Abstract:

For a type of measurement equations which can be transformed into pseudo-linear equalities immediately, a novel theoretical analysis framework is developed to position the source with a closed-form solution for passive location based on the constrained weighted least squares (CWLS). Firstly, a localization model based on the CWLS is constructed and then the unconstrained optimization is derived. Secondly, the estimated target status is got through the generalized eigenvalue decomposition and its algebraic form is present, which can be utilized to prove that the estimation is the globally optimal solution and its characteristic of reducing location bias. Finally, a location scenario with angle of arrival/ time difference of arrival (AOA/TDOA) measurements is used as an example to describe the application of the proposed theoretical framework. Simulation results indicate that this proposed algorithm can approximate the Cramer-Rao low bound (CRLB) performance and is much better than the weighted least squares (WLS) as for the estimation bias, especially when the observation time is short and the noise is loud. Simulations corroborate the advantages of the proposed theoretical analysis framework.