An efficient algorithm for WBAF estimation based on linear interpolation and its estimation error

Wideband ambiguity function (WBAF) plays an important role in radar, sonar, and GPS. However, the computational complexity of the conventional algorithms for WBAF is high. Moreover, because the signal is discretized the values between two sampling points of the sampled signal are unknown. These situations cause significant difficulty for the computation of the WBAF with Doppler stretch changing. To solve these problems, an algorithm based on linear interpolation is proposed to estimate the WBAF. According to the values of Doppler stretch and time delay, the locations of interpolation can be determined Based on these interpolation locations, the algorithm calculates the signal values, which are unknown but essential for WBAF, with linear interpolation; and then use the recovered values and original sampled values to estimate the WBAF. By using the linear interpolation, the algorithm does not need to utilize a great deal of the matched filters, and the conventional multirate sampling method is avoided. Therefore, the computational complexity of the algorithm can be reduced greatly. We analyzed the estimation error of WBAF to examine the performance of the algorithm. Moreover, we obtained the following results: the estimation error of the WBAF is mainly affected by the linear interpolation error, while the linear interpolation error depends on the time delay, Doppler stretch and sampling frequency. The estimation error is acceptable in the case of high sampling frequency. Numerical experiments verified the validity of the algorithm.