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Journal articles on the topic 'Gaussian measures Kalman filtering'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Gou, Linfeng, Ruiqian Sun, and Xiaobao Han. "FDIA System for Sensors of the Aero-Engine Control System Based on the Immune Fusion Kalman Filter." Mathematical Problems in Engineering 2021 (March 18, 2021): 1–17. http://dx.doi.org/10.1155/2021/6662425.

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The Kalman filter plays an important role in the field of aero-engine control system fault diagnosis. However, the design of the Kalman filter bank is complex, the structure is fixed, and the parameter estimation accuracy in the non-Gaussian environment is low. In this study, a new filtering method, immune fusion Kalman filter, was proposed based on the artificial immune system (AIS) theory and the Kalman filter algorithm. The proposed method was used to establish the fault diagnosis, isolation, and accommodation (FDIA) system for sensors of the aero-engine control system. Through a filtering calculation, the FDIA system reconstructs the measured parameters of the faulty sensor to ensure the reliable operation of the aero engine. The AIS antibody library based on single sensor fault was constructed, and with feature combination and library update, the FDIA system can reconstruct the measured values of multiple sensors. The evaluation of the FDIA system performance is based on the Monte Carlo method. Both steady and transient simulation experiments show that, under the non-Gaussian environment, the diagnosis and isolation accuracy of the immune fusion Kalman filter is above 95%, much higher than that of the Kalman filter bank, and compared with the Kalman particle filter, the reconstruction value is smoother, more accurate, and less affected by noise.

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Ali, Wasiq, Yaan Li, Zhe Chen, Muhammad Asif Zahoor Raja, Nauman Ahmed, and Xiao Chen. "Application of Spherical-Radial Cubature Bayesian Filtering and Smoothing in Bearings Only Passive Target Tracking." Entropy 21, no. 11 (November 7, 2019): 1088. http://dx.doi.org/10.3390/e21111088.

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In this paper, an application of spherical radial cubature Bayesian filtering and smoothing algorithms is presented to solve a typical underwater bearings only passive target tracking problem effectively. Generally, passive target tracking problems in the ocean environment are represented with the state-space model having linear system dynamics merged with nonlinear passive measurements, and the system is analyzed with nonlinear filtering algorithms. In the present scheme, an application of spherical radial cubature Bayesian filtering and smoothing is efficiently investigated for accurate state estimation of a far-field moving target in complex ocean environments. The nonlinear model of a Kalman filter based on a Spherical Radial Cubature Kalman Filter (SRCKF) and discrete-time Kalman smoother known as a Spherical Radial Cubature Rauch–Tung–Striebel (SRCRTS) smoother are applied for tracking the semi-curved and curved trajectory of a moving object. The worth of spherical radial cubature Bayesian filtering and smoothing algorithms is validated by comparing with a conventional Unscented Kalman Filter (UKF) and an Unscented Rauch–Tung–Striebel (URTS) smoother. Performance analysis of these techniques is performed for white Gaussian measured noise variations, which is a significant factor in passive target tracking, while the Bearings Only Tracking (BOT) technology is used for modeling of a passive target tracking framework. Simulations based experiments are executed for obtaining least Root Mean Square Error (RMSE) among a true and estimated position of a moving target at every time instant in Cartesian coordinates. Numerical results endorsed the validation of SRCKF and SRCRTS smoothers with better convergence and accuracy rates than that of UKF and URTS for each scenario of passive target tracking problem.

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Ali, Wasiq, Yaan Li, Muhammad Asif Zahoor Raja, Wasim Ullah Khan, and Yigang He. "State Estimation of an Underwater Markov Chain Maneuvering Target Using Intelligent Computing." Entropy 23, no. 9 (August 29, 2021): 1124. http://dx.doi.org/10.3390/e23091124.

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In this study, an application of deep learning-based neural computing is proposed for efficient real-time state estimation of the Markov chain underwater maneuvering object. The designed intelligent strategy is exploiting the strength of nonlinear autoregressive with an exogenous input (NARX) network model, which has the capability for estimating the dynamics of the systems that follow the discrete-time Markov chain. Nonlinear Bayesian filtering techniques are often applied for underwater maneuvering state estimation applications by following state-space methodology. The robustness and precision of NARX neural network are efficiently investigated for accurate state prediction of the passive Markov chain highly maneuvering underwater target. A continuous coordinated turning trajectory of an underwater maneuvering object is modeled for analyzing the performance of the neural computing paradigm. State estimation modeling is developed in the context of bearings only tracking technology in which the efficiency of the NARX neural network is investigated for ideal and complex ocean environments. Real-time position and velocity of maneuvering object are computed for five different cases by varying standard deviations of white Gaussian measured noise. Sufficient Monte Carlo simulation results validate the competence of NARX neural computing over conventional generalized pseudo-Bayesian filtering algorithms like an interacting multiple model extended Kalman filter and an interacting multiple model unscented Kalman filter.

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Mulimani, neshwari, and Aziz Makandar. "Sports Video Annotation and Multi- Target Tracking using Extended Gaussian Mixture model." International Journal of Recent Technology and Engineering 10, no. 1 (May 30, 2021): 1–6. http://dx.doi.org/10.35940/ijrte.a5589.0510121.

