Kalman滤波法在电感耦合等离子体原子发射光谱分析中的应用──Ⅱ．测定高纯氧化铕中的14种稀土杂质

本文研究了电感耦合等离子体原子发射光谱分析Ｋａｌｍａｎ滤波法测定高纯氧化铕中的１４种其他稀土杂质的方法。Ｋａｌｍａｎ滤波法有效地消除光谱干扰，可利用受干扰的光谱灵敏线，因而可提高灵敏度，是一种在大量基体存在下测定痕量杂质的有效方法。

Kalman滤波法消除光谱连续背景的研究

本文研究了Ｋａｌｍａｎ滤波法消除光谱连续背景，以电感耦合等离子体原子发射光谱法测量氧化铽中Ｌａ，Ｅｒ，Ｇｄ，Ｄｙ，Ｅｕ和Ｔｍ为例研究了不同背景情况下的结果。用新息序列的平均平方和及正交自相关系数超过出置信度极限以外数为评价函数，可评价所估计的背景形状。是一种不用测背景，用计算方法消除光谱连续背景的好方法。本方法不仅适用于电感耦合等离子体原子发射光谱，对分光光度、原子吸收等原则上都可适用。

Kalman滤波技术在电感耦合等离子体原子发射光谱分析中的应用

本文研究了Ｋａｌｍａｎ滤波技术在电感耦合等离子体原子发射光谱分析中的应用。以０．３２０ｍｇ／ｍｌ氧化铽中微克级镧，铕，钆，镝，饵和铥的测量为例具体叙述了方法，并提供实用计算机程序，为校正光谱干扰提出了一个实用方法。该方法无需化学分离富集，直接分析光谱干扰严重的样品。

A STUDY ON THE INDICATION OF UNEXPECTED COMPONENTS BY KALMAN FILTERING IN FLUOROSPECTROPHOTOMETRY

The potential of Kalman filtering for indication of unexpected components in a mixture was experimentally evaluated by taking the spectrofluorimetric analysis of the tricomponent system;oi phenylalanine, tryhtophen and tyrosine as an example. According to

ICP－AES分析中用Kalman滤波法校正光谱干扰时波长定位误差对结果的影响及消除

本工作以Ｋａｌｍａｎ滤波技术为光谱干扰校正方法，选择典型的光谱干扰为例，系统研究了波长定位误差影响滤波结果准确性的规律性，提出了改善波长定位精度的途径。对于谱线重叠干扰的校正，波长定位精度一般应优于０．１ｐｍ；利用新息序列零均白噪音特性建立指示函数优化扫描光谱峰位，大大提高了波长定位精度，保证了滤波结果的准确性。

Kalman滤波荧光光度法同时测定酪氨酸、色氨酸和苯丙氨酸

苯丙氨酸的荧光峰完全包含在酪氨酸荧光峰之中，酪氨酸和色氨酸的荧光峰也严重重叠。用卡尔曼滤波法解析该体系给出了令人满意的分析结果。回收率为９４．０～１０５％，相对标准偏差不大于３．６％（个别一点除外）。将试剂空白作为一个组分计算，从而免去了试剂空白扣不准给分析结果带来的影响。利用新息序列的白噪音特性来判断结果的可靠性。

荧光光度法中Kalman滤波法指示未知组分的研究

以苯丙氨酸、酪氨酸和色氨酸三组分体系的荧光光度分析为例,研究了Kalman滤波法指示未知组分的潜力.根据新息序列的白噪音特性,建立指示函数,并确定指示函数的临界值,指示未知组分存在;并根据相对新息序列的形状可大致估计未知组分的荧光光谱的形状和峰位.

COMPARATIVE-STUDY OF KALMAN FILTERING, SYNCHRONOUS EXCITATION AND NUMERICAL DERIVATIVE TECHNIQUES IN FLUOROMETRY

The performance of Kalman filtering, synchronous excitation and numerical derivative techniques for the resolution of overlapping emission spectra in spectrofluorimetry was studied. The extent of spectrum overlap was quantitatively described by the separation degree D(s), defined as the ratio of the peak separation to the full width at half-maximum of the emission spectrum of the interferent. For the system of Rhodamine B and Rhodamine 6G with a large D(s) of about 0.4, both Kalman filtering and synchronous techniques are able to resolve the overlapping spectra well and to give satisfactory results while the derivative spectra are still overlapped with each other. Moreover, the sensitivities are greatly decreased in derivative techniques. For more closely spaced spectra emitted by the complexes of Al and Zn with 7-iodo-8-hydroxyquinoline-5-sulphonic acid (Ferron)-hexadecyltrimethylammonium bromide, the synchronous excitation technique cannot completely separate the overlapping peaks, although it increases the separation degree from 0.25 in the conventional spectra to 0.37 in the synchronous spectra. On the other hand, Kalman filtering is capable of resolving this system. When the Al/Zn intensity ratio at the central wavelength of Al was > 1, however, the accuracy and precision of the estimates for Zn concentration produced by the Kalman filter became worse. In this event, the combination of synchronous excitation and Kalman filtering can much improve the analytical results.

