Numerical Comparison of Five Mean Frequency Estimators

Sirmans, Dale; Bumgarner, Bill

doi:10.1175/1520-0450(1975)014<0991:ncofmf>2.0.co;2

Cited by 112 publications

(41 citation statements)

References 5 publications

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“…Throughout this study, estimators from independent, spaced, and contiguous pulse pairs are compared to provide a continuum of statistics from equispaced tightly correlated to statistically independent pulse pairs. Spectral moment estimation by covariance argument techniques is increasing as an important signal processing tool in the analysis of pulse Doppler echoes from distributed scatterers [1]. Hyde and Perry [2] suggested a version of the covariance technique for first moment estimation, and Woodman and Hagfors [3] used it to measure mean ionospheric motions.…”

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confidence: 69%

Spectral Moment Estimates from Correlated Pulse Pairs

Zrnić

1977

IEEE Trans. Aerosp. Electron. Syst.

172

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Estimates statistics of the first two power spectrum moments from the pulse pair covariance are analyzed. The input signal is assumed to be colored Gaussian and the noise, white Gaussian. Perturbation formulas for the standard deviation of both mean frequency and spectrum width are applied to a Gaussian shaped power spectrum, and so is a perturbation formula for the bias in the width estimate.Mean frequency estimation from interlaced pulse pairs is presented. Throughout this study, estimators from independent, spaced, and contiguous pulse pairs are compared to provide a continuum of statistics from equispaced tightly correlated to statistically independent pulse pairs. Spectral moment estimation by covariance argument techniques is increasing as an important signal processing tool in the analysis of pulse Doppler echoes from distributed scatterers [1]. Hyde and Perry [2] suggested a version of the covariance technique for first moment estimation, and Woodman and Hagfors [3] used it to measure mean ionospheric motions. Independently, Rummler had proposed estimators of both mean and variance from pulse pair bursts [4], [5] . Hofstetter [6] and Miller and Rochwarger [7] established maximum likelihood properties of these estimators. Furthermore, Miller and Rochwarger analyzed the first and second order statistics of the estimators. The probability density of the mean frequency for a large number of independent pairs can be found in [3], while Berger [8] calculated the density for any arbitrary number of independent pairs. To process independent echo sample pairs requires much longer observation time; hence it has been suggested [4] that independence in a uniform pulse train can be created by changing the carrier frequency on altemate pairs. This, of course, considerably complicates the system's hardware. Moment estimation from contiguous pairs with constant carrier frequency is the most direct technique to implement on conventional radars. Arithmetic units that calculate spectral momnents using the fast Fourier transform algorithm also can be used. Although these units rapidly calculate the spectrum and its moments, all echo samples comprising the time series must be stored prior to calculations. When data fields consist of a thousand sample volumes along a radial and each volume generates a few hundred samples, the storage required normally exceeds a million bits. Estimates from contiguous pairs (with a common pulse among each two pairs) were analyzed by Benham et al. [9], and Berger and Groginsky [10] , who found the standard deviations of the mean and variance. In this paper the perturbation analysis of Benham et al. [Appendix A] is extended to include arbitrarily spaced pulse pairs. Under appropriate limiting conditions, it is shown how this more general situation reduces to previous results of Berger and Groginsky [10] (pair spacing equal to intrapair period), Miller and Rochwarger [7] (large spacing between pairs or uncorrelated pairs) and Lank et al. [11] (zero width spectrum or fully correlated signal sample...

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confidence: 69%

Spectral Moment Estimates from Correlated Pulse Pairs

Zrnić

1977

IEEE Trans. Aerosp. Electron. Syst.

172

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“…The former guarantees better performances for narrow spectra while the latter is more robust against spectral asymmetries. The most widely used equations in the Doppler weather radar community were derived in the '70s [16,17] however they cannot be applied to most spaceborne configurations since the resulting Doppler spectra do not respect the narrow spectrum constraints. Generalized equations to estimate the variance of Vz estimates for broader spectra were derived in [18].…”

Section: Radar Parameters and Doppler Observablesmentioning

confidence: 99%

Spaceborne Doppler radars for atmospheric dynamics and energy budget studies

Tanelli

Durden

et al. 2008

2008 IEEE Radar Conference

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The successful deployments of the first spaceborne precipitation radar (TRMMIPR KU-band, 1997 [1]) and spaceborne cloud radar (CloudSat/CPR W-band, 2006 [2]) have demonstrated the feasibility of monitoring atmospheric processes from space with vertical resolutions of a few hundred meters. Future missions being implemented (EarthCARE, Wband [3]) or envisaged (ACE, Ka-and W-band [4]) include use of coherent detection to measure the first moment of the Doppler spectrum to observe and analyze the dynamics of atmospheric systems. In this talk we discuss the main challenges and potentials of measuring the Doppler velocity of clouds and precipitation from space.

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“…Since this estimator is based on the periodogram, it will be herein called the periodogram-based (PB) estimator. Related references on this topic are [30] and [31].…”

Section: A Classical Estimatorsmentioning

confidence: 99%

“…The following statistics are evaluated: 1) BLM biases and given by (30) and (38), respectively; 2) BLM mean square errors (MSE's) and given by (31) and (39), respectively; 3) Cramér-Rao Bounds (CRB's) of parameters and with respect to the covariance sequence ; 4) sample mean biases and of the BLM, the MLM, the PPM, and the PBM ( denotes the sample mean of independent samples of random variable ); 5) BL estimates of and computed according to (15) and (16), respectively, whereas ML estimates of these parameters are given by (12) and (13), respectively; 6) Sample MSE's and of the BLM, the MLM, the PPM, and the PBM. The following remarks are in order.…”

Section: Performance Evaluationmentioning

confidence: 99%

Nonparametric estimation of mean Doppler and spectral width

Dias

Leitao

2000

IEEE Trans. Geosci. Remote Sensing

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Abstract-This paper proposes a new nonparametric method for estimation of spectral moments of a zero-mean Gaussian process immersed in additive white Gaussian noise. Although the technique is valid for any order moment, particular attention is given to the mean Doppler (first moment) and to the spectral width (square root of the centered second-spectral moment). By assuming that the power spectral density (PSD) of the underlying process is bandlimited, the maximum-likelihood estimates of its spectral moments are derived. A suboptimal estimate based on the sample covariance is also studied. Both methods are robust in the sense that they do not rely on any assumption concerning the PSD (besides being bandlimited). Under weak conditions, the set of estimates based on sample covariance is unbiased and strongly consistent. Compared with the classical pulse pair and the periodogram-based estimators, the proposed methods exhibit better statistical properties for asymmetric spectra and/or spectra with large spectral widths, while involving a computational burden of the same order.

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Numerical Comparison of Five Mean Frequency Estimators

Cited by 112 publications

References 5 publications

Spectral Moment Estimates from Correlated Pulse Pairs

Spectral Moment Estimates from Correlated Pulse Pairs

Spaceborne Doppler radars for atmospheric dynamics and energy budget studies

Nonparametric estimation of mean Doppler and spectral width

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