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Video offers solutions to many of the traditional problems with coach, trainer, commenter, umpires and other security issues of modern team games. This paper presents a novel framework to perform player identification and tracking technique for the sports (Kabaddi) with extending the implementation towards the event handling process which expands the game analysis of the third umpire assessment. In the proposed methodology, video preprocessing has done with Kalman Filtering (KF) technique. Extended Gaussian Mixture Model (EGMM) implemented to detect the object occlusions and player labeling. Morphological operations have given the more genuine results on player detection on the spatial domain by applying the silhouette spot model. Team localization and player tracking has done with Robust Color Table (RCT) model generation to classify each team members. Hough Grid Transformation (HGT) and Region of Interest (RoI) method has applied for background annotation process. Through which each court line tracing and labeling in the half of the court with respect to their state-of-art for foremost event handling process is performed. Extensive experiments have been conducted on real time video samples to meet out the all the challenging aspects. Proposed algorithm tested on both Self Developed Video (SDV) data and Real Time Video (RTV) with dynamic background for the greater tracking accuracy and performance measures in the different state of video samples.

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Guardeño, Rafael, Manuel J. López, and Víctor M. Sánchez. "MIMO PID Controller Tuning Method for Quadrotor Based on LQR/LQG Theory." Robotics 8, no. 2 (May 1, 2019): 36. http://dx.doi.org/10.3390/robotics8020036.

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In this work, a new pre-tuning multivariable PID (Proportional Integral Derivative) controllers method for quadrotors is put forward. A procedure based on LQR/LQG (Linear Quadratic Regulator/Gaussian) theory is proposed for attitude and altitude control, which suposes a considerable simplification of the design problem due to only one pretuning parameter being used. With the aim to analyze the performance and robustness of the proposed method, a non-linear mathematical model of the DJI-F450 quadrotor is employed, where rotors dynamics, together with sensors drift/bias properties and noise characteristics of low-cost commercial sensors typically used in this type of applications are considered. In order to estimate the state vector and compensate bias/drift effects in the measures, a combination of filtering and data fusion algorithms (Kalman filter and Madgwick algorithm for attitude estimation) are proposed and implemented. Performance and robustness analysis of the control system is carried out by employing numerical simulations, which take into account the presence of uncertainty in the plant model and external disturbances. The obtained results show the proposed controller design method for multivariable PID controller is robust with respect to: (a) parametric uncertainty in the plant model, (b) disturbances acting at the plant input, (c) sensors measurement and estimation errors.

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Tavakoli, Reza, Sanjay Srinivasan, and Mary F. Wheeler. "Rapid Updating of Stochastic Models by Use of an Ensemble-Filter Approach." SPE Journal 19, no. 03 (December 31, 2013): 500–513. http://dx.doi.org/10.2118/163673-pa.

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Summary Applying an ensemble Kalman filter (EnKF) is an effective method for reservoir history matching. The underlying principle is that an initial ensemble of stochastic models can be progressively updated to reflect measured values as they become available. The EnKF performance is only optimal, however, if the prior-state vector is linearly related to the predicted data and if the joint distribution of the prior-state vector is multivariate Gaussian. Therefore, it is challenging to implement the filtering scheme for non-Gaussian random fields, such as channelized reservoirs, in which the continuity of permeability extremes is well-preserved. In this paper, we develop a methodology by combining model classification with multidimensional scaling (MDS) and the EnKF to create rapidly updating models of a channelized reservoir. A dissimilarity matrix is computed by use of the dynamic responses of ensemble members. This dissimilarity matrix is transformed into a lower-dimensional space by use of MDS. Responses mapped in the lower-dimension space are clustered, and on the basis of the distances between the models in a cluster and the actual observed response, the closest models to the observed response are retrieved. Model updates within the closest cluster are performed with EnKF equations. The results of an update are used to resample new models for the next step. Two-dimensional, waterflooding examples of channelized reservoirs are provided to demonstrate the applicability of the proposed method. The obtained results demonstrate that the proposed algorithm is viable both for sequentially updating reservoir models and for preserving channel features after the data-assimilation process.

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Küper, Armin, and Steffen Waldherr. "Numerical Gaussian process Kalman filtering." IFAC-PapersOnLine 53, no. 2 (2020): 11416–21. http://dx.doi.org/10.1016/j.ifacol.2020.12.577.

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Garcia-Fernandez, Angel F., and Lennart Svensson. "Gaussian MAP Filtering Using Kalman Optimization." IEEE Transactions on Automatic Control 60, no. 5 (May 2015): 1336–49. http://dx.doi.org/10.1109/tac.2014.2372909.

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9

Niehsen, W. "Robust Kalman filtering with generalized Gaussian measurement noise." IEEE Transactions on Aerospace and Electronic Systems 38, no. 4 (October 2002): 1409–12. http://dx.doi.org/10.1109/taes.2002.1145765.

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10

Todescato, Marco, Andrea Carron, Ruggero Carli, Gianluigi Pillonetto, and Luca Schenato. "Efficient spatio-temporal Gaussian regression via Kalman filtering." Automatica 118 (August 2020): 109032. http://dx.doi.org/10.1016/j.automatica.2020.109032.

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Dovera, Laura, and Ernesto Della Rossa. "Multimodal ensemble Kalman filtering using Gaussian mixture models." Computational Geosciences 15, no. 2 (August 18, 2010): 307–23. http://dx.doi.org/10.1007/s10596-010-9205-3.

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12

Sasiadek, J. Z., and P. J. Wojcik. "Adaptive Kalman Filtering: A Simulation Result." Journal of Dynamic Systems, Measurement, and Control 110, no. 1 (March 1, 1988): 104–7. http://dx.doi.org/10.1115/1.3152639.

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This paper presents the algorithm for on-line adaptive Kalman filtering of sensor signals with unknown signal to noise ratio. A first order spectrum of a pure signal and white Gaussian measurement noise have been assumed. The results of the performance tests of the algorithm as well as the design methodology of the adaptive filter are given.

