Sanjeev Arulampalam

Comparison of the particle filter with range-parameterized and modified polar EKFs for angle-only tracking

The tracking performance of the Particle Filter is compared with that of the Range-Parameterised EKF (RPEKF) and Modified Polar coordinate EKF (MPEKF) for a single-sensor angle-only tracking problem with ownship maneuver. The Particle Filter is based on representing the required density of the state vector as a set of random samples with associated weights. This filter is implemented for recursive estimation, and works by propagating the set of samples, and then updating the associated weights according to the new received measurement. The RPEKF, which is essentially a weighted sum of multiple EKF outputs, and the MPEKF are known for their robust angle-only tracking performance. This comparative study shows that the Particle Filter performance is the best, although the RPEKF is only marginally worse. The superior performance of the Particle Filter is particularly evident for high noise conditions where the EKF type trackers generally diverge. Also, the Particle Filter and the RPEKF are found to be robust to the level of a priori knowledge of initial target range. On the contrary, the MPEKF exhibits degraded performance for poor initialisation.

A Gaussian-Sum Based Cubature Kalman Filter for Bearings-Only Tracking

Herein is presented an efficient nonlinear filtering algorithm called the Gaussian-sum cubature Kalman filter (GSCKF) for the bearings-only tracking problem. It is developed based on the recently proposed cubature Kalman filter and is built within a Gaussian-sum framework. The new algorithm consists of a splitting and merging procedure when a high degree of nonlinearity is detected. Simulation results show that the proposed algorithm demonstrates comparable performance to the particle filter (PF) with significantly reduced computational cost.

A Multiple Hypothesis Tracker for Multitarget Tracking With Multiple Simultaneous Measurements

Typical multitarget tracking systems assume that in every scan there is at most one measurement for each target. In certain other systems such as over-the-horizon radar tracking, the sensor can generate resolvable multiple detections, corresponding to different measurement modes, from the same target. In this paper, we propose a new algorithm called multiple detection multiple hypothesis tracker (MD-MHT) to effectively track multiple targets in such multiple-detection systems. The challenge for this tracker, which follows the multiple hypothesis framework, is to jointly resolve the measurement origin and measurement mode uncertainties. The proposed tracker solves this data association problem via an extension to the multiframe assignment algorithm. Its performance is demonstrated on a simulated over-the-horizon-radar multitarget tracking scenario, which confirms the effectiveness of this algorithm.

Comparison of nonlinear filtering algorithms in ground moving target indicator (GMTI) tracking

Tracking using the ground moving target indicator (GMTI) sensor measurements plays an important role in situation awareness of the battlefield, surveillance, and precision tracking of ground moving targets. The GMTI sensor measurements range, azimuth, and range-rate are nonlinear functions of the target state. The extended Kalman filter (EKF) is widely used to solve the GMTI filtering problem. Since the GMTI measurement model is nonlinear, the use of an EKF is sub-optimal. The sub-optimality depends on the degree of nonlinearity of the measurement function and GMTI measurement error covariance. We can convert polar measurements range and azimuth to Cartesian measurements and approximately treat the range-rate as a linear function of the target velocity by considering the radar line-of-sight (RLOS) vector as a constant. This allows the use linear Kalman filter (KF) with linearized measurements in an approximate way. The unscented Kalman filter (UKF) and particle filter (PF) have been shown recently as robust alternate algorithms for a wide range of nonlinear estimation problems. This paper compares the performance of the KF with linearized measurements, EKF, iterated EKF (IEKF), UKF, and PF for the GMTI measurement filtering problem using a wide range of operating conditions. Estimation accuracy, statistical consistency, and computational speed and storage are used to evaluate the performance of these estimators. We use Monte-Carlo simulations and calculate the average mean square error (MSE) matrix, normalized estimation error squared (NEES), and normalized innovation squared (NIS) to analyze the accuracy and statistical consistency.

