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Two algorithms for tracking in clutter, based on the Viterbi algorithm are presented: single-target Viterbi data association (ST-VDA) and multihypothesis VDA (MH-VDA). MH-VDA is designed specifically for multiple-target tracking (MTT), although ST-VDA still achieves good performance on MTT problems. The basic philosophy of both methods is to set up an optimisation problem for the sequence of measurement-to-target associations rather than directly seeking the target state estimates. The joint optimisation problem for the data association sequence is decomposed into a sequence of scalar optimisation problems by means of an approximate forward dynamic programming recursion to which the Viterbi algorithm is applicable. Once the data association problem is solved, the target state estimates can be retrieved by backtracking. The operation of the algorithms is easily visualised as a search on a trellis for the optimal path. For ST-VDA, nodes in the trellis correspond to measurements. For MH-VDA, nodes correspond to multitarget data association hypotheses. Conventional measurement gating is extended to work within this context. Results from simulations that compare the performance of ST-VDA and MH-VDA with four, standard, zero-scan-back tracking approaches are given. The performance assessment includes metrics for track loss and track swaps in a multiple crossing target context. The Viterbi data association (VDA) algorithms are shown to outperform the alternative algorithms. In particular the ST-VDA is found to have the best track swap performance, while MH-VDA has the lowest track loss figure. Average state estimation errors for both VDA algorithms are only about 10% larger than a Kalman filter with known data associations. While both variants of VDA are essentially batch processing approaches, the simulation results indicate that the algorithms can be implemented with a fixed processing lag of only a few scans without significant loss in performance.

We consider the problem of tracking a ''smart'' target. That is, a target that is aware it is being tracked and modifies its behaviour accordingly. To track such targets effectively it is necessary to modify the behaviour of the tracking sensor in response to the target. We consider that the best framework for such a problem is that of a mathematical game. In this paper, we consider an idealised version of this problem that illustrates some of the issues that can occur when attempting to track a smart target and the utility of a game theoretic framework.

When tracking targets using radars and sonars, the number of targets and the origin of data is uncertain. Data may be false measurements or clutter, or they may be detections from an unknown number of targets whose possible trajectories and detection processes can only be described in a statistical manner. Optimal all-neighbor multi-target tracking (MTT) in clutter enumerates all possible joint measurement-to-track assignments and calculates the a posteriori probabilities of each of these joint assignments. The numerical complexity of this process is combinatorial in the number of tracks and the number of measurements. One of the key differences between most MTT algorithms is the manner in which they reduce the computational complexity of the joint measurement-to-track assignment process. We propose an alternative approach, using a form of soft assignment, that enables us to bypass this step entirely. Specifically, our approach treats possible detections of targets followed by other tracks as additional clutter measurements. It starts by approximating the a~priori probabilities of measurement origin. These probabilities are then used to modify the clutter spatial density at the location of the measurements. A suitable single target tracking (STT) filter then uses the modified clutter intensity for updating the track state. In effect, the STT filter is transformed into an MTT filter with a numerical complexity that is linear in the number of tracks and the number of measurements. Simulations show the effectiveness of this approach in a number of different multi-target scenarios.

A fully automatic tracking algorithm must be able to deal with an unknown number of targets, unknown target initiation and termination times, false measurements and possibly time-varying target trajectory behaviour. An efficient algorithm for tracking in this environment is presented here. This approach makes use of estimates of the probability of target existence, which is an integral part of the algorithm. This allows for the efficient generation and management of possible target hypotheses, yielding an algorithm with performance that matches what can be obtained by multiple hypothesis tracking-based approaches, but at a significantly lower computational cost. This paper considers only the single target case for clarity. The extension to multiple targets is easily incorporated into this framework. Simulation studies are given that show the effectiveness of this approach in the presence of heavy and nonuniform clutter when tracking a target in an environment of low probability of detection and in an environment where the target performs violent manoeuvres.

This paper examines the problem of adaptive beam scheduling to minimise target tracking error with a phased array radar. It is shown that this can be posed in a framework that is similar to a particular type of dynamic programming problem known as the restless bandit problem. We will show that when the problem is put in this framework it has an indexable solution under certain circumstances.

Two algorithms are derived for the problem of tracking a manoeuvring target based on a sequence of noisy measurements of the state. Manoeuvres are modeled as unknown input (acceleration) terms entering linearly into the state equation and chosen from a discrete set. The expectation maximization (EM) algorithm is first applied, resulting in a multi-pass estimator of the MAP sequence of inputs. The expectation step for each pass involves computation of state estimates in a bank of Kalman smoothers tuned to the possible manoeuvre sequences. The maximization computation is efficiently implemented using the Viterbi algorithm. A second, recursive estimator is then derived using a modified EM-type cost function. To obtain a dynamic programming recursion, the target state is assumed to satisfy a Markov property with respect to the manoeuvre sequence. This results in a recursive but suboptimal estimator implementable on a Viterbi trellis. The transition costs of the latter algorithm, which depend on filtered estimates of the state, are compared with the costs arising in a Viterbi-based manoeuvre estimator due to Averbuch, et al. (1991). It is shown that the two criteria differ only in the weighting matrix of the quadratic part of the cost function. Simulations are provided to demonstrate the performance of both the batch and recursive estimators compared with Averbuch's method and the interacting multiple model filter.