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Hoteit, Ibrahim, Xiaodong Luo, and Dinh-Tuan Pham. "Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters." Monthly Weather Review 140, no. 2 (February 2012): 528–42. http://dx.doi.org/10.1175/2011mwr3640.1.

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This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter, but is different from it in that the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the associated covariance matrices in the Gaussian mixture. The authors show that this filter is an algorithm in between the Kalman filter and the particle filter, and therefore is referred to as the particle Kalman filter (PKF). In the PKF, the solution of a nonlinear filtering problem is expressed as the weighted average of an “ensemble of Kalman filters” operating in parallel. Running an ensemble of Kalman filters is, however, computationally prohibitive for realistic atmospheric and oceanic data assimilation problems. For this reason, the authors consider the construction of the PKF through an “ensemble” of ensemble Kalman filters (EnKFs) instead, and call the implementation the particle EnKF (PEnKF). It is shown that different types of the EnKFs can be considered as special cases of the PEnKF. Similar to the situation in the particle filter, the authors also introduce a resampling step to the PEnKF in order to reduce the risk of weights collapse and improve the performance of the filter. Numerical experiments with the strongly nonlinear Lorenz-96 model are presented and discussed.

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Brunot, Mathieu. "A Gaussian Uniform Mixture Model for Robust Kalman Filtering." IEEE Transactions on Aerospace and Electronic Systems 56, no. 4 (August 2020): 2656–65. http://dx.doi.org/10.1109/taes.2019.2953414.

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Nanda, Sumanta Kumar, Guddu Kumar, Vimal Bhatia, and Abhinoy Kumar Singh. "Kalman Filtering With Delayed Measurements in Non-Gaussian Environments." IEEE Access 9 (2021): 123231–44. http://dx.doi.org/10.1109/access.2021.3107466.

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Wang, Shan, and Cheng Gu. "A New Application of Kalman Filtering Algorithm Based on Interval Calculation in Navigation System." Applied Mechanics and Materials 538 (April 2014): 465–69. http://dx.doi.org/10.4028/www.scientific.net/amm.538.465.

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In traditional Kalman filtering algorithm, the system noise and observation noise should be assumed as zero-mean Gaussian white noise, meanwhile need the state-space model and relevant references be given and accurate. However, the white noise is just an ideal noise model that doesnt exist in real environment. This paper analyzed the effect to filtering result from the statistical estimation in traditional Kalman filtering algorithm and brought interval calculation into traditional Kalman filtering algorithm, which based on the concept of interval and could improve the robustness of the system, decrease the error caused by the statistical estimation of noise model.

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Burkhart, Michael C., David M. Brandman, Brian Franco, Leigh R. Hochberg, and Matthew T. Harrison. "The Discriminative Kalman Filter for Bayesian Filtering with Nonlinear and Nongaussian Observation Models." Neural Computation 32, no. 5 (May 2020): 969–1017. http://dx.doi.org/10.1162/neco_a_01275.

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The Kalman filter provides a simple and efficient algorithm to compute the posterior distribution for state-space models where both the latent state and measurement models are linear and gaussian. Extensions to the Kalman filter, including the extended and unscented Kalman filters, incorporate linearizations for models where the observation model [Formula: see text] is nonlinear. We argue that in many cases, a model for [Formula: see text] proves both easier to learn and more accurate for latent state estimation. Approximating [Formula: see text] as gaussian leads to a new filtering algorithm, the discriminative Kalman filter (DKF), which can perform well even when [Formula: see text] is highly nonlinear and/or nongaussian. The approximation, motivated by the Bernstein–von Mises theorem, improves as the dimensionality of the observations increases. The DKF has computational complexity similar to the Kalman filter, allowing it in some cases to perform much faster than particle filters with similar precision, while better accounting for nonlinear and nongaussian observation models than Kalman-based extensions. When the observation model must be learned from training data prior to filtering, off-the-shelf nonlinear and nonparametric regression techniques can provide a gaussian model for [Formula: see text] that cleanly integrates with the DKF. As part of the BrainGate2 clinical trial, we successfully implemented gaussian process regression with the DKF framework in a brain-computer interface to provide real-time, closed-loop cursor control to a person with a complete spinal cord injury. In this letter, we explore the theory underlying the DKF, exhibit some illustrative examples, and outline potential extensions.

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Fasano, Antonio, Alfredo Germani, and Andrea Monteriu. "Reduced-Order Quadratic Kalman-Like Filtering of Non-Gaussian Systems." IEEE Transactions on Automatic Control 58, no. 7 (July 2013): 1744–57. http://dx.doi.org/10.1109/tac.2013.2246474.

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Battilotti, Stefano, Filippo Cacace, Massimiliano d’Angelo, Alfredo Germani, and Bruno Sinopoli. "Kalman-like filtering with intermittent observations and non-Gaussian noise." IFAC-PapersOnLine 52, no. 20 (2019): 61–66. http://dx.doi.org/10.1016/j.ifacol.2019.12.127.

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Chen, Han-Fu, P. R. Kumar, and J. H. van Schuppen. "On Kalman filtering for conditionally Gaussian systems with random matrices." Systems & Control Letters 13, no. 5 (December 1989): 397–404. http://dx.doi.org/10.1016/0167-6911(89)90106-0.

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Li, Zhaoming, and Wenge Yang. "Spherical Simplex-Radial Cubature Quadrature Kalman Filter." Journal of Electrical and Computer Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/7863875.

