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System Identification Under Multi-rate Sensing Environment

Hiroshi Okajima, Risa Furukawa, Nobutomo Matsunaga

TL;DR

The paper tackles identifying discrete-time systems observed through sensors with different sampling rates. It introduces a cyclic reformulation that converts a multi-rate, periodically time-varying system into a time-invariant cycled model, enabling standard subspace identification on cycled data. A coordinate transformation then recovers per-rate state-space matrices, and numerical examples show that recovered transfer functions closely match the true plant, validating the approach. The method offers a computation-efficient solution for accurate identification in multi-sensor networks without requiring specially structured input signals.

Abstract

This paper proposes a system identification algorithm for systems with multi-rate sensors in a discrete-time framework. It is challenging to obtain an accurate mathematical model when the ratios of inputs and outputs are different in the system. A cyclic reformulation-based model for multi-rate systems is formulated, and the multi-rate system can be reduced to a linear time-invariant system to derive the model under the multi-rate sensing environment. The proposed algorithm integrates a cyclic reformulation with a state coordinate transformation of the cycled system to enable precise identification of systems under the multi-rate sensing environment. The effectiveness of the proposed system identification method is demonstrated using numerical simulations.

System Identification Under Multi-rate Sensing Environment

TL;DR

The paper tackles identifying discrete-time systems observed through sensors with different sampling rates. It introduces a cyclic reformulation that converts a multi-rate, periodically time-varying system into a time-invariant cycled model, enabling standard subspace identification on cycled data. A coordinate transformation then recovers per-rate state-space matrices, and numerical examples show that recovered transfer functions closely match the true plant, validating the approach. The method offers a computation-efficient solution for accurate identification in multi-sensor networks without requiring specially structured input signals.

Abstract

This paper proposes a system identification algorithm for systems with multi-rate sensors in a discrete-time framework. It is challenging to obtain an accurate mathematical model when the ratios of inputs and outputs are different in the system. A cyclic reformulation-based model for multi-rate systems is formulated, and the multi-rate system can be reduced to a linear time-invariant system to derive the model under the multi-rate sensing environment. The proposed algorithm integrates a cyclic reformulation with a state coordinate transformation of the cycled system to enable precise identification of systems under the multi-rate sensing environment. The effectiveness of the proposed system identification method is demonstrated using numerical simulations.

Paper Structure

This paper contains 15 sections, 4 theorems, 70 equations, 1 figure, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Cyclic Reformulation of Multirate System
  4. Time-invariant system expression
  5. Controllability and observability of cycled system
  6. Characteristics of Markov parameters
  7. System Identification Algorithm
  8. System identification using cycled signals
  9. Transformation of obtained state-space model
  10. System identification algorithm
  11. Numerical Example
  12. Setting of the multirate system
  13. Simulation result
  14. Conclusion
  15. Proof of Theorem \ref{['theo1']}

Key Result

Lemma 1

Consider the following $Ml\times Mm$ matrix. Then, $\check S_l^i \check H(i+j)\check S_m^j$ can be regarded as a block diagonal matrix with $l\times m$ block elements for any non-negative integers $i, j$. In addition, the following matrix: can be regarded as a cyclic matrix.

Figures (1)

  • Figure 1: System Identification for Multirate Sensing Environments

Theorems & Definitions (5)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Theorem 1
  • Proof 1