A Modest Power Consumption Maximum Likelihood Direct Position Determination Approach for Multiple Targets With Moving Sensor Arrays

Target localization is widely applied in wireless sensor networks (WSNs). In this article, we tackle the problem of position estimation for multiple stationary targets using Doppler frequency shifts and angles by moving sensor arrays. The computational load for the exhaustive maximum likelihood (ML) direct position determination (DPD) search is insufferable. Based on Pincus’ theorem and the importance sampling (IS) concept, we propose a novel noniterative ML DPD method, and the circular mean is used for superior position estimation performance; meanwhile, a concrete criterion is also proposed for the choice of the importance function. The computational complexity of the proposed method is modest, and the off-grid problem that most existing DPD techniques face is significantly alleviated. Moreover, it can be implemented in parallel separately. In addition, we present the closed-form Cramér–Rao lower bound (CRLB) for the DPD with moving sensor arrays and stationary targets. Simulation results demonstrate that the proposed ML DPD estimator can achieve better estimation accuracy than state-of-the-art DPD techniques. With a reasonable parameter choice, the estimation performance of the proposed technique is very close to the CRLB, even in the adverse conditions of low signal-to-noise ratio (SNR) levels.

I. Introduction

The localization of the target attracts much interest in radar, navigation, and wireless sensor networks (WSNs) [1], [2], [3], [4], [5]. Some researchers devoted their attention to the scenario that both target and receivers are stationary, where the target is an emitter that radiates the narrowband signal, and then, the angle of arrival (AOA) of the target can be measured by the sensor array in the receiver [6], [7]. The others turned interests to scenarios with moving receivers [8], [9], such as sonar, satellite positioning, and airplanes. The motion induces a Doppler frequency shift that is proportional to the radial velocity relatively between receiver and target; this additional information is the key for estimating the location and velocity of the target. In this article, we focus on locating multiple stationary targets by several moving platforms, each platform carrying a sensor array.