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Linear Least Squares Parameter Estimation

Drayton D. Boozer, Ph.D, PE

The need to fit mathematical models to measured data arises often in science and engineering. Parameter estimation is a discipline that provides estimates of unknown parameters in a system or process model based on measured data. The professional analyst can use the model that results from the application of parameter estimation to explain measured data to customers in a concise, compelling way.

The 4-hour course begins with a general, nonlinear system model and then focuses on a linear system model. Six basic assumptions about measurement errors are presented and their implications on the least squares estimator explained. Confidence limits for the estimated parameters for specified assumptions are developed.

Two comprehensive examples are presented which demonstrate the application of least squares parameter estimation. The first is a “position-velocity” estimation problem that arises in many engineering contexts. The second estimates the parameters for a triangular weir, a structure used to measure small stream flow in hydrology.

This course includes a multiple-choice quiz at the end, which is designed to enhance the understanding of the course materials.

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NY PE & PLS: You must choose courses that are technical in nature or related to matters of laws and ethics contributing to the health and welfare of the public. NY Board does not accept courses related to office management, risk management, leadership, marketing, accounting, financial planning, real estate, and basic CAD. Specific course topics that are on the borderline and are not acceptable by the NY Board have been noted under the course description on our website.