Improved Positioning Algorithms for Nonline-of-Sight Environments

Nonline-of-sight (NLOS) conditions pose a major challenge to radio positioning. In this paper, a constrained-optimization-based location algorithm is proposed to jointly estimate the unknown location and bias by using the sequential quadratic programming (SQP) algorithm. This method does not rely on any prior statistics information, and simulation results show that the proposed method considerably outperforms existing methods. To reduce the complexity of the SQP-based algorithm, we further propose a Taylor-series expansion-based linear quadratic programming (TS-LQP) algorithm. It is demonstrated that the computational complexity of the TS-LQP algorithm is only a fraction of that of the SQP algorithm, whereas the accuracy loss is limited. Also, maximum-likelihood (ML) algorithms that are suited for different NLOS error statistics are developed under several circumstances when there are different levels of a priori information. The analytical performance of the ML estimation (MLE) is investigated. Moreover, analytical expressions to approximate the variance of the MLE with and without model parameter mismatches are derived. Simulation results show that the approximate variance can be used as a better accuracy measure than the Cramer-Rao lower bound (CRLB).