CRLB for Estimating Time-Varying Rotational Biases in Passive Sensors

In target tracking systems involving data fusion it is common to encounter sensor measurement biases that contribute to the tracking errors. There is extensive research into estimating sensor biases, but very little research into bias estimation in the dynamic case, meaning that biases that change over time are addressed. This paper investigates the means for and necessity of estimating bias rates of change in addition to constant sensor biases to reduce the errors in the state estimates. This is explored by comparing the Cramér–Rao lower bound and root-mean-square error of simultaneous target state and bias estimates for rotational biases with three-dimensional passive sensors with roll, pitch, and yaw biases. The present work models the dynamic biases as linearly varying over time. The iterated least squares method is used for the search of the maximum likelihood estimate, and is shown to be statistically efficient via hypothesis testing.