MATLAB Simulation of Time Delay Estimation Using Correlation Method

Correlation-based time delay estimation is a classical signal processing technique for measuring temporal delays, widely applied in acoustic localization, radar ranging, and related fields. This method utilizes the cross-correlation function between signals, where the peak position identifies the time difference between two signals.

Implementing correlation-based time delay estimation in MATLAB enables analysis of arbitrary WAV files. The process begins by reading the target WAV file using audioread() to extract audio signals, followed by preprocessing steps like noise reduction or filtering with functions such as filter() or medfilt1(). The core computation involves calculating the cross-correlation function via MATLAB's xcorr() function, which efficiently returns correlation values and supports different normalization modes. The time delay corresponds to the index of the maximum absolute value in the cross-correlation output, adjustable for sampling rate using findpeaks() for robust peak detection.

Algorithm accuracy evaluation includes error analysis addressing noise, sampling rate constraints, and signal non-stationarity. Performance can be quantified under varying signal-to-noise ratio (SNR) conditions using awgn() to add noise or artificial delays. Metrics like Mean Squared Error (MSE) and Mean Absolute Error (MAE), computable with immse() and custom functions, assess robustness.

This simulation method suits both laboratory research and practical applications such as microphone array sound source localization or wireless sensor network synchronization, with extensibility to multi-channel signals and real-time processing.