Tracking of targets with state dependent measurement errors using recursive BLUE filters

In this paper, optimal best linear unbiased estimation (BLUE) filters are derived for cases where measurement errors depend on the state of the target. The standard Kalman filter fails to provide optimal estimates in these cases. Previously applied measurement models are reformulated in order to apply BLUE filters, and two new measurement models with state dependent biases are proposed. It is shown how the higher order unscented transform may be used to approximate the terms in the BLUE filter when they are not available analytically. The BLUE filters are shown by Monte Carlo simulations to have better performance than other suboptimal filters.