A quadratic correlation algorithm with variable sets of lags for frequency estimation

The range resolution is a critical element for accurately detecting an object in the frequency modulated continuous wave (FMCW) radar system. However, the efficacy of existing correlation-based range estimate algorithms suffers dramatically under the low signal-to-noise ratio (SNR). A quadratic correlation algorithm with variable sets of lags is proposed to improve the estimation accuracy in order to overcome this challenge. The time translation parameter is varied in the proposed method to reduce noise influence, and a method for selecting the lag sequence sets is proposed to reduce computing complexity. Firstly, a variable time translation parameter is utilized to extract two signal segments from the received signal. Then, the autocorrelation function of the first signal segment along with the cross-correlation function of the two signal segments are obtained, and the quadratic correlation of the above two correlation functions is calculated for a lag sequence set with an initial lag step. Moreover, the expression for the frequency estimation as well as the range estimation is derived, and the mean and standard deviation of range estimation can be statistically obtained from the range estimates. Finally, if the standard deviation of the range estimation is above the prefixed standard deviation threshold, the lag step is modified and the above range estimation process is repeated; otherwise, the range estimation is obtained. The simulation results show that the proposed quadratic correlation algorithm with variable sets of lags outperforms existing approaches in terms of range accuracy.