Binary-valued Output Observations Research Articles

System identification with binary-valued output observations under either-or communication and data packet dropout

The event-triggered mechanism can effectively save communication resources. However, if the packet loss occurs during data transmission, the receiving center is unable to distinguish between “no data has been sent since the event is not triggered” and “the data has been sent, but the packet is lost”. This paper aims to address this issue in the system identification with binary-valued output observations under either-or communication and data packet dropout. For the case that the packet loss probability is known, the identification algorithm is designed, and the strong convergence and asymptotic normality of the algorithm are given. For the case that the packet loss probability is unknown, a compensation-oriented identification approach is proposed by improving the either-or communication mechanism. The identification algorithm is designed to jointly estimate the system parameter and the packet loss probability, then its convergence and asymptotic normality are derived. The minimum communication rate is given within the allowable range of estimation error and the implementation of the optimal communication mechanism is provided. The validity and rationality of the results are verified by numerical simulation.

Channel Identification of Non-linear Systems with Binary-Valued Output Observations Based on Positive Definite Kernels

Nowadays, the kernel methods are increasingly developed, they are a significant source of advances, not only in terms of computational cost but also in terms of the obtained efficiencies in solving complex tasks, they are founded on the theory of reproducing kernel Hilbert spaces (RKHS). In this paper, we propose an algorithm for recursive identification of finite impulse response (FIR) nonlinear systems, whose outputs are detected by binary value sensors. This algorithm is based on a nonlinear transformation of the data using a kernel function. This transformation performs a basic change that allows the data to be projected into a new space where the relationships between the variables are linear. To test the accuracy of the proposed algorithm, we have compared it with another algorithm proposed in the literature, for that, we employ the practical frequency selective fading channel, called Broadband Radio Access Network (BRAN). Monte Carlo simulation results, in noisy environment and for various data length, demonstrate that the proposed algorithm can give better precision.

Event-triggered identification of FIR systems with binary-valued output observations

This paper investigates the identification of FIR (finite impulse response) systems whose output observations are subject to both the binary-valued quantization and the event-triggered scheme. Based on the a priori information of the unknown parameters and the statistical property of the system noise, a recursive stochastic-approximation-type identification algorithm is proposed. Under a class of persistently exciting inputs, the algorithm is proved to be strongly convergent and the convergence rate of the estimation error is also established, where the corresponding event-triggering conditions are provided. Moreover, the communication rate is discussed. A numerical example is included to verify the effectiveness of the results obtained.

Parameter estimation for systems with structural uncertainties based on quantised inputs and binary‐valued output observations

This study investigates the parameter estimation with general quantised inputs and binary-valued output observations for systems with structural uncertainties of the time-dependent bias and the non-linear model mismatch. Combining the empirical-measure-based technique and the least-squares optimisation, an identification algorithm is proposed by use of the output threshold information and the distribution function of the system noise. It is shown that the estimate of the unknown parameter can be sandwiched in between two constructed auxiliary sequences, whose limits are just a lower bound of the limit inferior of the algorithm and an upper bound of the limit superior, respectively. Moreover, probabilistic estimation error bounds are given. Numerical simulations are presented to illustrate the main theoretical results.

Identification of Wiener systems with quantized inputs and binary-valued output observations

This paper investigates identification of Wiener systems with quantized inputs and binary-valued output observations. By parameterizing the static nonlinear function and incorporating both linear and nonlinear parts, we begin by investigating system identifiability under the input and output constraints. Then a three-step algorithm is proposed to estimate the unknown parameters by using the empirical measure, input persistent patterns, and information on noise statistics. Convergence properties of the algorithm, including strong convergence and mean-square convergence rate, are established. Furthermore, by selecting a suitable transformation matrix, the asymptotic efficiency of the algorithm is proved in terms of the Cramér–Rao lower bound. Finally, numerical simulations are presented to illustrate the main results of this paper.

State reconstruction for linear time-invariant systems with binary-valued output observations

This paper focuses on state reconstruction problems for systems whose outputs are measured only by binary-valued sensors. A binary-valued sensor is characterized by its switching threshold or post-switching location and by its output that indicates only whether the system output is above or below the threshold. The traditional passive-type state reconstruction that does not require input design will fail in general, even if the system has a full-rank observability matrix. It is shown that under controllability conditions and bounded uncertainty on the initial state, it is always possible to construct a causal input that will cause the output to cross the sensor threshold in a designated time interval. Information on the time instants of threshold crossing is then used to reconstruct the initial state. It is proved that if the system is observable, such a reconstruction is always possible if the eigenvalues of the system are all real valued. If the eigenvalues of the system contain only purely imaginary and non-repeating values, it is sufficient that threshold crossing occurs within a relatively small time interval. In general without constraints on system eigenvalues, an input can always be randomized to ensure that the state can be reconstructed with probability one. These results lead to an active state reconstruction algorithm.

Identification Input Design for Consistent Parameter Estimation of Linear Systems With Binary-Valued Output Observations

Input design is of essential importance in system identification for providing sufficient probing capabilities to guarantee convergence of parameter estimates to their true values. This paper presents conditions on input signals that characterize their probing richness for strongly consistent parameter estimation of linear systems with binary-valued output observations. Necessary and sufficient conditions on periodic signals are derived for sufficient richness. These conditions are further studied under different system configurations including open-loop and feedback systems, and different scenarios of noises including actuator noise, input measurement noise, and output measurement noise. In addition to system parameter estimation, essential properties of identifiability and input conditions are also derived when sensor thresholds or noise distribution functions are unknown. The findings of this paper provide a foundation to study identification of systems that either use binary-valued or quantized sensors or involve communication channels, which mandate quantization of signals.

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.

Joint identification of plant rational models and noise distribution functions using binary-valued observations

System identification of plants with binary-valued output observations is of importance in understanding modeling capability and limitations for systems with limited sensor information, establishing relationships between communication resource limitations and identification complexity, and studying sensor networks. This paper resolves two issues arising in such system identification problems. First, regression structures for identifying a rational model contain non-smooth nonlinearities, leading to a difficult nonlinear filtering problem. By introducing a two-step identification procedure that employs periodic signals, empirical measures, and identifiability features, rational models can be identified without resorting to complicated nonlinear searching algorithms. Second, by formulating a joint identification problem, we are able to accommodate scenarios in which noise distribution functions are unknown. Convergence of parameter estimates is established. Recursive algorithms for joint identification and their key properties are further developed.

RATIONAL MODEL IDENTIFICATION WITH UNKNOWN NOISE DISTRIBUTION USING BINARY DATA

This paper introduces new methods in system identification with binary-valued output observations. It resolves two key issues, (a) regression structures for identifying a rational model that contain non-smooth nonlinearity, and (b) unknown noise distributions arising in practical identification problems. Optimal identification errors, time complexity, and input design are examined in a stochastic information framework.