An Analysis and Algorithm for Unknown Altitude Source Geo-location Using TDOA Measurements in the presence of Receiver Location Errors

This paper aims to deal with the problem of geo-location of a source whose altitude is unknown in the presence of random errors in receiver locations by minimizing the influences of errors on the final location estimate. This paper performs an analysis and provides an efficient algorithm for locating source using time difference of arrival (TDOA) measurements. The analysis starts with the Cramer-Rao lower bound (CRLB) with receiver location errors, and derives the increase in mean square error (MSE) in source location estimate with the constraint of the WGS84 oblate spheroid model if the source altitude is assumed accurate but in fact have error. And then, we derive the MSE of source location with the constraint of the WGS84 oblate spheroid model without altitude error. An LSSQP algorithm based on sequential quadratic programming (SQP) method is then proposed for this constrained nonlinear optimization problem to reduce the estimation error, and it is shown analytically, without any approximation, to achieve the CRLB accuracy for an unknown altitude source. Simulation results indicate the computationally efficient and superior performance of the proposed method as compared to the existing closed-form method and Taylor-series iterative based approach for the source geo-location.