The problem of constructing a frequency tracker for weak, narrowband signals with slowly varying frequency is considered. An extended Kalman filter is proposed that uses prior knowledge of the nature of the signal to overcome the difficulties presented by the inherent nonlinearity of the problem and the very low signal-to-noise ratios.

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.

Efficient collaborative self-localisation is a vital component of large scale sensor network applications. This paper presents a computationally efficient algorithm for performing this task using radio interferometric positioning. In this way it is possible to localise the nodes in the network without needing additional sensors. Simulation results show performance that is similar to that obtained with a centralised approach but with significantly lower computation and transmission costs.

We consider the problem of geolocating a target using relatively simple ground-based sensors with a high degree of accuracy. We show that by using cooperative receivers, it is possible to achieve the desired level of accuracy for a stationary target by utilizing time difference of arrival measurements. We then extend this approach to provide a recursive solution for tracking moving targets using the unscented Kalman filter. Simulation results indicate improved performance over traditional geolocation results with a single receiver.

This paper examines a sensor scheduling problem for target tracking using a network of distributed passive sensors. It considers how to schedule sensor activation to minimise bandwidth and battery usage while maintaining track accuracy. The sensor network is made up of simple acoustic, binary proximity sensors. Four different scheduling methods are considered. Two of these methods are heuristic while the other two are optimal, one-step ahead schedulers for differing objectives. The performance of all four algorithms is compared using simulations. The results show that it is possible to obtain adequate performance with only a subset of the sensor field active at any one time.

Advances in technology are making distributed networks of sensor platforms a reality for surveillance systems. Such networks provide many benefits including the ability to cover a broader area, to compute more accurate target estimates and provide a reduction in susceptibility to countermeasures. In spite of these advantages, many practical issues remain in the deployment of such networks. One such significant issue is bandwidth limitations on the communication channels between the sensor platforms. This paper examines the effect of bandwidth restrictions on a decentralised system architecture. In such a structure, each sensor tracks targets within its individual surveillance region and then transmits its track data to a global fusion centre. The minimum necessary data rates required to permit reconstruction of the global track estimates to a given level of accuracy are presented in the case when the track state can be represented by a Gauss-Markov system.

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.

This paper describes an algorithm for target tracking in a distributed network of binary proximity sensors that is robust to sensor failures. Tracking with such sensors is a difficult problem as they only tramsmit a single binary digit regarding the presence of a target. The operational status of these sensors may also not be accurately known. This paper describes a Gaussian mixture-based tracking algorithm that addresses these two issues.

In this paper we consider state estimation problems where there are multiple independent processses 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.

The ground moving target indicator (GMTI) radar is widely used to detect, geolocate, track, and classify ground-moving targets in all weather, day-night, and cluttered conditions. The measurements of a GMTI radar are slant range, azimuth, and range-rate or Doppler. These measurements are nonlinear functions of the target state. Until recently, a quantitative measure of the degree of nonlinearity (DoN) for nonlinear filtering problems was lacking. Recently, the DoN of a filtering problem with a nonlinear measurement model has been quantified using the differential geometry based measures of nonlinearity such as the parameter-effects curvature and intrinsic curvature. We calculate three types of parameter-effects curvature and intrinsic curvature for the nonlinear GMTI filtering problem for a variety of scenarios. We vary the distance between the target and the GMTI sensor in these scenarios using simulated data. We demonstrate that the state estimation mean square error (MSE) increases with increase in the DoN

This paper describes an algorithm for tracking a manoeuvring target in heavy clutter and/or with a low probability of detection. It is known that when tracking under such adverse conditions multi-scan tracking algorithms, such as the multi-hypothesis tracker (MHT), provide improved performance over single-scan trackers. This paper uses a computationally efficient algorithm for multi-scan target tracking based on the Viterbi algorithm, known as the Viterbi data association (VDA) algorithm. In this paper it is shown how the VDA algorithm can be combined with the well-known interacting multiple model (IMM) method to create an effective multi-scan manoeuvring target tracker. The performance of the IMM-VDA algorithm is shown by simulation. It is compared to another manoeuvring target algorithm based on the VDA approach which uses a hard decision manoeuvre detection scheme. In addition, it is compared to a single-scan tracking algorithm based on the probabilistic data association method.

