Quantized Output Observations Research Articles

Asymptotically efficient Quasi-Newton type identification with quantized observations under bounded persistent excitations

This paper is concerned with the optimal identification problem of dynamical systems in which only quantized output observations are available under the assumption of fixed thresholds and bounded persistent excitations. Based on a time-varying projection, a weighted Quasi-Newton type projection (WQNP) algorithm is proposed. With some mild conditions on the weight coefficients, the algorithm is proved to be mean square and almost surely convergent, and the convergence rate can be the reciprocal of the number of observations, which is the same order as the optimal estimate under accurate measurements. Furthermore, inspired by the structure of the Cramér–Rao lower bound, an information-based identification (IBID) algorithm is constructed with an adaptive design about weight coefficients of the WQNP algorithm, where the weight coefficients are related to the parameter estimates which leads to the essential difficulty of algorithm analysis. Beyond the convergence properties, this paper demonstrates that the IBID algorithm tends asymptotically to the Cramér–Rao lower bound, and hence is asymptotically efficient. A numerical example is simulated to show the effectiveness of the proposed algorithms.

Parameter estimation of quantized DARMA systems using weighted least squares

AbstractThis paper is concerned with parameter estimate of deterministic autoregressive moving average (DARMA) systems with uniform quantized output observations. By designing system input signals, the recursive least‐squares algorithm with designed weights is proved to have convergence properties under the uniform output signal quantizer. The authors analyse the properties of the size of quantization error, which implies that the convergence properties can be achieved when the quantization error satisfies some conditions. A numerical example is supplied to demonstrate the theoretical results.

Deep learning with transfer functions: new applications in system identification

Abstract This paper presents a linear dynamical operator described in terms of a rational transfer function, endowed with a well-defined and efficient back-propagation behavior for automatic derivatives computation. The operator enables end-to-end training of structured networks containing linear transfer functions and other differentiable units by exploiting standard deep learning software. Two relevant applications of the operator in system identification are presented. The first one consists in the integration of prediction error methods in deep learning. The dynamical operator is included as the last layer of a neural network in order to obtain the optimal one-step-ahead prediction error. The second one considers identification of general block-oriented models from quantized data. These block-oriented models are constructed by combining linear dynamical operators with static nonlinearities described as standard feed-forward neural networks. A custom loss function corresponding to the log-likelihood of quantized output observations is defined. For gradient-based optimization, the derivatives of the log-likelihood are computed by applying the back-propagation algorithm through the whole network. Two system identification benchmarks are used to show the effectiveness of the proposed methodologies.

Prediction-based event-triggered identification of quantized input FIR systems with quantized output observations

This paper addresses the identification of finite impulse response (FIR) systems withboth quantized and event-triggered observations.An event-triggered communication scheme for the binary-valued output quantization is introducedto save communication resources.Combining the empirical-measure-based identification techniqueand the weighted least-squares optimization,an algorithm is proposed to estimate the unknown parameterby full use of the received data and thenot-triggered condition.Under quantized inputs,it is shown that the estimate can strongly converge to the real valuesand the estimator is asymptotically efficient in terms of the Cramer-Rao lowerbound.Further, the limit of the average communication rate is derived and the tradeoff between this limitand the estimation performance is discussed.Moreover, the case of multi-threshold quantized observations is considered.Numerical examples are included to illustrate the obtained main results.

One-Bit Recursive Least-Squares Algorithm With Application to Distributed Target Localization

Adaptation and learning over low-cost wireless networks, meanwhile keeping an acceptable performance, are well motivated. This paper focuses on online parameter estimation over binary networks, which consist of noisy low-resolution sensors, each only giving coarsely one-bit quantized output observations and transmitting them to a fusion center. We develop a class of recursive least-squares (RLS) algorithms based on an expectation–maximization framework, which realizes adaptive parameter estimation from one-bit observations of the noisy output stream. The developed algorithms are, respectively, derived with and without prior knowledge of the noise variances, and their performances are theoretically and experimentally evaluated. Moreover, it is shown that, although the information contained in the one-bit observations is very limited, the proposed algorithms are comparable to the classical RLS algorithm using the original (nonquantized) observations. In addition, as a practical application, the proposed algorithm combined with array signal processing techniques is applied to bearing-only target localization over wireless sensor array networks, and its effectiveness is verified through simulation experiments.

Identification for Wiener‐Hammerstein systems under quantized inputs and quantized output observations

AbstractThis paper investigates the Wiener‐Hammerstein system identification with quantized inputs and quantized output observations. By parameterizing the static nonlinear function, system identifiability is discussed first. Then, for the identifiable system a three‐step algorithm is proposed to estimate the unknown parameters by employing the empirical measure‐based method and the quasi‐convex combination technique. Finally, the algorithm is proved to be strongly convergent, the mean‐square convergence rate is presented, and the asymptotic efficiency is given by selecting a suitable transformation matrix. A numerical simulation is included to demonstrate the main results obtained.

