This is the fifth part of a series of papers that provide a comprehensive survey of techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. Part I and Part II deal with target motion models. Part III covers measurement models and associated techniques. Part IV is concerned with tracking techniques that are based on decisions regarding target maneuvers. This part surveys the multiple-model methods $the use of multiple models (and filters) simultaneously - which is the prevailing approach to maneuvering target tracking in recent years. The survey is presented in a structured way, centered around three generations of algorithms: autonomous, cooperating, and variable structure. It emphasizes the underpinning of each algorithm and covers various issues in algorithm design, application, and performance.

Survey of maneuvering target tracking. Part V. Multiple-model methods

Performance evaluation of UKF-based nonlinear filtering

This paper proposes a numerical-integration perspective on the Gaussian filters. A Gaussian filter is approximation of the Bayesian inference with the Gaussian posterior probability density assumption being valid. There exists a variation of Gaussian filters in the literature that derived themselves from very different backgrounds. From the numerical-integration viewpoint, various versions of Gaussian filters are only distinctive from each other in their specific treatments of approximating the multiple statistical integrations. A common base is provided for the first time to analyze and compare Gaussian filters with respect to accuracy, efficiency and stability factor. This study is expected to facilitate the selection of appropriate Gaussian filters in practice and to help design more efficient filters by employing better numerical integration methods

A Numerical-Integration Perspective on Gaussian Filters

This paper is the second part in a series that provides a comprehensive survey of maneuvering target tracking without addressing the so-called measurement-origin uncertainty. It surveys motion models of ballistic targets used for target tracking. Models for all three phases (i.e., boost, coast, and reentry) of motion are covered.

Survey of Maneuvering Target Tracking. Part II: Motion Models of Ballistic and Space Targets

Tracking ground targets with airborne GMTI (ground moving target indicator) sensor measurements proves to be a challenging task due to high target density, high clutter, and low visibility. The exploitation of nonstandard background information such as road maps and terrain information is therefore highly desirable for the enhancement of track quality and track continuity. The present paper presents a Bayesian approach to incorporate such information consistently. It is particularly suited to deal with winding roads and networks of roads. The target dynamics is modeled in quasi one-dimensional road coordinates and mapped onto ground coordinates using linear road segments taking road map errors into account. The case of several intersecting roads with different characteristics, such as mean curvature, slope, or visibility, is treated within an interacting multiple model (IMM) scheme. Targets can be masked both by the clutter notch of the sensor and by terrain obstacles. Both effects are modeled using a sensor-target state dependent detection probability. The iterative filter equations are formulated within a framework of Gaussian sum approximations on the one hand and a particle filter approach on the other hand. Simulation results for single targets taken from a realistic ground scenario show strongly reduced target location errors compared with the case of neglecting road-map information. By modeling the clutter notch of the GMTI sensor, early detection of stopping targets is demonstrated

Road-map assisted ground moving target tracking

Tracking of a ballistic re-entry object from radar observations is a highly complex problem in nonlinear filtering. The paper adopts a one-dimensional vertical motion model with unknown ballistic coefficient, derives and analyses the posterior Cramer-Rao lower bounds (CRLBs) for this problem, and compares the error performance of three nonlinear filters against the theoretical CRLBs. The considered nonlinear filters include the extended Kalman filter, the unscented Kalman filter and the bootstrap (particle) filter. Taking into account the computational and statistical performance, the unscented Kalman filter is found to be the preferred choice for this application.

Performance bounds and comparison of nonlinear filters for tracking a ballistic object on re-entry

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.

A variable structure multiple model particle filter for GMTI tracking

The paper explores the subject of Cramer-Rao type lower bounds for tracking a manoeuvring target. Tar- get dynamics are modelled by the switching of multi- ple (possibly nonlinear) motion regimes. Two types of bounds are considered. The flrst is evaluated as the expected value over the regime sequences. The compu- tational complexity of this bound grows exponentially with time. The second bound is applicable only to the deterministic trajectories, and assumes that the knowl- edge of the particular regime sequence is known. Nu- merical examples are provided in support of theoretical considerations.

M.S. Arulampalam

Papers

Performance bounds and comparison of nonlinear filters for tracking a ballistic object on re-entry

A variable structure multiple model particle filter for GMTI tracking

Error performance bounds for tracking a manoeuvring target