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Effects of noise on the optimal processing of frequency-stepped cw radar data

We develop a nonlinear optimal signal processing algorithm for estimating the time delays and amplitudes of target reflections from a set of frequency-stepped continuous wave (FSCW) measurements in the presence of noise. The optimization algorithm solves the nonlinear problem directly in an iterative fashion after prewindowing a range for the estimation of the time delay. The optimal estimate of the corresponding amplitude is solved for each time delay in the range. A performance measure is calculated based on each of the solved amplitude and time delay pairs. The minima in the performance metric correspond to the locations of the reflections. The optimization algorithm is applicable to any set of FSCW measurements from which the target range resolution is to be maximized. The derivation is general in the number of reflections, and a uniform frequency interval between the FSCW measurements is not required. We quantify the effects of noise on the accuracy of estimation through analytic expressions and illustrate through simulation. We demonstrate the performance of this optimization algorithm using synthetic FSCW data in the presence of noise through comparison with the IFFT method. The results show this algorithm is robust in estimating target reflection ranges from noisy FSCW data.