A new look at the statistical identification of nonstationary systems

Niedźwiecki, Maciej; Ciolek, Marcin; Gancza, Artur

doi:10.1016/j.automatica.2020.109037

Cited by 23 publications

(20 citation statements)

References 20 publications

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“…For values of M lower than the minimum, the MSD is mostly defined by the noise component given by (38); as can be seen in (40), this noise component is approximately inversely proportional to M , and therefore the dependence is almost linear on a plot with logarithmic axis. For values of M higher than the minimum, the MSD is mostly defined by the approximation component given by (35). For binary signals and L = 1, the MSD approximation component a should provide the best match to the theoretical analysis presented in Section III.…”

Section: A Comparison Of Theoretical and Simulation Resultsmentioning

confidence: 98%

“…The authors were not aware of the work in [34], [35] when drafting this version of the paper. This paper will be updated to compare our results with the results in [34], [35].…”

Section: Notementioning

confidence: 99%

“…Thus, for a given power spectral density G h (ω) = (T /2)Gh(T ω/2), defining how fast h(t) varies in time, the MSD approximation component can be found using (54), (56) and (57) as shown in (35), where the integrals can be computed numerically.…”

Section: Appendix A: Msd Approximation Componentmentioning

confidence: 99%

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Adaptive Filtering Based on Legendre Polynomials

Shen¹,

Zakharov²,

Shi³

et al. 2020

Preprint

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Abstract:<div><br><div><pre><p>In system identification scenarios, classical adaptive filters, such as the recursive least squares (RLS) algorithm, predict the system impulse response. If a tracking delay is acceptable, interpolating estimators capable of providing more accurate estimates of time-varying impulse responses can be used; channel estimation in communications is an example of such applications. The basis expansion model (BEM) approach is known to be efficient for non-adaptive (block) channel estimation in communications. In this paper, we combine the BEM approach with the sliding-window RLS (SRLS) algorithm and propose a new family of adaptive filters. Specifically, we use the Legendre polynomials, thus the name the SRLS-L adaptive filter. The identification performance of the SRLS-L algorithm is evaluated analytically and via simulation. The analysis shows significant improvement in the estimation accuracy compared to the SRLS algorithm and a good match between the theoretical and simulation results. The performance is further investigated in application to the self-interference cancellation in full-duplex underwater acoustic communications, where a high estimation accuracy is required. A field experiment conducted in a lake shows significant improvement in the cancellation performance compared to the classical SRLS algorithm.</p> </pre></div></div>

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Section: A Comparison Of Theoretical and Simulation Resultsmentioning

confidence: 98%

“…The authors were not aware of the work in [34], [35] when drafting this version of the paper. This paper will be updated to compare our results with the results in [34], [35].…”

Section: Notementioning

confidence: 99%

See 1 more Smart Citation

Adaptive Filtering Based on Legendre Polynomials

Shen¹,

Zakharov²,

Shi³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Quite recently a new estimation paradigm for identification of linear time-varying processes, based on the concept of preestimation, was proposed [19]. Preestimates are raw estimates of process parameters -unbiased but with a very large variability.…”

Section: Introductionmentioning

confidence: 99%

“…The resulting two-stage identification procedure compares favorably with the existing solutions to the problem of parameter tracking as it offers, without compromising good tracking performance, significantly lower computational complexity and increased numerical robustness. The current paper aims to further improve, using the regularization technique, the solutions described in [18] and [19].…”

Section: Introductionmentioning

confidence: 99%

Regularized Local Basis Function Approach to Identification of Nonstationary Processes

Gancza

Niedźwiecki

Ciolek

2021

IEEE Trans. Signal Process.

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The problem of identification of nonstationary stochastic processes (systems or signals) is considered and a new class of identification algorithms, combining the basis functions approach with local estimation technique, is described. Unlike the classical basis function estimation schemes, the proposed regularized local basis function estimators are not used to obtain interval approximations of the parameter trajectory, but provide a sequence of point estimates corresponding to consecutive instants of time. Based on the results of theoretical analysis, the paper addresses and solves all major problems associated with implementation of the new class of estimators, such as optimization of the regularization matrix, adaptive selection of the number of basis functions and the width of the local analysis interval, and reduction of complexity of the computational algorithms.

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Nonparametric Tracking for Time-Varying Nonlinearities Using the Kernel Method

Joshi

Mzyk

2022

New Advances in Dependability of Networks and Systems

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A new look at the statistical identification of nonstationary systems

Cited by 23 publications

References 20 publications

Adaptive Filtering Based on Legendre Polynomials

Adaptive Filtering Based on Legendre Polynomials

Regularized Local Basis Function Approach to Identification of Nonstationary Processes

Nonparametric Tracking for Time-Varying Nonlinearities Using the Kernel Method

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