High Resolution Frequency Estimation in an FMCW Radar Application
Abstract: FMCW radars are widely used in the process industry for range estimation, usu- ally for estimating the liquid level in a tank. Since the tank system, often is an automatically controlled system, reliable estimates of the surface level are re- quired, e.g. to avoid the tank from pouring over or become empty. The goal of this thesis is to investigate methods which can distinguish fre- quencies closer to each other than the FFT resolution limit. Two properties are of interest, the accuracy and the resolution performance. Three such methods have been evaluated: one that tries to compensate for the leakage and interference of close frequencies, one subspace-based method and one deconvolution method. The deconvolution is performed with the iterative Lucy Richardson algorithm. The methods are evaluated against each other and against a typical FFT based algorithm. The methods sensitivity to amplitude differences is examined together with the robustness against noise and disturbances which appear due to imperfections in the radar unit. The deconvolution algorithm is the one that performs the best. The subspace-based method SURE requires prior knowledge of the number of ingoing frequencies which is difficult to know for real data from an FMCW radar. The leakage compensation method main weakness is the influence of the phase difference between close frequencies. The deconvolution algorithm is evaluated on some real data, and it is proven that it has better resolution performance than the FFT. However, the accuracy of the estimates are dependent on the number of iterations used. With a large num- ber of iterations, the algorithm finds peaks with small amplitude nearby the large peaks and they will thus interact and hence contribute to a worse accuracy even in the undisturbed case. If too few iterations are used in the deconvolution algo- rithm the resolution performance is about the same as the FFT algorithm. With a suitable choice of iterations about 40–50 mm, extra of continuous measurements are achieved. However, the estimation error of the gained resolution can in the worst case be about 40–50 mm.
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