Multistatic pseudolinear target motion analysis using hybrid measurements

• New pseudolinear estimators are proposed for multistatic target motion analysis.
• Hybrid sensor measurements of AOA, TDOA and FDOA are exploited.
• Proposed estimators are closed-form with low complexity and inherent stability.
• Complexity analysis confirms computational advantage of proposed estimators.
• WIV estimator is analytically and numerically shown to be asymptotically efficient.

This paper presents a new hybrid pseudolinear estimator (PLE) for target motion analysis of a constant-velocity target in the two-dimensional plane using angle-of-arrival, time-difference-of-arrival and frequency-difference-of-arrival measurements obtained from spatially distributed stationary passive receivers. The hybrid PLE is developed by linearizing the nonlinear measurement equations in the unknown target motion parameters. The resulting estimator is not only closed-form and has low computational complexity, but is also free from nuisance parameters, therefore avoiding the problems arising from the dependence of the nuisance parameters on the target motion parameters. However, the noise injected into the PLE data matrix causes biased estimates. To address this, a bias-compensated PLE is proposed based on an asymptotic bias analysis of the hybrid PLE. This estimator is then incorporated into a weighted instrumental variable (WIV) estimator to obtain asymptotically unbiased estimates of the target motion parameters. The WIV estimator is shown to be asymptotically efficient both analytically and through numerical simulation examples. Furthermore, it is observed that the WIV estimator performs similar to the computationally demanding maximum likelihood estimator, closely achieving the Cramér–Rao lower bound and producing negligible bias at moderate noise levels.