farms where a loss of jobs happens if and only if all buffers are full, MAIP is asymptotically optimal, as the number of servers tends to infinity under certain conditions associated with the large number of servers, as we have in a real server farm. Through extensive numerical simulations, we demonstrate the effectiveness of MAIP and its robustness to different job-size distributions, and observe that significant improvement in energy efficiency can be achieved by utilizing the knowledge of energy consumption rate of idle servers.

We consider the problem of fusing measurements in a sensor network, where the sensing regions overlap and data are nonnegative real numbers, possibly resulting from a count of indistinguishable discrete entities. Because of overlaps, it is generally impossible to fuse this information to arrive at an accurate value of the overall amount or count of material present in the union of the sensing regions. Here we study the computation of the range of overall values consistent with the data and provide several results. Posed as a linear programming problem, this leads to questions associated with the geometry of the sensor regions, specifically the arrangement of their nonempty intersections. We define a computational tool called the fusion polytope , based on the geometry of the sensing regions. Its properties are explored, and in particular, a topological necessary and sufficient condition for this to be in the positive orthant, a property that considerably simplifies calculations, is provided. We show that in two dimensions, inflated tiling schemes based on rectangular regions fail to satisfy this condition, whereas inflated tiling schemes based on hexagons do.

The principal difficultly in tracking in an urban terrain is the presence of multipaths. However by using proper modelling and signal processing techniques these multipaths can be used favourably. In this paper we consider a more robust model of the urban terrain by not assuming exact wall locations but rather allowing for small deviations. This is achieved by introducing a random phase shift to the radar equation. A MCMC based particle filter which uses an adaptive kernel to improve the mobility of the Markov Chain is proposed with supporting simulation results.

Tracking of the orientation of a rigid body based on directional measurements is a key issue in many applications. Configurations in this sense are precisely representable as elements of the rotation group SO(3), and the issue devolves to one of tracking on this group, for which and algorithm is described here. Its novelty derives from the use of maximum entropy distributions on these groups as models for the priors, and from the approximation algorithms that permit numerical implementation of such a model. These solutions can be written in a recursive form. While the general ideas apply in all dimensions, the focus of this paper is on the important 3-dimensional case. It is impossible to compute the exact solution; instead, obtained here is a highly effective approximation. It is shown that, in contrast with other approaches, the algorithm described here produces outputs which are both very accurate and statistically meaningful.

Each of a large number of nodes takes a measurement in sequence to decide between two hypotheses about the state of the world. Each node also has available the decisions of some of its immediate predecessors and uses these and its own measurement to make its decision. Each node broadcasts its decision through a binary symmetric channel, which randomly flips the decision. The question treated here is whether there exists a decision strategy consisting of a sequence of likelihood ratio tests such that the decisions approach the true hypothesis as the number of nodes increases. We show that if each node learns from bounded number of predecessors, then the decisions cannot converge to the underlying truth. We show that if each node learns from all predecessors then the decisions converge in probability to the underlying truth when the flipping probabilities are bounded away from 1/2. We also derive, in the case when the flipping probabilities tend to 1/2, a condition on the convergence rate of the flipping probabilities that is required for the decisions to converge to the true hypothesis in probability.

This paper presents a method that incorporates background subtraction and temporal persistency with the HOG pedestrian detector to detect pedestrians from videos captured by a fixed camera. We use a codebook based method and interpolation to extract a series of foreground sub-images for the HOG detector. This allows the detector to focus on pedestrian detection on smaller image regions and thereby reduce its computational cost and lower its false positive error rate. We employ a temporal persistency constraint to overcome problems that may arise from background subtraction. Compared to other state-of-art techniques, the performance of our method is pleasantly promising.

Estimation of multiple T2 components within single imaging voxels typically proceeds in one of two ways; a nonparametric grid approximation to a continuous distribution is made and a regularized nonnegative least squares algorithm is employed to perform the parameter estimation, or a parametric multicomponent model is assumed with a maximum likelihood estimator for the component estimation. In this work, we present a Bayesian algorithm based on the principle of progressive correction for the latter choice of a discrete multicomponent model. We demonstrate in application to simulated data and two experimental datasets that our Bayesian approach provides robust and accurate estimates of both the T2 model parameters and nonideal flip angles. The second contribution of the paper is to present a Cramér-Rao analysis of T2 component width estimators. To this end, we introduce a parsimonious parametric and continuous model based on a mixture of inverse-gamma distributions. This analysis supports the notion that T2 spread is difficult, if not infeasible, to estimate from relaxometry data acquired with a typical clinical paradigm. These results justify the use of the discrete distribution model.

