Simplex optimization of the adaptive kalman filter

A method for determining concentrations from overlapped spectral data when a complete model is not available is described. This approach combines simplex optimization with the adaptive Kalman filter to yield a method in which initial guesses for the adaptive filter are generated by the simplex algorithm. The performance of the method is demonstrated by deconvoluting overlapped synthetic data and spectral data.     

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.     

A one-dimensional kalman filter for peak resolution

A one-dimensional Kalman filter algorithm is presented that resolves several overlapped liquid chromatographic peaks without algebraic operations of matrices. The resolving powers or filtering reliability of the algorithm is independent of the number of peaks, but depends on both the peak overlap (resolution value R_s) and the signal-to-noise ratio more significantly than the usual multi-dimensional Kalman filter. The reliability is shown to be similar to that of the multi-dimensional filter for the resolution of overlapped Gaussian peaks with limited R_s and S/N values.     

Simultaneous kinetic determination of phenols by use of the kalman filter

A multicomponent analysis method based on the Kalman filter algorithm is proposed for the determination of phenolic compounds. The method relies on the oxidative coupling of phenols (phenol, 2-chlorophenol and 3-chlorophenol) to N,N-diethyl-p-phenylenediamine in the presence of hexacyanoferrate(III), the reaction being monitored via changes in the absorbance at 660 nm of the dye formed. Phenols can be determined individually over the concentration range 1.25-25 muM with a relative standard deviation of ca 0.6-0.8%. Differences in the kinetic behaviour of the three species were exploited by using the linear Kalman filter to resolve mixtures of the phenols at the muM level in a widely variable concentration ratios with errors less than 10%.     

Estimation of first-order kinetic parameters by using the extended kalman filter

A model for first-order kinetics is derived for spectra obtained while a reaction is taking place. A technique for nonlinear-regression analysis known as the extended Kalman filter is used to estimate the initial concentrations of the reactants and the rate constant from the spectral data. The effects of the magnitude of the rate constant and the identity of the absorbing species are examined for synthetic spectra containing overlapped responses. The technique is used successfully to obtain the rate constant for the dissociation reaction of a praseodymium complex. The filter is also shown to be useful for the detection of erros in the kinetic model employed to fit the data. The extended Kalman filter can be used to fit kinetic models other than the one discussed here, and may prove to be a valuable technique for estimation of kinetic parameters.     

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.     

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.     

Multicomponent determinations in flow-injection systems with square-wave voltammetric detection using the kalman filter

Electrochemical detection in flow-injection systems has become increasingly popular. Scanning electrochemical methods of detection have received less attention. The use of rapid square-wave voltammetric detection for flow injection is described. Experimental considerations for the use of square-wave voltammetric detection are discussed. Results of the application of this combination are shown for dopamine in 0.28 M sulfuric acid, and for lead(II) and thallium(I) in 0.9 M nitric acid. A linear, recursive estimator known as the Kalman filter is used to resolve overlapping responses. Empirical models consisting of the square-wave voltammetric responses of single species are used. Results are shown for mixtures of lead(II) and thallium(I) in 0.9 M nitric acid.     

Analysis of partially resolved liquid chromatographic peaks using dynamic modeling with the kalman filter

Establishing a calibration model is an important part of any mathematical method for multi-component determination. Use of a calibration model based on single spectra is subject to error, because the model spectrum chosen may not be representative of the response over the full range of the calibration. Alternative calibration models require more time to establish calibration, an these may not be convenient for real-time determinations. A novel calibration method is reported for use with Kalman filters. The method, dynamic modeling, is based on the use of libraries of calibration spectra. The set of used to describe the model at any time is based on component concentrations, estimated for the multi-component mixture, as determined from the Kalman filter, so that several spectra can be used to best describe a varying response. Through application of the dynamic modelingt to simulated and real chromatograms, it is demonstrated that use of the method decreases estimation errors cause by model data mismatches, and that full benefit can be obtained from relatively small libraries.     

Estimation of ester hydrolysis parameters by using fourier-transform infrared spectroscopy and the extended kalman filter

Fourier-transform (FTIR) spectroscopy has found a wide range of applications. Attempts have been made to make FTIR spectroscopy a reliable quantiative technique for obtaining chemical information foru complex systems, but it is often difficult to obtain even qualitative information about a complex system because of matrix, interaction, and background effects on the infrared on the spectra. In this study, FTIR spectroscopy was used in conjuction with the extended Kalaman filter, a recursive digital filter, to investigate the simple neutral hydrolysis of two esters in aqueous solutions. Interactions between the solvent, reactants and products of the hyrolysis perturb the spectrum, making a single-wavelength kinetic analysis impractical. With the extended Kalman filter, a range of frequencies where severe perturbation does not occur is processed to obtain not only the rate constant but also the initial reactant concentrations.     

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.     

