Convergence analysis of an online approach to parameter estimation problems based on binary observations

Jafari, Kian; Jerome, J. Terrence Jose; Roger, Morgan

doi:10.1016/j.automatica.2012.05.050

Cited by 41 publications

(18 citation statements)

References 13 publications

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“…In this paper, we extended the analysis of the LIMBO method [9] to a more general context involving measurement noise and no relaxation step. We demonstrated the convergence in the mean of the non-relaxed version of the method, in the absence of noise.…”

Section: Discussionmentioning

confidence: 99%

“…CONVERGENCE ANALYSIS IN THE PRESENCE OF NOISE In [9], the almost sure convergence of the algorithm presented in the previous section is demonstrated under some specific assumptions. In particular, the proof is established for a relaxed version of the algorithm by supposing b k = 0 (although a proof in the noise-free non-relaxed case could also be obtained by following the approach in [18]).…”

Section: Proposed Lms Approachmentioning

confidence: 99%

“…They have proved that the cumulative distribution function of the threshold does not have to be known a priori and can be estimated simultaneously with the system parameters. More recently, Jafari and his co-authors [9] have studied a recursive identification method which does not rely on a pseudogradient of a least-squares criterion and requires neither a known non-zero threshold value, nor a varying threshold. This online LMS-like identification method based on binary observations (LIMBO) has little storage requirements and low computational complexity.…”

Section: Introductionmentioning

confidence: 99%

“…Several identification methods based on binary or roughly quantized observations can be found in the literature [5], [6], [7], [8], [1], [9], [10], [11], [12], [13], [14]. For example, Wigren [5], [6] has developed a least-mean-square (LMS) approach to the problem of online parameter estimation from quantized observations, based on an approximation of the quantizer.…”

Section: Introductionmentioning

confidence: 99%

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Convergence analysis of an online approach to parameter estimation problems based on binary noisy observations

Bourgois

Jerome

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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The convergence analysis of an online system identification method based on binary-quantized observations is presented in this paper. This recursive algorithm can be applied in the case of finite impulse response (FIR) systems and exhibits low computational complexity as well as low storage requirement. This method, whose practical requirement is a simple 1-bit quantizer, implies low power consumption and minimal silicon area, and is consequently well-adapted to the test of microfabricated devices. The convergence in the mean of the method is studied in the presence of measurement noise at the input of the quantizer. In particular, a lower bound of the correlation coefficient between the nominal and the estimated system parameters is found. Some simulation results are then given in order to illustrate this result and the assumptions necessary for its derivation are discussed.

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Section: Discussionmentioning

confidence: 99%

Section: Proposed Lms Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Convergence analysis of an online approach to parameter estimation problems based on binary noisy observations

Bourgois

Jerome

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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“…The authors of [43] proposed an algorithm based on the recursive prediction error method to estimate the linear part of Wiener systems, which can be used to deal with quantized output models, but both quantizers and the range of parameters were assumed to be known. A least-squares algorithm was developed in [22] to recursively estimate finite impulse response systems. For the theoretical results the authors assumed that the inputs have a positivemeasure support and that the threshold is known.…”

Section: B Related Workmentioning

confidence: 99%

Network Weight Estimation for Binary-Valued Observation Models

Fang

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which agents exchange and display binary outputs. Sufficient conditions are given to ensure stability of the observation sequence and identifiability of the system parameters. It is shown that stability and identifiability can be guaranteed under the assumption of independent standard Gaussian disturbances. Via a maximum likelihood approach, the estimation problem is transformed into an optimization problem, and it is verified that its solution is the true parameter vector under the independent standard Gaussian assumption. A recursive algorithm for the estimation problem is then proposed based on stochastic approximation techniques. Its strong consistency is established and convergence rate analyzed. Finally, numerical simulations are conducted to illustrate the results and to show that the proposed algorithm is insensitive to small unmodeled factors.

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Recursive system identification method from binary input/output measurements

Oualla

Pouliquen

Frikel

et al. 2023

Asian Journal of Control

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This paper presents two online identification algorithms of finite impulse response (FIR) systems using binary measurements both on the input and on the output. These algorithms are based on the least mean square (LMS) technique and on the estimation of the correlation functions of the input and output from binary data. Note that the second algorithm is a simplified version of the first one in the case of a white noise on the input. The convergence and variance analyses are provided. A numerical example is given to demonstrate the effectiveness of the proposed algorithms.

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Convergence analysis of an online approach to parameter estimation problems based on binary observations

Cited by 41 publications

References 13 publications

Convergence analysis of an online approach to parameter estimation problems based on binary noisy observations

Convergence analysis of an online approach to parameter estimation problems based on binary noisy observations

Network Weight Estimation for Binary-Valued Observation Models

Recursive system identification method from binary input/output measurements

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