Efficient Algorithms for Linear System Identification with Particular Symmetric Filters

Applied Sciences

Laura-Maria Dogariu¹  Constantin Paleologu¹  Silviu Ciochină¹  Ionuţ-Dorinel Fîciu¹  Jacob Benesty² 

[1] Department of Telecommunications, University Politehnica of Bucharest, 1-3, Iuliu Maniu Blvd., 061071 Bucharest, Romania;INRS-EMT, University of Quebec, Montreal, QC H5A 1K6, Canada;

关键词: adaptive filters;    echo cancellation;    impulse response decomposition;    nearest Kronecker product;    recursive least-squares (RLS) algorithm;    symmetric filter;   

DOI  :  10.3390/app12094263

来源: DOAJ

【 摘 要 】

In linear system identification problems, it is important to reveal and exploit any specific intrinsic characteristic of the impulse responses, in order to improve the overall performance, especially in terms of the accuracy and complexity of the solution. In this paper, we focus on the nearest Kronecker product decomposition of the impulse responses, together with low-rank approximations. Such an approach is suitable for the identification of a wide range of real-world systems. Most importantly, we reformulate the system identification problem by using a particular symmetric filter within the development, which allows us to efficiently design two (iterative/recursive) algorithms. First, an iterative Wiener filter is proposed, with improved performance as compared to the conventional Wiener filter, especially in challenging conditions (e.g., small amount of available data and/or noisy environments). Second, an even more practical solution is developed, in the form of a recursive least-squares adaptive algorithm, which could represent an appealing choice in real-time applications. Overall, based on the proposed approach, a system identification problem that can be conventionally solved by using a system of $L=L_1{L}_2$ equations (with L unknown parameters) is reformulated as a combination of two systems of $P{L}_1$ and $P{L}_2$ equations, respectively, where usually $P\ll L_2$ (i.e., a total of $P{L}_1+P{L}_2$ parameters). This could lead to important advantages, in terms of both performance and complexity. Simulation results are provided in the framework of network and acoustic echo cancellation, supporting the performance gain and the practical features of the proposed algorithms.

【 授权许可】

Unknown