Batch Optimal FIR Smoothing: Increasing State Informativity in Nonwhite Measurement Noise Environments

In this paper, the optimal finite impulse response (OFIR) with embedded unbiasedness (EU) filter is derived by minimizing the mean square error (MSE) subject to the unbiasedness constraint for discrete time-invariant state-space models. Un like the OFIR filter, the OFIR-EU filter does not require the initial conditions. In terms of accuracy, the OFIR-EU filter occupies an intermediate place between the UFIR and OFIR filters. With a two-state harmonic model, we show that the OFIR-UE filter has higher immunity against errors in the noise statistics and better robustness against temporary model uncertainties than the OFIR and Kalman filters.

Fast optimal estimates are often required in control and signal processing. In this paper, we discuss an approach to optimal finite impulse response (OFIR) filtering for discrete time-variant systems using finite measurements. The mean square error is minimized to obtain the batch OFIR algorithm which requires measurements on an a finite horizon of N points. Fast iterative algorithm is found using recursions. It is shown that each recursion has a predictor/corrector Kalman filter (KF)-like format with special initial conditions. In this sense, the KF is considered as a special case of the proposed iterative OFIR filtering algorithm when N approaches infinity for known initial conditions. It has been confirmed by simulation that the iterative form of the OFIR filter operates much faster than the batch form.

In this paper, Rauch-Tung-Striebel(RTS) optimal smoothing algorithm is applied to improving off-line satellite attitude determination accuracy. The measurements are first processed by the forward filter, and then, a separate backward smoothing pass is used for obtaining the smoothing solution. The performances between RTS and extended Kalman filter(EKF) in gyro/star-sensor integrated system are compared. RTS smoother exhibits better accuracy and robustness than EKF under the situation of lower sensors precision, different length of data and larger initial attitude error. The results verify the effectiveness and practicability of RTS smoothing algorithm in satellite attitude determination.

Application of ARIMA-RTS optimal smoothing algorithm in gas well production prediction

The well-known Jazwinski's limited memory filter, Schweppe's finite memory filter, and Kwon's optimal finite impulse response (FIR) filter are compared in the filter structures, system models, and optimality criterions, and are shown to be equivalent on condition that they are applied to the discrete system with no process noise and unknown prior information of the system state. The different properties such as stability and computation burden are briefly discussed. Kwon's optimal FIR filter is shown to have some advantages in terms of stability and modeling constraints.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The authors present a general framework of the construction of biorthogonal wavelets based on Bernstein bases along with theory analysis and application. The presented framework possesses the largest possible regularity, the required vanishing moments and the passband flatness of frequency response of filters. Based on this concept, the authors establish explicit formulas for filters of biorthogonal wavelets with arbitrary odd lengths. Meanwhile, a new family of parametric filters with symmetry is constructed. The choice of filter bank in wavelet compression is a critical issue that affects image quality. In this study, an optimal model of FIR aiming at image compression is brought forward, and the optimal finite impulse response (FIR) filters can be obtained correspondingly through sequential quadratic programming (SQP) and genetic algorithm (GA). The authors demonstrate the performance of the new family of filters given in this study for image compression with very encouraging results.

An efficient method is proposed for the design of finite impulse response (FIR) filter with arbitrary pass band edge, stop band edge frequencies and transition width. The proposed FIR band stop filter is designed using craziness based particle swarm optimization (CRPSO) approach. Given the filter specifications to be realized, the CRPSO algorithm generates a set of optimal filter coefficients and tries to meet the ideal frequency response characteristics. In this paper, for the given problem, the realizations of the optimal FIR band pass filters of different orders have been performed. The simulation results have been compared with those obtained by the well accepted evolutionary algorithms, such as Parks and McClellan algorithm (PMA), genetic algorithm (GA) and classical particle swarm optimization (PSO). Several numerical design examples justify that the proposed optimal filter design approach using CRPSO outperforms PMA and PSO, not only in the accuracy of the designed filter but also in the convergence speed and solution quality.

The finite impulse response (FIR) approach is known to be more robust than the Kalman approach. In this paper, we derive a batch q-lag maximum likelihood (ML) FIR smoother for full covariance matrices and represent it with an iterative algorithm using recursions for diagonal covariance matrices. It is shown that, under ideal conditions of fully known model, the ML FIR smoother occupies an intermediate place between the more accurate Rauch-Tung-Striebel (RTS) smoother and the less accurate unbiased FIR smoother. With uncertainties and errors in noise covariances, ML FIR smoothing is significantly superior to RTS smoothing. It is also shown experimentally that ML FIR smoothing is more robust than RTS smoothing against measurement outliers.

