Analysis of suboptimal Kalman tracking algorithms

Abstract

The standard Kalman filter has been applied extensively to the trackingof non-maneuveringtargets. Although thisfilter tracks these targets accurately it requires a heavy computational burden. This paper studies several suboptimal Kalman filtering schemes which require less computational burden than the standard Kalman filter while yielding nearly optimal performance during both transient and steady-state filtering. It is shown that these suboptimal filters are viable alternatives to the standard Kalman filtel: I INTRODUCTIONOver the past several years, a great deal of research has been published on the application of Kalman filters to target tracking problems. Much effort has been focused on developing computationally efficient Kalman filtering algorithms has proposed a suboptimal method of computing the Kalman gain based upon the steady-state analysis of Kalman filters in the twodimensional case [5] and the three dimensional case [6,7]. Singer and Sea [2] attempt to decrease the computational load of the Kalman filter by developing an iterative method of computing the error covariance matrix. Daum and Fitzgerald [3] study the performance of the Kalman filter when it is decoupled in various coordinate systems. Farooq and Horsman [4] compare the computational and storage requirements of the coupled and decoupled forms of the standard Kalman filter and various adaptive Kalman filtering algorithms. Mendel [8]presents the general computational and storage requirements of the discrete Kalman filter, and Gura and Bierman [9] compare the computational and storage requirements of several tracking algorithms, including the standard and the stabilized Kalman filters, the sequential least-squares filter, and several square root filters.In this paper the computing time and storage requirements of five tracking algorithms are compared. These algorithms are: the standard coupled Kalman filter , the decoupled Kalman filter, the partially-decoupled Kalman filter, the Baheti approach which is formulated in [ 11, and a modified Baheti approach that has been developed by the authors. Simulation results for two target tracks are presented in order to demonstrate the relative accuracy of the tracking algorithms. I1 TARGET MOTION MODELAgeneral target motion model in discrete time can be expressed as follows:(1) where x k is the target state vector in Cartesian coordinates at time t i , @L is the linear state transition matrix, B is the input matrix, and u k is the input acceleration of the target at time t k . The measurement equation is: Zf = HXk f vk where H is the linear observation matrix, and vk is the zero mean, white Gaussian noise associated with the measurement vector .zk.The measurement vector is originally obtained inspherical coordinates as:where r, b and e represent range, bearing and elevation respectively. The superscripts m and a represent measured and actual values and v,, is a zero mean Gaussian white noise sequence with the covariance matrix as:$ , and d are the variances of the noise in the range, bearing and elev...

Multiple structure adaptive target tracking

“…An analysis of Baheti's filter [9] has demonstrated that his algorithm, as described in [2], will only track accurately during steady State conditions. Baheti's algorithm calculates the Kalman gain using equation (4).…”

“…Rather than use the standard Kalman filter, a computationally more efficient filter, which is a modified version of the filter presented by Baheti in [ 11, was selected for implementation [9].…”