Recipes for degrees of freedom of frequency stability estimators

Greenhall, C. A.

doi:10.1109/19.119780

Cited by 68 publications

(49 citation statements)

References 9 publications

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“…More rigorously, this quantity is defined as half the expectation of squared differences between adjacent nonoverlappinḡ y t (τ ): Despite there exist several estimators of the AV, we solely focus on the maximal-overlap estimator proposed in [26] which present some superior statistical properties. Such an estimator is defined as:…”

Section: Allan Hadamard and Total Variance Techniquesmentioning

confidence: 99%

Constrained expectation-maximization algorithm for stochastic inertial error modeling: study of feasibility

Stebler¹,

Guerrier²,

Skaloud³

et al. 2011

Meas. Sci. Technol.

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Abstract. Stochastic modeling is a challenging task for low-cost sensors which errors can have complex spectral structures. This makes the tuning process of the INS/GNSS Kalman filter often sensitive and difficult. For example, first-order Gauss-Markov processes are very often used in inertial sensor models. But the estimation of their parameters is a non-trivial task if the error structure is mixed with other types of noises. Such estimation is often attempted by computing and analyzing Allan variance plots. This contribution demonstrates solving situations when the estimation of error parameters by graphical interpretation is rather difficult. The novel strategy performs direct estimation of these parameters by means of the Expectation-Maximization (EM) algorithm. The algorithm results are first analyzed with a critical and practical point of view using simulations with typically encountered error signals. These simulations show that the EM algorithm seems to perform better than the Allan variance and offers a procedure to estimate first-order Gauss-Markov processes mixed with other types of noises. At the same time, the conducted tests revealed limits of this approach that are related to the convergence and stability issues. Suggestions are given to circumvent or mitigate these problems when complexity of error structure is "reasonable". This work also highlights the fact that the suggested approach via EM algorithm and the Allan variance may not be able to estimate reasonably well parameters of complex error models, and shows the need for new estimation procedures to be developed in this context. Finally, an empirical scenario is presented to support the former findings. There, the positive effect of using the more sophisticated EM-based error modeling on a filtered trajectory is highlighted.

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Section: Allan Hadamard and Total Variance Techniquesmentioning

confidence: 99%

Constrained expectation-maximization algorithm for stochastic inertial error modeling: study of feasibility

Stebler¹,

Guerrier²,

Skaloud³

et al. 2011

Meas. Sci. Technol.

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“…Along a plot of MAVAR(τ), confidence intervals are negligible for short τ and widen moving to longer τ, where fewer terms are averaged [34] [36]. In our results, therefore, we excluded MAVAR values computed for largest n.…”

Section: A the Modified Allan Variancementioning

confidence: 99%

Output Traffic Characterization of Policers and Shapers with Long-Range Dependent Input Traffic

Bregni

Giacomazzi

Saddemi

2007

IEEE GLOBECOM 2007-2007 IEEE Global Telecommunications Conference

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“…An alternative estimator for the WV is based on the Discrete Wavelet Transform (DWT) coefficients (see Greenhall 1991;Percival and Guttorp 1994), for which the wavelet filter is applied to the process in (1) in a different manner. More specifically, the DWT filters a sequence {X t } on non-overlapping windows yielding the DWT wavelet coefficients…”

Section: Robust Estimation Of the Wavelet Variancementioning

confidence: 99%

Estimation of Time Series Models via Robust Wavelet Variance

Guerrier

Molinari

Victoria‐Feser

2014

AJS

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A robust approach to the estimation of time series models is proposed. Taking from a new estimation method called the Generalized Method of Wavelet Moments (GMWM) which is an indirect method based on the Wavelet Variance (WV), we replace the classical estimator of the WV with a recently proposed robust M-estimator to obtain a robust version of the GMWM. The simulation results show that the proposed approach can be considered as a valid robust approach to the estimation of time series and state-space models.

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Recipes for degrees of freedom of frequency stability estimators

Cited by 68 publications

References 9 publications

Constrained expectation-maximization algorithm for stochastic inertial error modeling: study of feasibility

Constrained expectation-maximization algorithm for stochastic inertial error modeling: study of feasibility

Output Traffic Characterization of Policers and Shapers with Long-Range Dependent Input Traffic

Estimation of Time Series Models via Robust Wavelet Variance

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