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A spherical simplex-radial cubature quadrature Kalman filter (SSRCQKF) is proposed in order to further improve the nonlinear filtering accuracy. The Gaussian probability weighted integral of the nonlinear function is decomposed into spherical integral and radial integral, which are approximated by spherical simplex cubature rule and arbitrary order Gauss-Laguerre quadrature rule, respectively, and the novel spherical simplex-radial cubature quadrature rule is obtained. Combined with the Bayesian filtering framework, the general form and the specific form of SSRCQKF are put forward, and the numerical simulation results indicate that the proposed algorithm can achieve a higher filtering accuracy than CKF and SSRCKF.

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Zehnwirth, Ben. "Linear Filtering and Recursive Credibility Estimation." ASTIN Bulletin 15, no. 1 (April 1985): 19–35. http://dx.doi.org/10.2143/ast.15.1.2015030.

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AbstractRecursive credibility estimation is discussed from the viewpoint of linear filtering theory. A conjunction of geometric interpretation and the innovation approach leads to general algorithms not developed before. Moreover, covariance characterizations considered by other researchers drop our elegantly as a result of geometric considerations. Examples are presented of Kalman type filters valid for non-Gaussian measurements.

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Emara-Shabaik, Hosam E. "Filtering of Linear Systems With Unknown Inputs." Journal of Dynamic Systems, Measurement, and Control 125, no. 3 (September 1, 2003): 482–85. http://dx.doi.org/10.1115/1.1591804.

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State estimation of linear systems under the influence of both unknown deterministic inputs as well as Gaussian noise is considered. A Kalman like filter is developed which does not require the estimation of the unknown inputs as is customarily practiced. Therefore, the developed filter has reduced computational requirements. Comparative simulation results, under the influence of various types of unknown disturbance inputs, show the merits of the developed filter with respect to a conventional Kalman filter using disturbance estimation. It is found that the developed filter enjoys several practical advantages in terms of accuracy and fast tracking of the system states.

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Wang, Jiaolong, Chengxi Zhang, Jin Wu, and Ming Liu. "An Improved Invariant Kalman Filter for Lie Groups Attitude Dynamics with Heavy-Tailed Process Noise." Machines 9, no. 9 (August 27, 2021): 182. http://dx.doi.org/10.3390/machines9090182.

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Attitude estimation is a basic task for most spacecraft missions in aerospace engineering and many Kalman type attitude estimators have been applied to the guidance and navigation of spacecraft systems. By building the attitude dynamics on matrix Lie groups, the invariant Kalman filter (IKF) was developed according to the invariance properties of symmetry groups. However, the Gaussian noise assumption of Kalman theory may be violated when a spacecraft maneuvers severely and the process noise might be heavy-tailed, which is prone to degrade IKF’s performance for attitude estimation. To address the attitude estimation problem with heavy-tailed process noise, this paper proposes a hierarchical Gaussian state-space model for invariant Kalman filtering: The probability density function of state prediction is defined based on student’s t distribution, while the conjugate prior distributions of the scale matrix and degrees of freedom (dofs) parameter are respectively formulated as the inverse Wishart and Gamma distribution. For the constructed hierarchical Gaussian attitude estimation state-space model, the Lie groups rotation matrix of spacecraft attitude is inferred together with the scale matrix and dof parameter using the variational Bayesian iteration. Numerical simulation results illustrate that the proposed approach can significantly improve the filtering robustness of invariant Kalman filter for Lie groups spacecraft attitude estimation problems with heavy-tailed process uncertainty.

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Jiang, Ping, Liang Chen, Hang Guo, Min Yu, and Jian Xiong. "Novel indoor positioning algorithm based on Lidar/inertial measurement unit integrated system." International Journal of Advanced Robotic Systems 18, no. 2 (March 1, 2021): 172988142199992. http://dx.doi.org/10.1177/1729881421999923.

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As an important research field of mobile robot, simultaneous localization and mapping technology is the core technology to realize intelligent autonomous mobile robot. Aiming at the problems of low positioning accuracy of Lidar (light detection and ranging) simultaneous localization and mapping with nonlinear and non-Gaussian noise characteristics, this article presents a mobile robot simultaneous localization and mapping method that combines Lidar and inertial measurement unit to set up a multi-sensor integrated system and uses a rank Kalman filtering to estimate the robot motion trajectory through inertial measurement unit and Lidar observations. Rank Kalman filtering is similar to the Gaussian deterministic point sampling filtering algorithm in structure, but it does not need to meet the assumptions of Gaussian distribution. It completely calculates the sampling points and the sampling points weights based on the correlation principle of rank statistics. It is suitable for nonlinear and non-Gaussian systems. With multiple experimental tests of small-scale arc trajectories, we can see that compared with the alone Lidar simultaneous localization and mapping algorithm, the new algorithm reduces the mean error of the indoor mobile robot in the X direction from 0.0928 m to 0.0451 m, with an improved accuracy rate of 46.39%, and the mean error in the Y direction from 0.0772 m to 0.0405 m, which improves the accuracy rate of 48.40%. Compared with the extended Kalman filter fusion algorithm, the new algorithm reduces the mean error of the indoor mobile robot in the X direction from 0.0597 m to 0.0451 m, with an improved accuracy rate of 24.46%, and the mean error in the Y direction from 0.0537 m to 0.0405 m, which improves the accuracy rate of 24.58%. Finally, we also tested on a large-scale rectangular trajectory, compared with the extended Kalman filter algorithm, rank Kalman filtering improves the accuracy of 23.84% and 25.26% in the X and Y directions, respectively, it is verified that the accuracy of the algorithm proposed in this article has been improved.

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Gao, Lian Zhou. "Study on WSN Localization Algorithm and Simulation Model for Intelligent Transportation System." Applied Mechanics and Materials 539 (July 2014): 867–73. http://dx.doi.org/10.4028/www.scientific.net/amm.539.867.

