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

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data.Comment: 10 pages, 4 figure

Bayesian kernel-based system identification with quantized output data

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo (MCMC) methods to provide an estimate of the system. In particular, we show how to design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods when employed in identification of systems with quantized data.Comment: Submitted to IFAC SysId 201

A Recursive System Identification Method Based on Binary Measurements

An online approach to parameter estimation problems based on binary observations is presented in this paper. This recursive identification method relies on a least-mean squares approach which makes it possible to estimate the coefficients of a finite-impulse response system knowing only the system input and the sign of the system output. The impulse response is identified up to a positive multiplicative constant. The role of the regulative coefficient is investigated thanks to simulated data. The proposed method is compared with another online approach: it is shown that the proposed method is competitive with the other one in terms of estimation quality and of calculation complexity

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

Abstract 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

Convergence Analysis of an Online Approach to Parameter Estimation Problems Based on Binary Noisy Observations

International audienceThe 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 coe cient 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 discusse

A Novel Kernel Algorithm for Finite Impulse Response Channel Identification, Journal of Telecommunications and Information Technology, 2023, nr 2

Over the last few years, kernel adaptive filters have gained in importance as the kernel trick started to be used in classic linear adaptive filters in order to address various regression and time-series prediction issues in nonlinear environments.In this paper, we study a recursive method for identifying finite impulse response (FIR) nonlinear systems based on binary-value observation systems. We also apply the kernel trick to the recursive projection (RP) algorithm, yielding a novel recursive algorithm based on a positive definite kernel. For purposes, our approach is compared with the recursive projection (RP) algorithm in the process of identifying the parameters of two channels, with the first of them being a frequency-selective fading channel, called a broadband radio access network (BRAN B) channel, and the other being a a theoretical frequency-selective channel, known as the Macchi channel. Monte Carlo simulation results are presented to show the performance of the proposed algorith