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Empirical investigations show that at low and moderate signal-to-noise ratios, maximum entropy (ME) Doppler shift and spectral width estimates of VHF radar signals have significantly higher accuracies than conventional periodogram estimates with noise thresholding. The variances of the ME estimates decrease with decreasing spectral width and clearly indicate a limiting signal-to-noise ratio below which the Doppler shift estimates are dominated by cosmic and instrumental noise rather than fluctuating radar signals. Two criteria are derived empirically that yield estimates of the optimum ME prediction error filter lengths for computing the Doppler shift and spectral width of individual radar signals. At small signal-to-noise ratios the Doppler shift criterion produces variances that are close to the minimum variance bounds of spectral methods. Fast ME algorithms for computing signal power, Doppler shift, and spectral width are described. At large signal-to-noise ratios the ME Doppler shift estimator is faster than the corresponding periodogram estimator based on a fast Fourier tranform, whereas at low signal-to-noise ratios, it is slower. For computing a typical height profile of the mean radial velocity in the troposphere and lower stratosphere, the ME estimator is as fast as the periodogram estimator, whereas for a height profile of the mean spectral width, it needs approximately 3 times as much computation time as the periodogram estimator.