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We develop a non-linear 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 non-linear problem directly in an iterative fashion after pre-windowing 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.

We derive a complex nonlinear optimal signal-processing algorithm for estimating target ranges from a set of frequency-stepped continuous wave (FSCW) measurements. It is a generalization of a prior optimization algorithm in that the reflection amplitudes are modeled as phasors rather than real-valued scalars. The algorithm solves this nonlinear problem by separating it into its linear and nonlinear parts. The amplitudes of the reflections are first optimized by solving a set of linear equations in the least-squares sense. A performance measure is then calculated and scanned to find its global minimum to yield a set of reflection amplitudes and time-delay estimates. We derive analytical expressions for the performance measure and for the effects of noise in the measurement data. Finally, we present experimental results to demonstrate the performance of our algorithm.

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