Bias Compensation Method for 3D AOA-TMA with Uncertainty in Sensor Positions

This paper focuses on the problem of target motion analysis (TMA) in 3D-space using angle of arrival (AOA) measurements taken by a moving sensor whose positions are inaccurate. The AOA measurement consists of a pair of azimuth and elevation angles in 3D where azimuth and elevation angles are used jointly to estimate target motion parameters. To start with, the maximum likelihood estimator, the pseudolinear estimator (PLE), the weighted instrumental variable estimator (WIVE) and the selective-angle-measurement (SAM)-WIVE with uncertainty in sensor positions are derived. Under the effect of sensor position errors, the WIVE would be no longer asymptotically unbiased due to the correlation between the instrumental variable (IV) matrix and the pseudolinear noise vector. As a result, the bias of the WIVE is theoretically analyzed by modeling the sensor position error as the additional azimuth and elevation noises. Then a new bias compensated SAM-WIVE (BCSAM-WIVE) is derived based on the bias analysis, which can mitigate the bias of the PLE and IV-based methods caused by both AOA measurements and sensor position errors. Moreover, the Cramer-Rao lower bound is derived when sensor positions are not precisely known. Simulation results validate the superior performance of the proposed BCSAM-WIVE over other existing methods.