Estimation of electrochemical charge transfer parameters with the Kalman filter

Abstract

A discussion Is presented of the application of the Kalman filter to systems where the model Is neither linear nor In closed form. The system studied here Involves the modeling of linear scan voltammetrlc responses, where heterogeneous kinetic parameters are estimated. Results are presented for synthetic data and for reduction of Cr(III) and Pb(II) In perchlorate media. It Is demonstrated, using state estimation, that the Cr(III) reduction follows Volmerlan kinetic law.Recently, it has been recognized that modeling of responses obtained from analytical measurements has a number of important applications. Among these are smoothing, the ability to remove noise efficiently without distorting or biasing the signal, and deconvolution, the ability to accurately separate the effects of two processes whose responses couple with one

Correction for temperature variations in kinetic methods of analysis with the extended Kalman filter

“…Large numbers of iterations are also due in part to the lack of noise in the synthetic data, as more iterations are necessary to achieve the higher precision results obtainable with noise-free data. These observations are expected with the extended filter because this form of the algorithm has inherent errors caused by the truncation of Taylor series expansion of the f and h functions necessary to linearize the model (21,22). These errors render the extended filter statistically nonoptimal.…”

Simultaneous Determination of Four Components in Composite Vitamin B Tablets Using a Square-Root Kalman Filter

“…H T (k) is the measurement function row vector (1×n) consisting of the absorptivities of the involved components at wavelength k. Superscript T denotes the transpose of the matrix. The Potter-Schmidt squareroot algorithm [12][13][14] is given in Table 1. This square-root algorithm is usually less susceptible to round-off error, and is particularly effective in stabilizing the filter in spite of square-root filter with a larger computational burden than that of the ordinary Kalman filter algorithm.…”

Adaptive Kalman Filtering

“…The Potter-Schmidt square-root algorithm, one implementation of the Kalman filter [18], is given in table 1. The details of this algorithm have been discussed elsewhere [18,19]. Initial guesses for the filter states and for the covariance matrix P are required to start the filter.…”