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.     

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

This 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.     

Identification of cascaded systems with linear and quantized observations

This paper studies identification of systems that can be decomposed into cascaded subsystems. The benefits of using additional sensors for identifying subsystems are investigated in terms of identification accuracy and time complexity. Identification algorithms, input design, and time complexity are first developed for subsystems, under various sensor types and locations. Overall reduction in estimation errors and time complexity is then analyzed to understand optimal selection of sensor locations and impact of sensor types on identification accuracy and time complexity. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Blind system identification using precise and quantized observations

This paper studies the blind identification of multi-channel FIR systems using precise and quantized observations. First, a new deterministic blind identification (DBI) algorithm is presented for multi-channel FIR systems using precise observations, in which the system parameters can be consistently estimated and the common source signal can be stably recovered. When the observed samples are quantized by a static finite-level quantizer, an iterative deterministic blind identification (IDBI) method is then provided. The asymptotic characters of the proposed IDBI method are discussed and the quantization effect on the identification performance is analyzed. Numerical simulations are given to support the developed DBI method and IDBI method.     

Identification of FIR systems under difference-driven scheduled quantized observations

In networked system identification, how to effectively use communication resources and improve convergence speed is the focus of attention. However, there is an inherent contradiction between the two tasks. In this paper, the event-driven communication is used to save communication resources for the identification of finite impulse response systems, and the input design is carried out to meet the requirements of convergence speed. First, a difference-driven communication is proposed. Then, the performance of the communication mechanism is analyzed, and the calculation method of its communication rate is given. After that, according to the communication rate and the convergence rate of the identification algorithm, the input design problem is transformed into a constrained optimization problem, and the algorithm for finding the optimal solution is given. In addition, considering the case that the output is quantized by multiple thresholds, the way to calculate its communication rate is given and the influence of threshold number on communication rate is discussed. Finally, the effectiveness of the algorithm is verified by simulation.     

Stabilization of impulsive hybrid systems using quantized input and output feedback

In this paper, we consider the feedback stabilization of impulsive control systems with quantized input and output signals. To study the problem, the notions of quasi‐invariant sets and attracting sets for impulsive systems with quantization are introduced first, and then applied to the control design. Hybrid quantized control schemes are proposed to stabilize the considered impulsive linear or nonlinear systems via either input or output feedback. Mathematical analysis and numerical simulations are given to show the principle and effectiveness of the proposed designs. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Identification of the gain system with quantized observations and bounded persistent excitations

System identification with quantized observations and persistent excitations is a fundamental and difcult problem.As the first step,this paper takes the gain system for example to investigate the identification with quantized observations and bounded persistently exciting inputs.Firstly,the identification with single threshold quantization is considered.A projection recursive algorithm is proposed to estimate the unknown parameter.By use of the conditional expectation of quantized observations with respect to the estimates,the algorithm is shown to be both mean-square and almost surely convergent.The upper bound of the convergence rate is also obtained,which has the same order as the one of the optimal estimation in the case where the system output is exactly known.Secondly,for the multi-threshold quantization,the identification algorithm is similarly constructed and its asymptotic property is analyzed.Using a multi-linear transformation,the optimal scheme of quantization values and thresholds is given.A numerical example is simulated to demonstrate the efectiveness of the algorithms and the main results obtained.     

Identification of Wiener systems with binary-valued output observations

This work is concerned with identification of Wiener systems whose outputs are measured by binary-valued sensors. The system consists of a linear FIR (finite impulse response) subsystem of known order, followed by a nonlinear function with a known parametrization structure. The parameters of both linear and nonlinear parts are unknown. Input design, identification algorithms, and their essential properties are presented under the assumptions that the distribution function of the noise is known and the nonlinearity is continuous and invertible. It is shown that under scaled periodic inputs, identification of Wiener systems can be decomposed into a finite number of core identification problems. The concept of joint identifiability of the core problem is introduced to capture the essential conditions under which the Wiener system can be identified with binary-valued observations. Under scaled full-rank conditions and joint identifiability, a strongly convergent algorithm is constructed. The algorithm is shown to be asymptotically efficient for the core identification problem, hence achieving asymptotic optimality in its convergence rate. For computational simplicity, recursive algorithms are also developed.     

