A sequential converted measurement Kalman filter in the ECEF coordinate system for airborne Doppler radar

Abstract

For an airborne Doppler radar, the carrying platform is moving and has time-varying attitudes. The filtering algorithms applicable to local coordinate system are not suitable anymore. In this paper, we propose a sequential converted measurement Kalman filter (SCMKF) with Doppler, which is based on the earth-centered earth-fixed (ECEF) coordinate system. First, to effectively utilize Doppler measurement with probable correlation with slant range, the correlated Doppler and range are decorrelated by the Cholesky factorization. The range component remains unchanged while the Doppler component is changed. Second, by a series of coordinate transformations with unchanged range component and other observations, the converted position measurement is obtained. Meanwhile, the corresponding error covariance is derived by using Taylor series expansion. With the resulting converted measurement and covariance, the target state is filtered by the converted measurement Kalman filter (CMKF), which is extended to the ECEF system. Finally, the filtered state is updated sequentially with the changed Doppler. Compared with the posterior Cramer–Rao lower bound as well as the CMKF, the proposed SCMKF is shown to be an efficient solution, and is superior to the CMKF. Although the gain brought from low-accuracy Doppler is limited, the introduction of high-accuracy Doppler can improve tracking performance significantly.