Time delay estimation of an observed signal is a problem of considerable interest in real systems. The Cramer-Rao inequality provides a lower bound on the error of the maximum likelihood estimator. With high signal-to-noise ratio, the estimation error approaches the lower bound. However, as the signal-to-noise ratio degrades beyond a threshold, the error variance deviates from the lower bound, indicating the degradation of estimation accuracy. In practical applications, it is usually desirable to predict the signal-to-noise ratio threshold to guarantee an acceptable estimation error. In this paper, a new method of predicting the signal-to-noise ratio threshold is proposed. Afterwards, as the use of spread-spectrum technique prevails in positioning systems, the method is applied to delay estimation via the spreading code. Both Cramer-Rao lower bound and the signal-to-noise ratio threshold are deduced. Simulation based on the Monte Carlo method was conducted. The results were consistent with our theoretical analysis. Besides, the influence of sample numbers and code rate on the estimation error was analyzed through simulation. The conclusion is that the error variance can be reduced by increasing the number of samples or using a higher code rate.
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