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 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

The canonical variate analysis (CVA) approach for system identification, filtering, and adaptive control is developed. The past/future Markov property provides a starting point for defining a reduced-order prediction problem. The solution is a canonical variate analysis that is characterized by a generalized singular value decomposition. State-space model estimation requires only simple regression, and state order selection involves the optimal Akaike information criterion procedure. The CVA method extends to time-varying and abruptly changing systems. A reduce-rank stochastic model predictive control problem is shown to be equivalent to the CVA problem. Also discussed are computational aspects, applications, and an example illustrating the method. New extensions to the identification of general nonlinear systems are briefly discussed. The CVA method provides an approach giving reliable, automatic implementation of identification, filtering, and control for online adaptive control. >

Canonical variate analysis in identification, filtering, and adaptive control

One of the most important tasks in integration of GPS/INS is to choose the realistic dynamic model covariance matrix Q and measurement noise covariance matrix R for use in the Kalman filter. The performance of the methods to estimate both of these matrices depends entirely on the minimization of dynamic and measurement update errors that lead the filter to converge. This paper evaluates the performances of adaptive Kalman filter methods with different adaptations. Innovation and residual based adaptive Kalman filters were employed for adapting R and Q. These methods were implemented in a loose GPS/INS integration system and tested using real data sets. Their performances have been evaluated and compared. Their limitations in real-life engineering applications are discussed.

Evaluating the Performances of Adaptive Kalman Filter Methods in GPS/INS Integration

The vector control of an induction motor by speed estimation using an extended Kalman filter (EKF) is described. The rotor speed is regarded as a parameter, and the composite state is composed of the original state and the rotor speed. The EKF is employed to identify the speed of an induction motor and rotor magnetic flux based on the measured quantities such as stator currents and DC link voltage. The estimated speed is used for vector control and overall speed control. The current control is performed in the synchronous rotating reference frame, and the estimated speed information is used for reference frame transformation of the current controller. Computer simulation of the speed control has been carried out to confirm the usefulness of the speed estimation algorithm. The error between the real speed and the estimated speed is within a few RPM even in the low speed range of about 20 RPM. >

Speed sensorless vector control of an induction motor using an extended Kalman filter

Analysis tools are developed that can be effectively used to study the performance degradation of a filter when incorrect models of the state and measurement noise covariances are used. For a linear time-variant system with stationary noise processes, it is shown that under certain stability conditions on the system model, the one-step prediction error covariance matrix will converge to a steady-state solution even when the filter gain is not optimal. On the other hand, if the state transition matrix has an unreachable mode outside a unit circle, then the modeling errors in the noise covariances may cause the filter to diverge. Bounds on the asymptotic filter performance are computed when the range of errors in the noise covariance matrices are known. Using simple examples, insights into the behavior of a Kalman filter under nonideal conditions are provided. >

Analysis of discrete-time Kalman filtering under incorrect noise covariances

An indirect adaptive control scheme is applied to the design of an autopilot for missiles using bank-to-turn steering. Controller design is based on a discretization of the short-period approximation to the linearized longitudinal motion. Parameter estimation is based on a first-order vector ARMA representation of the discretized system. Controller gains are derived in terms of functions of the estimated system parameters with the objective of the control to achieve tracking of a commanded acceleration with stability of the closed-loop system.

Adaptive Control Applied to Missile Autopilots

Technical communique: Invariant system description of the stochastic realization

Two approaches to tracking a maneuverable target are presented. The tracking filter comprises two main parts: acceleration estimation and maneuver detection. The acceleration estimator is implemented first by assuming piecewise constant acceleration levels. Maneuver detection is performed to justify the validity of the assumption, i.e. if the acceleration has remained constant. If a maneuver is declared, the filter is reinitialized and a new level of constant acceleration is identified. The second approach is based on a nonlinear state model which gives better tracking for planar maneuvers and non constant accelerations.

Maneuver detection and tracking with a nonlinear target model

A design procedure for minimal-order observers which is applicable to linear, observable, time-invariant systems is developed based on certain polynomial matrices associated with the transfer functions of the plant. The approach is to select the observer dynamics so that the feedback control law is satisfied with a minimal-order system. The method is a frequency domain technique but is significantly different from earlier results. Necessary and sufficient conditions for construction of a minimal-order observer to observe several linear functions of the state are given.

T. E. Bullock

Papers

Analysis of discrete-time Kalman filtering under incorrect noise covariances

Adaptive Control Applied to Missile Autopilots

Technical communique: Invariant system description of the stochastic realization

Maneuver detection and tracking with a nonlinear target model

A frequency domain approach to minimal-order observer design for several linear functions of the state