Tracking with Estimate-Conditioned Debiased 2-D Converted Measurements

John N. Spitzmiller, Reza R. Adhami

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DOI: 10.4236/iim.2010.23033                

Abstract

This paper describes a new algorithm for the 2­D converted-measurement Kalman filter (CMKF) which estimates a target’s Cartesian state given polar position measurements. At each processing index, the new algorithm chooses the more accurate of (1) the sensor’s polar 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 polar-measurement-conditioned bias and covariance and shows the resulting polar-measurement-conditioned CMKF’s mathematical equivalence with the 2­D 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 2­D MUCMKF.

Keywords

Tracking, Converted Measurements, Kalman Filter, Unscented Transformation

Conflicts of Interest

The authors declare no conflicts of interest.

References

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