The computational burden of cross-ambiguity function is very large for measuring the time delay difference and the Doppler frequency shift of passive radar

which is difficult to meet the real-time requirements by the general algorithms. This paper proposes two fast algorithms of cross-ambiguity function for passive radar:the multi-stage decimation FFT algorithm and the pre-weighting multi-stage decimation FFT algorithm. The multi-stage decimation FFT algorithm decreases the length of the anti-aliasing filters and save the computational amount and the storage. The pre-weighting multi-stage decimation FFT algorithm avoids the cycle of the first-stage filter multiplication in different time delays and further increases the computational efficiency at the expense of the large storage. Experimental results show that the proposed algorithms can effectively increases the computational efficiency.