A new kernel-based approach to system identification with quantized output data

Bottegal, Giulio; Hjalmarsson, Håkan; Pillonetto, Gianluigi

doi:10.1016/j.automatica.2017.07.053

Cited by 47 publications

(20 citation statements)

References 41 publications

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“…In [1], [19], the EM algorithm was used to optimize the likelihood function, while in [37] a variational approximation approach was utilized. Additionally, Bayesian frameworks were applied in, e.g., [9]. 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.…”

Section: B Related Workmentioning

confidence: 99%

“…See Appendix C Remark 9. This theorem is the key to establish the consistent estimation of the weighted adjacency matrix A * , since it shows that θ * = vec (A * c * ) can be obtained by optimizing (9). Because of its significance, one of the future works of this paper is to generalize the disturbance assumption.…”

Section: A An Objective Function and Its Concavitymentioning

confidence: 99%

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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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Section: B Related Workmentioning

confidence: 99%

Section: A An Objective Function and Its Concavitymentioning

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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“…Recently, a number of set-valued identification algorithms have been developed. They can be classified roughly from system models, e.g., for linear systems, there are FIR models [9][10][11][12][13][14]; for nonlinear systems, there are Wiener [15] and Hammerstein [16] models. Besides, they can also be categorized in terms of the quantization schemes, e.g., fixed-level quantizer and uniform quantizer.…”

Section: Introductionmentioning

confidence: 99%

“…Besides, they can also be categorized in terms of the quantization schemes, e.g., fixed-level quantizer and uniform quantizer. In particular, for FIR models with finite quantization levels, there are empirical measure approach [9,17] which has good properties of unbiasedness and strong consistency, EM algorithm [10,11] which has a exponent convergent speed under certain conditions, kernel-based method [12], and quadratic programming-based method [13].…”

Section: Introductionmentioning

confidence: 99%

FIR system identification with set-valued and precise observations from multiple sensors

Zhang

Wang

Zhao

2019

Sci. China Inf. Sci.

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This paper considers the system identification problem for FIR (finite impulse response) systems with set-valued and precise observations received from multiple sensors. A fusion estimation algorithm based on some suitable identification algorithms for different types of observations is proposed. In particular, least square method is chosen for FIR systems with precise observations, while empirical measure method and EM algorithm are chosen for FIR systems with set-valued observations in the cases of periodic and general system inputs, respectively. Then, the quasi-convex combination estimator (QCCE) fusing the two different estimators by a linear combination with appropriate weights is constructed. Furthermore, the convergence properties are theoretically analyzed in terms of strong consistency and asymptotic efficiency. The fused estimator QCCE is proved to achieve the Cramér-Rao (CR) lower bound asymptotically under periodic inputs. Extensive numerical simulations validate the superiority of the fusion estimation algorithm under both periodic and general inputs.

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“…Zhao et al [12] considered linear system identification with batched binary‐valued observations and constructed an iterative parameter estimate algorithm to achieve the maximum likelihood estimate. Bottegal et al [13] modelled the impulse response as a zero‐mean Gaussian process whose covariance (kernel) was given by the recently proposed stable spline kernel and introduced a novel method for linear system identification with quantised output data. Zhao et al [14] addressed the recursive non‐parametric identification of non‐linear systems with adaptive binary sensors.…”

Section: Introductionmentioning

confidence: 99%