The Histogram Probabilistic Multi-Hypothesis Tracker (H-PMHT) is a parametric track-before-detect algorithm that has
been shown to give good performance at a relatively low computation cost. Recent research has extended the algorithm
to allow it to estimate the signature of targets in the sensor image. This paper shows how this approach can be adapted to
address the problem of group target tracking where the motion of several targets is correlated. The group structure is treated
as the target signature, resulting in a two-tiered estimator for the group bulk-state and group element relative position.
The problem of tracking multiple maneuvering targets is considered. The usual multiple model approach is adopted in which maneuvering target motion is modeled by assuming that the target motion at each point in time can be described by one of a finite set of dynamic models. Transitions between each mode of target motion are assumed to be Markovian. Target positions are measured in polar coordinates leading to a nonlinear measurement equation. A particle filter is proposed as a solution to the problem. The proposed algorithm seeks to improve upon the performance of a previously proposed particle filter by using measurement-directed proposals and exploiting the structure of the measurement likelihood. The performance analysis focuses on targets which perform coordinated turn maneuvers. An improved model for target motion in this regime is suggested. The performance analysis, using Monte Carlo simulations, demonstrates the improved performance of the proposed algorithm compared to the previously proposed particle filter and the standard Gaussian approximation, the IMM-JPDAF.
Track-before-detect (TBD) refers to a tracking scheme where detection of a target is not made by placing a threshold on the sensor data. Rather, the complete sensor data is used to detect and track a target in the absence of a data threshold. By using all of the sensor data a TBD algorithm can detect and track targets which have a lower signal power than could be detected by using a standard detection and tracking scheme.
This paper presents an efficient particle filter TBD algorithm, which models the signal processing stages which may be found in a sensor such as radar. In this type of sensor the noise is modelled as the magnitude of a complex Gaussian process, which is Rayleigh distributed. This noise model and the model of the sensor signal processing is incorporated into the filter derivation. It is shown that in a simple simulation the algorithm can detect and track targets with a signal-to-noise ratio as low as 3dB.
The assumption of Gaussian noise in the system and measurement model has been standard practice for target tracking algorithm development
for many years. For problems involving manoeuvring targets this is known to be an over-simplification and a potentially poor approximation. In this paper the use of heavy-tailed distributions is suggested as a means of efficiently modelling the behaviour of manoeuvring targets with a single dynamic model. We exploit the fact
that all heavy-tailed distributions can be written as scale mixture of Normals to propose a Rao-Blackwellised particle filter (SMNPF) where particles sample the history of the continuous scale parameter and a Kalman filter is used to conduct the associated filtering for each particle. Schemes are proposed for making the proposal of new particles efficient. Performance of a heavy-tailed system model implemented via the SMNPF filter is compared against an IMM for a sample trajectory taken from a benchmark problem.
Over-the-horizon radar (OTHR) uses the refraction of high frequency radiation through the ionosphere in order to detect targets beyond the line-of-sight horizon. The complexities of the ionosphere can produce multipath propagation, which may result in multiple resolved detections for a single target. When there are multipath detections, an OTHR tracker will produce several spatially separated tracks for each target. Information conveying the state of the ionosphere is required in order to determine the true location of the target and is available in the form of a set of possible propagation paths, and a transformation from measured coordinates into ground coordinates for each path. Since there is no a-priori information as to how many targets are in the surveillance region, or which propagation path gave rise to which track, there is a joint target and propagation path association ambiguity which must be resolved using the available track and ionospheric information. The multipath track association problem has traditionally been solved using a multiple hypothesis technique, but a shortcoming of this method is that the number of possible association hypotheses increases exponentially with both the number of tracks and the number of possible propagation paths. This paper proposes an algorithm based on a combinatorial optimisation method to solve the multipath track association problem. The association is formulated as a two-dimensional assignment problem with additional constraints. The problem is then solved using Lagrangian relaxation, which is a technique familiar in the tracking literature for the multidimensional assignment problem arising in data association. It is argued that due to a fundamental property of relaxations convergence cannot be guaranteed for this problem. However, results show that a multipath track-to-track association algorithm based on Lagrangian relaxation, when compared with an exact algorithm, provides a large reduction in computational effort, without significantly degrading association accuracy.