Modeling of the grounding resistance variation using ARMA models

This study addresses the problem of modeling the variation of the grounding resistance during the year. An AutoRegressive Moving Average (ARMA) model is fitted (off-line) on the provided actual data using the Corrected Akaike Information Criterion (AICC). The developed model is shown to fit the data in a successful manner. Difficulties occur when the provided data includes noise or errors and also when an on line/adaptive modeling is required. In both cases, and under the assumption that the provided data can be represented by an ARMA model, simultaneous order and parameter estimation of ARMA models under the presence of noise is necessary. In this paper, a new method based on the multi-model partitioning theory which is also applicable to on line/adaptive operation, is used for the solution of the above mentioned problem. The simulations show that the proposed method succeeds in selecting the correct ARMA model order and estimates the parameters accurately in very few steps and even with a small sample size. For validation purposes the method introduced is compared with three other established order selection criteria presenting very good results. The proposed method can be extremely useful in the studies of electrical engineer designers, since the variation of the grounding resistance during the year affects significantly power systems performance and must be definitely considered.     

On the identifiability of non-Gaussian ARMA models using cumulants

A fixed set of output cumulants of order greater than two guarantees unique identification of known-order causal ARMA (autoregressive moving-average) models, which are driven by unobservable non-Gaussian i.i.d. noise. The models are allowed to be non-minimum-phase, and their outputs may be corrupted by additive colored Gaussian noise of unknown covariance. The ARMA parameters can be estimated either by means of linear equations and closed-form expressions or by minimizing quadratic cumulant matching criteria. The latter approach requires computation of cumulants in terms of the ARMA parameters, which is carried out in the state space using Kronecker products     

基于脉冲响应的输出误差模型的辨识

基于系统脉冲响应参数, 利用相关分析方法, 提出了一种辨识输出误差模型参数的方法. 该方法是利用有限脉冲响应模型逼近输出误差模型, 通过依次递增脉冲响应参数的数目N来提高逼近精度. 理论分析表明, 只要N足够大, 模型的辨识精度可以满足实际要求. 提出的辨识方法可以在假设阶次N =1的条件下, 依次递增计算N较大时的脉冲响应参数和目标函数值, 从而根据脉冲响应确定系统的参数. 仿真试验说明提出的方法估计输出误差模型的参数是有效的.     

On identification of FIR systems having quantized output data

In this paper, we present a novel algorithm for estimating the parameters of a linear system when the observed output signal is quantized. This question has relevance to many areas including sensor networks and telecommunications. The algorithms described here have closed form solutions for the SISO case. However, for the MIMO case, a set of pre-computed scenarios is used to reduce the computational complexity of EM type algorithms that are typically deployed for this kind of problem. Comparisons are made with other algorithms that have been previously described in the literature as well as with the implementation of algorithms based on the Quasi-Newton method.     

Global output feedback stabilization for a class of nonlinear systems with quantized input and output

In this paper, we aim at addressing the problem of global output feedback stabilization for a class of uncertain nonlinear systems with quantized input and output. The nonlinear functions of the system are assumed to satisfy high‐order growth condition on the unmeasurable states. Based on the homogeneous domination approach and sector bound approach, a homogeneous quantized controller computed from quantized output is constructed, and a guideline is derived to select the parameters of the quantizers. Further, it is proved that, with the proposed scheme, the closed‐loop system is globally asymptotically stable. Copyright © 2016 John Wiley & Sons, Ltd.     