Recursive Identification of Quantized Linear Systems

This paper studies the identification of linear systems with quantized output observations. Recursive estimates for the linear system and the quantization thresholds are derived by the stochastic approximation algorithms with expanding truncations (SAAWET). Under suitable conditions, it is shown that the estimates converge to the true values almost surely.

FIR systems identification under quantized output observations and a large class of persistently exciting quantized inputs

This paper investigates the FIR systems identification with quantized output observations and a large class of quantized inputs. The limit inferior of the regressors’ frequencies of occurrences is employed to characterize the input’s persistent excitation, under which the strong convergence and the convergence rate of the two-step estimation algorithm are given. As for the asymptotical efficiency, with a suitable selection of the weighting matrix in the algorithm, even though the limit of the product of the Cramer-Rao (CR) lower bound and the data length does not exist as the data length goes to infinity, the estimates still can be asymptotically efficient in the sense of CR lower bound. A numerical example is given to demonstrate the effectiveness and the asymptotic efficiency of the algorithm.

Asymptotically efficient identification of FIR systems with quantized observations and general quantized inputs

This paper introduces identification algorithms for finite impulse response systems under quantized output observations and general quantized inputs. While asymptotically efficient algorithms for quantized identification under periodic inputs are available, their counterpart under general inputs has encountered technical difficulties and evaded satisfactory resolutions. Under quantized inputs, this paper resolves this issue with constructive solutions. A two-step algorithm is developed, which demonstrates desired convergence properties including strong convergence, mean-square convergence, convergence rates, asymptotic normality, and asymptotical efficiency in terms of the Cramér–Rao lower bound. Some essential conditions on input excitation are derived that ensure identifiability and convergence. It is shown that by a suitable selection of the algorithm’s weighting matrix, the estimates become asymptotically efficient. The strong and mean-square convergence rates are obtained. Optimal input design is given. Also the joint identification of noise distribution functions and system parameters is investigated. Numerical examples are included to illustrate the main results of this paper.

Identification of FIR Systems with Quantized Inputs and Observations

This paper introduces identification algorithms for finite impulse response systems under quantized output observations and general quantized inputs. While asymptotically efficient algorithms for quantized identification under periodic inputs are available, their counterpart under general inputs has encountered technical difficulties and evaded satisfactory resolutions. Under quantized inputs, this paper resolves this issue with constructive solutions. A two-step algorithm is developed, which demonstrates desired convergence properties including strong convergence, mean-square convergence, convergence rates, asymptotic normality, and asymptotical efficiency in terms of the Cramér-Rao lower bound. Some essential conditions on input excitation are derived that ensure identifiability and convergence. It is shown that by a suitable selection of the algorithm’s weighting matrix, the estimates become asymptotically efficient. The strong and mean-square convergence rates are explicitly obtained. Optimal input design is discussed. Numerical examples are included to illustrate the main results of this paper

Identification of ARMA models using intermittent and quantized output observations

This paper studies system identification of ARMA models whose outputs are subject to finite-level quantization and random packet dropouts. Using the maximum likelihood criterion, we propose a recursive identification algorithm, which we show to be strongly consistent and asymptotically normal. We also propose a simple adaptive quantization scheme, which asymptotically achieves the minimum parameter estimation error covariance. The joint effect of finite-level quantization and random packet dropouts on identification accuracy are exactly quantified. The theoretical results are verified by simulations.

Space and time complexities and sensor threshold selection in quantized identification

This work is concerned with system identification of plants using quantized output observations. We focus on relationships between identification space and time complexities. This problem is of importance for system identification in which data-flow rates are limited due to computer networking, communications, wireless channels, etc. Asymptotic efficiency of empirical measure based algorithms yields a tight lower bound on identification accuracy. This bound is employed to derive a separation principle of space and time complexities and to study sensor threshold selection. Insights gained from these understandings provide a feasible approach for optimal utility of communication bandwidth resources in enhancing identification accuracy.

Asymptotically efficient parameter estimation using quantized output observations

This paper studies identification of systems in which only quantized output observations are available. An identification algorithm for system gains is introduced that employs empirical measures from multiple sensor thresholds and optimizes their convex combinations. Strong convergence of the algorithm is first derived. The algorithm is then extended to a scenario of system identification with communication constraints, in which the sensor output is transmitted through a noisy communication channel and observed after transmission. The main results of this paper demonstrate that these algorithms achieve the Cramér–Rao lower bounds asymptotically, and hence are asymptotically efficient algorithms. Furthermore, under some mild regularity conditions, these optimal algorithms achieve error bounds that approach optimal error bounds of linear sensors when the number of thresholds becomes large. These results are further extended to finite impulse response and rational transfer function models when the inputs are designed to be periodic and full rank.