Recently there has been increasing interest in estimating the distribution of relaxation times contributing to a magnetic resonance signal. This paper shows that it is impractical to estimate the spread of such a distribution from typical measurements. Instead, a Bayesian estimator is developed for a discrete distribution, which is very robust to noise. Although the distribution spread is not modelled, the estimates capture the main features of the distribution such as the mode locations and often provide improved myelin water fraction estimates in simulation examples.

An information-geometric approach to sensor management is introduced that is based on following geodesic curves in a manifold of possible sensor configurations. This perspective arises by observing that, given a parameter estimation problem to be addressed through management of sensor assets, any particular sensor configuration corresponds to a Riemannian metric on the parameter manifold. With this perspective, managing sensors involves navigation on the space of all Riemannian metrics on the parameter manifold, which is itself a Riemannian manifold. Existing work assumes the metric on the parameter manifold is one that, in statistical terms, corresponds to a Jeffreys prior on the parameter to be estimated. It is observed that informative priors, as arise in sensor management, can also be accommodated. Given an initial sensor configuration, the trajectory along which to move in sensor configuration space to gather most information is seen to be locally defined by the geodesic structure of this manifold. Further, divergences based on Fisher and Shannon information lead to the same Riemannian metric and geodesics.

Robust multiple object tracking is the backbone of many higher-level applications such as people counting, behavioral analytics and biomedical imaging. We enhance multiple hypothesis tracker robustness to the problems of split, merge, occlusion and fragment through hierarchical approach. Foreground segmentation and clustered optical flow are used as the first-level tracker input. Only associated track of the first level is fed into the second level with the additional of two virtual measurements. Occlusion predictor is obtained by using the predicted data of each track to distinguish between merge and occlusion. Kalman filter is used to predict and smooth the track's state. Gaussian modelling is used to measure the quality of the hypotheses. Histogram intersection is applied to limit the size expansion of the track. The results show improvement both in terms of accuracy and precision compared to the benchmark trackers [1, 2].

We study the detection error probability associated with a balanced binary relay tree, where the leaves of the tree correspond toNidentical and independent sensors. The root of the tree represents a fusion center that makes the overall detection decision. Each of the other nodes in the tree is a relay node that combines two binary messages to form a single output binary message. Only the leaves are sensors. In this way, the information from the sensors is aggregated into the fusion center via the relay nodes. In this context, we describe the evolution of the Type I and Type II error probabilities of the binary data as it propagates from the leaves toward the root. Tight upper and lower bounds for the total error probability at the fusion center as functions ofNare derived. These characterize how fast the total error probability converges to 0 with respect toN, even if the individual sensors have error probabilities that converge to 1/2.

Nonlinear spatial encoding fields for magnetic resonance imaging (MRI) hold great promise to improve on the linear gradient approaches by, for example, enabling reduced imaging times. Imaging schemes that employ general nonlinear encoding fields are difficult to analyze using traditional measures. In particular, the resolution is spatially varying, characterized by a position-dependent point spread function (PSF). Likewise, the use of nonlinear encoding fields creates an additional spatial dependence on the signal-to-noise ratio (SNR). Although the two properties of resolution and SNR are linked, in this work we focus on the latter. To this end, we examine the pixel variance, which requires a computation that is often not feasible for nonlinear encoding schemes. This paper presents a general formulation for the performance analysis of imaging schemes using arbitrary encoding fields. The analysis leads to the derivation of a practical and computationally efficient performance metric, which is demonstrated through simulation examples.

When tracking a target using phase-only signal returns, range ambiguities are a major issue. In this work, a look-up table between phase measurement space and target location space is constructed for phase measurement mapping. Solving such problems via solutions to Diophantine equations has been used to locate candidate locations. Here we show how such target location ambiguity can also be resolved over time when the underlying target is in motion and where issues of clutter are treated via a phase distribution discrimination method. That is, a probability density function of the ambiguous phase-only measurement that takes both sensor noise and target motion distributions into account is derived based on directional statistics. This approach to solving phase ambiguity under significant clutter conditions has promising results.

