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

Thijssen, P.C.; Wolfrum, Stefan; Kateman, G.; Smit, H.C.

doi:10.1016/s0003-2670(00)85540-3

Cited by 47 publications

(7 citation statements)

References 12 publications

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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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Section: Discussionmentioning

confidence: 99%

Shannon Information Retrieved from Overlapped Chromatographic Peaks with Kaiman Filter

1989

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“…Complete details of this example are found elsewhere [1]. Figure I shows the performance of a multi-rule procedure [4] for N=2 and N=4. For an unstable measurement procedure having a frequency of errors of 0.10 (or 10%), doing more quality control actually provides higher quality and higher productivity.…”

Section: Quality-productivity Modelsmentioning

confidence: 99%

Design of cost-effective QC procedures for clinical-chemistry assays

Westgard¹

1988

J. RES. NATL. BUR. STAN.

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“…This is a consequence of the recursive nature of the filter algorithm. A more general version of the algorithm allows the measurement to take the form of a vector, rather than a scalar, and results in a required matrix inversion in equation (7). However, most problems of analytical interest (even three-dimensional problems) can be reduced to a scalar measurement format.…”

Section: R ( K ) = E [~( K )~( J ) L a J K (4)mentioning

confidence: 99%

Kalman filtering approaches for solving problems in analytical chemistry

Rutan

1987

J. Chemometrics

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SUMMARYThe application of the Kalman filter to the solution of a variety of problems in analytical chemistry is reviewed. Five examples are selected from the literature to illustrate the use of Kalman filtering techniques for obtaining least-squares estimates for several parameters of analytical importance. These examples include multicomponent curve resolution and concentration estimation, correction for variable background responses, calibration with drift compensation, and estimation of kinetic parameters for first-order reactions and for heterogeneous charge-transfer reactions. An adaptive Kalman filtering technique is required for the solution of the background correction problem, and the extended Kalman filter algorithm is required for the solution of the nonlinear kinetic problems. For each case, the results that were obtained are summarized, and some advantages of Kalman filtering over traditional least-squares approaches are discussed. KEY WORDS Kalman filter Calibration Curve resolution Parameter estimationThere are many instances in chemistry when parameters must be determined from analytical data. Chemical species concentrations, kinetic parameters and calibration parameters are examples of some of the most important parameters which can be obtained from spectroscopic, chromatographic or electrochemical measurements. Parameter estimation methods used for chemical problems are usually based on least-squares techniques. One method which has been employed recently for solving these sorts of problems is the Kalman filter. The Kalman filter is a recursive, digital filtering algorithm which allows the estimation of states and parameters from noisy measurements. This approach is convenient for determining some of the important chemical parameters described above, and it offers a flexible approach in these cases. An extensive review of Kalman filter applications in analytical chemistry has been published recently; it includes a discussion of the algorithm and a comprehensive survey of recent applications. 'Here, the focus is a more detailed discussion of some specific examples from the literature which demonstrate the flexibility of the Kalman filter for the solution of specific chemical problems. Five examples have been chosen which illustrate the essential features of the Kalman filter. These examples include multicomponent curve resolution and concentration kinetic parameter estimation, 5 s 6 calibration with drift correction, '-lo compensation for variable background responses, and estimation of electrochemical kinetic parameters in conjunction with digital filtering techniques.

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

Cited by 47 publications

References 12 publications

Shannon Information Retrieved from Overlapped Chromatographic Peaks with Kaiman Filter

Shannon Information Retrieved from Overlapped Chromatographic Peaks with Kaiman Filter

Design of cost-effective QC procedures for clinical-chemistry assays

Kalman filtering approaches for solving problems in analytical chemistry

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