1,721,017 research outputs found
Binary input reconstruction for linear systems: A performance analysis
No full textRecovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have been developed for this purpose in the last decades, addressed to different models and performance/complexity requirements. In this paper, we implement a straightforward algorithm to reconstruct the binary input of a one-dimensional linear system with known probabilistic properties. Although suboptimal, this algorithm presents two main advantages: it works online (given the current output measurement, it decodes the current input bit) and has very low complexity. Moreover, we can theoretically analyze its performance: using results on convergence of probability measures, Markov processes, and Iterated Random Functions we evaluate its long-time behavior in terms of mean square erro
Analysis of reduced-search BCJR algorithms for input estimation in a jump linear system
No full textLinear systems with unknown finite-valued inputs are of interest in all those hybrid frameworks where switches or jumps may change the continuous dynamics of a linear system. Many models have been proposed in this sense; in most cases, a probabilistic distribution on the input is assumed to be known and used as prior information for estimation. In this paper, we propose a simple model of jump linear system and develop low complexity algorithms, based on BCJR, to retrieve the input. We consider systems over a possibly infinite time horizon, which motivates the study of on-line, causal algorithms. Our main purpose is to provide a rigorous theoretical analysis of the performance of the proposed techniques: an error function is defined and its distribution is proved to converge, exploiting mathematical tools from Markov Processes theory and ergodic theorem
Deconvolution of quantized-input linear systems: Analysis via Markov Processes of a low-complexity algorithm
No full textThis paper is concerned with the problem of the
deconvolution, which consists in recovering the unknown input
of a linear system from a noisy version of the output. The
case of a system with quantized input is considered and a
low-complexity algorithm, derived from decoding techniques,
is introduced to tackle it. The performance of such algorithm
is analytically evaluated through the Theory of Markov Processes. In this framework, results are shown which prove the
uniqueness of an invariant probability measure of a Markov
Process, even in case of non-standard state space. Finally, the
theoretic issues are compared with simulations’ outcomes
Analysis of a Deconvolution Algorithm for quantized-input linear systems through Iterated Random Functions
No full textDeconvolution consists in recovering the unknown input of a system given noisy measurements of the output. If the input is quantized, the problem can be faced via Information and Decoding techniques, which provide the suitable tools to work in hybrid contexts, namely when discrete signals are transmitted through analog communication systems. Derived from BCJR, a low-complexity, recursive decoding algorithm has been developed by Fagnani and Fosson (2009) and is here applied to tackle deconvolution of one-dimensional linear systemswith binary input. The aim of the paper is to provide a rigorous mathematical analysis of the performance of such algorithm, in terms of a mean square error and for long time transmissions. This task is accomplished by means of Iterated Random Function
A decoding approach to fault tolerant control of linear systems with quantised disturbance input
No full textFault tolerant control aims at removing or at least reducing the negative effects of disturbances in an automation system, in order to maintain the best performance as far as possible. Such a task is performed in three steps: the fault detection, the fault identification, and the consequent process recovery. Let us consider a hybrid model in which a continuous, time invariant, linear system is excited by a quantised disturbance signal: a decoding approach can be undertaken to perform detection and identification. For this purpose, in this article we propose a low-complexity, recursive decoding algorithm, which has been developed using techniques from information and coding theory and here adapted to the control framework. Our aim is to analyse and test the decoding approach to control in the case of binary quantisation, in a flight control scenario. We report both theoretical and simulations' results and derive optimal design criteri
Recovery of Binary Sparse Signals From Compressed Linear Measurements via Polynomial Optimization
Full text linkThe recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the com-pressed sensing framework, tailored methods have been recently proposed to deal with the case of finite-valued sparse signals. In this letter, we focus on binary sparse signals and we propose a novel formulation, based on polynomial optimization. This approach is analyzed and compared to the state-of-the-art binary compressed sensing methods
Non-convex approach to binary compressed sensing
Full text linkWe propose a new approach for the recovery of binary signals in compressed sensing, based on the local minimization of a non-convex cost functional. The desired signal is proved to be a local minimum of the functional under mild conditions on the sensing matrix and on the number of measurements. We develop a procedure to achieve the desired local minimum, and, finally, we propose numerical experiments that show the improvement obtained by the proposed approach with respect to classical convex methods
Online Optimization in Dynamic Environments: A Regret Analysis for Sparse Problems
Full text linkTime-varying systems are a challenge in many scientific and engineering areas. Usually, estimation of time-varying parameters or signals must be performed online, which calls for the development of responsive online algorithms. In this paper, we consider this problem in the context of the sparse optimization; specifically, we consider the Elastic-net model. Following the rationale in [1], we propose a novel online algorithm and we theoretically prove that it is successful in terms of dynamic regret. We then show an application to recursive identification of time-varying autoregressive models, in the case when the number of parameters to be estimated is unknown. Numerical results show the practical efficiency of the proposed method
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