Incorporation of a positivity constraint into a Kalman-filter-basedalgorithm for correction of spectrometric data

Improving the resolution of spectrometric analyses by numerical processing of spectrometric data subject to systematic errors of an instrumental type, as well as to random errors, is addressed. It is assumed that the model of the spectrometric data has the form of an integral, convolution-type equation of the first kind. The method for improving the resolution consists of numerically solving this equation on the basis of the acquired data. A new algorithm for dealing with this problem is proposed; it is based on the Kalman filter constrained in such a way that the negative values of the solution are suppressed. The efficiency of this constrained algorithm is demonstrated using both synthetic and real-world data     

Spline-based variational method with constraints forspectrophotometric data correction

The raw results of spectrophotometric measurements are subject to systematic errors of an instrumental type which may be reduced provided a mathematical model of the instrumental imperfections is identified. It is assumed that this model has the form of an integral, convolution-type equation of the first kind. The correction of the spectrometric data consists in numerically solving this equation on the basis of the raw results of measurements. An algorithm of correction is proposed which is based on the approximation of the solution with a spline function whose parameters are determined using a variational method with the positivity constraint imposed on the set of feasible solutions. The efficiency of the incorporation of this constraint into the algorithm of correction is demonstrated using synthetic data. The possibility of improving resolution of spectrometric data is shown on a set of real spectrophotometric measurements     

Kalman-filter-based algorithms of spectrophotometric datacorrection III. Use of splines for approximation of spectra

An alternative method to that presented in the first paper of the series for improving the resolution of spectrophotometric measurements via processing of spectrometric data is proposed. It is based on the approximation of the solution with a spline function the parameters of which are determined by means of a recursive Kalman-filter-based algorithm. It is assumed in the paper that the model of the spectrophotometric data has the form of an integral, convolution-type equation of the first kind. It is shown, using synthetic and real-world spectrophotometric data, that the proposed method allows for significant reduction of computational requirements as well as an improvement in the quality of correction     

Using rational filters for digital correction of a spectrometricmicrotransducer

Raw spectrometric data are subject to systematic errors of an instrumental type that may be reduced, provided a mathematical model of the spectrometer, or its pseudoinverse, i.e., an operator of reconstruction, is identified. The idea of identifying this operator, directly during calibration of the spectrometer, is developed in this paper. The applicability of an operator of reconstruction, having the form of a rational filter, is studied when it is used for correction of the instrumental errors introduced by a low-resolution spectrometric microtransducer (SMT) that is intended for designing a microspectrometer. Several algorithms of correction are developed and systematically studied using real-world spectra and a nonlinear mathematical model of the microtransducer, proposed by the authors in a previous publication     

State estimation of a boiler model using the unscented Kalman filter

The state estimation of a 300 MW drum-type boiler is examined, using an unscented Kalman filter to improve estimation accuracy by preserving the nonlinearities of the boiler equations. The boiler is modelled by a system of differential state equations for the dynamics of the circulation loop and another set of partial differential equations for the heat exchangers such as the superheaters, reheater and economiser. These modelling equations are the results of first principle balance equations, which have a form that is unsuitable for the extended Kalman filter method because of errors between the linear and nonlinear propagation of the boiler states and the difficulties in obtaining the Jacobian of the state model for the propagation of model uncertainties. An unscented Kalman filter is used to circumvent this problem as it treats the system model as a black box. Filtering results from simulated plant data are presented to demonstrate the effectiveness of the filter application.     

Adaptive filter solution for processing lidar returns: optical parameter estimation

Joint estimation of extinction and backscatter simulated profiles from elastic-backscatter lidar return signals is tackled by means of an extended Kalman filter (EKF). First, we introduced the issue from a theoretical point of view by using both an EKF formulation and an appropriate atmospheric stochastic model; second, it is tested through extensive simulation and under simplified conditions; and, finally, a first real application is discussed. An atmospheric model including both temporal and spatial correlation features is introduced to describe approximate fluctuation statistics in the sought-after atmospheric optical parameters and hence to include a priori information in the algorithm. Provided that reasonable models are given for the filter, inversion errors are shown to depend strongly on the atmospheric condition (i.e., the visibility) and the signal-to-noise ratio along the exploration path in spite of modeling errors in the assumed statistical properties of the atmospheric optical parameters. This is of advantage in the performance of the Kalman filter because they are often the point of most concern in identification problems. In light of the adaptive behavior of the filter and the inversion results, the EKF approach promises a successful alternative to present-day nonmemory algorithms based on exponential-curve fitting or differential equation formulations such as Klett's method.     

