Assumed density filter with application to homing missile guidance
Sivasubramanya Nadar Balakrishnan, Jason Lee Speyer · Journal of Guidance Control and Dynamics · 1989
A maximum likelihood estimation method is developed for a class of problems where the dynamics are linear and the measurement function is nonlinear. In this method, called the density filter,' the form of the conditional probability density function is selected to be a function of a finite number of quantities. These quantities, which describe the approximate shape of conditional probability density function around the mode, are propagated through each measurement interval. At the measurement, the conditional probability density function is updated using Bayes theorem, and its mode, computed numerically, is defined to be the best estimate of the state. The posteriori conditional probability density function is then approximated by a Taylor series expansion about its mode to preserve the assumed functional form. The numerical results for a target-intercept problem indicate that the assumed density filter is superior to the extended Kalman filter. However, the assumed density filter has a negative range bias. It is analytically proved, with some approximations, that the maximum likelihood range estimates are smaller than the mean range estimates.