Tracking with spherical-estimate-conditioned debiased converted measurements

This paper presents a new algorithm for the 3-D converted-measurement Kalman filter (CMKF) [1]-[3]. At each index, the new algorithm chooses the more accurate of (1) the spherical measurement provided by a sensor and (2) a spherical prediction computed from the CMKF´s prediction information. The new algorithm next debiases the raw converted measurement with the raw converted measurement´s error bias conditioned on the chosen spherical estimate. The new algorithm then computes the debiased converted measurement´s error covariance conditioned on the chosen spherical target-position estimate, thus allowing the standard Kalman-filter algorithm´s application. The paper gives closed-form solutions for the measurement-conditioned bias and covariance. The paper also describes a novel method, based on the unscented transformation [4], for approximating the prediction-conditioned bias and covariance. Simulation results show the new algorithm´s improved tracking performance and statistical credibility over those of the 3-D modified unbiased CMKF.