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This paper conducts research on the algorithm to improve the location of Wireless Sensor Network (WSN) in Intelligent Transportation System (ITS). The localization algorithm introduced an improved RSSI vehicle localization algorithm based on multi-path effect and Gaussian white noise. The localization results under different values of Gaussian white noise and different density of beacon nodes are analyzes, and Kalman filtering algorithm is introduced to reduce the influence of signal noise. Finally, a simulation model of ITS is developed to test the algorithm based on mixed noise and Kalman filtering algorithm, which is used to simulate the localization of real vehicles. The simulation shows the algorithm has effect to improve location accuracy and to application

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Li, Zheng Feng, and Lian Zhou Gao. "Study on WSN Localization Algorithm and Simulation Model for Intelligent Transportation System." Applied Mechanics and Materials 548-549 (April 2014): 1407–14. http://dx.doi.org/10.4028/www.scientific.net/amm.548-549.1407.

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This paper conducts research on the algorithm to improve the location of Wireless Sensor Network (WSN) in Intelligent Transportation System (ITS). The localization algorithm introduced an improved RSSI vehicle localization algorithm based on multi-path effect and Gaussian white noise. The localization results under different values of Gaussian white noise and different density of beacon nodes are analyzes, and Kalman filtering algorithm is introduced to reduce the influence of signal noise. Finally, a simulation model of ITS is developed to test the algorithm based on mixed noise and Kalman filtering algorithm, which is used to simulate the localization of real vehicles. The simulation shows the algorithm has effect to improve location accuracy and to application

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Kai, Zhang, and Gan Lin Shan. "Nonlinear Non-Gaussian Filtering Algorithm Based on Cubature Kalman and Particle Filter." Applied Mechanics and Materials 380-384 (August 2013): 1323–26. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.1323.

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To resolve the nonlinear non-Gaussian tracking problem effectively, a novel filtering algorithm based on Cubature Kalman Filter (CKF) and Particle Filters (PF) is proposed, which is called Cubature Kalman Particle Filter (CPF). CKF is used to generate the importance density function for PF. It linearizes the nonlinear functions using statistical linear regression method through a set of Gaussian cubature points. It need not compute the Jacobian matrix. Moreover, it makes efficient use of the latest observation information into system state transition density, thus greatly improving the filter performance. The simulation results show that CPF has higher estimation accuracy and less computational load comparing against the widely used Unscented Particle Filter (UPF).

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Bocquet, M. "Ensemble Kalman filtering without the intrinsic need for inflation." Nonlinear Processes in Geophysics 18, no. 5 (October 20, 2011): 735–50. http://dx.doi.org/10.5194/npg-18-735-2011.

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Abstract. The main intrinsic source of error in the ensemble Kalman filter (EnKF) is sampling error. External sources of error, such as model error or deviations from Gaussianity, depend on the dynamical properties of the model. Sampling errors can lead to instability of the filter which, as a consequence, often requires inflation and localization. The goal of this article is to derive an ensemble Kalman filter which is less sensitive to sampling errors. A prior probability density function conditional on the forecast ensemble is derived using Bayesian principles. Even though this prior is built upon the assumption that the ensemble is Gaussian-distributed, it is different from the Gaussian probability density function defined by the empirical mean and the empirical error covariance matrix of the ensemble, which is implicitly used in traditional EnKFs. This new prior generates a new class of ensemble Kalman filters, called finite-size ensemble Kalman filter (EnKF-N). One deterministic variant, the finite-size ensemble transform Kalman filter (ETKF-N), is derived. It is tested on the Lorenz '63 and Lorenz '95 models. In this context, ETKF-N is shown to be stable without inflation for ensemble size greater than the model unstable subspace dimension, at the same numerical cost as the ensemble transform Kalman filter (ETKF). One variant of ETKF-N seems to systematically outperform the ETKF with optimally tuned inflation. However it is shown that ETKF-N does not account for all sampling errors, and necessitates localization like any EnKF, whenever the ensemble size is too small. In order to explore the need for inflation in this small ensemble size regime, a local version of the new class of filters is defined (LETKF-N) and tested on the Lorenz '95 toy model. Whatever the size of the ensemble, the filter is stable. Its performance without inflation is slightly inferior to that of LETKF with optimally tuned inflation for small interval between updates, and superior to LETKF with optimally tuned inflation for large time interval between updates.

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Chen, Cheng, Xiaogang Wang, Wutao Qin, and Naigang Cui. "Vision-based relative navigation using cubature Huber-based filtering." Aircraft Engineering and Aerospace Technology 90, no. 5 (July 2, 2018): 843–50. http://dx.doi.org/10.1108/aeat-01-2017-0006.

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Purpose A novel vision-based relative navigation system (VBRNS) plays an important role in aeronautics and astronautics fields, and the filter is the core of VBRNS. However, most of the existing filtering algorithms used in VBRNS are derived based on Gaussian assumption and disregard the non-Gaussianity of VBRNS. Therefore, a novel robust filtering named as cubature Huber-based filtering (CHF) is proposed and applied to VBRNS to improve the navigation accuracy in non-Gaussian noise case. Design/methodology/approach Under the Bayesian filter framework, the third-degree cubature rule is used to compute the cubature points which are propagated through state equation, and then the predicted mean and the associated covariance are taken. A combined minimum l1 and l2-norm estimation method referred as Huber’s criterion is used to design the measurement update. After that, the vision-based relative navigation model is presented and the CHF is used to integrate the line-of-sight measurements from vision camera with inertial measurement of the follower to estimate the precise relative position, velocity and attitude between two unmanned aerial vehicles. During the design of relative navigation filter, the quaternions are used to represent the attitude and the generalized Rodrigues parameters are used to represent the attitude error. The simulation is conducted to demonstrate the effectiveness of the algorithm. Findings By this means, the VBRNS could perform better than traditional VBRNS whose filter is designed by Gaussian filtering algorithms. And the simulation results demonstrate that the CHF could exhibit robustness when the system is non-Gaussian. Moreover, the CHF has more accurate estimation and faster rate of convergence than extended Kalman Filtering (EKF) in face of inaccurate initial conditions. Originality/value A novel robust nonlinear filtering algorithm named as CHF is proposed and applied to VBRNS based on cubature Kalman filtering (CKF) and Huber’s technique. The CHF could adapt to the non-Gaussian system effectively and perform better than traditional Gaussian filtering such as EKF.