Kalman滤波流动注射化学发光法同时测定铂钯的研究

利用Luminol H2O2 OP Pt(Pd)化学发光新体系以及Kalman滤波化学计量学方法建立了流动注射化学发光法同时测定铂钯的新方法。方法的检出限:铂为2.2×10-8g mL、钯为2.4×10-8g mL,铂钯相对标准偏差分别为0.9%和3%。采用阳离子交换树脂静态吸附分离,消除贱金属离子的干扰。可用于贫铂矿中铂、钯的同时测定。     

Resolution of overlapped chromatograms by means of the kalman filter : Dimensional reduction of error covariance matrices and state estimate vectors

If many samples are successively injected into a high-performance liquid chromatograph at short intervals, then overlapped chromatograms will be obtained. A simplified version of the Kalman-filter algorithm is described for rapid resolution of several such overlapped peaks on small laboratory computers; the dimensionalities of the error covariance matrix Pk and state estimate vector X?k are reduced to far less than the total number of the peaks. Computer simulation shows that at least twenty partially overlapped Gaussian peaks, used as a model of the successive injections can be successfully resolved, with the 4 × 4 matrix Pk and 4-vector X?k. This version is independent of the number of injections and is effective for the resolution of a finite number of peaks in that injection mode. The algorithm of small dimensions is applicable to a wide variety of peak resolution procedures.     

Comparison of the simplex,marquardt, and extended and iterated extended kalman filter procedures in the estimation of parameters from voltammetric curves

The use of the simplex, Marquardt, and extended and iterated extended Kalman filter nonlinear least-squares curve-fitting methods is examined for evaluation of parameters in linear-sweep and cyclic voltammetric curves. The EE mechanism (two-electron transfer) is considered as a reference process and the relevant results are compared on the basis of accuracy, computing time and robustness. The E° values for l-β-3,4-dihydroxyphenylalanine are calculated.     

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.     

A kalman filter for calibration,evaluation of unknown samples and quality control in drifting systems: Part 2. Optimal Designs

It is well known that the optimal design for linear calibration is found at the extremes of the concentration range. For the evaluation of unknown samples, the precision is maximal at the mean value of the calibration standards. If the static model is replaced and stochastic behaviour of the parameters with extension to drift is assumed, only minor differences on these generalizations are obtained. The intelligent analyzer described here integrates on line procedures for calibration, evaluation, quality control and optimization.     

Modifications to an analytical mass spectrometer for the soft-landing experiment

Modifications to a hybrid geometry beam mass spectrometer are described that allow its use for soft-landing of ions onto a stainless steel surface intercepting the ion beam at the site of the intermediate detector. Initial success is documented through the presence of metal ions brought to the surface as part of a complex, metal-containing cluster ion. Further, organic cations have also been soft landed at the collector surface, and electrospray ionization (ESI) and ESI tandem mass spectrometry analysis of the surface wash solution confirm preservation of the original organic structure. Future directions for predictable surface density collection strategies are described.     

Background subtraction for fluorescence detection in thin-layer chromatography with derivative spectrometry and the adaptive Kalman filter

Background signals must be removed from analyte responses before reliable qualitative and quantitative results can be obtained. For cases in which a reliable estimate for the background response cannot be obtained, the combination of two mathematical approaches yields accurate quantitative results. First-derivative spectrometric methods, in conjunction with a curve-resolution approach based on the adaptive Kalman filter, are used to compensate for difficulties caused by background responses which are not reproducible. Derivative spectrometric techniques reduce the relative magnitude of low-frequency systematic deviations in the spectra. In this case, this has the effect of localizing model errors to restricted regions of the spectra, which in turn meets the major requirement for successful utilization of the adaptive Kalman filter. The approach is applied to fluorimetric detection for thin-layer chromatography in the quantification of polynuclear atomatic hydrocarbon compounds. Results are given which demonstrate that this combined approach yields accurate estimates for concentrations of components in overlapped chromatographic zones. A derivative spectrometric approach in conjunction with a regular Kalman-filter fit gives less accurate results, and an adaptive Kalman filter used to fit the raw spectral data fails to give any reliable quantitative information. The combined approach using derivative spectrometry anal the adaptive Kalman filter is shown to give 8-fold lower detection limits for anthracene when compared to traditional background-subtraction methods.     

Modifications to increase the efficiency of the fluorometric cycling assay for cyclic ADP-ribose

Cyclic ADP-ribose (cADPR) is an intracellular messenger that triggers the release of calcium ions from intracellular stores in a variety of cell types. The fluorometric cycling assay has become the preferred method for measuring cADPR due to its high level of sensitivity (in the sub-nanomolar range) and its use of commercially available reagents. Additionally, the assay is performed in multiwell plates, making it suitable for high throughput screening using a fluorescence plate reader. The findings reported in this paper present several problems that may be encountered during various stages of the assay, and provide solutions to these problems. Modifications to the assay address reduced recovery of sample and cADPR with removal of perchloric acid (PCA) using organic solvent, reduction in diaphorase activity with heat treatment, and effects on resorufin fluorescence by pH range. Using these modifications, we report an increase of approximately 15% in recovery of brain cADPR, and show that between-subject variability is greatly reduced. We hope that these observations will encourage more widespread application of this valuable assay.