Identification of dynamic errors-in-variables models: Approaches based on two-dimensional ARMA modeling of the data

In this paper we propose a parametric and a non-parametric identification algorithm for dynamic errors-in-variables model. We show that the two-dimensional process composed of the input-output data admits a finite order ARMA representation. The non-parametric method uses the ARMA structure to compute a consistent estimate of the joint spectrum of the input and the output. A Frisch scheme is then employed to extract an estimate of the joint spectrum of the noise free input-output data, which in turn is used to estimate the transfer function of the system. The parametric method exploits the ARMA structure to give estimates of the system parameters. The performances of the algorithms are illustrated using the results obtained from a numerical simulation study.     

Discrete-event models of quantized systems for diagnosis

The paper concerns the model-based diagnosis of continuous-variable systems whose state can only be measured through a quantizer. The diagnosis is based on the investigation whether the observed discrete input and output sequences are consistent with a discrete-event model of the quantized system. The paper describes a necessary and sufficient condition for the discrete-event model to be suitable for diagnosis. This condition is independent of the specific model form and of the diagnostic algorithm applied to the model. Within a hierarchy of models with increasing accuracy all of which satisfy this modelling requirement the quality of the diagnostic result increases. The results are illustrated by an example.     

Identification of Wiener models using optimal local linear models

Identification of a Wiener model using optimal local linear models (LLMs) is presented. The model consists of a discrete-time transfer function and piece-wise linear functions. Parameter estimation as well as partitioning of the LLMs is simultaneously accomplished by the algorithm. The optimality is threefold: first, each local model is linear in the parameters, thus leading to an optimal solution. Second, the model size of each LLM is adaptively optimized using a chi-squared criterion, explicitly incorporating the measurement noise level. Third, the resulting model has a minimum of parameters for a given performance. Simulation results document that the output noise is balanced with the systems nonlinearity.     

Computing and estimating information matrices of weak ARMA models

Numerous time series admit weak autoregressive-moving average (ARMA) representations, in which the errors are uncorrelated but not necessarily independent nor martingale differences. The statistical inference of this general class of models requires the estimation of generalized Fisher information matrices. Analytic expressions are given for these information matrices, and consistent estimators, at any point of the parameter space, are proposed. The theoretical results are illustrated by means of Monte Carlo experiments and by analyzing the dynamics of daily returns and squared daily returns of financial series.     

Iterative least-squares parameter estimation for ARMA pulse response and output disturbance

The parameters of an ARMA system and of additive ARMA output disturbance with mutually different poles were estimated from a record of the disturbed output on a single pulse input. Alternating the steps of iterative inverse filtering with iterations according to generalized least squares appeared very economical for this system. This procedure converged for second-order simulations. Statistics of the estimates were evaluated from these simulation results for two signal-to-noise ratios.     

Fixed-order FIR approximation of linear systems from quantized input and output data

The problem of identifying a fixed-order FIR approximation of linear systems with unknown structure, assuming that both input and output measurements are subjected to quantization, is dealt with in this paper. A fixed-order FIR model providing the best approximation of the input–output relationship is sought by minimizing the worst-case distance between the output of the true system and the modeled output, for all possible values of the input and output data consistent with their quantized measurements. The considered problem is firstly formulated in terms of robust optimization. Then, two different algorithms to compute the optimum of the formulated problem by means of linear programming techniques are presented. The effectiveness of the proposed approach is illustrated by means of a simulation example.     

Rank pattern-based selection of input/output ARMA model order

Rational transfer functions are standard models for radar targets and adaptive beamforming. Fitting these models essentially involves estimating the transfer function “poles and zeroes.” A key preliminary step in this estimation process is to determine the numbers of poles and zeros, or equivalently to determine the order of the corresponding ARMA model. A pattern-based method of order selection using matrix ranks is proposed for input/output (I/O) ARMA models, where ARMA model inputs and outputs are each observed in additive noise with known variances. This I/O ARMA model encompasses two distinct scenarios: observational studies in which all observations—those of both inputs and outputs—are erred, and controlled experiments in which outputs are observed with error while inputs are known without error. The proposed rank pattern method exploits the eigenvalue structure of the covariance matrices associated with the observed data and performs well for short data records at moderate SNRs.