Relationship Between Geometric Translations and TLS Estimation Bias in Bearings-Only Target Localization

This paper analyzes the effects of local coordinate translations and rotations on the bias and mean-squared error performance of the total least squares (TLS) bearings-only target localization algorithm. The TLS estimator was originally proposed to alleviate the severe bias problems associated with the traditional pseudolinear estimator. An interesting property of the TLS estimator, which is not shared by the pseudolinear estimator, is that its bias is sensitive to where the origin of the local Cartesian coordinates is placed. The paper provides a formal proof of this observation, discusses its implication on bias minimization, and proposes a simple and effective method for TLS bias reduction. The findings of the paper are illustrated with comprehensive simulation examples.