Recursive LMMSE filtering for target tracking with range and direction cosine measurements

Due to the nonlinear relationship between Cartesian coordinates and range-direction-cosine coordinates, target tracking of state described in Cartesian coordinates with range and direction cosine measurements is a nonlinear filtering problem. Measurement conversion based Kalman filter available for this type of problem has some serious drawbacks. Depending on whether measurement of the third direction cosine is directly available, two recursive linear minimum mean-squared error (LMMSE) filters for target tracking with range and direction cosine measurements are developed in this paper. Illustrative numerical examples show that in terms of credibility and accuracy, the proposed filters should be preferred.