Analysis of a Kalman filter based method for on-line estimation of atmospheric dispersion parameters using radiation monitoring data

A Kalman filter method is discussed for on-line estimation of radioactive release and atmospheric dispersion from a time series of off-site radiation monitoring data. The method is based on a state space approach, where a stochastic system equation describes the dynamics of the plume model parameters, and the observables are linked to the state variables through a static measurement equation. The method is analysed for three simple state space models using experimental data obtained at a nuclear research reactor. Compared to direct measurements of the atmospheric dispersion, the Kalman filter estimates are found to agree well with the measured parameters, provided that the radiation measurements are spread out in the cross-wind direction. For less optimal detector placement it proves difficult to distinguish variations in the source term and plume height; yet the Kalman filter yields consistent parameter estimates with large associated uncertainties. Improved source term assessment results, when independent estimates of the plume height can be used. Perspectives for using the method in the context of nuclear emergency management are discussed, and possible extensions to the present modelling scheme are outlined, to account for realistic accident scenarios.     

被动定向浮标阵卡尔曼滤波目标跟踪研究

文章研究利用被动定向浮标阵定位跟踪水下机动目标的方法,基于卡尔曼滤波(Kalman Filter, KF)原理提出一种定位跟踪滤波器的具体实现方法。该方法能够整合多枚浮标现在及过去有误差的测量数据,提高定位精度,同时连续输出水下目标运动参数估计从而锁定目标运动轨迹。该方法实现的关键在于建立水下目标与浮标阵的数学迭代运算模型,包括状态空间的动态与观测过程。由于被动定向浮标阵目标跟踪是一个非线性估计问题,而卡尔曼滤波器是线性的,因此文章设计了近似的线性观测方程以利用卡尔曼滤波来解决这个问题。通过计算机仿真研究该滤波器的跟踪效果并与最小二乘法进行比较,估计精度明显高于最小二乘法。同时通过仿真验证该滤波器可以自适应跟踪目标的非稳态运动过程。该方法在工程实践上具有一定应用前景与指导意义。     

Spatio-temporal analysis with short- and long-memory dependence: a state-space approach

This paper deals with the estimation and prediction problems of spatio-temporal processes by using state-space methodology. The spatio-temporal process is represented through an infinite moving average decomposition. This expansion is well known in time series analysis and can be extended straightforwardly in space–time. Such an approach allows easy implementation of the Kalman filter procedure for estimation and prediction of linear time processes exhibiting both short- and long-range dependence and a spatial dependence structure given on the locations. Furthermore, we consider a truncated state-space equation, which allows to calculate an approximate likelihood for large data sets. The performance of the proposed Kalman filter approach is evaluated by means of several Monte Carlo experiments implemented under different scenarios, and it is illustrated with two applications.     

Application of a digital signal processor for correction ofspectrophotometric measurements

The results of spectrophotometric measurements are subject to systematic errors of an instrumental type which may be partially corrected provided a mathematical model of the instrumental imperfections is identified. It is assumed that this model has the form of an integral, convolution-type equation of the first kind. The correction of the results of measurements, subject to random measurement errors, consists of numerically solving this equation on the basis of these results. A correction algorithm, based on the Tikhonov method of frequency-domain regularization, has been implemented using the DSP 56001 digital signal processor. The results of its application are compared with those obtained by means of PC-MATLAB software for the same synthetic data. It is shown that a considerable gain in speed of computation is attained without significant reduction of the accuracy     

An application-specific processor dedicated to Kalman-filter-basedcorrection of spectrometric data

An application-specific processor dedicated to Kalman-filter-based measurand reconstruction in spectrometric applications is proposed. It is intended to act as coprocessor of a host processor, performing relatively sophisticated processing of measurement data subject to systematic errors of an instrumental type and to random errors of various natures, it is basically designed for improving the resolution of spectrometric measurements commonly used in environmental laboratories, but it may be useful in other applications where similar processing of measurement data is required. Examples of applications of the processor in spectrometric measurements, its metrological advantages and limitations, as well as perspectives of its development, are presented     

