Distributed Angle Estimation by Multiple Frequencies Synthetic Array in Wireless Sensor Localization System

In this paper, we address the problem of distributed angle estimation in wireless sensor localization system. Given that the practical limitations on size and cost, i.e., anchor node cannot equip a complicated antenna or antenna array, we devise an alternative measure based on a fixed-spacing two-antenna equipment. Through the multiple frequencies tuning, a virtual non-uniform linear array, called multiple frequencies synthetic array (MFSA), can be rebuilt independently at each sensor node. We first provide in theory the angle unambiguity conditions for such virtual array and then propose two different algorithms to achieve the distributed angle of departure (AOD) estimation. The first algorithm is based on the spectral searching technique, which is an improved version of the conventional rank reduction estimator (RARE) and has the same performance but less computational complexity. To further alleviate the computational burden at sensor node end, we convert the above angle estimation into a congruence problem and provide another closed-form solution based on Chinese remainder theorem (CRT). We also derive the Cramer-Rao bound for the MFSA and demonstrate theoretically that the latter algorithm from the perspective of cumulative circular distance is suboptimal when compared with the former one. Numerical examples are provided to show the validity of the proposed algorithms and the corresponding conclusions.