| An analysis of bias in the Extended Kalman Filter has been performed leading to the identification of its cause, an estimate of its magnitude and the synthesis of a filter in which this bias is substantially reduced. These results are reported with respect to a particular, but very important, nonlinear estimation problem: passive target tracking. An approach integrating both analytic (mathematical) and empirical (simulation) investigations is used. Observations made in simulation studies are examined mathematically and the consequent analytic formulations are validated using further simulation experiments.; The Extended Kalman Filter is a simple recursive algorithm that uses a stochastic linearization to utilize the form of the standard linear Kalman Filter equations to estimate the state trajectory of a system when the dynamical and/or the measurement equations are nonlinear. The use of this linearization, which is based on the filter's a priori state estimate, leads to a complex stochastic relationship between the sequence of gain matrices and the sequence of measurement residuals. The fact that these two sequences are correlated is the cause of the observed bias, and a unique stochastic perturbation analysis yields a prediction of the bias introduced into the filter's state estimate at each measurement update.; This prediction of the bias and an estimate of it based on quantities available to the filter itself are studied and modified using an empirical method. A filter is synthesized using these results and its performance is shown to be a substantial improvement over the standard method.; Two other methods for avoiding the bias inherent in the Extended Kalman Filter are presented and tested. |
