TOA-Based Robust Wireless Geolocation and Cramér-Rao Lower Bound Analysis in Harsh LOS/NLOS Environments

Abstract

Abstract-We consider time-of-arrival based robust geolocation in harsh line-of-sight/non-line-of-sight environments. Herein, we assume the probability density function (PDF) of the measurement error to be completely unknown and develop an iterative algorithm for robust position estimation. The iterative algorithm alternates between a PDF estimation step, which approximates the exact measurement error PDF (albeit unknown) under the current parameter estimate via adaptive kernel density estimation, and a parameter estimation step, which resolves a position estimate from the approximate log-likelihood function via a quasi-Newton method. Unless the convergence condition is satisfied, the resolved position estimate is then used to refine the PDF estimation in the next iteration. We also present the best achievable geolocation accuracy in terms of the Cramér-Rao lower bound. Various simulations have been conducted in both real-world and simulated scenarios. When the number of received range measurements is large, the new proposed position estimator attains the performance of the maximum likelihood estimator (MLE). When the number of range measurements is small, it deviates from the MLE, but still outperforms several salient robust estimators in terms of geolocation accuracy, which comes at the cost of higher computational complexity.Index Terms-Adaptive kernel density estimation (AKDE), Cramér-Rao lower bound (CRLB), non-line-of-sight (NLOS) mitigation, robust geolocation, time-of-arrival (TOA).

EM- and JMAP-ML Based Joint Estimation Algorithms for Robust Wireless Geolocation in Mixed LOS/NLOS Environments

“…being calculated in light of (13). Since y i,k is discrete-valued, the global optimal solution to (19) must be the one among…”

“…Besides, there may exist other applications, cf. [13,, where the measurement error samples are truly i.i.d. and follow a mixture distribution.…”

“…The numerical evaluation of x (η+1) attempts to minimize f 1 (x) via the BFGS quasi-Newton method which involves another iterative procedure similar to [13,Algorithm 2]. Analogously, we count the FLOPs required for one iteration of this local search.…”

“…This idea was initially proposed for robust multiuser detection in impulsive noise channels in [12] and revisited for robust TOA based geolocation in mixed LOS/NLOS environments in [13]. Therein, the developed robust iterative nonparametric (RIN) algorithm seeks to approximate the actual measurement error PDF (albeit unknown) using the adaptive kernel density estimation (AKDE) and update the position estimate in an attempt to maximize the approximated log-likelihood function.…”

“…In this paper, we reconsider the geolocation problem in [13] except that we explicitly appoint a specific two-mode mixture distribution to represent the measurement error. To avoid offline calibration, we set the mixture model parameters to be unknown.…”