{'fraction_non_alphanumeric': 0.029829545454545456, 'fraction_numerical': 0.0, 'mean_word_length': 4.7317073170731705, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
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.