This is the first part of a comprehensive and up-to-date survey of the techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. It surveys various mathematical models of target motion/dynamics proposed for maneuvering target tracking, including 2D and 3D maneuver models as well as coordinate-uncoupled generic models for target motion. This survey emphasizes the underlying ideas and assumptions of the models. Interrelationships among models and insight to the pros and cons of models are provided. Some material presented here has not appeared elsewhere.

Survey of maneuvering target tracking. Part I. Dynamic models

This paper assumes a requirement for an unmanned multiunit satellite to be assembled in orbit. The requirement to be met is to bring the satellites together so tha t they do not collide but actually rendezvous. The equations of motion of the rendezvous satellite in a relative coordinate system are derived and used to compute a final injection velocity which would effect collision after a time r. The velocity is corrected periodically by a command guidance system and just before impact retrothrust is applied. A terminal infrared homing sj^stem is required to actually accomplish physical contact and joining of the satellites. The first satellite placed in orbit is the "control satellite" and controls all the satellites to be assembled and contains the ccmputer, command guidance equipment, precision orientation equipment, and other features necessary to effect rendezvous. The succeeding satellites contain a propulsion system, a rough at t i tude control system, and a command receiver plus whatever scientific equipment they carry to perform their basic mission. This paper presents the following:

Terminal Guidance System for Satellite Rendezvous

Multiple hypothesis tracking (MHT) is generally accepted as the preferred method for solving the data association problem in modern multiple target tracking (MTT) systems. This paper summarizes the motivations for MHT, the basic principles behind MHT and the alternative implementations in common use. It discusses the manner in which the multiple data association hypotheses formed by MHT can be combined with multiple filter models, such as used by the interacting multiple model (IMM) method. An overview of the studies that show the advantages of MHT over the conventional single hypothesis approach is given. Important current applications and areas of future research and development for MHT are discussed.

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Multiple hypothesis tracking for multiple target tracking

MULTISENSOR DATA FUSION Introduction to Multisensor Data Fusion, D. Hall and J. Llinas The JDL Data Fusion Process Model, A. Steinberg and C. Bowman Introduction to the Algorithms of Data Association in Multiple-Target Tracking, J.K. Uhlmann The Principles and Practice of Image and Spatial Data Fusion, E. Waltz Data Registration, R. Brooks and L. Grewe Data Fusion Automation: A Top-Down Perspective, R. Antony Contrasting Approaches to Combine Evidence, J. Carl ADVANCED TRACKING AND ASSOCIATION METHODS Target Tracking Using Probabilistic Data Association-Based Techniques and Applications to Sonar, Radar, and EO Sensors, T. Kirubarajan and Y. Bar-Shalom An Introduction to the Combinatorics of Optimal and Approximate Data Association, J.K. Uhlmann A Bayesian Approach to Multiple-Target Tracking, L. Stone Data Association Using Multiple Frame Assignments, A. Poore, S. Lu, and B.J. Suchomel General Decentralized Data Fusion with Covariance Intersection, S. Julier and J. Uhlmann Data Fusion in Non-Linear Systems, S. Julier and J. Uhlmann Random Set Theory for Target Tracking and Identification, R. Mahler SYSTEMS ENGINEERING AND IMPLEMENTATION Requirements Derivation for Data Fusion Systems, E. Waltz and D. Hall A Systems Engineering Approach for Implementing Data Fusion Systems, C. Bowman and A. Steinberg Studies and Analyses with Project Correlation: An In-Depth Assessment of Correlation Problems and Solution Techniques, J. Llinas, L. McConnell, C. Bowman, D. Hall, and P. Applegate Data Management Support to Tactical Data Fusion, R. Antony Removing the HCI Bottleneck: How the Human-Computer Interface (HCI) Affects the Performance of Data Fusion Systems, M.J. Hall, S.A. Hall, and T. Tate Assessing the Performance of Multisensor Fusion Processes, J. Llinas Dirty Secrets in Data Fusion, D. Hall and A. Steinberg SAMPLE APPLICATIONS A Survey of Multisensor Data Fusion Systems, M. Nichols Data Fusion for Developing Predictive Diagnostics for Electromechanical Systems, C. Byington and A. Garga Information Technology for NASA in the 21st Century, R.J. Hansen, D. Cooke, K. Ford, and S. Zornetzer Data Fusion for a Distributed Ground-Based Sensing System, R. Brooks An Evaluation Methodology for Fusion Processes Based on Information Needs, H. Keithley RESOURCES Web Sites Related to Multi-Sensor Data Fusion Index

