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.