Neil J. Gordon

Bearings-only tracking of manoeuvring targets using particle filters

We investigate the problem of bearings-only tracking of manoeuvring targets using particle filters (PFs). Three different (PFs) are proposed for this problem which is formulated as a multiple model tracking problem in a jump Markov system (JMS) framework. The proposed filters are (i) multiple model PF (MMPF), (ii) auxiliary MMPF (AUX-MMPF), and (iii) jump Markov system PF (JMS-PF). The performance of these filters is compared with that of standard interacting multiple model (IMM)-based trackers such as IMM-EKF and IMM-UKF for three separate cases: (i) single-sensor case, (ii) multisensor case, and (iii) tracking with hard constraints. A conservative CRLB applicable for this problem is also derived and compared with the RMS error performance of the filters. The results confirm the superiority of the PFs for this difficult nonlinear tracking problem.

A variable structure multiple model particle filter for GMTI tracking

The problem of tracking ground targets with GMTI sensors has received some attention in the recent past. In addition to standard GMTI sensor measurements, one is interested in using non-standard information such as road maps, and terrain-related visibility conditions to enhance tracker performance. The conventional approach to this problem has been to use the variable structure IMM (VS-IMM), which uses the concept of directional process noise to model motion along particular roads. In this paper, we present a particle filter based approach to this problem which we call variable structure multiple model particle filter (VS-MMPF). Simulation results show that the performance of the VS-MMPF is much superior to that of VS-IMM.

Detection and Tracking Using Particle-Filter-Based Wireless Sensor Networks

The work reported in this paper investigates the performance of the Particle Filter (PF) algorithm for tracking a moving object using a wireless sensor network (WSN). It is well known that the PF is particularly well suited for use in target tracking applications. However, a comprehensive analysis on the effect of various design and calibration parameters on the accuracy of the PF has been overlooked. This paper outlines the results from such a study. In particular, we evaluate the effect of various design parameters (such as the number of deployed nodes, number of generated particles, and sampling interval) and calibration parameters (such as the gain, path loss factor, noise variations, and nonlinearity constant) on the tracking accuracy and computation time of the particle-filter-based tracking system. Based on our analysis, we present recommendations on suitable values for these parameters, which provide a reasonable trade-off between accuracy and complexity. We also analyze the theoretical Cramér-Rao Bound as the benchmark for the best possible tracking performance and demonstrate that the results from our simulations closely match the theoretical bound. In this paper, we also propose a novel technique for calibrating off-the-shelf sensor devices. We implement the tracking system on a real sensor network and demonstrate its accuracy in detecting and tracking a moving object in a variety of scenarios. To the best of our knowledge, this is the first time that empirical results from a PF-based tracking system with off-the-shelf WSN devices have been reported. Finally, we also present simple albeit important building blocks that are essential for field deployment of such a system.

On target classification using kinematic data

Abstract The use of kinematic measurements for target classification has been explored recently by several authors. This paper formulates the general framework for optimal Bayesian estimation of target state and class. Since target class is a non-evolutionary attribute, the solution is conceptually based on a static multiple-class filter. When applied to linear/Gaussian estimation using acceleration limits, the class-matched filters can be aggregated into a single IMM filter, thus reducing the described general solution to the joint tracking and classification approach presented in earlier publications.

Detection and tracking using wireless sensor networks

Target detection and tracking is a well-established area of research. However, a majority of proposed solutions in existing literature rely on expensive and specialized sensors, which often have limited coverage. Using low cost sensor nodes is an attractive and complementary approach to scalable target detection and tracking applications. However, tracking with low cost Wireless Sensor Network (WSN), presents its own challenges, namely real time decision making, high frequency sampling, multi-modal sensing, complex signal processing, and data fusion. In this work, we investigate the use of inexpensive off-the-shelf WSN devices for ground surveillance. Our system estimates and tracks a target based on the spatial differences of the target objects signal strength detected by the monitoring sensors at different locations.

Littoral tracking using particle filter

Littoral tracking refers to the tracking of targets on land and in sea near the boundary of the two regions. A ground-moving target continues to move on land and can not enter the sea. Similarly, a sea-moving target moves in the sea and the land serves as an infeasible region. Enforcing infeasible regions or hard constraints in the framework of the Kalman filter or interacting multiple model (IMM) estimator is not natural. However, these hard constraints can be easily enforced using the particle filter algorithm. We formulate the littoral tracking problem as a joint tracking and classification problem, where we assign a target class for each isolated land or water region. We use a reflecting boundary condition to enforce the region constraint. We demonstrate this concept for a single target using the airborne ground moving target indicator measurements. Numerical results show that the proposed algorithm produces robust classification probabilities using kinematic measurements.

Particle-Based Track-Before-Detect in Rayleigh Noise

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.

Multipath track association for over-the-horizon radar using Lagrangian relaxation

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.

Target tracking through a coordinated turn

Allowing for perturbations in speed and turn rate, the state of a target moving in a coordinated turn obeys a nonlinear stochastic differential equation which cannot be discretised exactly. Existing algorithms for coordinated turn tracking avoid this problem by ignoring perturbations in the continuous-time model and adding process noise only after discretisation. We retain this modelling by discretising using first and second order Taylor approximations to the continuous-time coordinated turn dynamic model. The discrete-time models are used as the basis for a particle filter for tracking a target moving in a coordinated turn. The performances of the discretisation techniques and the effect of different coordinate systems on tracking performance are examined.

Performance bounds for recursive sensor registration

A pre-requisite to successful multi-sensor in- tegration is that the data from reporting sensors be trans- ferred to a common reference frame free of errors. This is referred to as sensor registration. In this paper we consider the problem of recursive sensor registration al- gorithms, which carry out simultaneous registration and tracking. Cramer-Rao pe flormance bounds are derived for recursive sensor registration assuming asynchronous dis- similar sensors. The statistical error pelformance of the EKF applied to the recursive sensor registration problem is compared with the bounds.