Adaptive Kalman filtering used to compensate for model errors in multicomponent methods

An adaptive Kalman filtering technique is developed and evaluated as a tool for compensation of model errors that commonly occur in multicomponent problems. Results presented demonstrate that the adaptive Kalman filter should be of considerable value for obtaining accurate concentrations and spectral information from multicomponent responses. The restrictions of the technique are that the model must be correct for a portion of the response, and the errors must be attributable to a single component. Concentration estimates are accurate for those components which are modeled correctly, but the concentration estimate obtained for the component not included in the model may not always be reliable. The technique is evaluated for multicomponent problems in spectroscopy and voltammetry.     

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.     

Quantitative line selection with the Kalman filter approach for inductively coupled plasma atomic emission spectrometry

With the Kalman filter approach, the true detection limit (i.e. the detection limit in the sample solution) only depends on the height of the total background signal, and is not determined by the uncertainties in interfering background signals. Based on the background equivalent interferent concentration, the true detection limit can be directly estimated in sample solutions containing various amounts of interferent. This eases the application of the true detection limit as quantitative criterion for line selection. Following this approach, quantitative line selection is demonstrated for Pb and Cd determinations in river sediments (Fe interferences).     

Kalman filter quantitative resolution of shifted ESCA spectra after optimal alignment by simulated annealing

Summary The quantitative separation of overlapped responses accomplished by the Kalman filter algorithm is deteriorated by the errors in the model due to shifts of the component peaks. This is particularly true for spectral resolution in Electron Spectroscopy for Chemical Analysis (ESCA). A computational approach for the quantitative resolution of overlapping ESCA spectra when there is loss of collinearity between the pure component peaks and the mixture peak, has been developed. The procedure makes itera tive use of the Kalman filter for resolving the mixture spectrum with the component spectra aligned according to some values of the position parameters, and of the simulated annealing algorithm to find the optimal alignment. The performance of simulated annealing in pursuing this task, has been compared with those of simplex and steepest descent, by analyzing a set of overlapped synthetic spectra and some ESCA spectra of powder mixtures of lead compounds.     

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.     

Quantitative Auger electron spectroscopic analysis of carbides,nitrides and carbonitrides

A novel method for the quantitative evaluation of Auger electron spectra based on peak areas is presented. Sample and reference spectra in integral mode are filtered by an area conserving digital filter. This transforms the peak shapes influenced by chemical effects into standard peak shapes. After filtering a linear combination of reference spectra, differentiated spectra accounting for peak shifts and some low order polynomials to account for variations in the background is fitted to the sample spectrum by a least squares method. The need to approximate the spectrum of the secondary electron background explicitly for direct calculation of peak areas is thus eliminated. Filters of different widths are applied to reduce errors by chemical effects. The composition of the sample is computed from the composition of the reference samples and the coefficients obtained from the fit.To demonstrate the validity of this technique it has been applied to both, Gaussian model peaks and spectra of titanium carbonitrides. A further test on an alloy series is under investigation. The results show that the method works as predicted and gives accurate quantification.     

Kalman filter deconvolution after cubic splines background removal in the HPLC determination of Cr(III) and Al(III) as 8-hydroxyquinolines

Summary A procedure for the simultaneous quantitation of Al(III) and Cr(III) ions by reversed-phase HPLC, after pre-column complexation with 8-hydroxyquinoline, is described. The deconvolution of the partially overlapped peaks was by the Kalman filter method which yielded accurate and precise results. Background removal from the chromatograms was by a new approach employing cubic splines as interpolators between the peak valleys. Finally, it is shown that the Kalman filter deconvolution, after subtraction of the background by cubic spline interpolation, allowed quantitation of Al(III) and Cr(III) down to 25 ppb for each metal. These concentrations were not detectable by conventional integration methods due to a very low signal-to-noise ratio.     

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.     

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。     

衍生化气相色谱-质谱法测定植物油中植物甾醇

植物油样品经氢氧化钾甲醇溶液皂化后,硅烷化衍生,采用气相色谱-质谱(GC-MS)法建立了植物油中菜籽甾醇、菜油甾醇、豆甾醇、β-谷甾醇4种植物甾醇含量的分析方法,研究了各植物甾醇衍生物的质谱特征和断裂机理。该方法方便快捷、准确可靠,检出限为0.01 g/kg,用于植物油样品中植物甾醇的组成和含量测定,结果满意。     

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.     

Matched filtering with background suppression for improved quality of base peak chromatograms and mass spectra in liquid chromatography-mass spectrometry

A time domain filter that combines the properties of matched filtering and two-fold differentiation is presented. The filter coefficients are given by the second derivative of a Gaussian model peak, controlled by the setting of two parameters related to the chromatographic system. The fundamental characteristics of the filter were derived, and its applicability demonstrated for real liquid chromatography-mass spectrometry (LC-MS) data. The filter is primarily intended as a fast pre-processing step, for a mass chromatogram with 320 scans over 700 mass channels the computation time was 0.6 s on a standard PC. Base peak chromatograms with improved peak detection capability and mass spectra useful for compound identification were obtained with filtered data. The most significant effect of the described filter is background reduction due to the differentiation, which in combination with the matched filter can be performed with maintained or even improved signal-to-noise ratio.     

