Multistatic time-of-arrival (TOA) localization has recently attracted great attention due to performance advantages offered by multistatic radar. In target localization, the relative sensor-target geometry is an important factor that can significantly affect the localization performance. In this paper, we analyze the optimal geometries for a two-dimensional TOA localization configuration commonly presented in the literature with a single transmitter and multiple receivers. Our analysis is based on minimizing the area of estimation confidence region, which is equivalent to maximizing the determinant of the Fisher information matrix. If the coordinate system is rotated such that the bearing angle of the transmitter with respect to the target is zero, an optimal geometry is obtained when a subset of the receivers are collinear with the target at a bearing angle of π/3 rad and the remaining receivers at a bearing angle of -π/3 rad. The arrangement of the receivers on either branch of the bearing angles, i.e., π/3 rad or -π/3 rad, is decided based on the measurement noise variances at the receivers. We conclude the study with numerical solutions generated by the genetic algorithm and simulation examples for UAV path optimization to verify the accuracy of the analytical findings.

Despite its stability and computational complexity advantages, the pseudolinear Kalman filter (PLKF) suffers from severe bias problems in bearings-only target tracking applications. This paper develops new variants of the PLKF with significant performance improvement. First, a detailed analysis of the PLKF bias is provided for nearly constant-velocity target dynamics. This analysis uncovers the specific reasons of bias in state estimation and leads to a new bias-compensated PLKF (BC-PLKF) algorithm with the improved bias performance. The bias arising from the correlation between the measurement vector and pseudolinear noise is tackled by a novel instrumental-variable Kalman filter (IVKF). While the method of instrumental variables has been successfully applied to batch pseudolinear estimation algorithms, its extension to the PLKF is new. The IVKF embeds the method of recursive IV estimation into the BC-PLKF and employs the BC-PLKF to construct instrumental variable vectors with desired properties. The IVKF is further improved by adopting the method of selective angle measurements (SAM), which ensures that the performance of the IVKF is not degraded by a weak correlation between the instrumental variable vector and measurement vector in low signal-to-noise ratio (SNR) situations. Comparative simulation examples are presented to demonstrate the performance improvement of the proposed recursive estimators (the BC-PLKF, IVKF and SAM-IVKF) over the conventional PLKF and the extended Kalman filter. The SAM-IVKF is observed to provide the best estimation performance among the proposed estimators by producing a negligible estimation bias and mean squared error close to the posterior Cramér-Rao lower bound at moderate noise levels.

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.