A Fast Algorithm of Direct Position Determination Using TDOA and FDOA

Weiss's Direct position determination (WDPD) method compensate the received signals of the M stations to the transmitted signals by the Delay-Doppler operator, and Delay-Doppler operator is computed M times to compensate the time delay and Doppler shift for every search point, and the dimension of the Delay-Doppler operator is related to the size of data points N. And Delay-Doppler operator is equal to four matrices multiplying continuously, whose size is N×N, and matrix multiplication needs lots of time and memory, limiting the size of N. This paper deduces the DPD that don't need to compensate to the transmitted signals. In practice, any one of M stations maybe is the reference station, and the signal of the reference station can compensate to the receiving signals of other stations by Delay-Doppler operator, and the objective function of the DPD is given. Through the DPD, Delay Doppler operator only is calculated M-1 times for every search point, and reduce the computation complexity, especially M is small. And for DPD algorithm, there are a lot of redundant computations in the Delay Doppler operator, so the fast algorithm of DPD (FDPD) is proposed. The experimental results verify that DPD reduce the computation complexity and FDPD saves the computation time and maintain the performance of the DPD algorithm simultaneously.