Correlation and sequential filtering with Doppler measurements

Two sequential filters are developed for Doppler radar measurements in the presence of correlation between range and range rate measurement errors. Two ideal linear measurement equations with the pseudo measurements are constructed via block-partitioned Cholesky factorization and the practical measurement equations with the pseudo measurements are obtained through the direction cosine estimation and error compensation. The resulting sequential filters make the position measurement be possibly processed before the pseudo measurement and hence the more accurate direction cosine estimate can be obtained from the filtered position estimate rather than the predicted state estimate. The numerical simulations with different rangerange rate correlation coefficients show that the proposed two sequential filters are almost equivalent in performance but both superior to the conventional extended Kalman filter for different correlation coefficients.