Source Localization: Algorithms and Analysis

Abstract

Time of arrival (TOA), time difference of arrival (TDOA), time sum of arrival (TSOA), received signal strength (RSS), and direction of arrival (DOA) of the emitted signal are commonly used measurements for source localization. This chapter introduces two categories of positioning algorithms based on TOA, TDOA, TSOA, RSS, and DOA measurements. The first category works on the nonlinear equations directly obtained from the nonlinear relationships between the source and measurements. Corresponding examples, namely, nonlinear least squares (NLS) and maximum likelihood (ML) estimators, are presented. The second category attempts to convert the equations to linear. The chapter discusses the linear least squares, weighted linear least squares (WLLS), and subspace approaches. It develops the mean and variance expressions for any positioning method which can be formulated as an unconstrained optimization problem. The Cramer‐Rao lower bound (CRLB), which is a lower bound on the variance attainable by any unbiased location estimator using the same data, is also discussed.