Adaptive Fuzzy Strong Tracking Extended Kalman Filtering for GPS Navigation

The well-known extended Kalman filter (EKF) has been widely applied to the Global Positioning System (GPS) navigation processing. The adaptive algorithm has been one of the approaches to prevent the divergence problem of the EKF when precise knowledge on the system models are not available. One of the adaptive methods is called the strong tracking Kalman filter (STKF), which is essentially a nonlinear smoother algorithm that employs suboptimal multiple fading factors, in which the softening factors are involved. Traditional approach for selecting the softening factors heavily relies on personal experience or computer simulation. In order to resolve this shortcoming, a novel scheme called the adaptive fuzzy strong tracking Kalman filter (AFSTKF) is carried out. In the AFSTKF, the fuzzy logic reasoning system based on the Takagi-Sugeno (T-S) model is incorporated into the STKF. By monitoring the degree of divergence (DOD) parameters based on the innovation information, the fuzzy logic adaptive system (FLAS) is designed for dynamically adjusting the softening factor according to the change in vehicle dynamics. GPS navigation processing using the AFSTKF will be simulated to validate the effectiveness of the proposed strategy. The performance of the proposed scheme will be assessed and compared with those of conventional EKF and STKF     

Angular velocity estimation from measurement vectors of star tracker

In most spacecraft, there is a need to know the craft's angular rate. Approaches with least squares and an adaptive Kalman filter are proposed for estimating the angular rate directly from the star tracker measurements. In these approaches, only knowledge of the vector measurements and sampling interval is required. The designed adaptive Kalman filter can filter out noise without information of the dynamic model and inertia dyadic. To verify the proposed estimation approaches, simulations based on the orbit data of the challenging minisatellite payload (CHAMP) satellite and experimental tests with night-sky observation are performed. Both the simulations and experimental testing results have demonstrated that the proposed approach performs well in terms of accuracy, robustness, and performance.     

One step-ahead ANFIS time series model for forecasting electricity loads

In electric industry, electricity loads forecasting has become more and more important, because demand quantity is a major determinant in electricity supply strategy. Furthermore, accurate regional loads forecasting is one of principal factors for electric industry to improve the management performance. Recently, time series analysis and statistical methods have been developed for electricity loads forecasting. However, there are two drawbacks in the past forecasting models: (1) conventional statistical methods, such as regression models are unable to deal with the nonlinear relationships well, because of electricity loads are known to be nonlinear; and (2) the rules generated from conventional statistical methods (i.e., ARIMA), and artificial intelligence technologies (i.e., support vector machines (SVM) and artificial neural networks (ANN)) are not easily comprehensive for policy-maker. Based on these reasons above, this paper proposes a new model, which incorporates one step-ahead concept into adaptive-network-based fuzzy inference system (ANFIS) to build a fusion ANFIS model and enhances forecasting for electricity loads by adaptive forecasting equation. The fuzzy if-then rules produced from fusion ANFIS model, which can be understood for human recognition, and the adaptive network in fusion ANFIS model can deal with the nonlinear relationships. This study optimizes the proposed model by adaptive network and adaptive forecasting equation to improve electricity loads forecasting accuracy. To evaluate forecasting performances, six different models are used as comparison models. The experimental results indicate that the proposed model is superior to the listing models in terms of mean absolute percentage errors (MAPE).     

Using forecasts and managerial accounting information to enhance closed-loop supply chain management

This paper develops a generic forecasting framework for product returns that combines concepts used in different disciplines. If more-step ahead forecasts of product returns are required, estimating sales data is necessary. This is accomplished by adopting growth curve models based on the extended Kalman filter. In order to capture the process generating product returns more adequately than in the literature, we propose an adaptive Bayesian approach to forecast future returns. The combination of these two concepts enables us to conduct more-step ahead forecasts. We evaluate the robustness of this approach against Holts approach, a Kalman filter based approach, and the model by Toktay et al. (Manag Sci 46:1412–1426, 2000) for varying degrees of misspecification. In addition, we create a link between forecasting accuracy and the economic value added. This enables the user to choose the economically worthwhile forecasting method that trades-off additional operating costs and savings in working capital. Our theoretical and numerical results indicate that our approach operates on high accuracy even in situations when the underlying assumptions are obviously violated.     

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.     

