Estimation With Range Dependent Sensor Model

Abstract

This paper focuses on the improvement of target tracking accuracy taking into account the sensor’s reading degradation as the relative range increases. The approach is based on the assumption that range measurement error depends on the actual range. Specifically, we model the measurement error as a proportional to the actual range term plus a zero-mean, Gaussian distributed, and uncorrelated process. We present two approaches to tracking a target with constant velocity model. The first approach uses Extended Kalman Filter (EKF) framework to estimate target's states and the unknown proportionality coefficient with linearization on the observation model on the predicted states at each time step. The second one uses a measurement conversion method to estimate the target's scaled by the unknown constant term states, which is shown to be unbiased. This conversion results in linear state and observation models, hence the standard Kalman filter can be applied. The actual target state is computed by application of back scaling with the estimate of unknown scale factor. We evaluate the approaches in desktop simulations.