A Generalized Converted Measurement Kalman Filter

Abstract

This report derives a generalized, converted measurement Kalman filter for the class of filtering problems with a linear state equation and nonlinear measurement equation, for which a bijective mapping exists between the state and measurement coordinate systems. For these problems, a procedure is developed for mapping the observed measurements and their covariance matrices from measurement coordinates to state coordinates, such that the converted measurements are unbiased and the converted measurement covariance matrices are independent of the states and observed measurements. In cases where not all measurement coordinates are observed, predicted measurements of these coordinates are introduced as substitutes, and the impact of these measurements on the filter is mitigated by an information zeroing operation on the corresponding rows and columns of the converted measurement inverse-covariance matrix. Filter performance is demonstrated on two well-known target-tracking problems and is compared with the performance of the standard extended and unscented Kalman filters for these problems. These examples show the proposed filter obtains lower mean squared error, better consistency, and less track loss than either the extended Kalman filter or the unscented Kalman filter.