A New Optimized Algorithm with Nonlinear Filter for Ultra-Tightly Coupled Integrated Navigation System of Land Vehicle

The extended particle filter (EPF) assisted by the Takagi-Sugeno (T-S) fuzzy logic adaptive system (FLAS) is used to design the ultra-tightly coupled GPS/INS (inertial navigation system) integrated navigation, which can maneuver the vehicle environment and the GPS outages scenario. The traditional integrated navigation designs adopt a loosely or tightly coupled architecture, for which the GPS receiver may lose the lock due to the interference/jamming scenarios, high dynamic environments, and the periods of partial GPS shading. An ultra-tight GPS/INS architecture involves the integration of I (in-phase) and Q (quadrature) components from the correlator of a GPS receiver with the INS data. The EPF is a particle filter (PF) which uses the extended Kalman filter (EKF) to generate the proposal distribution. The PF depends mostly on the number of particles in order to achieve a better performance during the high dynamic environments and GPS outages. The T-S FLAS is one of these approaches that can prevent the divergence problem of the filter when the precise knowledge on the system models is not available. The results show that the proposed fuzzy adaptive EPF (FAEPF) can effectively improve the navigation estimation accuracy and reduce the computational load as compared with the EPF and the unscented Kalman filter (UKF).     

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.     

基于多尺度Kalman数据融合滤波

本文通过分析基于小波变换的动态系统模型,提出一种基于小波多尺度的Kalman数据滤波方法,本文利用小波的多尺度特点,把初始估计序列多尺度分解,并在不同尺度层上进行Kalman滤波估计,再利用小波重构来融合各层的估计信息,把标准Kalman滤波只在单一尺度和时间轴上对状态估计值和误差协方差进行数据更新,改进为基于小波变换的尺度轴和时间轴上的双向数据更新,该算法将小波多尺度分解去噪和Kalman滤波相结合,对实际中含较强噪声的动态系统的状态估计效果较好.算法也可用于多分辨率多传感器数据融合.     

Kernel Entropy Based Extended Kalman Filter for GPS Navigation Processing

This paper investigates the kernel entropy based extended Kalman filter (EKF) as the navigation processor for the Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS). The algorithm is effective for dealing with non-Gaussian errors or heavy-tailed (or impulsive) interference errors, such as the multipath. The kernel minimum error entropy (MEE) and maximum correntropy criterion (MCC) based filtering for satellite navigation system is involved for dealing with non-Gaussian errors or heavy-tailed interference errors or outliers of the GPS. The standard EKF method is derived based on minimization of mean square error (MSE) and is optimal only under Gaussian assumption in case the system models are precisely established. The GPS navigation algorithm based on kernel entropy related principles, including the MEE criterion and the MCC will be performed, which is utilized not only for the time-varying adaptation but the outlier type of interference errors. The kernel entropy based design is a new approach using information from higher-order signal statistics. In information theoretic learning (ITL), the entropy principle based measure uses information from higher-order signal statistics and captures more statistical information as compared to MSE. To improve the performance under non-Gaussian environments, the proposed filter which adopts the MEE/MCC as the optimization criterion instead of using the minimum mean square error (MMSE) is utilized for mitigation of the heavy-tailed type of multipath errors. Performance assessment will be carried out to show the effectiveness of the proposed approach for positioning improvement in GPS navigation processing.     

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.     

Advances in real-time flood forecasting

This paper discusses the modelling of rainfall-flow (rainfall-run-off) and flow-routeing processes in river systems within the context of real-time flood forecasting. It is argued that deterministic, reductionist (or 'bottom-up') models are inappropriate for real-time forecasting because of the inherent uncertainty that characterizes river-catchment dynamics and the problems of model over-parametrization. The advantages of alternative, efficiently parametrized data-based mechanistic models, identified and estimated using statistical methods, are discussed. It is shown that such models are in an ideal form for incorporation in a real-time, adaptive forecasting system based on recursive state-space estimation (an adaptive version of the stochastic Kalman filter algorithm). An illustrative example, based on the analysis of a limited set of hourly rainfall-flow data from the River Hodder in northwest England, demonstrates the utility of this methodology in difficult circumstances and illustrates the advantages of incorporating real-time state and parameter adaption.     

Short-term forecasting of electricity prices in the colombian electricity market

The restructuring of the electricity-generating industry from protected monopoly to an open competitive market has presented producers with a problem scheduling generation: finding the optimal bidding strategy to maximise their profits. In order to solve this scheduling problem, a reliable system capable of forecasting electricity prices is needed. This work evaluates the forecasting capabilities of several modelling techniques for the next-day-prices forecasting problem in the Colombian market, measured in USD/MWh. The models include exogenous variables such as reservoir levels and load demand. Results show that a segmentation of the prices into three intervals, based on load demand behaviour, contribute to an important standard deviation reduction. Regarding the models under analysis, Takagi?Sugeno?Kang models and ARMAX models identified by means of a Kalman filter perform the best forecasting, with an error rate below 6%.     

