Converting bistatic radar measurements to Cartesian position for tracking

Tracking with 2-D bistatic radar measurements is a challenging problem due to the nonlinear relationship between the sine-space radar measurements and the Cartesian coordinates, especially for long distances. For 2-D bistatic radar, this nonlinearity leads to a non-elliptical measurement uncertainty region in 2-D Cartesian coordinates, similar to a crescent, that causes consistency problems for a tracking filter. A solution is suggested by developing an unbiased and statistically consistent conversion of the position measurements to Cartesian coordinates, based on second order Taylor expansion. Such an approach was successfully used for monostatic radars but considered impractical for the bistatic case due to the difficulty to derive explicit conversion expressions. The implementation includes conversion of the bistatic range (r_b) and sine-space angle measurement (u) to Cartesian position coordinates and tracking with a standard linear Kalman filter using the converted measurements, now linear in the state. This method is compared to the best-known existing filter, the converted measurement sigma point Kalman filter. Results show improved performance especially in terms of tracker consistency, keeping the state estimation error covariance statistically consistent with the actual estimation errors.