Neural filtering of colored noise based on Kalman filter structure

In this paper, adaptive filtering approaches of colored noise based on the Kalman filter structure using neural networks are proposed, which need not extend the dimensions of the filter. The colored measurement noise is first modeled from a Gaussian white noise through a shaping filter. The Kalman filtering model of colored noise is then built by adopting an equivalent observation equation, which can avoid the dimension extension and complicated computations. An observation correlation-based algorithm is suggested to estimate the variance of the measurement noise by use of a single layer neural network. The Kalman gain can be obtained when a perfect knowledge of the plant model and noise variances is given. However, in some cases, the difficulties of the correlative method and the Kalman filter equations are the amount of computations and memory requirements. A neural estimator based on the Kalman filter structure is also analyzed as an alternative in this paper. The Kalman gain is replaced by a feedforward neural network whose weight adjustment permits minimization of the estimation error. The estimator has the capability of estimating the states of the plant in a stochastic environment without knowledge of noise statistics. If the noise of the plant is white and Gaussian and its statistics are well known, the neural estimator and the Kalman filter produce equally good results. The neural filtering approaches of colored noise based on the Kalman filter structure are applied to restore the cephalometric images of stomatology. Several experimental results demonstrate the feasibility and good performances of the approaches.     

卡尔曼滤波器在光电经纬仪中的应用

为了解决光电经纬仪电视跟踪系统脱靶量滞后对控制系统跟踪精度及稳定性的影响，将预测滤波技术应用到光电跟踪系统中，提出了极坐标下卡尔曼滤波算法，目标模型采用等速运动并附有时间相关的随机加速度，增加了延时补偿。仿真结果表明，跟踪误差减小，当跟踪目标从视场消失时，控制系统按照预测的目标信息跟踪。     

Variational Bayesian Based IMM Robust GPS Navigation Filter

This paper investigates the navigational performance of Global Positioning System (GPS) using the variational Bayesian (VB) based robust filter with interacting multiple model (IMM) adaptation as the navigation processor. The performance of the state estimation for GPS navigation processing using the family of Kalman filter (KF) may be degraded due to the fact that in practical situations the statistics of measurement noise might change. In the proposed algorithm, the adaptivity is achieved by estimating the time-varying noise covariance matrices based on VB learning using the probabilistic approach, where in each update step, both the system state and time-varying measurement noise were recognized as random variables to be estimated. The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning. One of the two major classical adaptive Kalman filter (AKF) approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate (MMAE). The IMM algorithm uses two or more filters to process in parallel, where each filter corresponds to a different dynamic or measurement model. The robust Huber's M-estimation-based extended Kalman filter (HEKF) algorithm integrates both merits of the Huber M-estimation methodology and EKF. The robustness is enhanced by modifying the filter update based on Huber's M-estimation method in the filtering framework. The proposed algorithm, referred to as the interactive multi-model based variational Bayesian HEKF (IMM-VBHEKF), provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors, such as the multipath effect. Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.     

Static and dynamic novelty detection methods for jet engine health monitoring

Novelty detection requires models of normality to be learnt from training data known to be normal. The first model considered in this paper is a static model trained to detect novel events associated with changes in the vibration spectra recorded from a jet engine. We describe how the distribution of energy across the harmonics of a rotating shaft can be learnt by a support vector machine model of normality. The second model is a dynamic model partially learnt from data using an expectation-maximization-based method. This model uses a Kalman filter to fuse performance data in order to characterize normal engine behaviour. Deviations from normal operation are detected using the normalized innovations squared from the Kalman filter.     

A real-time filtering method for the drift data of a laser Doppler velocimeter

To effectively reduce the random drift of a laser Doppler velocimeter (LDV), a real-time filtering model is presented for filtering the drift data of an LDV, which is a combination of the metabolic grey model (1, 1) and the metabolic time series model AR (2). The basic principle of the metabolic grey-time series model is introduced in detail first. Then, the model is established for the static and dynamic drift data, and a Kalman filter is used to filter the drift data based on the model. The variance analysis method and the Allan variance method are employed to analyse the static drift data. The dynamic drift data are also compared before and after being modelled and filtered. The results demonstrate that the metabolic grey-time series method cannot only effectively reduce the static random drift of an LDV, but can also reduce the dynamic random drift in real time.     