一种水下GPS系统及其在蛙人定位导航中的应用

研究了一种适用于蛙人导航的水下GPS系统。针对蛙人执行水下任务所需的高精度导航,提出了一种由主动声纳浮标作为定位基站的GPS定位系统,介绍了该系统基于延时测量的定位原理和求解方法,给出了Kalman滤波器和扩展Kalman滤波器的设计,并通过数值仿真进行了验证,结果表明：为提高定位精度,在定位解算的基础上进行滤波平滑是必要的。     

未知激励下的无迹卡尔曼滤波新方法

无迹卡尔曼滤波（UKF）是一种识别非线性系统的有效方法,然而传统的UKF方法需要观测外部激励,这限制了UKF的应用范围。迄今为止,国内外对未知激励情况下的UKF方法的研究还非常少。该文在传统UKF的基础上,推导出在未知激励情况下的无迹卡尔曼滤波（UKF-UI）方法的递推公式,通过对观测误差的最小化,利用非线性方程求解,识别未知外部激励,进而识别非线性结构系统状态与结构未知参数。进一步采用融合部分观测的加速度响应及位移响应,消除识别结果的漂移问题。分别通过白噪声和未知地震作用下识别非线性迟滞模型的两个数值算例,考虑观测噪声对非线性系统进行识别,从而验证提出新方法的有效性。结果表明,该文所提出的UKF-UI方法,能够在部分观测结构系统响应的情况下,有效地识别非线性结构参数和未知激励。     

Evaluating adaptive smoothing models: some guidelines for implementation

A number of multiple-parameter adaptive exponential smoothing models have been proposed and demonstrated over the last two decades for short range forecasting. There have been conflicting results on their performance and no systematic study has been conducted to compare them in a controlled environment. The work reported here fills this void by testing a set of well known multiple-parameter adaptive procedures against the three-parameter Winters' model. First, sets of synthetic time series with known characteristics are used to compare performance for the different approaches using the standard deviation of forecast errors. Second, the information gathered at this point is used to predict the technique's performance on six empirical time series. And third, general guidelines are presented for model selection.     

Error sources and algorithms for white-light fringe estimation at low light levels

We address the problem of highly accurate phase estimation at low light levels, as required by the Space Interferometry Mission (SIM). The most stringent SIM requirement in this regard is that the average phase error over a 30-s integration time correspond to a path-length error of approximately 30 pm. Most conventional phase-estimation algorithms exhibit significant enough bias at the signal levels at which the SIM will be operating so that some correction is necessary. Several algorithms are analyzed, and methods of compensating for their bias are developed. Another source of error in phase estimation occurs because the phase is not constant over the integration period. Errors that are due to spacecraft motion, the motion of compensating optical elements, and modulation errors are analyzed and simulated. A Kalman smoothing approach for compensating for these errors is introduced.     

拖曳阵阵形估计的自适应Kalman滤波算法

柔性拖曳阵在水下拖动时受拖船拖动及海流等的扰动,因此拖曳阵的阵形估计问题是个存在未知输入的系统状态估计问题。文中采用了一个自适应的KALMAN滤波算法来解决这一问题。自适应Kalman滤波器包括两部分:一部分是没有输入的Kalman滤波,另一部分是自适应加权的Kalman滤波用于估计快时变的余量偏差。在迭代的每一步,均利用M-估计器和Huber函数相结合构造作为更新偏差函数的遗忘因子。数值仿真与海试结果表明,该方法比传统的状态估计方法估计效果好。     

Star spot location estimation using Kalman filter for star tracker

Star pattern recognition and attitude determination accuracy is highly dependent on star spot location accuracy for the star tracker. A star spot location estimation approach with the Kalman filter for a star tracker has been proposed, which consists of three steps. In the proposed approach, the approximate locations of the star spots in successive frames are predicted first; then the measurement star spot locations are achieved by defining a series of small windows around each predictive star spot location. Finally, the star spot locations are updated by the designed Kalman filter. To confirm the proposed star spot location estimation approach, the simulations based on the orbit data of the CHAMP satellite and the real guide star catalog are performed. The simulation results indicate that the proposed approach can filter out noises from the measurements remarkably if the sampling frequency is sufficient.     

Adaptive forecasting techniques

The class of exponential smoothing models which vary the values of their parameters to adapt to changing conditions in a time series are referred to as adaptive forecasting techniques. In this article criteria for evaluating forecasting models are presented and the features of a simple exponential smoothing model that are exploited by the adaptive techniques are discussed. Several adaptive forecasting schemes are described and classified, and examples of the performance of these techniques 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.