Tracking in a multipath environment poses many challenges. It is worth while to quantify the achievable performance bounds in such an environment. However finding the performance bounds could be challenging. This requires calculating derivatives of parameters that are functions of reflection points on walls, with respect to target related quantities. We propose a method to calculate the lower bound for minimum mean squared error (MMSE) in target state estimation in a multipath environment. A novel measurement model is introduced taking into account a general setup with locations of obstacle walls known. Furthermore we model the wall reflectivities as random variables. Simulation results are provided in which we have obtained the bound for various setups.

Estimating the coefficients of a noisy polynomial phase signal is important in many fields including radar, biology and radio communications. One approach to estimation attempts to perform polynomial regression on the phase of the signal. This is complicated by the fact that the phase is wrapped modulo 2π and therefore must be unwrapped before the regression can be performed. A recent approach suggested by the authors is to perform the unwrapping in a least squares manner. It was shown by Monte Carlo simulation that this produces a remarkably accurate estimator. In this paper we describe the asymptotic properties of this estimator, showing that it is strongly consistent and deriving its central limit theorem. We hypothesise that the estimator produces very near maximum likelihood performance.

In this paper, we present a method for tracking pedestrians in video sequences captured by a fixed camera. Pedestrians are detected in every video frame using the human detector proposed by Dalal and Triggs. An interacting multiple model method is used to predict and update pedestrian trajectories from current frame to the next one. We employ a stationary model and a constant velocity model in our method to handle cases such as when a pedestrian suddenly stops or changes walking direction. We smooth the colour histogram that describes the appearance of each detected pedestrian using kernel density estimation. Our experimental results show that our tracking method outperforms one that uses the Kalman filter and colour histograms.

Traditional magnetic resonance imaging (MRI) studies are based on image contrast and qualitative analysis. However, there is an increasing interest in quantifying the physical parameters of the object such as the free induction decay rate, T*2. In this paper, a new Bayesian algorithm is proposed for the estimation of T*2from gradient echo MRI scans. Current estimation methods use a simple signal model based on Fourier reconstruction which imposes a trade-off between the signal-to-noise ratio (SNR) and image distortion, and results in estimation bias. The proposed algorithm uses a Gibbs sampler in a Bayesian framework to account for image distortion allowing data samples to be acquired with increased SNR, improving the estimation accuracy. Estimation results on simulated objects and in vivo experimental data demonstrate the effectiveness of the algorithm.

Principal Components Analysis (PCA) and Linear Discriminant Analysis (LDA) are the two popular techniques in the context of dimensionality reduction and classification. By extracting discriminant features, LDA is optimal when the distributions of the features for each class are unimodal and separated by the scatter of means. On the other hand, PCA extract descriptive features which helps itself to outperform LDA in some classification tasks and less sensitive to different training data sets. The idea of Parametric Subspace Analysis (PSA) proposed in this paper is to include a parameter for regulating the combination of PCA and LDA. By combining descriptive (of PCA) and discriminant (of LDA) features, a better performance for dimensionality reduction and classification tasks is obtained with PSA and can be seen via our experimental results.

An algorithm for trajectory optimization of autonomous aerial vehicles performing multiple target tracking is proposed. The problem is approached by formulating it as a partially observed Markov decision process (POMDP) and developing a moving-horizon solution taking into account short and long term costs. To evaluate the effectiveness of the approach a simulation involving multiple UAVs and targets is performed.

We describe a method to analyze materials on a conveyor belt using natural gamma spectra collected with a BGO (Bismuth Germanate) gamma ray detector, which collects emissions from Potassium (K), Uranium (U), and Thorium (Th) in the materials. A statistical model is proposed based on a Poisson process and an approximate maximum likelihood (ML) technique via the expectation-maximization (EM) algorithm is then used to estimate the amount of each of the three elements in the material. A refinement of the statistical model is used to estimate linear drift in the detector.

Node localisation in wireless sensor networks is a difficult problem due to the large number of parameters to be estimated and the nonlinear relationship between the measurements and the parameters. Assuming the presence of a number of anchor nodes with known positions and a centralised architecture, a Bayesian algorithm for node localisation in wireless sensor networks is proposed. The algorithm is a refinement of an existing importance sampling method referred to as progressive correction. A simulation analysis shows that, with only a few anchor nodes, the proposed method is capable of accurately localising a large number of nodes.

