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Efficient Least-squares State Estimation Using Uniform Sampling.

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Efficient Least-squares State Estimation Using Uniform Sampling.

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Efficient Least-Squares State Estimation Using Uniform Sampling.

Reza Vafaee¹, Milad Siami¹

¹Electrical and Computer Engineering Department, Northeastern University, Boston, MA 02115 USA.

Ifac-Papersonline

|August 25, 2025

View abstract on PubMed

Summary

This summary is machine-generated.

This study introduces a new method for state estimation in large systems. Uniformly sampling rows approximates statistical leverage scores, enabling efficient least-squares problem solutions.

Keywords:

Large-scale LTI dynamics Least-squares problem Leverage scores Randomization Sparse sensing State estimation Unifrom sampling

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Area of Science:

Control Systems Engineering
Numerical Analysis
Computational Mathematics

Background:

State estimation for large-scale, discrete-time, linear time-invariant systems is often formulated as a least-squares problem.
Computational challenges arise due to increasing problem dimensions over time.
Randomized sampling offers approximations but requires calculating statistical leverage scores, which is difficult.

Purpose of the Study:

To propose an alternative, computationally feasible method for approximating statistical leverage scores.
To enable efficient approximation and solution of large-scale least-squares state estimation problems.
To provide theoretical guarantees for the proposed approximation method.

Main Methods:

Developing an approach to approximate statistical leverage scores using uniform row sampling.

Applying this approximation to the least-squares state estimation problem for linear time-invariant systems.

Analyzing the theoretical guarantees of the uniform sampling approximation.

Main Results:

Uniform row sampling provides a sufficiently weak approximation for estimating leverage scores.
The proposed method yields a reasonable approximation of leverage scores.
This approximation is suitable for solving the least-squares estimation problem efficiently.

Conclusions:

Uniform row sampling offers a practical alternative for approximating leverage scores in large-scale state estimation.
The method simplifies the computational complexity associated with randomized sampling techniques.
This research contributes to more efficient and scalable solutions for linear system state estimation.