A novel time difference of arrival source localization method based on constrained scoring algorithm with a calibration emitter

In this paper, we focus on the radiation source localization problem based on time‐difference‐of‐arrival (time difference of arrival (TDOA)) measurements in the presence of sensor position errors. In order to alleviate the estimation degradation in locating a radiation source caused by the sensor position uncertainty, we propose to use a single calibration source and develop a novel two‐stage localization algorithm based on the constrained scoring algorithm (CSA). In the first stage, we use the information of the calibration source to reduce the sensor position deviation, and here the CSA method is utilised to solve a quadratic constrained maximum likelihood (ML) objective function which is formulated from a set of underdetermined pseudo‐linear equations. In the second stage, using the updated sensor positions and the TDOA measurements of the radiation source, another ML estimation problem with quadratic constraints is formulated, and we again invoke the CSA method to jointly estimate the source and sensor positions. Moreover, the asymptotically optimal performance of the proposed algorithm is mathematically analysed and proved based on the first‐order error analysis. The simulation results verify the excellent performance of our algorithm and also demonstrate its robustness of resisting large measurement noise and sensor position errors.