System Identification Based on Tensor Decompositions: A Trilinear Approach

System identification problems are always challenging to address in applications that involve long impulse responses, especially in the framework of multichannel systems. In this context, the main goal of this review paper is to promote some recent developments that exploit decomposition-based approaches to multiple-input/single-output (MISO) system identification problems, which can be efficiently solved as combinations of low-dimension solutions. The basic idea is to reformulate such a high-dimension problem in the framework of bilinear forms, and to then take advantage of the Kronecker product decomposition and low-rank approximation of the spatiotemporal impulse response of the system. The validity of this approach is addressed in terms of the celebrated Wiener filter, by developing an iterative version with improved performance features (related to the accuracy and robustness of the solution). Simulation results support the main theoretical findings and indicate the appealing performance of these developments.

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A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms

Algorithms ◽

10.3390/a11120211 ◽

2018 ◽

Vol 11 (12) ◽

pp. 211 ◽

Cited By ~ 3

Author(s):

Laura-Maria Dogariu ◽

Silviu Ciochină ◽

Constantin Paleologu ◽

Jacob Benesty

Keyword(s):

Kalman Filter ◽

Wiener Filter ◽

Identification Problem ◽

Lms Algorithm ◽

Bilinear Forms ◽

Least Mean Square ◽

Spatiotemporal Model ◽

Single Output ◽

Multiple Input ◽

Output System

The system identification problem becomes more challenging when the parameter space increases. Recently, several works have focused on the identification of bilinear forms, which are related to the impulse responses of a spatiotemporal model, in the context of a multiple-input/ single-output system. In this framework, the problem was addressed in terms of the Wiener filter and different basic adaptive algorithms. This paper studies two types of algorithms tailored for the identification of such bilinear forms, i.e., the Kalman filter (along with its simplified version) and an optimized least-mean-square (LMS) algorithm. Also, a comparison between them is performed, which shows interesting similarities. In addition to the mathematical derivation of the algorithms, we also provide extensive experimental results, which support the theoretical findings and indicate the good performance of the proposed solutions.

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System Identification of Static Nonlinear Elements: A Unified Approach of Active Learning, Over-fit Avoidance, and Model Structure Determination

10.36227/techrxiv.12149874.v1 ◽

2020 ◽

Author(s):

Nalika Ulapane ◽

Karthick Thiyagarajan ◽

sarath kodagoda

Keyword(s):

System Identification ◽

Active Learning ◽

Computationally Efficient ◽

Single Input Single Output ◽

Domain Identification ◽

Single Output ◽

Crucial Component ◽

Long Time ◽

Polynomial Models ◽

Noisy Measurements

Systems containing linear ﬁrst-order dynamics and static nonlinear elements (i.e., nonlinear elements whose outputs depend only on the present value of inputs) are often encountered; for example, certain automobile engine subsystems. Therefore, system identiﬁcation of static nonlinear elements becomes a crucial component that underpins the success of the overall identiﬁcation of such dynamical systems. In relation to identifying such systems, we are often required to identify models in differential equation form, and consequently, we are required to describe static nonlinear elements in the form of functions in time domain. Identiﬁcation of such functions describing static elements is often a black-box identiﬁcation exercise; although the inputs and outputs are known, correct mathematical models describing the static nonlinear elements may be unknown. Therefore, with the aim of obtaining computationally efﬁcient models, calibrating polynomial models for such static elements is often attempted. With that approach comes several issues, such as long time requirements to collect adequate amounts of measurements to calibrate models, having to test different models to pick the best one, and having to avoid models over-ﬁtting to noisy measurements. Given that premise, this paper proposes an approach to tackle some of those issues. The approach involves collecting measurements based on an uncertainty-driven Active Learning scheme to reduce time spent on measurements, and simultaneously ﬁtting smooth models using Gaussian Process (GP) regression to avoid over-ﬁtting, and subsequently picking best ﬁtting polynomial models using GP-regressed smooth models. The principles for the single-input-single-output (SISO) static nonlinear element case are demonstrated in this paper through simulation. These principles can easily be extended to MISO systems.

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System Identification of Static Nonlinear Elements: A Unified Approach of Active Learning, Over-fit Avoidance, and Model Structure Determination

10.36227/techrxiv.12149874 ◽

2020 ◽

Author(s):

Nalika Ulapane ◽

Karthick Thiyagarajan ◽

sarath kodagoda

Keyword(s):

System Identification ◽

Active Learning ◽

Computationally Efficient ◽

Single Input Single Output ◽

Domain Identification ◽

Single Output ◽

Crucial Component ◽

Long Time ◽

Polynomial Models ◽

Noisy Measurements

Systems containing linear ﬁrst-order dynamics and static nonlinear elements (i.e., nonlinear elements whose outputs depend only on the present value of inputs) are often encountered; for example, certain automobile engine subsystems. Therefore, system identiﬁcation of static nonlinear elements becomes a crucial component that underpins the success of the overall identiﬁcation of such dynamical systems. In relation to identifying such systems, we are often required to identify models in differential equation form, and consequently, we are required to describe static nonlinear elements in the form of functions in time domain. Identiﬁcation of such functions describing static elements is often a black-box identiﬁcation exercise; although the inputs and outputs are known, correct mathematical models describing the static nonlinear elements may be unknown. Therefore, with the aim of obtaining computationally efﬁcient models, calibrating polynomial models for such static elements is often attempted. With that approach comes several issues, such as long time requirements to collect adequate amounts of measurements to calibrate models, having to test different models to pick the best one, and having to avoid models over-ﬁtting to noisy measurements. Given that premise, this paper proposes an approach to tackle some of those issues. The approach involves collecting measurements based on an uncertainty-driven Active Learning scheme to reduce time spent on measurements, and simultaneously ﬁtting smooth models using Gaussian Process (GP) regression to avoid over-ﬁtting, and subsequently picking best ﬁtting polynomial models using GP-regressed smooth models. The principles for the single-input-single-output (SISO) static nonlinear element case are demonstrated in this paper through simulation. These principles can easily be extended to MISO systems.

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