The Identification of the Wind Parameters Based on the Interactive Multi-Models

The wind as a natural phenomenon would cause the derivation of the pesticide drops during the operation of agricultural unmanned aerial vehicles (UAV). In particular, the changeable wind makes it difficult for the precision agriculture. For accurate spraying of pesticide, it is necessary to estimate the real-time wind parameters to provide the correction reference for the UAV path. Most estimation algorithms are model based, and as such, serious errors can arise when the models fail to properly fit the physical wind motions. To address this problem, a robust estimation model is proposed in this paper. Considering the diversity of the wind, three elemental time-related Markov models with carefully designed parameter α are adopted in the interacting multiple model (IMM) algorithm, to accomplish the estimation of the wind parameters. Furthermore, the estimation accuracy is dependent as well on the filtering technique. In that regard, the sparse grid quadrature Kalman filter (SGQKF) is employed to comprise the computation load and high filtering accuracy. Finally, the proposed algorithm is ran using simulation tests which results demonstrate its effectiveness and superiority in tracking the wind change.     

On-line identification, flutter testing and adaptive notching of structural mode parameters for V-22 tiltrotor aircraft

New algorithms and results are presented for flutter testing and adaptive notching of structural modes in V-22 tiltrotor aircraft based on simulated and flight-test data from Bell Helicopter Textron, Inc. (BHTI). For flutter testing and the identification of structural mode frequencies, dampings and mode shapes, time domain state space techniques based on Deterministic Stochastic Realization Algorithms (DSRA) are used to accurately identify multiple modes simultaneously from sine sweep and other multifrequency data, resulting in great savings over the conventional Prony method. Two different techniques for adaptive notching are explored in order to design an Integrated Flight Structural Control (IFSC) system. The first technique is based on on-line identification of structural mode parameters using DSRA algorithm and tuning of a notch filter. The second technique is based on decoupling rigid-body and structural modes of the aircraft by means of a Kalman filter and using rigid-body estimates in the feedback control loop. The difference between the two approaches is that on-line identification and adaptive notching in the first approach are entirely based on the knowledge of structural modes, whereas the Kalman filter design in the second approach is based on the rigid-body dynamic model only. In the first IFSC design, on-line identification is necessary for flight envelope expansion and to adjust the notch filter frequencies and suppress aero-servoelastic instabilities due to changing flight conditions such as gross weight, sling loads, and air speed. It is shown that by tuning the notch filter frequency to the identified frequency, the phase lag is reduced and the corresponding structural mode is effectively suppressed and stability is maintained. In the second IFSC design using Kalman filter design, the structural modes are again effectively suppressed. Furthermore, the rigid-body estimates are found to be fairly insensitive to both natural frequency and damping factor variations and therefore stability is maintained. The Kalman filter design might be a better choice when the rigid-body dynamics are well known because no adaptation is necessary in this case.     

Study on Posture Estimation Using Delayed Measurements for Mobile Robots

1Introduction Mobilerobotsaredevelopingtowardsintellectualization,whichdependsonthedevelopmentofsensor technologytotheutmostextent.Theinformationfusiontechnologyhasovercomethedrawbackresul tingfromtheapplicationofasingletonsensor.Forthesamereason,inordertoenhancetheposition precisionofthemobilerobot,morethanonesensorisoftenneededtogenerateandmaintainarelia blestateestimation[1].Furthermore,thecomputationcomplexityofdealingwiththesensordatawil oftenbringonsignificanttimedelaysfromtheacquisition…     

卫星跟踪中位置预测的序列匹配算法

针对卫星跟踪中的位置预测问题,分析了动力学模型方法的预测误差组成,提出一种用测量数据来计算预测数据时间误差的序列匹配算法,并讨论了空间误差的计算方法。仿真结果表明,提出的时间校正和空间误差补偿方法的预测精度比动力学模型和Kalman滤波法的预测精度高;即在相同的精度要求下,序列匹配算法能预测的时间范围是Kalman滤波法的1.5倍以上。