Target tracking based on Kalman-type filters combined with recursive estimation of model disturbances

Clearly, the problem of deriving accurate algorithms for tracking of the dynamics of various kinds of targets has received considerable interest. This problem is central in many applications, such as radar and sonar. A large number of methods based on Kalman filter theory have been proposed. Design of a tracker based on a Kalman filter typically involves a trade-off between tracking performance and noise sensitivity. In particular, the Kalman filter depends on certain second-order statistics, namely the measurement noise variance and the variance of the (presumably random) target acceleration. Since these latter quantities can not be expected to be a priori known, a recursive least squares type algorithm which provides estimates thereof is suggested here. This method utilizes intermediate results obtained in the Kalman filter and hence, is evaluated in parallel. The usefulness of the proposed method is demonstrated by means of application to an extended Kalman filter, EKF. The considered EKF is based on a three-state filter model for tracking of the position and velocity of a moving target as well as estimation of possible nonlinearities in the measurements of the target position. Next, as an interesting alternative to the EKF, a recursive prediction error method, RPEM is proposed. As opposed to the extended Kalman filter, EKF, the suggested RPEM algorithm does not require knowledge of, or estimation of the statistics of the noise and the dynamics of the target motion. Instead, the proposed RPEM adjusts to changing target dynamics by means of on-line adjustment of a forgetting factor, which is calculated from filtered values of the prediction error. Hence, the resulting algorithm is less complex than the EKF. In addition, it is shown here how the EKF is related to the RPEM by means of specific choices of the time-varying estimates of the measurement noise variance and the covariance matrix of the system time variations. It is demonstrated by means of a numerical example that the tracking capability of the proposed RPEM is essentially as good as that of the EKF. Although, the transient, (initial) behavior of the EKF is somewhat better than that of the RPEM. Furthermore, the performance of the EKF is significantly enhanced using the suggested method for on-line recursive estimation of the unknown second-order quantities. However, this improvement is achieved at the expense of a noticeable increase in the computational burden.