Handbook of multisensor data fusion

Nonlinear filters can provide estimation accuracy that is vastly superior to extended Kalman filters for some important practical applications. We compare several types of nonlinear filters, including: particle filters (PFs), unscented Kalman filters, extended Kalman filters, batch filters and exact recursive filters. The key practical issue in nonlinear filtering is computational complexity, which is often called "the curse of dimensionality". It has been asserted that PFs avoid the curse of dimensionality, but this is generally incorrect. Well-designed PFs with good proposal densities sometimes avoid the curse of dimensionality, but not otherwise. Future research in nonlinear filtering will exploit recent progress in quasi-Monte Carlo algorithms (rather than boring old Monte Carlo methods), as well as ideas borrowed from physics (e.g., dimensional interpolation) and new mesh-free adjoint methods for solving PDEs. This tutorial was written for normal engineers, who do not have nonlinear filters for breakfast.

Nonlinear filters: beyond the Kalman filter

The Kalman estimation technique is examined from the point of view of the asymptotic behavior of the errors in the estimates. It is shown that, under certain conditions, the mean-square errors may become unbounded with time, and that this divergence may or may not be correctable by increasing the intensity of process noise assumed in the filtering model General results are derived for multidimensional systems, and both "true" and "apparent" divergence are demonstrated by a simple scalar system. Divergence due to numerical inaccuracies is considered, and an example problem in orbital navigation is used to demonstrate divergence and its elimination.

Divergence of the Kalman filter

A simplified form of probabilistic data association (PDA) logic was developed for real-time multitarget tracking by a microprocessor associated with a radar track-while-scan system. A variety of practical problems with the method led to a relatively complex set of algorithms, while certain fundamental shortcomings of the approach still threatened performance due to anomalous behavior in some situations. Ultimately, the weighted-average updating feature of the PDA approach was abandoned in favor of a "nearest-neighbor PDA" method, which utilizes the PDA association probabilities to associate a single measurement with each track.

Development of Practical PDA Logic for Multitarget Tracking by Microprocessor

Attention is called to the phenomenon of ?range-Doppler coupling,? characteristic of linear FM (chirp) waveforms, and the strong effect this coupling may have on tracking accuracy. Numerical results are presented for simple three-state filters and for a realistic reentry vehicle tracking problem.

Effects of Range-Doppler Coupling on Chirp Radar Tracking Accuracy

Kalman filters have been used in numerous phased array radars to track satellites, reentry vehicles, and missiles. This paper considers the design of these filters to reduce computational requirements, ill-conditioning, and the effects of nonlinearities. Several special coordinate systems used to represent the Kalman filter error covariance matrix are described. These covariance coordinates facilitate the approximate decoupling required for practical filter design. A tutorial discussion and analysis of ill-conditioning in Kalman filters is used to motivate these design considerations. This analysis also explains several well-known phenomena reported in the literature. In addition, a discussion of nonlinearities and methods to mitigate their ill effects is included.

Decoupled Kalman filters for phased array radar tracking

This paper discusses several theoretical issues related to the score function for the measurement-to-track association/assignment decision in the track-oriented version of the multiple hypothesis tracker (MHT). This score function is the likelihood ratio: the ratio of the probability density function (pdf) of a measurement having originated from a track, to the pdf of this measurement having a different origin. The likelihood ratio score is derived rigorously starting from the fully Bayesian MHT (hypothesis oriented, based on combinatorial analysis of the general multitarget problem), which is shown to be amenable under some (reasonable) assumptions to the track-oriented MHT (TOMHT). The latter can be implemented efficiently using multidimensional assignment (MDA). The main feature of a likelihood ratio is the fact that it is a (physically) dimensionless quantity and, consequently, can be used for the association of different numbers of measurements and/or measurements of different dimension. The explicit forms of the likelihood ratio are discussed both for the commonly used Kalman tracking filter, as well as for the interacting multiple model (IMM) estimator. The issues of measurements of different dimension and different coordinate systems together with the selection of certain MHT design parameters - the spatial densities of the false measurements and new targets - are also discussed.

Robert J. Fitzgerald

Papers

Divergence of the Kalman filter

Development of Practical PDA Logic for Multitarget Tracking by Microprocessor

Effects of Range-Doppler Coupling on Chirp Radar Tracking Accuracy

Decoupled Kalman filters for phased array radar tracking

Dimensionless score function for multiple hypothesis tracking