A methodology for using Kalman filter to determine material parameters from uncertain measurements

TL;DR

This paper presents a practical methodology for applying the Kalman filter to estimate material parameters from uncertain measurements, emphasizing initial value prediction and error selection to improve convergence and stability.

Contribution

It introduces a two-step approach to predict initial parameters and errors, enhancing Kalman filter performance in material parameter estimation from noisy data.

Findings

Method reduces iteration time significantly.

Effective for a wide range of initial guesses.

Achieves accurate results with real bovine bone data.

Abstract

A Kalman filter can be used to determine material parameters using uncertain experimental data. However, starting with inappropriate initial values for material parameters might include false local attractors or even divergence. Also, inappropriate choices of covariance errors of initial state, present state, and measurements might affect the stability of the prediction. The present method suggests a simple way to predict the parameters and the errors, required to start Kalman filter based on known parameters that are used to generate the data with different noises used as 'measurement data'. The method consists of two steps. First, an appropriate range of parameter values is chosen based on a graphical representation of the mean square error. Second, the Kalman filter is used based on the selected range and the suggested parameters and errors. The method of the filter significantly reduces the iteration time, and covers a wide range of initial suggested values for the parameters compared with the standard Kalman filter. When the methodology is applied to real data, very good results are obtained. Diffusion coefficient for bovine bone is chosen to be a case study in this work.