A Kalman filter for calibration, evaluation of unknown samples and quality control in drifting systems

Thijssen, P.C.; Prop, L.T.M.; Kateman, G.; Smit, H.C.

doi:10.1016/s0003-2670(00)84362-7

Cited by 28 publications

(3 citation statements)

References 12 publications

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“…It has been suggested that assay calibrations may be improved by using recursive estimation algorithms. Application of linear filtering techniques to drifting calibration systems has been discussed in several recent papers (Vecchia et al, 1989;Brown, 1986;Thijssen et al, 1984). These algorithms combine present calibration parameter estimates with appropriately weighted past estimates to produce "optimal" values of regression parameters.…”

Section: Resultsmentioning

confidence: 99%

Rapid Immunoassay Technique for Process Monitoring of Animal Cell Fermentations

Jervis

Kilburn

1991

Biotechnology Progress

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A calibration and quality control technique suited to process monitoring with immunoassay is demonstrated. The particle concentration fluorescence immunoassay (PC-FIA) is shown to provide a sensitive and rapid method for the quantification of specific biomolecules in cell cultures. Smoothing of linear calibration parameters is performed by forming weighted averages of standard points as the run progresses. These estimates are then used to determine slope and intercept values for improved calibration. The nonuniformity of the fluorescent signal variance is also considered, and a weight model is developed to describe the relationship between signal fluorescence and signal variance for weighted linear curve fitting. Pooling calibration results over the process run improves overall assay performance as determined by using standard control chart analysis. This method is suitable for semicontinuous monitoring of animal cell fermentations and has been used here to measure cell-associated and culture supernatant concentrations of monoclonal antibody (Ab) from hybridoma cells. The cell-associated Ab concentration correlates with cell-specific production rate. Assay times on the order of 10 min for supernatant and 25-30 min for cell-associated Ab concentrations can be achieved, making this procedure suitable for process monitoring and control. Under these conditions the assay has a detection limit of approximately 10 ng/mL, providing a sensitive and specific method for the quantification of cell culture constituents.

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Section: Resultsmentioning

confidence: 99%

Rapid Immunoassay Technique for Process Monitoring of Animal Cell Fermentations

Jervis

Kilburn

1991

Biotechnology Progress

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“…[16][17][18][19] The information measures of Thijssen et al, however, need the often troublesome calculation of matrices and do not share the simplicity of the formula and the intelligible chemometric meaning of the mutual information which are characteristic of FUMI. The computational and chemometric advantages of FUMI, due to the scalar description of the mutual information, come from the adoption of the algorithm of the onedimensional Kalman filter for peak resolution.…”

Section: Discussionmentioning

confidence: 99%

Shannon Information Retrieved from Overlapped Chromatographic Peaks with Kaiman Filter

1989

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A function (FUMI) which describes the Shannon mutual information in chromatography is derived. FUMI covers two subjects in one formula: (i) the degree of peak overlap and the noise level; (ii) the mathematical formalism of peak deconvolution and quantitation based on the one-dimensional Kalman filter for peak resolution. Computer simulation demonstrates that a sufficient amount of mutual information can be retrieved from overlapped peaks (Gaussian) through (i) observation and (ii) data processing. A practical advantage of FUMI is logical evaluation and optimization of chromatographic experiments without resort to experience: the optimal can be defined as the chromatogram which can transmit the maximal amount of mutual information in a unit time. KeywordsInformation theory, Kalman filter, mutual information, chromatography, optimizationAnalytical systems provide us with information in various forms and ways.An important aim in analytical chemistry is to elaborate a method through which more information can be transmitted from samples of interest. Logical evaluation of an overall analytical system, therefore, should be founded on the quantitative description of the information.As an example, high performance liquid chromatography (HPLC) is taken here. We focus our discussion on quantitative analysis. We can easily guess that superior chromatographic separation of target materials will yield more information.However, the amount of useful information is not only regulated by the elution pattern: reliability of the information also depends on analytical powers of data processing because of the inevitable noise-contamination, baseline drift, etc., in the measurement process.The Shannon mutual information will serve for the quantitative evaluation of the system (see below), but should cover at least two subjects: (i) the degree of peak overlap in a noise level; (ii) mathematical formalism of a data processing.We review the fundamental concepts of information theory to clarify our reasoning. Let 1[Q] be the amount of information concerning an unknown quantity Q to be estimated. If the probability of Q is known or welldefined, I[SO] can be calculated according to the Shannon equation.' We cannot know any details of the quantity Q before measurement of Q, but the complete or undistorted transmission of the information I[Q] through analytical media is always thwarted by various error sources such as calibration, interference, drift, etc. In general, the useful information which we can actually collect from an ensemble !P of the measure- If ambiguity is absent (1[Q/ !PJ 0), then we can retrieve from the measurements !V all of the original information on the unknown quantity Q. In other words, we can establish the estimation for Q with 100% certainty. If I[Q/ VI takes the largest value (=1[Q]), then nothing can be known concerning the information source Q. Chromatography achieves a decrease in the ambiguity I[Q/ !P] by separating peaks of interest, increasing the sensitivity of detection systems, etc. Data processing is also...

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“…When used on-line to correct for drift in flow injection analysis systems, the variance of the slope and intercept estimates can be decreased by using an off-line smoothing filter. 32* 33 Another potential problem which can affect the accuracy and precision of calibration procedures for on-line processes is an abrupt change that affects instrumental sensitivity (the slope) or the background (the intercept). These difficulties can arise for a number of reasons, including changes in the sample matrix and power fluctuations to the instrument.…”

Section: Zero-lag Jltermentioning

confidence: 99%

Recursive parameter estimation

Rutan

1990

Journal of Chemometrics

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SUMMARYThe use of recursive filtering techniques for parameter estimation in a variety of areas is reviewed. In particular, the Kalman filter algorithm is described, along with several variations, including square-root, UDUT and information filters. The solution to parameter estimation problems is discussed for both linear and non-linear models. Applications described include calibration, curve resolution in spectroscopy, chromatography, electrochemistry, kinetic analysis and process monitoring.

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A Kalman filter for calibration, evaluation of unknown samples and quality control in drifting systems

Cited by 28 publications

References 12 publications

Rapid Immunoassay Technique for Process Monitoring of Animal Cell Fermentations

Rapid Immunoassay Technique for Process Monitoring of Animal Cell Fermentations

Shannon Information Retrieved from Overlapped Chromatographic Peaks with Kaiman Filter

Recursive parameter estimation

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