In a Bayesian framework, all single target tracking problems reduce to recursive computation of the posterior density of the target state. Particle filters approximate the optimal Bayesian recursion by propagating a set of random samples with associated weights. In the last decade, there have been numerous contributions to the theory and applications of particle filters. Much study has focussed on design issues such as appropriate selection of the importance density, the use of resampling techniques which mitigate sample degeneracy and the choice of a suitable random variable space upon which to implement the particle filter in order to minimise numerical complexity. Although the effect of these design choices is, in general, well known, their relevance to target tracking problems has not been fully established. These design issues are considered for single target tracking applications involving target manoeuvres and clutter. Two choices of importance density are studied and methods for enhancing particle diversity through the avoidance of particle duplication in the resampling step are considered for each importance density. The possibility of reducing the dimension of the space over which the particle filter is implemented is considered. Based on simulation results, a few key observations are drawn about which aspects of particle filter design most influence their performance in target tracking applications. The numerical simulations also provide insights into the relationship between the state dimension and the number of particles needed to improve upon the performance of the standard tracking filters.
A dynamic infrared scene projector based on IR luminescent devices has many potential advantages compared with existing systems based on micro-resistor arrays. These include very fast response times, as individual devices can be driven at frequencies greater than 1 MHz, and no need for cryogenic cooling. Additionally, luminescent sources can not only appear hot to an IR observer when in forward bias, but also appear cold in reverse bias (commonly referred to as negative luminescence), so that a large apparent temperature range around ambient can be simulated. For a scene projector a large array of photodiodes is required, where each photodiode can be biased individually. As a precursor to the manufacture of a scene projector, we have already fabricated large area MW devices, consisting of arrays of photodiodes, suitable for use as calibration sources in IR cameras. To reduce the currents needed to achieve maximum dynamic temperature range, we have used a novel micromachining technique to fabricate integrated optical concentrators in InSb/InAlSb devices. We present here recent results from a large area (~0.86cm<sup>2</sup>) medium wavelength (MW) device, consisting of an array of photodiodes each with an integrated optical concentrator. The reverse saturation current of the device was measured to be ~2.3A/cm<sup>2</sup>, which is significantly smaller than the value of ~9A/cm<sup>2 </sup>reported previously for similar devices without optical concentrators. The device also displays a large apparent temperature range in line with device modelling. Finally, we will discuss the perspectives on using similar devices for dynamic infrared scene projection.
For many dynamic estimation problems involving nonlinear and/or non-Gaussian models, particle filtering offers improved performance at the expense of computational effort. This paper describes a scheme for efficiently tracking multiple targets using particle filters. The tracking of the individual targets is made efficient through the use of Rao-Blackwellisation. The tracking of multiple targets is made practicable using Quasi-Monte Carlo integration. The efficiency of the approach is illustrated on synthetic data.
Proc. SPIE. 4728, Signal and Data Processing of Small Targets 2002
KEYWORDS: Radar, FDA class I medical device development, Detection and tracking algorithms, Sensors, Particles, Kinematics, Monte Carlo methods, Particle filters, Systems modeling, Filtering (signal processing)
Target tracking is usually performed using data from sensors such as radar, whilst the target identification task usually relies on information from sensors such as IFF, ESM or imagery. The differing nature of the data from these sensors has generally led to these two vital tasks being performed separately. However, it is clear that an experienced operator can observe behavior characteristics of targets and, in combination with knowledge and expectations of target type and likely activity, can more knowledgeably identify the target and robustly predict its track than any automatic process yet defined. Most trackers are designed to follow targets within a wide envelope of trajectories and are not designed to derive behavior characteristics or include them as part of their output. Thus, there is potential scope for both applying target type knowledge to improve the reliability of the tracking process, and to derive behavioral characteristics which may enhance knowledge about target identity and/or activity. In this paper we introduce a Bayesian framework for joint tracking and identification and give a robust and computationally efficient particle filter based algorithm for numerical implementation of the resulting recursions. Simulation results illustrating algorithm performance are presented.
