A batch processing algorithm for target tracking using frequency measurements

Abstract

This paper develops a batch processing algorithm that can be used to track a moving ground target emitter with measurements of received frequency. A constant velocity track that best fits the frequency measurements is computed. The target's position will be defined u sing W GS84 longitude, latitude, and altitude. We will assume the following about the target: an estimate of initial position is available, the east and north velocity components are constant during the observation period, and altitude is either known or can be computed using a local datum. The 3 parameters to be estimated are the 2 velocity components and a receiver measurement bias. These parameters are treated as random variables with known a priori distributions, so the tracking problem is one of Maximum A Posteriori (MAP) estimation. The a priori distribution provides a statistical bound on parameter values and keeps the algorithm stable when sensor-target geometry is poor. The frequency measurements used for tracking are nonlinear functions of target position and velocity, thereby requiring that a nonlinear optimal estimation problem be solved. Batch processing of all sensor measurements and Iterated Least-Squares (ILS) are used to solve this problem. Each update of ILS requires the target's position time history in order to compute the objective function value being minimized. Target tracking is treated as a parameter identification or inverse problem, i.e., the target's position is the output of an ordinary differential equation having unknown parameters to be estimated. As a result, the target's position time history is found using numerical integration, the given initial position and the current velocity estimates. This process also gives the system sensitivity matrix needed to compute the parameter estimation error covariance matrix. The model used for this algorithm contrasts with that used for the design of recursive estimators such as an extended Kalman filter, where the target's position is t he output of a dynamic system driven by white noise. A Kalman filter will provide good estimates of target position and velocity when the frequency of the target's transmitted signal is stable or the target's velocity is fairly constant. However, when neither of these conditions is met, the filter m ay produce a nerratic t rack t hat differs significantly from truth. The constant velocity track produced by this algorithm is less erratic than one produced by a recursive estimator when the transmitter frequency drifts and the target maneuvers. In these unfavorable conditions, the batch processor is more robust and can provide the user with a target direction vector. This direction vector can be combined with a map of the area of interest to inform the user as to the target's most likely route and location.