Isolating Random and Bias Covariances in Tracks

Abstract

In addition to the typical random errors that vary between consecutive measurements, the measurements for most all sensors used for target tracking include bias errors that remain relatively fixed during a target tracking episode and are typically characterized by an a priori mean and covariance. Since the bias errors are approximately fixed during a tracking episode, those errors violate the typical assumption of the measurement errors being white noise. Inflating the measurement covariance of the random errors by adding the bias covariance gives track covariances that poorly represent the true errors. The Schmidt-Kalman filter can be used to prevent the track covariances from becoming artificially too small. However, the Schmidt-Kalman filter produces a track covariance that encompasses the random and bias errors. In this paper, the authors formulate the target tracking as a least-square estimation (LSE) problem and show that the track covariance due to the bias errors can be isolated from the track covariance due the random errors. The authors utilize Monte Carlo simulations to verify and illustrate the accuracy of isolation of the bias and random covariances.