Tracking error bounds of adaptive nonstationary filtering

Eweda, Eweda; Macchi, Odile

doi:10.1016/0005-1098(85)90062-7

Cited by 68 publications

(25 citation statements)

References 11 publications

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“…By using a state-space realization of a one-step prediction filter of arbitrary structure, the expressions (1), (4), and (5) could be iterated to obtain explicit, but very involved, expressions for the one-step prediction error. Similar expressions form the basis of many works; see, e.g., [8]- [13]. Even for the LMS case, a strict analysis becomes very difficult.…”

Section: Introductionmentioning

confidence: 86%

“…In the book [19] by Macchi (see also [8] and [12] for a similar definition), the DNS is for the purpose of LMS analysis characterized by the quantity (43) Parameter variations are considered slow if this quantity is always small. For vanishing parameter-drift-to-noise ratios , the variations will be slow according to (43).…”

Section: Neglecting the Time-varying Feedbackmentioning

confidence: 99%

“…This recursion must converge (convergence in MSE). The use of (47) For and independent inputs with constant modulus, , (8) and (14) give as…”

Section: Appendix B Proof Of Lemmamentioning

confidence: 99%

See 2 more Smart Citations

Analysis of Stability and Performance of Adaptation Algorithms With Time-Invariant Gains

Åhlén

Lindbom

Sternad

2004

IEEE Trans. Signal Process.

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Section: Introductionmentioning

confidence: 86%

Section: Neglecting the Time-varying Feedbackmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of Stability and Performance of Adaptation Algorithms With Time-Invariant Gains

Åhlén

Lindbom

Sternad

2004

IEEE Trans. Signal Process.

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“…There is considerable research discussing the LMS tracker [1], [8], [9], [26]. Different papers report similar results.…”

Section: Appendix Amentioning

confidence: 99%

“…Therefore, the best a conservative tracker can do is to copy the weights of a target network whenever . That is if if (8) We will call a conservative tracker that follows this update procedure the optimal conservative tracker. Note that in this case, for .…”

Section: A Optimal Conservative Tracking Algorithmmentioning

confidence: 99%

Comparison of tracking algorithms for single layer threshold networks in the presence of random drift

Kuh

1997

IEEE Trans. Signal Process.

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This paper analyzes the behavior of a variety of tracking algorithms for single-layer threshold networks in the presence of random drift. We use a system identification model to model a target network where weights slowly change and a tracking network. Tracking algorithms are divided into conservative and nonconservative algorithms. For a random drift rate of , we find upper bounds for the generalization error of conservative algorithms that are O(2=3) and for nonconservative algorithms that are O(). Bounds are found for the Perceptron tracker and the least mean square (LMS) tracker. Simulations show the validity of these bounds and show that the bounds are tight when is small and the number of inputs n is large. These results show that the Perceptron tracker and the LMS tracker can work well in slowly changing nonstationary environments.

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Exponential convergence of products of random matrices: application to adaptive algorithms

Moustakides

1998

Int. J. Adapt. Control Signal Process.

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We introduce a novel methodology for analysing well known classes of adaptive algorithms. Combining recent developments concerning geometric ergodicity of stationary Markov processes and long existing results from the theory of Perturbations of Linear Operators we first study the behaviour and convergence properties of a class of products of random matrices, this is turn allows for the analysis of the first and second order statistics of adaptive algorithms without the need of any restrictive conditions imposed on the data (as essential boundedness). Efficient estimates of the convergence rate of adaptive algorithms during the initial transient phase are also presented. These estimates do not rely on the unrealistic Independence Assumption as it is commonly the case in existing literature. © 1998 John Wiley & Sons, Ltd.

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Tracking error bounds of adaptive nonstationary filtering

Cited by 68 publications

References 11 publications

Analysis of Stability and Performance of Adaptation Algorithms With Time-Invariant Gains

Analysis of Stability and Performance of Adaptation Algorithms With Time-Invariant Gains

Comparison of tracking algorithms for single layer threshold networks in the presence of random drift

Exponential convergence of products of random matrices: application to adaptive algorithms

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