A New Class of Moment Matching Filters for Nonlinear Tracking and Estimation Problems

In this paper a new algorithm is proposed for tracking problems, in which the state evolves according to a linear difference equation and the measurement is a nonlinear function of a noise corrupted version of the state. The algorithm recursively generates Gaussian approximations of the conditional distribution of the target state given the current and past measurements. It differs from other `moment matching' algorithms, such as the extended Kalman filter and its refinements, because it is based on an exact calculation of the mean and covariance of the updated conditional distribution. A special case of the algorithm, applicable to bearings-only tracking problems, is called the shifted Rayleigh filter. Simulations indicate that the shifted Rayleigh filter can match the accuracy of high order particle filters while significantly reducing the computational burden, even in some scenarios where the extended Kalman filter gives poor estimates or fails altogether. It is expected that the new algorithms will offer similar advantages for other kinds of tracking algorithms, including those involving range-only measurements.