Tracking with estimate-conditioned debiased 3-D converted measurements

This paper describes a new algorithm for the 3-D converted-measurement Kalman filter (CMKF) which estimates a target´s Cartesian state given spherical position measurements. At each processing index, the new algorithm chooses the more accurate of (1) the sensor´s spherical position measurement and (2) the CMKF´s Cartesian position prediction. The new algorithm then computes the raw converted measurement´s error bias and the corresponding debiased converted measurement´s error covariance conditioned on the chosen position estimate. The paper derives explicit expressions for the spherical-measurement-conditioned bias and covariance and shows the resulting spherical-measurement-conditioned CMKF´s mathematical equivalence with the 3-D modified unbiased CMKF (MUCMKF). The paper also describes a method, based upon the unscented transformation, for approximating the raw converted measurement´s error bias and the debiased converted measurement´s error covariance conditioned on the CMKF´s Cartesian position prediction. Simulation results demonstrate the new CMKF´s improved tracking performance and statistical credibility as compared to those of the 3-D MUCMKF.