Multicomponent-analysis computations based on kalman filtering

A theoretical introduction to the use of Kalman filtering in analytical chemistry is based on multicomponent-analysis computations with the non-recursive least-squares estimation method as a starting point. An initial value for the computation of the error covariance matrix is given and some new practical applications (determination of number of components, estimation of constant systematic error) are derived and demonstrated. Theory and practice suggest a new possible design for experimental measurements and novel applications of on-line computation and computer control. The excellent performance of the Kalman filter algorithm is demonstrated.     

自适应卡尔曼滤波分光光度法同时测定撒痛风注射液中各组分的含量

本文应用自适应卡尔曼滤波分光光度法同时测定了撒痛风注射液中各组分的含量,水杨酸钠、咖啡因、安替比林三组分平均回收率均为100.0％,相对标准偏差(％)依次为0.57、0.61和0.75,结果优于常规卡尔曼滤波法。自适应卡尔曼滤波法为不经分离直接测定相互干扰的多组分体系分析提供了一种新的途径。     

Comparison of robust regression methods based on least-median and adaptive kalman filtering approaches applied to linear calibration data

Five algorithms for data analysis are evaluated for their abilities to discriminate against outliers in small data sets (4–10 points). These methods included least-squares regression, the least absolute -deviation method, the least median of squares method, and two techniques based on an adaptive Kalman filter. For data sets consisting of 4–9 points with one outlier, the average errors in the estimation of the slope were found to be 18.9 % by least-squares, 17.7% by the least absolute deviation method, 0.5% by the least median of squares algorithm, 9.1% by an adaptive Kalman filter algorithm, and 0.9% by a zero-lag adaptive Kalman filter algorithm. Based on these results, the conclusion is that the zero-lag adaptive Kalman filter and the least median of squares approaches are best suited for the detection of outliers in small calibration data sets.     

Two-dimensional and three-dimensional fitting of enzyme kinetic data with the kalman filter

The availability of instrumentation which is capable of collecting multidimensional data has put increased demands on the data-processing methods utilized to obtain information about reaction kinetics. An enzyme-catalyzed reaction, the hydrolysis of p-nitrophenyl phosphate to p-nitrophenol, is examined so that various data-processing methods and data-collection formats can be examined and compared. The extended Kalman filter is used to obtain rate constants and values for the initial substrate concentration for three-dimensional data, and for two-dimensional kinetically perturbed data. In addition, non-linear least-squares regression with the simplex algorithm, and linear least-squares regression methods are used to analyze absorbance/time curves for this reaction. These results are compared to the results from a two-point kinetic method, and the accuracy and precision of each of the methods is evaluated. It is found that the methods based on the Kalman filter yielded results which were equivalent to or better than the results obtained from the other approaches.     

Modifications to the simplex-optimized adaptive kalman filter

New response functions for the simplex-optimized adaptive Kalman filter have been examined as a means of improving the estimation of known components in the presence of unknown components or other matrix effects. Four response functions based on the innovations sequence have been tested with respect to increasing the computational speed of the filter and reducing the estimation error for the quantitated components. The response function based on the area under the innovations sequence with a penalty function was found to provide the best estimates for synthetic data and ultraviolet-visible spectra.     

Simultaneous kinetic determinations with the kalman filter

The linear Kalman filter is successfully applied to the processing of data for simultaneous kinetic determinations. The Kalman filter offrs all of the advantages of linear least squares over traditional methods of data processing, but is simpler and more efficient than batch-mode least squares. The viability of the Kalman filter is demonstrated with synthetic data and it is then applied to the analysis of amino acid mixtures by their reaction with trinitrobenzenesulfonic acid. Mixtures of glycine and asparagine are successfully analyzed even though their pseudeo-first-order rate constants differ by a factor of only 2.5. The potential of the Kalman filter for real-time application is discussed.     

Characterization of a Stable Adaptive Calibration Model Using Near-Infrared Spectroscopy and Partial Least Squares with a Kalman Filter

The calibration model of near-infrared (NIR) spectra established using the Kalman filter-partial least square (partial least squares combined with a Kalman filter) method can be adapted to outdated equipment, environmental changes, external samples, and other applications. However, the variance of the measurement noise estimation for NIR spectrum measurements cannot be easily obtained using Kalman filter-partial least squares; therefore, the variance in the measurement noise is often assumed to be zero for the Kalman filter-partial least square calibration model, which affects the stability of the model. In this study, the measured input and output data were used effectively, and the gamma test method for estimating the measurement noise variance was used to improve the stability of the Kalman filter-partial least square calibration model. First, an accurate estimation of the measurement noise variance was obtained, and accurate modeling was then performed using Kalman filter-partial least squares. Finally, 600 abandoned drilling fluid samples were used to confirm the validity of the proposed method. The Kalman filter-partial least square and gamma test-Kalman filter-partial least square methods are compared. Testing of external samples 401–600 demonstrated that the stability of the Kalman filter-partial least square model decreased. The root mean square error of the prediction of the Kalman filter-partial least square model was 27.135, which was worse than that of the gamma test-Kalman filter-partial least square model (20.307). The validation results show that the proposed method has better stability in tracking the evolution of the NIR spectrometer’s measurement state.     

The Kalman Filter as an On-Line Drift Compensator in Multicomponent Analysis Determinations

Abstract

A method is proposed for the on-line compensation of linear drift in analytical measurements. The robustness of the compensator, which is based on the Kalman filter, has been investigated by means of a parametric study. Special emphasis is given to the choice of the initial error covariance matrix, which is an important design quantity for the Kalman filter. The presented method can be applied when there is uncertainty about the presence of drift in the measurements. Some results are compared with results obtained with the non-recursive least squares method. The excellent performance of the on-line compensator suggests a possible solution for the linear drift problem. Of some theoretical importance is the fact that the proposed solution has a strong intuitive appeal: the linear drift can be considered as “two extra components” in a spectrum or equivalently as the time varying mean of the measurement noise.     

One-dimensional Kalman filter in a robot system for total analysis of solid dosage formulations

A one-dimensional Kalman filter for peak resolution is applied to a totally automated robot system for liquid chromatographic analysis of solid dosage formulations. Sample solutions were prepared from four tablets of clemastine fumarate (1 mg/tablet) and injected automatically at regular, short intervals onto the column by the robot system. The overlapped peaks in the resulting complicated chromatogram were resolved and evaluated quantitatively by the one-dimensional filter. The peak-resolving powers are shown to be reliable by comparison with a multidimensional Kalman filter. The applicability of the whole analytical system with the linear Kalman filter is discussed.     

Comparison of the extended kalman filter and marquardt algorithms for processing kinetic data

The extended Kalman filter and Marquardt's gradient expansion algorithm for nonlinear least squares are compared with respect to accuracy and precision of parameter extimates, computational burden, sensitivity to initial parameter estimates and ability to indicate model errors. Fits of synthetic first-order data and combined first- and zero-order data produce estimates of equivalent precision and accuracy in most cases. Similar results were obtained for both simulated and experimental data for combined zero-order/first-order processes. However, for the simulated zero-order/first-order data with small zero-order components processed over two half-lives of the first-order process, the Kalman filter overestimated the zero-order rate constant by a substantially larger amount than the Marquardt algorithm. Significant differences in computational burden and sensitivity to initial parameter estimates are demonstrated; however, neither algorithm has a significant advantage over the other for the detection of model error.