Analysis of cigarette mainstream smoke for 1,1-dimethylhydrazine and vinyl acetate by gas chromatography-mass spectrometry

1,1-Dimethylhydrazine, also known as unsymdimethylhydrazine (UDMH) and vinyl acetate (VA), are both classified by the International Agency for Research on Cancer as 2B carcinogens (possibly carcinogenic to humans) and listed as cigarette smoke constituents; however, there is little or no quantitative data available on them. For UDMH in cigarette smoke, neither a yield nor a method has been published. For VA, the most recent information on yields dates back to 1965. To bridge this gap, we have developed new gas chromatographic-mass spectrometric methods for both compounds to determine their yields in cigarette smoke. UDMH is determined by derivatization with 2-nitrobenzaldehyde in methanol and is not found in cigarette smoke at levels above the detection limit of 19 ng/cig. In further experiments, when UDMH is added to the smoke stream or air stream of lit or unlit cigarettes, the derivative 2-nitrobenzaldehyde-2,2-dimethylhydrazone is found only in the air stream of the unlit cigarettes. From this, we conclude that UDMH is either not formed during smoking at all or, if it is, it reacts immediately and quantitatively with other smoke constituents (e.g., aldehydes) and is therefore not detectable in cigarette smoke. VA is determined by trapping in acetone at -78 degrees C and is found at a concentration of 270 ng/cig for a standard reference cigarette with a cellulose acetate filter (the reference cigarette 1 R4F). In the literature, VA is reported at concentrations of 1.6 microg/cig for a cigarette with a cellulose acetate/charcoal filter and 4 microg/cig for a cigarette with a cellulose acetate filter and for an unfiltered cigarette.     

Adaptive wavelet transform suppresses background and noise for quantitative analysis by Raman spectrometry

Discrete wavelet transform (DWT) provides a well-established means for spectral denoising and baseline elimination to enhance resolution and improve the performance of calibration and classification models. However, the limitation of a fixed filter bank can prevent the optimal application of conventional DWT for the multiresolution analysis of spectra of arbitrarily varying noise and background. This paper presents a novel methodology based on an improved, second-generation adaptive wavelet transform (AWT) algorithm. This AWT methodology uses a spectrally adapted lifting scheme to generate an infinite basis of wavelet filters from a single conventional wavelet, and then finds the optimal one. Such pretreatment combined with a multivariate calibration approach such as partial least squares can greatly enhance the utility of Raman spectroscopy for quantitative analysis. The present work demonstrates this methodology using two dispersive Raman spectral data sets, incorporating lactic acid and melamine in pure water and in milk solutions. The results indicate that AWT can separate spectral background and noise from signals of interest more efficiently than conventional DWT, thus improving the effectiveness of Raman spectroscopy for quantitative analysis and classification.     

Detailed peak fitting analysis of the Zn 2p photoemission spectrum for metallic films and its initial oxidation stages

The metallic Zn 2p photoemission spectra hold a complex background that requires individual assignment of Shirley background for each peak comprising the spectra. For this reason, a close fit requires the use of the Shirley‐Vegh‐Salvi‐Castle background‐type under the active background approach. We found that the intensity of the plasmon peaks and their associated background cannot be described through existing energy loss (intrinsic and extrinsic) formalisms. We also analyzed the Zn 2p and O 1s spectra for the initial stages of oxide formation at various oxygen exposures. We found that the composition of the oxide layer is ZnO_1.00±0.10 for all exposures, suggesting that our assessment of the primary function of metallic Zn is accurate and can be employed for quantitative studies. We also present a set of parameters to accurately fit and resolve the metallic and oxide Zn 2p peaks.     

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.     

Mass spectrometric studies of some novel sulfonamides

A recent paper described the overall 5-endo cyclisation of homoallylic sulfonamides to give pyrrolidines. This reaction was also used to prepare polycyclic systems. Mass spectrometric analysis using classical electron ionisation spectra and accurate mass measurement played a vital role in confirming the proposed structures for the products. These materials were not amenable to newer mass spectrometric methods and this study shows the continuing importance of older techniques.     

Software algorithm for automatic interpretation of mass spectra of glycerolipids

A new software algorithm for automatic interpretation of mass spectra of glycerolipids has been developed. The algorithm utilizes a user-specified list of parameters needed to process the spectra. The compounds in mass spectra are identified according to range of measured m/z values, after which the spectra are automatically corrected by the content of naturally occurring isotopes and ion intensities of identified compounds by response correction factors. Automatic processing of the spectra was shown to be accurate and reliable by testing with numerous spectra of glycerophospholipids obtained by liquid chromatography/electrospray ionization mass spectrometry and by comparing the results with manual interpretation of the spectra. If quantitative analysis using internal standards is performed, all the identified compounds in the sample are quantified automatically. A dilution factor may be defined for each sample and is applied to correct the alterations in sample concentration during sample preparation. Processing of several replicate spectra simultaneously produces mean results with standard deviations. The software may also be used to subtract the results of two analyses and to calculate the mean result of replicate subtractions. The algorithm was shown to save time and labor in repetitive processing of mass spectra of similar type. It may be applied to processing of spectra obtained by various mass spectrometric methods.     

Neue Methode zur quantitativen Analyse von AES-Spektren

Summary The quantitative analysis of Auger electron spectra may lead to problems using Auger peak-to-peak heights (APPH), especially in connection with chemical peak deformation and peak overlap. To eliminate these problems a method has been developed and was applied to metalnonmetal compounds. An integral spectrum is fitted with reference spectra and correction spectra, background differences are compensated. To deal with chemical effects a digital filter process is used. In order to test this method a copper-palladium alloy series has been measured and evaluated according to this method. The results show that a more accurate quantification could be obtained than by using APPHs and sensitivity factors. As a further advantage, relative sensitivity factors are no longer necessary due to peak/background standardization.     

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.