The use of complementary codes as a means of reducing radar range sidelobes is well-known, but lack of resilience to Doppler is often cited as a reason not to deploy them. This work describes techniques for providing Doppler resilience with an emphasis on tailoring Doppler performance to the specific aim of target tracking. The Doppler performance can be varied by suitably changing the order of transmission of multiple sets of complementary waveforms. We have developed a method that improves Doppler performance significantly by arranging the transmission of multiple copies of complementary waveforms according to the first order Reed-Muller codes. Here we demonstrate significant tracking gains in the context of accelerating targets by the use of adaptively chosen waveform sequences of this kind, compared to both a fixed sequence of similar waveforms, and an LFM waveform.

We describe a method of constructing a sequence (pulse train) of phase-coded waveforms, for which the ambiguity function is free of range sidelobes along modest Doppler shifts. The constituent waveforms are Golay complementary waveforms which have ideal ambiguity along the zero Doppler axis but are sensitive to nonzero Doppler shifts. We extend this construction to multiple dimensions, in particular to radar polarimetry, where the two dimensions are realized by orthogonal polarizations. Here we determine a sequence of two-by-two Alamouti matrices where the entries involve Golay pairs and for which the range sidelobes associated with a matrix-valued ambiguity function vanish at modest Doppler shifts. The Prouhet–Thue–Morse sequence plays a key role in the construction of Doppler resilient sequences of Golay complementary waveforms.

An algorithm is developed for joint tracking and detection of multiple maneuvering targets using a wireless sensor network. The target existence probability framework is adopted in which a collection of tentative tracks, each characterised by a posterior density and existence probability, is maintained. Track state posterior densities are approximated using the unscented Kalman filter and the interacting multiple model algorithm. The advantage of this approach compared to particle filter- based approaches is that it enables more computationally efficient tracking of multiple targets. The performance of the algorithm is examined as a function of signal-to-noise ratio and the number of bits per observation for a scenario involving three maneuvering targets. Good performance is achieved in all cases considered.

A new method of applying the unscented transformation to conditionally linear transformations of Gaussian random variables is proposed. This method exploits the structure of the model to reduce the required number of sigma points. A common application of the unscented transformation is to nonlinear filtering where it used to approximate the moments required in the Kalman filter recursion. The proposed procedure is applied to a nonlinear filtering problem which involves tracking a falling object.

Target tracking using a radar array system is considered. A signal model which includes the effects of path loss, signal delay, Doppler shift and angle-of-arrival is adopted. The conventional approach to radar tracking assumes that the raw measurements are processed to produce a collection of candidate target detections. We propose a new approach in which the raw received measurements are used for tracking. Performance bounds and a simulation analysis of filters developed for each model demonstrate the performance gains which can be achieved by tracking with raw sensor measurements.

In this paper, we propose a method to exploit waveform agility in modern radars to improve performance in the challenging task of detecting small targets on the ocean surface in heavy clutter. The approach exploits the compound-Gaussian model for sea clutter returns to achieve clutter suppression by forming an orthogonal projection of the received signal into the clutter subspace. Waveform scheduling is then performed by incorporating the information about the clutter into the design of the next transmitted waveform. A simulation study demonstrates the effectiveness of our approach.

This paper describes a new radar primitive that enables instantaneous radar polarimetry at essentially no increase in signal processing complexity. This primitive coordinates transmission of distinct waveforms on orthogonal polarizations and applies a unitary matched filter bank on receive. This avoids the information loss inherent in single-channel matched filters. A further advantage of this scheme is the elimination of range sidelobes

In this paper we consider state estimation problems where there are multiple independent processes evolving but the estimation scheme can only select a limited set of processes to measure at each time step. Within a Gauss-Markov framework, we show the optimality of a scheduling scheme under various scenarios. These types of problems are common in sensor scheduling applications