A localization and tracking algorithm for an early-warning tracking system based on the information fusion of Infrared (IR) sensor and Laser Detection and Ranging (LADAR) is proposed. The proposed Kalman filter scheme incorporates Out-of-Sequence Measurements (OOSMs) to address long-range, high-speed incoming targets to be tracked by networked Remote Observation Sites (ROS) in cluttered environments. The Rauch–Tung–Striebel (RTS) fixed lag smoothing algorithm is employed in the proposed technique to further improve tracking accuracy, which, in turn, is used for target profiling and efficient filter initialization at the targeted platform. This efficient initialization increases the probability of target engagement by increasing the distance at which it can be effectively engaged. The increased target engagement range also reduces risk of any damage from debris of the engaged target. Performance of the proposed target localization algorithm with OOSM and RTS smoothing is evaluated in terms of root mean square error (RMSE) for both position and velocity, which accurately depicts the improved performance of the proposed algorithm in comparison with existing retrodiction-based OOSM filtering algorithms. The effects of assisted target state initialization at the targeted platform are also evaluated in terms of Time to Impact (TTI) and true track retention, which also depict the advantage of the proposed strategy.

Acquired images in hyperspectral imagery are disturbed by additive noise which is usually assumes as zero-mean white one. In fact, there is still non-white noise in hyperspectral images (HSIs). The 2-dimensional filtering methods and multidimensional tensor decomposition algorithms cannot be used to remove non-white noise from HSIs directly. Therefore, a prewhitening denoising solution based on tensor decomposition is proposed in this paper. The prewhitening procedure can help to transform the non-white noise into a white one and the tensor decomposition method removes the noise without affecting the related information between image planes. The simulation results show that this non-white noise reducing approach has promising prospects in this field compared to existing denoising methods.

PPP-based UAV modeling using Galileo HAS orbit/clock products and RTS smoother

The noise in the acquired hyperspectral image (HSI) is generally assumed as additive white Gaussian noise (WGN), while the estimation of the noise in each band of the real-world HSI shows that the noise is not white. Reducing the additive non-white noise is an important preprocessing step to further analyze the information in the HSIs by classification. A PMWF method, prewhitening and MWF (multidimensional Wiener filtering), was suggested and the non-white noise could be whitened by a pre-whitening procedure. While this method is time-consuming due to both the pre-whitening step and the estimation of three ranks of the MWF method. In this paper, we introduce a powerful multilinear algebra model, named parallel factor analysis (PARAFAC), which has only one rank and need not the pre-whitening procedure. To improve the classification, the rank of PARAFAC decomposition is estimated according to the maximum of the overall accuracy (OA) of the support vector machine (SVM) classification. The experiment results show that the PARAFAC model has high efficiency in the reduction of non-white noise and is a preferable preprocessing method for the accuracy improvement of the SVM classification.

The electrocardiogram (ECG) signals provide information for making decisions about different kinds of heart diseases. During decades various approaches have been developed to denoise ECG data and extract useful features, although further increase in the accuracy is required. In this paper, we view the ECG signal as a quasi periodic process and employ the unbiased finite impulse response (UFIR) smoother on optimal horizons. It is shown that the UFIR smoother applied to a harmonic ECG model performs better than that recently developed for polynomial ECG models. Extensive investigation are provided for diverse ECG data. The results are compared in terms of the mean square error and signal-to-noise ratio.

Variational Bayesian State Space Model for dynamic process fault detection

An unbiased finite impulse response (UFIR) filtering algorithm is designed in the discrete-time state-space for industrial processes with unknown measurement data covariance. By assuming an inverse-Wishart distribution, the data noise covariance is recursively estimated using the variational Bayesian (VB) approach. The optimal averaging horizon length N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> is estimated in real time by incorporating the estimated data noise covariance into the full-horizon UFIR filter and specifying N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> at a point, where the estimation error covariance reaches a minimum. The proposed VB-UFIR algorithm is applied to a quadrupled water tank system and moving target tracking. It is demonstrated that the VB-UFIR filter self-estimates N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> more accurately than known solutions. Furthermore, the VB-UFIR filter is not prone to divergence and produces more stable and more reliable estimates than the VB-Kalman filter.