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Yang, Baojian, Lu Cao, Dechao Ran, and Bing Xiao. "Centered error entropy Kalman filter with application to satellite attitude determination." Transactions of the Institute of Measurement and Control 43, no. 13 (June 21, 2021): 3055–70. http://dx.doi.org/10.1177/01423312211019867.

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Due to unavoidable factors, heavy-tailed noise appears in satellite attitude estimation. Traditional Kalman filter is prone to performance degradation and even filtering divergence when facing non-Gaussian noise. The existing robust algorithms have limited accuracy. To improve the attitude determination accuracy under non-Gaussian noise, we use the centered error entropy (CEE) criterion to derive a new filter named centered error entropy Kalman filter (CEEKF). CEEKF is formed by maximizing the CEE cost function. In the CEEKF algorithm, the prior state values are transmitted the same as the classical Kalman filter, and the posterior states are calculated by the fixed-point iteration method. The CEE EKF (CEE-EKF) algorithm is also derived to improve filtering accuracy in the case of the nonlinear system. We also give the convergence conditions of the iteration algorithm and the computational complexity analysis of CEEKF. The results of the two simulation examples validate the robustness of the algorithm we presented.

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Snyder, Chris, Thomas Bengtsson, Peter Bickel, and Jeff Anderson. "Obstacles to High-Dimensional Particle Filtering." Monthly Weather Review 136, no. 12 (December 1, 2008): 4629–40. http://dx.doi.org/10.1175/2008mwr2529.1.

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Abstract Particle filters are ensemble-based assimilation schemes that, unlike the ensemble Kalman filter, employ a fully nonlinear and non-Gaussian analysis step to compute the probability distribution function (pdf) of a system’s state conditioned on a set of observations. Evidence is provided that the ensemble size required for a successful particle filter scales exponentially with the problem size. For the simple example in which each component of the state vector is independent, Gaussian, and of unit variance and the observations are of each state component separately with independent, Gaussian errors, simulations indicate that the required ensemble size scales exponentially with the state dimension. In this example, the particle filter requires at least 1011 members when applied to a 200-dimensional state. Asymptotic results, following the work of Bengtsson, Bickel, and collaborators, are provided for two cases: one in which each prior state component is independent and identically distributed, and one in which both the prior pdf and the observation errors are Gaussian. The asymptotic theory reveals that, in both cases, the required ensemble size scales exponentially with the variance of the observation log likelihood rather than with the state dimension per se.

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Battaglin, Paulo David, and Gilmar Barreto. "Kalman Filtering Solution Converges on a Personal Computer." Journal of Circuits, Systems and Computers 26, no. 01 (October 4, 2016): 1750005. http://dx.doi.org/10.1142/s0218126617500050.

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Instantaneous observability is used to watch a system output with very fast signals as well as it is a system property that enables to estimate system internal states. This property depends on the pair of discrete matrices [Formula: see text] and it considers that the system state equations are known. The problem is that the system states are inside and they are not always accessible directly. A process, which is a time-varying running program in four parts composes the system under investigation here. It is shown it is possible to apply Kalman filtering on a digital personal computer’s system with particularly the four parts like the ones under investigation. A computing process is performed during a period of time called latency. The calculation of latency considers it as a random variable with Gaussian distribution. The potential application of the results attained is the forecasting of data traffic-jam on a digital personal computer, which has very fast signals inside. In a broader perspective, this method to calculate latency can be applied on other digital personal computer processes such as processes on random access memory. It is also possible to apply this method on local area networks and mainframes.

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Sun, Xu, Jinqiao Duan, Xiaofan Li, and Xiangjun Wang. "State estimation under non-Gaussian Lévy noise: A modified Kalman filtering method." Banach Center Publications 105 (2015): 239–46. http://dx.doi.org/10.4064/bc105-0-14.

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Wu, H., and G. Chen. "Suboptimal Kalman filtering for linear systems with Gaussian-sum type of noise." Mathematical and Computer Modelling 29, no. 3 (February 1999): 101–25. http://dx.doi.org/10.1016/s0895-7177(99)00034-5.

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Ruskeepä, Heikki. "Conditionally gaussian distributions and an application to kalman filtering with stochastic regressors." Communications in Statistics - Theory and Methods 14, no. 12 (January 1985): 2919–42. http://dx.doi.org/10.1080/03610928508829086.

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Xu, Changhui, Xiaoping Rui, Xianfeng Song, and Jingxiang Gao. "Generalized reliability measures of Kalman filtering for precise point positioning." Journal of Systems Engineering and Electronics 24, no. 4 (August 2013): 699–705. http://dx.doi.org/10.1109/jsee.2013.00081.

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Li, Wan Ge, Jin Feng Hu, Hui Ai, Zhi Rong Lin, and Ya Xuan Zhang. "Parameter Estimation of Polynomial Phase Signal by Unscented Kalman Filtering." Applied Mechanics and Materials 644-650 (September 2014): 4253–56. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.4253.

