Information and Statistical Efficiency When Quantizing Noisy DC Values

Moschitta, Antonio; Schoukens, Joannes; Carbone, Paolo

doi:10.1109/tim.2014.2341372

Cited by 13 publications

(17 citation statements)

References 21 publications

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“…Conversely, both estimators tend to provide similar results. Moreover, observe that already for σ = 0.2, the normalized standard deviation ofθ GM1 approximately achieves the square-root of the Cramer-Rao lower bound applicable to unbiased estimators of a quantized constant in Gaussian noise with known variance [9]. This becomes evident in Fig.…”

Section: Simulation Resultsmentioning

confidence: 60%

“…Consider however that model 2 can be reduced to model 1 if the known value of the noise standard deviation is substituted by an estimate of it obtained using alternative Fig. 6 and the corresponding Cramer-Rao lower bound for unbiased estimators, derived using an expression published in [9]. estimators as in [15] [21].…”

Section: Simulation Resultsmentioning

confidence: 99%

“…where ω is a known constant, (9) represents the well known model of the three-parameter sine fit [15]. In the following, the properties of a quantile-based estimator applied to all these cases will be illustrated.…”

Section: The DC and Ac Parametric Signal Modelsmentioning

confidence: 99%

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Parametric System Identification Using Quantized Data

Moschitta

Schoukens

Carbone

2015

IEEE Trans. Instrum. Meas.

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The estimation of signal parameters using quantized data is a recurrent problem in electrical engineering. As an example, this includes the estimation of a noisy constant value, and of the parameters of a sinewave that is its amplitude, initial record phase and offset. Conventional algorithms, such as the arithmetic mean, in the case of the estimation of a constant, are known not to be optimal in the presence of quantization errors. They provide biased estimates if particular conditions regarding the quantization process are not met, as it usually happens in practice. In this paper a quantile-based estimator is presented that is based on the Gauss-Markov theorem. The general theory is first described and the estimator is then applied to both DC and AC input signals with unknown characteristics. By using simulations and experimental results it is shown that the new estimator outperforms conventional estimators in both problems, by removing the estimation bias.

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Section: Simulation Resultsmentioning

confidence: 60%

Section: Simulation Resultsmentioning

confidence: 99%

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Parametric System Identification Using Quantized Data

Moschitta

Schoukens

Carbone

2015

IEEE Trans. Instrum. Meas.

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“…In the plots, the approximate regime boundaries are computed to be ξ 1 = {0.1098, 3.85 × 10 −2 , 9.56 × 10 −3 } and ξ 2 = {0.2296, 0.3132, 0.3737} for K = {5, 25, 125}, respectively, confirming that Regime II expands as K increases. In Regime I, the NMSE performance of all estimators on K = 5 < Z =" Regime I Regime II Regime III NMSE(mean) NMSE(mid) NVar(GGML) NCRB (7 Regime I Regime II Regime III NMSE(mean) NMSE(mid) NVar(GGML) Regime I Regime II Regime III NMSE(mean) NMSE(mid) NVar(GGML) Regime I Regime II Regime III NMSE(mean) NMSE(mid) Fig. 7: The results of our Monte Carlo simulations lead to a simplified decision process for when and how to use dither.…”

Section: A Normalized Mse Vs σ Z /∆mentioning

confidence: 99%

Estimation From Quantized Gaussian Measurements: When and How to Use Dither

Rapp

Dawson

Goyal

2019

IEEE Trans. Signal Process.

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Subtractive dither is a powerful method for removing the signal dependence of quantization noise for coarselyquantized signals. However, estimation from dithered measurements often naively applies the sample mean or midrange, even when the total noise is not well described with a Gaussian or uniform distribution. We show that the generalized Gaussian distribution approximately describes subtractively-dithered, quantized samples of a Gaussian signal. Furthermore, a generalized Gaussian fit leads to simple estimators based on order statistics that match the performance of more complicated maximum likelihood estimators requiring iterative solvers. The order statisticsbased estimators outperform both the sample mean and midrange for nontrivial sums of Gaussian and uniform noise. Additional analysis of the generalized Gaussian approximation yields rules of thumb for determining when and how to apply dither to quantized measurements. Specifically, we find subtractive dither to be beneficial when the ratio between the Gaussian standard deviation and quantization interval length is roughly less than 1/3. If that ratio is also greater than 0.822/K 0.930 for the number of measurements K > 20, we present estimators more efficient than the midrange.

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“…As an example, consider the quantization of a constant signal affected by white Gaussian noise. Moschitta et al [3] show that the amount of information at the quantizer output vanishes when the noise standard deviation tends to zero.…”

Section: Introductionmentioning

confidence: 99%

Quick Estimation of Periodic Signal Parameters From 1-Bit Measurements

Carbone

Schoukens

Moschitta

2020

IEEE Trans. Instrum. Meas.

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Information and Statistical Efficiency When Quantizing Noisy DC Values

Cited by 13 publications

References 21 publications

Parametric System Identification Using Quantized Data

Parametric System Identification Using Quantized Data

Estimation From Quantized Gaussian Measurements: When and How to Use Dither

Quick Estimation of Periodic Signal Parameters From 1-Bit Measurements

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