Networks of small low-cost sensors for target tracking are becoming increasingly important for many applications. A major problem is that these small sensors usually have limited observability due to power constraints and the transition between sensor observation and target states is nonlinear. As a consequence, nonlinear filtering techniques, such as particle filtering, are often chosen by researchers in this context. We focus on a network of sensors where each sensor provides binary data at each epoch: target present or target absent. At this point it is not clear that existing approaches can effectively handle the tracking of multiple targets using such networks. In addition, algorithmic computational complexity is an issue if particle filters are used. In this paper, we present a new method, the virtual measurement (VM) approach, for multi-target tracking using distributed binary sensor networks. The central idea of this approach is to define a mapping between the space of binary sensor observations and the so-called VM space, such that, any point within a VM space is a transform of the target state, as if it were generated by an equivalent "large sensor". With VMs, conventional multi-target tracking (MTT) algorithms can be used in a straightforward way for tracking multiple targets over the sensing field of binary sensor networks. Computer simulated examples of MTT demonstrate the effectiveness and robustness of the VM approach

We investigate the theory of the finite discrete Heisenberg-Weyl group in relation to the development of adaptive radar. We contend that this group can form the basis for the representation of the radar environment in terms of operators on the space of waveforms. We also demonstrate, following recent developments in the theory of error correcting codes, that the finite discrete Heisenberg-Weyl group provides a unified basis for the construction of useful waveforms/sequences for radar, communications and the theory of error correcting codes.

Modern radar systems have considerable flexibility in their modes of operation. In particular, it is possible to modify the waveform on a pulse to pulse basis, and electronically steered phased arrays can quickly point the radar beam in any feasible direction. Such flexibility calls for new methods of scheduling, both of the waveform and the beam direction so as to optimize the radar performance. We consider a radar system capable of rapid beam steering and of waveform switching. The transmit waveform is chosen from a small library. The operational requirement of the radar is to track a number of manoeuvring targets while performing surveillance for new potential targets. Tracking is accomplished by means of an LMIPDA (linear multitarget integrated probabilistic data association) tracker. An interacting multiple models (IMM) method is used to model manoeuvering targets in the tracker. LMIPDA provides a probability of track existence, permitting adoption of a track-before-detect technique. False alarm tracks are maintained until the probability of track existence falls below a threshold. Our aim is to maintain the tracks of the existing targets to within a specified accuracy as determined by the absolute value of the track error covariance matrix. However, this has to be done within the time available, given that a full scan has to be performed within a prescribed interval. We give an algorithm for scheduling revisits to measure the targets while maintaining surveillance.

In this paper, we present the true Cramer-Rao lower bounds (CRLBs) for the estimation of phase offset for common quadrature amplitude modulation (QAM), PSK, and PAM signals in AWGN channels. It is shown that the same analysis also applies to the QAM, FSK, and PAM CRLBs for frequency offset estimation. The ratio of the modulated to the unmodulated CRLBs is derived for all QAM, PSK, and PAM signals and calculated for specific cases of interest. This is useful to determine the limiting performance of synchronization circuits for coherent receivers without the need to simulate particular algorithms. The hounds are compared to the existing true CRLBs for an unmodulated carrier wave (CW), BPSK, and QPSK. We investigated new and existing QAM phase estimation algorithms in order to verify the new phase CRLB. This showed that new minimum distance estimator performs close to the QAM bound and provides a large improvement over the power law estimator at moderate to high signal-to-noise ratios.

This paper contains results on the design of optimum equalizers to eliminate intersymbol interference in linear non-minimum phase channels conveying binary signals. The optimization is with respect to an open eye condition with a given delay. For causal stable channels with non-minimum phase zeros, we argue that this problem requires only the consideration of the FIR modified channel that has all the non-minimum phase zeros of the original channel. We show that if this modified channel can be equalized to yield an equalized system that is open eye with a specified delay, then the optimizing equalizer is, in fact FIR with all zeros outside the unit circle, and the impulse response of the equalised channel does not extend beyond the delay. We also give a simple necessary and sufficient condition to determine if for a particular delay, a given channel can be equalized to achieve an equalized response that is open eye.

Artificial neural networks are a powerful tool for analyzing data sets where there are complicated nonlinear interactions between the measured inputs and the quantity to be predicted. We show that the results obtained when neural networks are applied to survival data depend critically on the treatment of censoring in the data. When the censoring is modeled correctly, neural networks are a robust model independent technique for the analysis of very large sets of survival data.