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The parameter estimation of the Polynomial Phase Signals (PPS) is one of the core issues. In this paper, UKF-based algorithm is proposed to estimate the parameter of PPS embedded in Gaussian noise. The algorithm constructs an adequate state-space model to represent the PPS and the model can also be implied in real radar signal. Unscented Kalman filtering is applied to estimate the signal parameters. The method achieves the lower SNR threshold, the faster convergence speed, the higher accuracy and more stable estimation performance compared with the existing methods. Simulation also verifies the efficiency of the proposed method.

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Liu, Bo, Boujemaa Ait-El-Fquih, and Ibrahim Hoteit. "Efficient Kernel-Based Ensemble Gaussian Mixture Filtering." Monthly Weather Review 144, no. 2 (February 1, 2016): 781–800. http://dx.doi.org/10.1175/mwr-d-14-00292.1.

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Abstract The Bayesian filtering problem for data assimilation is considered following the kernel-based ensemble Gaussian mixture filtering (EnGMF) approach introduced by Anderson and Anderson. In this approach, the posterior distribution of the system state is propagated with the model using the ensemble Monte Carlo method, providing a forecast ensemble that is then used to construct a prior Gaussian mixture (GM) based on the kernel density estimator. This results in two update steps: a Kalman filter (KF)-like update of the ensemble members and a particle filter (PF)-like update of the weights, followed by a resampling step to start a new forecast cycle. After formulating EnGMF for any observational operator, the influence of the bandwidth parameter of the kernel function on the covariance of the posterior distribution is analyzed. Then the focus is on two aspects: (i) the efficient implementation of EnGMF with (relatively) small ensembles, where a new deterministic resampling strategy is proposed preserving the first two moments of the posterior GM to limit the sampling error; and (ii) the analysis of the effect of the bandwidth parameter on contributions of KF and PF updates and on the weights variance. Numerical results using the Lorenz-96 model are presented to assess the behavior of EnGMF with deterministic resampling, study its sensitivity to different parameters and settings, and evaluate its performance against ensemble KFs. The proposed EnGMF approach with deterministic resampling suggests improved estimates in all tested scenarios, and is shown to require less localization and to be less sensitive to the choice of filtering parameters.

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Busu, Cristian, and Mihail Busu. "An Application of the Kalman Filter Recursive Algorithm to Estimate the Gaussian Errors by Minimizing the Symmetric Loss Function." Symmetry 13, no. 2 (January 31, 2021): 240. http://dx.doi.org/10.3390/sym13020240.

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Kalman filtering is a linear quadratic estimation (LQE) algorithm that uses a time series of observed data to produce estimations of unknown variables. The Kalman filter (KF) concept is widely used in applied mathematics and signal processing. In this study, we developed a methodology for estimating Gaussian errors by minimizing the symmetric loss function. Relevant applications of the kinetic models are described at the end of the manuscript.

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Omkar Lakshmi Jagan, B., and S. Koteswara Rao. "Underwater surveillance in non-Gaussian noisy environment." Measurement and Control 53, no. 1-2 (January 2020): 250–61. http://dx.doi.org/10.1177/0020294019877515.

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The aim of this paper is to evaluate the performance of different filtering algorithms in the presence of non-Gaussian noise environment for tracking underwater targets, using Doppler frequency and bearing measurements. The tracking using Doppler frequency and bearing measurements is popularly known as Doppler-bearing tracking. Here the measurements, that is, bearings and Doppler frequency, are considered to be corrupted with two types of non-Gaussian noises namely shot noise and Gaussian mixture noise. The non-Gaussian noise sampled measurements are assumed to be obtained (a) randomly throughout the process and (b) repeatedly at some particular time samples. The efficiency of these filters with the increase in non-Gaussian noise samples is discussed in this paper. The performance of filters is compared with that of Cramer-Rao Lower Bound. Doppler-bearing extended Kalman filter and Doppler-bearing unscented Kalman filter are chosen for this work.

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Wang, Yu, Yun Xu, and Xin Hua Zhu. "A Novel Filtering Method for the Random Drift of MEMS Gyroscope." Advanced Materials Research 901 (February 2014): 73–79. http://dx.doi.org/10.4028/www.scientific.net/amr.901.73.

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In engineering application, the nonlinearity effect of the environment noise is inconsistent with the successive starting state of MEMS gyroscope which will induce the random drifts. It manifests as the weak nonlinearity, non stability and slow time varying which cannot be compensated by the conventional method. In order to overcome the problems of the great random drift error model established based on the time series for MEMS gyroscope and the non Gaussian noise, the method of Iteration Unscented Kalman Particle Filter (IUKPF) is proposed in this paper. This method is based on the Particle Filter combing the Unscented Transformation (UT) with Iteration Kalman Filter (IKF), and it solved the instability of the precision for the conventional filtering methods and the degradation for the weight of the particle filter. The filtering result shows that the method of IUKPF can effectively restrain the random drift error under nonlinear and non Gaussian noise. The standard deviation for the output noise of MEMS gyroscope has decreased 81.9% by IUKPF which verifies the efficiency and superiority of this method.

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43

Yuan, Xianghui, Feng Lian, and Chongzhao Han. "Multiple-Model Cardinality Balanced Multitarget Multi-Bernoulli Filter for Tracking Maneuvering Targets." Journal of Applied Mathematics 2013 (2013): 1–16. http://dx.doi.org/10.1155/2013/727430.

