Tracking with estimate-conditioned debiased 3-D converted measurements

Abstract

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.1 2