Subhash Challa

Joint target tracking and classification using radar and ESM sensors

Bayesian target classification methods using radar and electronic support measure (ESM) data are considered. A joint treatment of target tracking and target classification problems is introduced. First, a method for target classification using radar data and class-dependent kinematic models is presented. Second, a target classification method using ESM data is presented. Then, a Bayesian radar and ESM data fusion algorithm, referred to as direct identity fusion (DIF), for target classification is presented. This algorithm exploits the dependence of target state on target class via the use of class dependent kinematic models but fails to exploit the dependence of target class on target state. We then introduce a method, referred to as joint tracking and classification (JTC), for treating target tracking and classification problems jointly, by exploiting the dependence of target class on target state via flight-envelope-dependent classes and the dependence of target state on target class via class dependent kinematic models. A two-dimensional example demonstrates the relative merits of these methods. It is shown that, while the incorporation of the two-way dependence between target state and class (i.e., JTC) promises some benefits over the method that incorporates only a one-way dependence (i.e., DIF), there are severe filter implementation difficulties for the former. The results also demonstrate that the fusion of information from radar and ESM sensors via the DIF approach results in improvements over classification methods based on either of the individual sensors.

Joint sensor registration and track-to-track fusion for distributed trackers

Sensor registration deals with the correction of registration errors and is an inherent problem in all multisensor tracking systems. Traditionally, it is viewed as a least squares or a maximum likelihood problem independent of the fusion problem. We formulate it as a Bayesian estimation problem where sensor registration and track-to-track fusion are treated as joint problems and provide solutions in cases 1) when sensor outputs (i.e., raw data) are available, and 2) when tracker outputs (i.e., tracks) are available. The solution to the latter problem is of particular significance in practical systems as band limited communication links render the transmission of raw data impractical and most of the practical fusion systems have to depend on tracker outputs rather than sensor outputs for fusion. We then show that, under linear Gaussian assumptions, the Bayesian approach leads to a registration solution based on equivalent measurements generated by geographically separated radar trackers. In addition, we show that equivalent measurements are a very effective way of handling sensor registration problem in clutter. Simulation results show that the proposed algorithm adequately estimates the biases, and the resulting central-level trucks are free of registration errors.

A Bayesian solution and its approximations to out-of-sequence measurement problems☆

Abstract Target tracking using delayed, out-of-sequence measurements is a problem of growing importance due to an increased reliance on networked sensors interconnected via complex communication network architectures. In such systems, it is often the case that measurements are received out-of-time-order at the fusion center. This paper presents a Bayesian solution to this problem and provides approximate, implementable algorithms for both cluttered and non-cluttered scenarios involving single and multiple time-delayed measurements. Such an approach leads to a solution involving the joint probability density of current and past target states. In contrast, existing solutions in the literature modify the sensor measurement equation to account for the time delay and explicitly deal with the resulting correlations that arise in the process noise and current target state. In the Bayesian solution proposed in this paper, such cross correlations are treated implicitly. Under linear Gaussian assumptions, the Bayesian solution reduces to an augmented state Kalman filter (AS-KF) for scenarios devoid of clutter and an augmented state probabilistic data association filter (AS-PDA) for scenarios involving clutter. Computationally efficient versions of AS-KF and AS-PDA are considered in this paper. Simulations are presented to evaluate the performance of these solutions.

Manoeuvring target tracking in clutter using particle filters

A particle filter (PF) is a recursive numerical technique which uses random sampling to approximate the optimal solution to target tracking problems involving nonlinearities and/or non-Gaussianity. A set of particle filtering methods for tracking and manoeuvering target in clutter from angle-only measurements is presented and evaluated. The aim is to compare PFs to a well-established tracking algorithm, the IMM-PDA-EKF (interacting multiple model, probabilistic data association, extended Kalman filter), and to provide an insight into which aspects of PF design are of most importance under given conditions. Monte Carlo simulations show that the use of a resampling scheme which produces particles with distinct values offers significant improvements under almost all conditions. Interestingly, under all conditions considered here,using this resampling scheme with blind particle proposals is shown to be superior, in the sense of providing improved performance for a fixed computational expense, to measurement-directed particle proposals with the same resampling scheme. This occurs even under conditions favourable to the use of measurement-directed proposals. The IMM-PDA-EKF performs poorly compared with the PFs for large clutter densities but is more effective when the measurements are precise.

Nonlinear filter design using Fokker-Planck-Kolmogorov probability density evolutions

The Fokker-Planck-Kolmogorov equation (FPKE) in conjunction with Bayes conditional density update formula provides optimal estimates for a general continuous-discrete nonlinear filtering problem. It is well known that the analytical solution of FPKE and Bayes formula are extremely difficult to obtain except in a few special cases. Hence, we address this problem using numerical approaches. The efficient numerical solution of FPKE presented relies on the key issue of adaptively calculating the domain over which the state probability density function is to be evaluated, which is done using Chebyshevs inequality. Application to a passive tracking example shows that this approach can provide consistent estimators when measurement nonlinearities and noise levels are high.

Nonlinear filtering via generalized Edgeworth series and Gauss-Hermite quadrature

In this correspondence, an approximate nonlinear filter is presented for systems with continuous time dynamics and discrete time measurements. The filter is based on a combination of generalized Edgeworth series (GES) expansion of probability density functions and Gauss-Hermite quadrature (GHQ); application to a passive tracking problem is also presented.

Bayesian approaches to track existence - IPDA and random sets

Most target tracking algorithms implicitly assume that target exists. There are only a few techniques that address the target existence problem along with target tracking. For example, (Integrated Probabilistic Data Association) IPDA filter addresses the target tracking and target existence problems simultaneously and it does so under at most one target assumption. In recent times random sets have been proposed as a general framework for multiple target tracking problem. However, its relationship to well understood existing tracking algorithms like IPDA has not been explored. In this paper, we show that under appropriate conditions random sets provide appropriate mathematical framework for solving the joint target existence and state estimation problem and subsequently show that it results in IPDA under appropriate simplifying assumptions.

Can we trust trusted nodes in wireless sensor networks

In this paper we extend our previously designed trust model in wireless sensor networks to include both; communication trust and data trust. Trust management in wireless sensor networks is predominantly based on routing messages; whether the communication has happened or not (successful and unsuccessful transactions). The uniqueness of sensing data in wireless sensor networks introduces new challenges in calculating trust between nodes (data trust). If the overall trust is based on just the communication trust, it might mislead the network, that is; untrustworthy nodes in terms of sensed data can be classified as trusted nodes due to their communication capabilities. Hence we need to develop new trust models to address the issue of the actual sensed data. Here we are comparing the two trust models and proving that one model by itself is not enough to decide on the trustworthiness of a node, so new techniques are required to combine both data trust and communication trust.

Gating techniques for maneuvering target tracking in clutter

Gating techniques for maneuvering target tracking using an IMM-PDA filter are considered in this paper. Existing gating techniques, namely, centralized gating and model based gating are reviewed and new gating techniques, called model probability weighted gating and two-stage model probability weighted gating, are proposed. A benchmark trajectory and a random scenario are considered for performance evaluation of the gating techniques in terms of RMS errors, percentage of track loss and computational load.

RBATMWSN: Recursive Bayesian Approach to Trust Management in Wireless Sensor Networks

This paper introduces a new trust model and a reputation system for wireless sensor networks based on a sensed continuous data. It establishes the continuous version of the beta reputation system and applied to binary events and presents a new Gaussian reputation system for sensor networks (GRSSN) . We introduce a theoretically sound Bayesian probabilistic approach for mixing second-hand information from neighbouring nodes with directly observed information.