A Partially Uniform Target Birth Model for Gaussian Mixture PHD/CPHD Filtering

The conventional GMPHD/CPHD filters require the PHD for target births to be a Gaussian mixture (GM), which is potentially inefficient because careful selection of the mixture parameters may be required to ensure good performance. Here we present approximations which allow part of the birth PHD to be uniformly distributed, obviating the need to use a large GM to model target births. The benefits of this approach are demonstrated by simulations on a bearings-only filtering scenario.

Performance of the shifted Rayleigh filter in single-sensor bearings-only tracking

The problem of single-sensor bearings-only tracking continues to present challenges to tracking algorithms, particularly in certain difficult scenarios such as ones with high bearing rates. In such scenarios, the performance of the recently introduced shifted Rayleigh filter (SRF) is compared with that of other techniques such as extended Kalman filter (EKF), unscented Kalman filter (UKF) and particle filter (PF). The results are also compared with the theoretical Cramer-Rao Lower Bound (CRLB). The SRF is a moment matching algorithm, and its key feature is that it generates the exact conditional distribution of target motion, given normal approximation to the prior. Simulations show that the SRF is superior to other moment matching algorithms such as EKF and UKF and is able to achieve comparable performance to PF while being orders of magnitude faster.

Introduction to the issue on multitarget tracking

Multitarget tracking has a long history spanning over 50 years and it refers to the problem of jointly estimating the number of targets and their states from sensor data. Today, multitarget tracking has found applications in diverse disciplines, including, air traffic control, intelligence, surveillance, and reconnaissance (ISR), space applications, oceanography, autonomous vehicles and robotics, remote sensing, computer vision, and biomedical research. During the last decade, advances in multitarget tracking techniques, along with sensing and computing technologies, have opened up numerous research venues as well as application areas. The multitarget tracking problem in the presence of false alarm and sensor probability of detection less than unity is much more complex than the standard filtering problem. Apart from process and measurement noises in the dynamic and measurement models, respectively, one has to contend with much more complex sources of uncertainty, such as the measurement origin uncertainty, data association, false alarm, missed detections, and births and deaths of targets. The goal of this special issue is to explore recent advances in the theory and applications of multitarget tracking with a focus on novel algorithms and methods.

Void Probabilities and Cauchy–Schwarz Divergence for Generalized Labeled Multi-Bernoulli Models

The generalized labeled multi-Bernoulli (GLMB) is a family of tractable models that alleviates the limitations of the Poisson family in dynamic Bayesian inference of point processes. In this paper, we derive closed form expressions for the void probability functional and the Cauchy–Schwarz divergence for GLMBs. The proposed analytic void probability functional is a necessary and sufficient statistic that uniquely characterizes a GLMB, while the proposed analytic Cauchy–Schwarz divergence provides a tractable measure of similarity between GLMBs. We demonstrate the use of both results on a partially observed Markov decision process for GLMBs, with Cauchy–Schwarz divergence based reward, and void probability constraint.

Differential geometry measures of nonlinearity for filtering with nonlinear dynamic and linear measurement models

In our previous work, we presented an algorithm to quantify the degree of nonlinearity of nonlinear filtering problems with linear dynamic models and nonlinear measurement models. A quantitative measure of the degree of nonlinearity was formulated using differential geometry measures of nonlinearity, the parameter-effects curvature and intrinsic curvature. We presented numerical results for a number of practical nonlinear filtering problems of interest such as the bearing-only filtering, ground moving target indicator filtering, and video filtering problems. In this paper, we present an algorithm to compute the degree of nonlinearity of a nonlinear filtering problem with a nonlinear dynamic model and a linear measurement model. This situation arises for the bearing-only filtering problem with modified polar coordinates and log polar coordinates. We present numerical results using simulated data.

Gaussian-Sum Cubature Kalman Filter with Improved Robustness for Bearings-only Tracking

This letter presents a Gaussian-sum cubature Kalman filter with improved robustness compared to the original algorithm proposed by the authors in , which demonstrated excellent accuracy and efficiency for the bearings-only tracking problem. Modifications are made in the splitting and merging procedure of the Gaussian components in the algorithm. Simulation results confirm the improved robustness of the modified algorithm against the choice of threshold level for the splitting procedure.