Nonlinear Observer State Estimation From Seeker Measurements and Seeker-Radar Measurements Fusion

Abstract

This paper deals with the estimation of line of sight rates and angles of evader with respect to pursuer from the available measurements from (i) noisy seeker alone and also from (ii) noisy seeker together with radar. During terminal guidance, the on board seeker of pursuer acquires the measurements of range rate, gimbal angles and line of sight rates along yaw and pitch planes. Generally the gimbal angles are contaminated by correlated bore sight error. The line of sight rates are very noisy and correlated with glint, radar cross section fluctuation and thermal noise. Also due to eclipsing there is an aperiodic data loss in line of sight rate measurements. Since the noise are generally modeled as white Gaussian in Kalman filter applications the present study using Extended Kalman Filter (EKF) and Unscented Kalman filter (UKF) is worked out to provide a bench mark solution for comparison with non white and non Gaussian model results that could be available later on. The line of sight rates and angles with observer states are worked out under the above practical constraints. The system state kinematic equations have been used in both Cartesian and Polar frame and the available measurements are in seeker gimbal frame. The present results from EKF and UKF under white Gaussian noise assumption have been found to be consistent. Thus the UKF, which accounts for system nonlinearity better than EKF shows the adequacy of the latter in the present case. Hence the EKF under the above Gaussian assumption has been used as against UKF to estimate the line of sight rates and observer states when using both seeker and radar measurements. The estimation algorithm has been validated in a simulated environment and the results are encouraging. The adequacy of the present filter model with all the inadequate modelling has been shown to be adequate in the present scenario. Further research to be carried out by modelling non Gaussian measurement noise is also provided.