This paper presents new pseudolinear estimation algorithms for angle-of-arrival (AOA) target motion analysis when the sensor locations are not precisely known. Sensor location errors can cause significant performance degradation for the existing pseudolinear estimator (PLE) and its variants. In particular, we analytically show that, in the presence of sensor location errors, the well-known weighted instrumental variable estimator (WIVE) is no longer asymptotically unbiased due to the non-vanishing correlation between the instrumental variable matrix and the pseudolinear noise vector. To ameliorate this bias problem, a novel bias compensation method is developed for the WIVE, which is proven to be approximately efficient for a large number of measurements under the small noise assumption. In addition, a selective-angle-measurement (SAM) strategy is integrated into the bias-compensated WIVE (BCWIVE) to strengthen the correlation between the instrumental variable matrix and the measurement matrix, alleviating the performance degradation in large AOA and sensor location noises, and unfavourable geometries. The performance advantages of the proposed BCWIVE and SAM-BCWIVE over the PLE, its WIVE variants and the maximum likelihood estimator are demonstrated by way of extensive simulation examples.

This paper considers the problem of robust three-dimensional (3D) angle-of-arrival (AOA) source localization in the presence of impulsive alpha-stable noise based on the lp-norm minimization criterion. The iteratively reweighted least-squares algorithm (IRLS) is a well-known technique for solving lp-norm minimization with the desirable global convergence property. Adopting the IRLS for 3D AOA localization requires nonlinear-to-pseudolinear transformation of azimuth and elevation angle measurement equations, thus resulting in a new variant of the IRLS, called the iteratively reweighted pseudolinear least-squares estimator (IRPLE). Unfortunately, there exists correlation between the measurement matrix and noise vector in the pseudolinear measurement equations, which consequently makes the IRPLE biased. To counter the bias problem of the IRPLE, a new iteratively reweighted instrumental-variable estimator (IRIVE) is proposed based on the exploitation of instrumental variables. The IRIVE is analytically shown to achieve the theoretical covariance of the general least lp-norm estimation. Extensive simulation studies are presented to demonstrate the performance advantages of the IRIVE over the IRPLE as well as other existing least-squares and least lp-norm estimators. The IRIVE is observed to produce nearly unbiased estimates with mean squared error performance very close to the Cramer-Rao lower bound.

This letter presents a new three-dimensional (3-D) instrumental variable based Kalman filter (3D-IVKF) algorithm for angle-of-arrival target tracking from azimuth and elevation angle measurements. First, a 3-D pseudolinear Kalman filter (KF) algorithm is derived by applying the classical linear KF to a pseudolinear state-space model. To counter the severe bias problems with this algorithm, bias compensation and recursive instrumental variable (IV) methods are considered. A selective-angle-measurement strategy is also adopted to satisfy requisite conditions for IV estimation. The resulting 3D-IVKF algorithm inherits the low computational complexity and robust performance of pseudolinear estimation techniques. It is shown through simulation examples that the 3D-IVKF algorithm can achieve a similar tracking performance to the sigma-point KFs by producing a negligible bias and a mean-square error close to the posterior Cramér-Rao lower bound at a much reduced computational complexity, while outperforming the extended KFs at high noise levels.

This paper develops a closed-form three-dimensional passive bearings-only localization algorithm based on the method of instrumental variables. The proposed localization algorithm is shown to attain a significant reduction in bias and root-mean-square error vis-à-vis orthogonal vector and pseudolinear estimators. It also has less computational requirements than a maximum likelihood estimator thanks to involving no iterative computations that are prone to instability problems. Further complexity reduction is shown to be achievable by averaging bearing measurements over finite-length non-overlapping windows. Simulation studies are provided to illustrate the effectiveness of the proposed instrumental variable estimation algorithm in a radar localization application.

This paper presents new closed-form estimators for 3-D source localization using Doppler measurements collected by a moving sensor platform. Two estimators, based on bias compensation and instrumental variables, are developed with significant performance improvement over a previously proposed least-squares estimator (LSE). First, a refined variant of the LSE, called bias-compensated weighted LSE (BCWLSE), is presented utilizing a weighting matrix and a bias compensation step. A weighted instrumental variable estimator is then developed based on a modified pseudolinear equation for the LSE to avoid pseudolinear noise amplification that may deteriorate the BCWLSE performance at large noise. Comparative simulation studies are presented to demonstrate the performance advantages of the proposed estimators over the severely biased LSE and divergence-prone maximum likelihood estimator. The proposed estimators are observed to produce almost no bias and achieve a mean-squared-error performance close to the Cramér-Rao lower bound.