This paper describes an application of sequential Monte Carlo estimation (particle filtering) to the problem of tracking targets occasionally hidden in the blind Doppler zones of a radar. A particle filter which incorporates the prior knowledge of the blind Doppler zone limits has been designed. The simulation results suggest significant improvement in track continuity over the standard Extended Kalman filter. As an operationally viable solution a hybrid tracker is envisaged which can switch between the EKF (with possible built-in data association logic) and the particle filter, depending on the tracking conditions.
We consider the problem of tracking a group of point targets via a sensor with limited resolution and a finite field of view. Measurement association uncertainty and measurement process non-linearity are major difficulties with such cases. It is shown that a Bayesian estimator can be directly implemented using the particle filter technique.
Proc. SPIE. 3809, Signal and Data Processing of Small Targets 1999
KEYWORDS: Target detection, Detection and tracking algorithms, Particles, Computer simulations, Monte Carlo methods, Time metrology, Signal processing, Electronic filtering, Filtering (signal processing), Expectation maximization algorithms
In this paper we consider the problem of tracking a maneuvering target in clutter. We apply an original on-line Monte Carlo filtering algorithm to perform optimal state estimation. Improved performance of the resulting algorithm over standard IMM/PDAF based filters is demonstrated.
The problem of tracking point targets moving in a group, or features of an extended object, is formulated via a general two component model. An example involving translation, scaling, rotation and pattern distortion is presented. It is assumed that measurements of the points are unlabelled, which, together with a significant clutter level, leads to measurement association uncertainty. A Bayesian bootstrap filter is used to implement a nonlinear, multiple hypothesis, recursive estimator.
While single model filters are sufficient for tracking targets having fixed kinematic behavior, maneuvering targets require the use of multiple models. Jump Markov linear systems whose parameters evolve with time according to a finite state-space Markov chain, have been used in these situations with great success. However, it is well-known that performing optimal estimation for JMLS involves a prohibitive computational cost exponential in the number of observations. Many approximate methods have been proposed in the literature to circumvent this including the well-known GPB and IMM algorithms. These methods are computationally cheap but at the cost of being suboptimal. Efficient off- line methods have recently been proposed based on Markov chain Monte Carlo algorithms that out-perform recent methods based on the Expectation-Maximization algorithms. However, realistic tracking systems need on-line techniques. In this paper, we propose an original on-line Monte Carlo filtering algorithm to perform optimal state estimation of JMLS. The approach taken is loosely based on the bootstrap filter which, wile begin a powerful general algorithm in its original form, does not make the most of the structure of JMLS. The proposed algorithm exploits this structure and leads to a significant performance improvement.
Proc. SPIE. 3816, Mathematical Modeling, Bayesian Estimation, and Inverse Problems
KEYWORDS: Signal to noise ratio, Environmental monitoring, Statistical analysis, Modulation, Fourier transforms, Computer simulations, Image analysis, Monte Carlo methods, Signal detection, Statistical modeling
General frequency modulated signals can be used to characterize many vibrations in dynamic environments, with applications to engine monitoring and sonar. Most work in to parameter estimation of such signals assumes knowledge of the number of carrier frequencies present in the signal. In this paper, we make no such assumption, and use Bayesian techniques to address jointly the problem of model selection and parameter estimation. Following the work of Andrieu and Doucet, who addressed the problem of joint Bayesian model selection and parameter estimation for non-modulated sinusoids in white Gaussian noise, a posterior distribution for the parameter and model order is obtained. This distribution is to o complicated to evaluate analytically, so we use a reversible jump Markov chain Monte Carlo algorithm to draw samples for the distribution. Some simulated examples are presented to illustrate the algorithm's performance.
The sampling based bootstrap filter is applied to the problem of maintaining track on a target in the presence of intermittent spurious objects. This problem is formulated in a multiple hypothesis framework and the bootstrap filter is applied to generate the posterior distribution of the state vector of the required target - i.e. to generate the target track. The bootstrap technique facilitates the integration of the available information in a near-optimal fashion without the need to explicitly store and manage hypotheses from previous time steps.
