Improvement of The Ziv-Zakai lower bound for time delay estimation

In time-delay parameter estimation theory, predicting the performance of the Maximum Likelihood Estimator (MLE) is of great interest. The Cramèr-Rao Bound (CRB) is widely used to estimate the variance of the MLE. But, in the case of low signal to noise ratio, the CRB becomes inefficient. The Ziv-Zakai Bound (ZZB) was therefore developed to estimate this variance at low SNR by taking into account the a priori parameter density. We propose in this paper an improvement of the ZZB which predicts a more accurate MLE variance. Moreover, we derive a closed-form expression of this improved ZZB using the saddlepoint approximation method.