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By integrating the cardinality balanced multitarget multi-Bernoulli (CBMeMBer) filter with the interacting multiple models (IMM) algorithm, an MM-CBMeMBer filter is proposed in this paper for tracking multiple maneuvering targets in clutter. The sequential Monte Carlo (SMC) method is used to implement the filter for generic multi-target models and the Gaussian mixture (GM) method is used to implement the filter for linear-Gaussian multi-target models. Then, the extended Kalman (EK) and unscented Kalman filtering approximations for the GM-MM-CBMeMBer filter to accommodate mildly nonlinear models are described briefly. Simulation results are presented to show the effectiveness of the proposed filter.

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Hu, Fengjun. "Target Centroid Position Estimation of Phase-Path Volume Kalman Filtering." Journal of Sensors 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/4879293.

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For the problem of easily losing track target when obstacles appear in intelligent robot target tracking, this paper proposes a target tracking algorithm integrating reduced dimension optimal Kalman filtering algorithm based on phase-path volume integral with Camshift algorithm. After analyzing the defects of Camshift algorithm, compare the performance with the SIFT algorithm and Mean Shift algorithm, and Kalman filtering algorithm is used for fusion optimization aiming at the defects. Then aiming at the increasing amount of calculation in integrated algorithm, reduce dimension with the phase-path volume integral instead of the Gaussian integral in Kalman algorithm and reduce the number of sampling points in the filtering process without influencing the operational precision of the original algorithm. Finally set the target centroid position from the Camshift algorithm iteration as the observation value of the improved Kalman filtering algorithm to fix predictive value; thus to make optimal estimation of target centroid position and keep the target tracking so that the robot can understand the environmental scene and react in time correctly according to the changes. The experiments show that the improved algorithm proposed in this paper shows good performance in target tracking with obstructions and reduces the computational complexity of the algorithm through the dimension reduction.

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Sen, Subhamoy, and Baidurya Bhattacharya. "Non-Gaussian parameter estimation using generalized polynomial chaos expansion with extended Kalman filtering." Structural Safety 70 (January 2018): 104–14. http://dx.doi.org/10.1016/j.strusafe.2017.10.009.

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Ait-El-Fquih, Boujemaa, and Ibrahim Hoteit. "Fast Kalman-Like Filtering for Large-Dimensional Linear and Gaussian State-Space Models." IEEE Transactions on Signal Processing 63, no. 21 (November 2015): 5853–67. http://dx.doi.org/10.1109/tsp.2015.2468674.

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Karavasilis, Vasileios, Christophoros Nikou, and Aristidis Likas. "Visual tracking using the Earth Mover's Distance between Gaussian mixtures and Kalman filtering." Image and Vision Computing 29, no. 5 (April 2011): 295–305. http://dx.doi.org/10.1016/j.imavis.2010.12.002.

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Lei, Jing, Peter Bickel, and Chris Snyder. "Comparison of Ensemble Kalman Filters under Non-Gaussianity." Monthly Weather Review 138, no. 4 (April 1, 2010): 1293–306. http://dx.doi.org/10.1175/2009mwr3133.1.

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Abstract Recently various versions of ensemble Kalman filters (EnKFs) have been proposed and studied. This work concerns, in a mathematically rigorous manner, the relative performance of two major versions of EnKF when the forecast ensemble is non-Gaussian. The approach is based on the stability of the filtering methods against small model violations, using the expected squared L2 distance as a measure of the deviation between the updated distributions. Analytical and experimental results suggest that both stochastic and deterministic EnKFs are sensitive to the violation of the Gaussian assumption, while the stochastic filter is relatively more stable than the deterministic filter under certain circumstances, especially when there are wild outliers. These results not only agree with previous empirical studies, but also suggest a natural choice of a free parameter in the square root Kalman filter algorithm.

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Llerena Caña, Juan Pedro, Jesús García Herrero, and José Manuel Molina López. "Forecasting Nonlinear Systems with LSTM: Analysis and Comparison with EKF." Sensors 21, no. 5 (March 5, 2021): 1805. http://dx.doi.org/10.3390/s21051805.

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Certain difficulties in path forecasting and filtering problems are based in the initial hypothesis of estimation and filtering techniques. Common hypotheses include that the system can be modeled as linear, Markovian, Gaussian, or all at one time. Although, in many cases, there are strategies to tackle problems with approaches that show very good results, the associated engineering process can become highly complex, requiring a great deal of time or even becoming unapproachable. To have tools to tackle complex problems without starting from a previous hypothesis but to continue to solve classic challenges and sharpen the implementation of estimation and filtering systems is of high scientific interest. This paper addresses the forecast–filter problem from deep learning paradigms with a neural network architecture inspired by natural language processing techniques and data structure. Unlike Kalman, this proposal performs the process of prediction and filtering in the same phase, while Kalman requires two phases. We propose three different study cases of incremental conceptual difficulty. The experimentation is divided into five parts: the standardization effect in raw data, proposal validation, filtering, loss of measurements (forecasting), and, finally, robustness. The results are compared with a Kalman filter, showing that the proposal is comparable in terms of the error within the linear case, with improved performance when facing non-linear systems.

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Inoue, A., Y. Nakano, and V. Anh. "Linear filtering of systems with memory and application to finance." Journal of Applied Mathematics and Stochastic Analysis 2006 (February 28, 2006): 1–26. http://dx.doi.org/10.1155/jamsa/2006/53104.

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We study the linear filtering problem for systems driven by continuous Gaussian processes V(1) and V(2) with memory described by two parameters. The processes V(j) have the virtue that they possess stationary increments and simple semimartingale representations simultaneously. They allow for straightforward parameter estimations. After giving the semimartingale representations of V(j) by innovation theory, we derive Kalman-Bucy-type filtering equations for the systems. We apply the result to the optimal portfolio problem for an investor with partial observations. We illustrate the tractability of the filtering algorithm by numerical implementations.

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