Bearings-only target localization using total least squares

A total least-squares (TLS) algorithm is developed for two-dimensional location estimation of a stationary target by using only passive bearing measurements of the target. This problem has been studied extensively for several decades and has applications in electronic warfare, surveillance, passive sonar, interference location and suppression, and so forth. The nonlinear nature of the estimation problem poses a number of challenges related to complexity, convergence and estimation bias. After a critical review of the least-squares (LS) algorithms, a TLS estimation algorithm is developed based on the method of orthogonal vectors with the advantage of simplicity and reduced bias in the presence of bearing noise and observer position errors. A constrained TLS (CTLS) algorithm is also developed to improve the estimation accuracy, especially in the case of large measurement errors. Numerical examples are provided to compare the performance of the TLS and CTLS algorithms with the LS target localization algorithms, viz. the maximum likelihood estimator, Stansfield estimator and the method of orthogonal vectors.