Modern phased array radars, with flexible waveform generation and beam steering capability, are able to adapt their performance to a variety of environments. The ultimate goal of our work is to “close the loop” in radar signal processing by producing algorithms for scheduling beam directions, beam shapes, waveforms and other radar modalities so as to optimally extract information from the environment. In order to achieve this goal several tasks must be performed. Briefly these are: 1) estimate the total environment (clutter and targets); 2) assess the effectiveness of a given modality in a given environment; and 3) select the optimal modality for each of a number of future epochs. This paper concentrates on the performance of the second task when the goal is optimal waveform scheduling. That is, we examine a method for measuring the effectiveness of waveforms in sampling an environment for which an estimate is available.

This paper presents a new single-target tracking filter. Similar in structure to track-oriented MHT, the Integrated track splitting (ITS) filter is a multi-scan tracking algorithm that, like IPDA, integrates target state estimation with the estimation of target existence. The ITS filter models each track as a set of components, where each component is defined with a unique measurement history which consists of zero or one measurement received each scan. For each component the state estimate and the a-posteriori probability of component existence are computed recursively. After each scan, a new component is formed from each pair of "existing component, associated measurement". The probability of the new component existence is the probability that the parent component exists and that the measurement used to create the new component is the target measurement. The probability of target existence, mean and covariance of the state estimate for the track are then calculated and used for track maintenance and track output. ITS-MAP filter uses a-priori clutter density information provided by a clutter map, analytically or by some other means to better discriminate clutter from target measurements. Simulations are be used to verify the performance of the ITS-MAP algorithm and to compare its performance with that of other target tracking algorithms in a dense and non-homogeneous clutter environment.

Modern phased array radars are able to adaptively modify their performance to the environment. To make full use of this capability, scheduling algorithms need to be designed. This paper poses the problem of adaptive waveform scheduling for detecting new targets in the context of finite horizon stochastic dynamic programming. The result is a scheduling algorithm that minimises the time taken to detect new targets, detecting these targets in accordance with importance, while minimising the use of radar resources.

This paper presents new algorithms for mulfi-scan, single target and multi target tracking in clutter. The algorithms from the Integrated Track Splif- ring (ITS) family offilters model each track as a set of components, where each component has a unique meas- uremenf history which consists ofzero or one measure- men1 received each scan. For each componenf, as well as for each track, the state estimate and the a-posferiori probability of component existence are computed recur- sively. Three algorithms are presenfed in fhis paper. The ITSfilfer is a single target tracking algorithm. The Joint ITS (JITS) filter is a multi target tracking algorithm which calculafes the a-posteriori probabilities of all pos- sible measurement-to-track assignmenfs, from which a- posteriori probabilities of component and track existence are computed. In each scan, fhe number of assignments grows exponentially in the number of trach and the num- ber of measuremenfs involved. The Linear Joint ITS (I-IITS) filter is anofher multi targef tracking algorifhm which decouples individual tracks in a mulfi-hack sifua- tion using the a-priori probabilities of possible measure- ment origins. In each scan, the LJlTSfilfer has a number of operations which is linear in the number offracks and the number of measurements involved.

This paper discusses the problem of designing a frequency tracker using the extended Kalman filter (EKF). The design trade-off between balancing noise rejection and tracking at a maximal slew rate is considered, as are the effect of varying design noise covariance values. The performance penalties for over- and under-design of noise covariances are examined and theoretically supported design guidelines are suggested. These are illustrated via simulation results. >

This paper examines the problem of eliminating a vibrational disturbance from the output of a linear, time-invariant and unknown system. Theory is presented which shows that it is possible to design an adaptive controller which will converge to a stable controller which regulates the system. Moreover, using this adaptive control scheme, it is possible to estimate consistently the frequency of the disturbance. This contrasts with the well-known bias that occurs when estimating the frequency of a sinusoid in open loop.

Considers the effects on track association of two features that are often neglected in analysis. These two features are the cross-covariance between two tracks of the same target and the effects of a loss of resolution in a sensor. The sensors modelled in this paper are nonhomogeneous in both the state space and the measurement space, and a method for calculating the cross-covariance for such dissimilar sensors is derived. Also, a simple resolution model is proposed. The paper uses Monte Carlo simulations to illustrate the effects of these two features on a number of track association methods.

This paper presents a new approach for multitarget tracking in a cluttered environment. Optimal all neighbour multi-target tracking (MTT) in clutter enumerates all possible joint measurement-to-target assignments and calculates the a posteriori probabilities of each of these joint assignments, e.g. J(I)PDA and MHT. The numerical complexity of this process is exponential in the number of tracks and the number of measurements involved. Our approach starts with an all-neighbour single-target tracking (STT) filter which provides the a priori probabilities of measurement origin; e.g. IPDA, IMM-PDA, ITS. These probabilities are used to modify the clutter density at the location of the selected measurements. In effect, the STT filter is transformed into a MTT filter with a numerical complexity which is linear in the number of tracks and the number of measurements. Measurement features, such as amplitude, can also be incorporated. Simulations are used to verify the approach when tracking crossing targets in an environment of heavy and non-uniform clutter.