RESOLUTION OF CLOSELY SPACED LINES WITH KALMAN FILTERING IN INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTROMETRY

Effects of some factors on the performance of our Kalman filter in discrimination of closely spaced overlapping signals were investigated. The resolution power of the filter for overlapping lines can be strengthened by reduction of the step size in scans. The minimum peak separation of two lines which the Kalman filter can effectively handle generally equals two to three times the step size in scans. Significant difference between the profiles of the analysis and interfering lines and multiple lines from matrix in the spectral window of the analysis line are very helpful for the Kalman filter to discern closely spaced analysis and interfering signals correctly, which allow the filter well to resolve the line pair with very small peak distance or even the entirely coincident lines.

Kalman滤波技术校正电感耦合等离子体原子发射光谱分析中严重重叠的谱线干扰

针对ICP-AES中严重重叠谱线干扰的校正,研究了若干因素对Kalman滤波器性能的影响.减小扫描步长可以增强Kalman滤波法解析重叠谱线的能力.当重叠线对轮廓基本相同且扫描窗口内干扰元素只有一条谱线时,Kalman滤波法能分辨的重叠线对的最小峰间距为扫描步长的2～3倍.扫描窗口内较多的干扰元素谱线和重叠线对轮廓的显著差异有利于Kalman滤波器正确识别分析信号和干扰信号,可以利用这两个因素有效地分辨峰间距很小甚至完全重叠的谱线.

KALMAN FILTERING FOR RESOLUTION OF OVERLAPPING LINES IN INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTROMETRY

A Kalman filter was developed for resolving overlapping lines in inductively coupled plasma atomic emission spectrometry (ICP-AES) and evaluated experimentally with the determination of La in the presence of Ho, and Cu in the presence of Pr. The whiteness of the innovation sequence for an optimal filter was explored to be the criterion for the correction of the wavelength positioning errors which may occur in spectral scans. Under the conditions of the medium-resolution spectrometer and 1.5 pm step size in scans, the filter effectively resolved the Cu/Pr line pair having a small peak separation of 4.8 pm. For the La/Ho line pair with a peak distance of 9.8 pm, an unbiased estimate for La concentration was still obtained even when the signal-to-background ratio was down to 0.048. Favourable detection limits for real samples were achieved. Unstructured backgrounds were modeled theoretically and all spectral scans therefore did not require the correction for solvent.

EVALUATION OF THE RELIABILITY OF KALMAN FILTERING RESULTS IN INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTROMETRY

This paper deals with the evaluation of the reliability of the analytical results obtained by Kalman filtering. Two criteria for evaluation were compared: one is based on the autocorrelation analysis of the innovation sequence, the so-called NAC criterion; the other is the innovations number, which actually is the autocorrelation coefficient of the innovation sequence at the initial wavelength. Both criteria allow compensation for the wavelength positioning errors in spectral scans, but there exists a difference in the way they work. The NAC criterion can provide information about the reliability of an individual result, which is very useful for the indication of unmodelled emissions, while the innovations number should be incorporated with the normalization of the innovations or seek the help of the sequence itself for the same purpose. The major limitation of the NAC criterion is that it does not allow the theoretical modelling of continuous backgrounds, which, however, is convenient in practical analysis and can be taken with the innovations number criterion.

电感耦合等离子体原子发射光谱法中Kalman滤波法解析重叠谱线的研究

考察了Kalman滤波技术校正ICP-AES中谱线重叠干扰的潜力.以新息序列的平均平方和为评价函数优化扫描光谱的峰位,消除扫描过程中可能产生的波长定位误差,从而保证滤波结果的准确性,并使实际检出限显著改善.在中等分辨率光谱仪和扫描步长为1.5pm的条件下,滤波器能有效地分辨峰间距只有4.8pm且峰形基本相同的重叠线对.对峰间距为9.8pm的重叠线对,当线背比低至0.05左右时仍能获得满意结果.连续背景用理论描述,因而样品溶液和纯组分溶液的光谱扫描无需扣除溶剂空白.

EVALUATION OF THE EFFECT OF WAVELENGTH POSITIONING ERRORS ON KALMAN FILTERING RESULTS IN INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION-SPECTROMETRY

This work evaluates the effect of wavelength positioning errors in spectral scans on analytical results when the Kalman filtering technique is used for the correction of line interferences in inductively coupled plasma atomic emission spectrometry (ICP-AES). The results show that a positioning accuracy of 0.1 pm is required in order to obtain accurate and precise estimates for analyte concentrations. The positioning error in sample scans is more crucial than that in model scans. The relative bias in measured analyte concentration originating from a positioning error in a sample scan increases linearly with an increase in the magnitude of the error and the peak distance of the overlapping lines, but is inversely proportional to the signal-to-background ratio. By the use of an optimization procedure for the positions of scans with the innovations number as the criterion, the wavelength positioning error can be reduced and, correspondingly, the accuracy and precision of analytical results improved.

Segmenting Foreground Objects from a Dynamic Textured Background via a Robust Kalman Filter

The algorithm presented in this paper aims to segment the foreground objects in video (e.g., people) given time-varying, textured backgrounds. Examples of time-varying backgrounds include waves on water, clouds moving, trees waving in the wind, automobile traffic, moving crowds, escalators, etc. We have developed a novel foreground-background segmentation algorithm that explicitly accounts for the non-stationary nature and clutter-like appearance of many dynamic textures. The dynamic texture is modeled by an Autoregressive Moving Average Model (ARMA). A robust Kalman filter algorithm iteratively estimates the intrinsic appearance of the dynamic texture, as well as the regions of the foreground objects. Preliminary experiments with this method have demonstrated promising results.