Proc. SPIE. 3373, Signal and Data Processing of Small Targets 1998
KEYWORDS: Target detection, Statistical analysis, Detection and tracking algorithms, Sensors, Control systems, Monte Carlo methods, Velocity measurements, Algorithm development, Stochastic processes, Systems modeling
Many tracking and guidance problems may be formulated as a terminating stochastic game in which the distribution of outcomes is affected by the intermediate actions. Traditional technique ignore this interaction. In this paper we develop an information gathering strategy which maximizes the expected gain of the outcome. For example, the objective could be a function of the terminal miss distance and target identify with penalties for missing a valid target or attacking a friendly one. Several trade-offs are addressed: the increased information available from taking more measurements, the fact that an increased number of measurement may adversely affect change of success and the fact that later measurements may be more informative but also may be of little use since there my not be enough time available for reaction to this extra information. The problem is formulated so that we are required to choose, under uncertainty, an alternative from a set of possible decisions. This set has a discrete uncertainty as to the number of measurements to be taken and a continuous uncertainty as to where and when the measurements should be taken. Preferences over consequences are modeled with a utility function. We propose to choose as optimal the alternative which maximizes expected utility. A simulation based approximation to the solution of this stochastic optimization problem is outlined. This relies on recent developments in dimensions swapping Markov Chain Monte Carlo (MCMC) techniques. The use of MCMC methodology allow us to explore the expected utility surface and thus select a measurement strategy. The resulting algorithm is demonstrated on a simple guidance problem.
A Bayesian technique is applied to the target acquisition problem at handover from the fire control to the missile seeker. This is a multiple hypothesis scheme which includes an explicit model of the possible misalignment or bias between the fire control and seeker coordinate frames. This method is compared with a linear least cost assignment technique which may be implemented via the Munkres fast search algorithm.
A standard assumption of most multiple target tracking filters is that all the targets move independently of one another. However, in many cases, it is known a-priori that the targets move (at least approximately) as a group: this dependency should not be ignored. In this paper we describe an approach to multiple target tracking where the target dynamics are taken to be the superposition of a group effect which is common to all group members and an individual effect which is taken to be independent between members of the group. The method also allows for the presence of clutter and missed target detections. This is done by embedding the dependent target motion model within a multiple hypothesis framework. A closed form solution is derived for the special linear-Gaussian case and simulation results illustrating performance are presented. This paper is a recursive extension of the selection method presented at last year's conference.
The following problem is considered: a group of point targets is observed via an imperfect sensor and one of the measurements chosen. The measurements of each target position is corrupted by an independent error, although every object is detected. Two processes then act to move and distort the group: one is a bulk effect that acts equally on all members of the group while the other is independent for each target. The group is observed again by a (possibly different) imperfect sensor which may not detect every target. The problem is to construct the posterior distribution of the chosen target's position, given the two sets of measurements. Probability models of the sensors and of the pattern distortion processes are assumed to be available. A formal general solution has been obtained for this problem. For the special linear-Gaussian case this reduces to a closed form analytic expression. To facilitate implementation, a hypothesis pruning technique is given. A simulation example illustrating performance is provided.
Proc. SPIE. 2561, Signal and Data Processing of Small Targets 1995
KEYWORDS: Radar, Detection and tracking algorithms, Digital filtering, Monte Carlo methods, Gaussian filters, Electronic filtering, Nonlinear filtering, Autoregressive models, Systems modeling, Filtering (signal processing)
When tracking targets with radar, changes in target aspect with respect to the observer can cause the apparent center of radar reflections to wander significantly. The resulting noisy angle errors are called target glint. Glint may severely affect the tracking accuracy, particularly when tracking large targets at short ranges (such as might occur in the final homing phase of a missile engagement). The effect of glint is to produce heavy-tailed, time correlated non-Gaussian disturbances on the observations. It is well known that the performance of the Kalman filter degrades severely in the presence of such disturbances. In this paper we propose a random sample based implementation of a Bayesian recursive filter. This filter is based on the Metropolis-Hastings algorithm and the Gaussian sum approach. The key advantage of the filter is that any nonlinear/non-Gaussian system and/or measurement models can be routinely implemented. Tracking performance of the filter is demonstrated in the presence of glint.