Optimal estimation of sensor biases for asynchronous multi-sensor data fusion

Abstract

An important step in a multi-sensor surveillance system is to estimate sensor biases from their noisy asynchronous measurements. This estimation problem is computationally challenging due to the highly nonlinear transformation between the global and local coordinate systems as well as the measurement asynchrony from different sensors. In this paper, we propose a novel nonlinear least squares (LS) formulation for the problem by assuming the existence of a reference target moving with an (unknown) constant velocity. We also propose an efficient block coordinate decent (BCD) optimization algorithm, with a judicious initialization, to solve the problem. The proposed BCD algorithm alternately updates the range and azimuth bias estimates by solving linear least squares problems and semidefinite programs (SDPs). In the absence of measurement noise, the proposed algorithm is guaranteed to find the global solution of the problem and the true biases. Simulation results show that the proposed algorithm significantly outperforms the existing approaches in terms of the root mean square error (RMSE).

Radar networks: A review of features and challenges

“…This method has been extended in [96] to asynchronous sensors. The case of asynchronous sensors has also been considered in [97] where the registration problem has been tackled by non-linear optimization assuming a target with a nearly-constantvelocity model.…”

An Enhanced SDR Based Global Algorithm for Nonconvex Complex Quadratic Programs With Signal Processing Applications

“…Problem (CQP) finds many important signal processing applications, including multi-input multi-output (MIMO) detection [2], [3], unimodular radar code design [4], [5], [6], virtual beamforming [7], phase recovery [8], sensor bias estimation [9], and angular synchronization [10]; see Section II further ahead. For more applications of problem (CQP) in signal processing and communications, please refer to [11] and [12] and references therein.…”

“…Most of existing algorithms for solving problem (CQP) are approximation algorithms, local optimization algorithms, or other heuristics (e.g., [3], [4], [5], [8], [10], [11], [13], [14], [19], [20], [21]). These algorithms generally cannot guarantee to find the global solutions of problem (CQP), except only for some special cases [9], [10], [22], [23]. A straightforward way of globally solving problem (CQP) is to first reformulate the problem as an equivalent real QP by representing the complex variables by their real and imaginary components and then apply the existing general-purpose global algorithms (e.g., algorithms proposed in [24], [25]) for solving the equivalent real reformulation.…”

Tightness of a New and Enhanced Semidefinite Relaxation for MIMO Detection

“…In the last two decades, the semidefinite relaxation (SDR) based algorithms have been widely studied in the signal processing and wireless communication community [26]. For various SDR based algorithms for problems (CQP) and (UQP) under different signal processing and wireless communication scenarios, we refer the interested reader to [2,14,15,13,18,23,25,27,28,31,35,40,44,47] and the references therein. The SDR based algorithms generally perform very well in some signal processing and wireless communication applications, as pointed out in [3].…”