Efficient Least-Squares State Estimation Using Uniform Sampling

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.