scholarly journals Spherical Simplex-Radial Cubature Quadrature Kalman Filter

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Zhaoming Li ◽  
Wenge Yang
Keyword(s):  
Kalman Filter ◽  
Nonlinear Filtering ◽  
Arbitrary Order ◽  
Nonlinear Function ◽  
Quadrature Rule ◽  
Specific Form ◽  
Bayesian Filtering ◽  
The Novel ◽  
Weighted Integral ◽  
Spherical Simplex

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.

scholarly journals A Novel Fifth-Degree Cubature Kalman Filter for Real-Time Orbit Determination by Radar

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Zhaoming Li ◽  
Wenge Yang ◽  
Dan Ding ◽  
Yurong Liao
Keyword(s):  
Kalman Filter ◽  
Real Time ◽  
Orbit Determination ◽  
Nonlinear Function ◽  
State Equation ◽  
Bayesian Filtering ◽  
Measurement Equation ◽  
J2 Perturbation ◽  
Cubature Kalman Filter ◽  
Weighted Integral

A novel fifth-degree cubature Kalman filter is proposed to improve the accuracy of real-time orbit determination by ground-based radar. A fully symmetric cubature rule, approaching the Gaussian weighted integral of a nonlinear function in general form, is introduced, and the specific points and weights are calculated by matching the monomials of degree not greater than five with the exact values. On the basis of the above rule, a novel fifth-degree cubature Kalman filter, which can achieve a higher accuracy than UKF and CKF, is derived under the Bayesian filtering framework. Then, to describe the nonlinear system more accurately, the orbital dynamics equation with J2 perturbation is used as the state equation, and the nonlinear relationship between the radar measurement elements and orbital states is built as the measurement equation. The simulation results show that, compared with the traditional third-degree algorithm, the proposed fifth-degree algorithm has a higher accuracy of orbit determination.

scholarly journals Application of Improved Simplex Quadrature Cubature Kalman Filter in Nonlinear Dynamic System

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ting Cao ◽  
Huo-tao Gao ◽  
Chun-feng Sun ◽  
Yun Ling ◽  
Guo-bao Ru
Keyword(s):  
Kalman Filter ◽  
Dynamic System ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic System ◽  
Quadrature Rule ◽  
Estimation Accuracy ◽  
Nonlinear State Estimation ◽  
Cubature Kalman Filter ◽  
Weighted Integral ◽  
Spherical Simplex

A novel spherical simplex Gauss–Laguerre quadrature cubature Kalman filter is proposed to improve the estimation accuracy of nonlinear dynamic system. The nonlinear Gaussian weighted integral has been approximately evaluated using the spherical simplex rule and the arbitrary order Gauss–Laguerre quadrature rule. Thus, a spherical simplex Gauss–Laguerre cubature quadrature rule is developed, from which the general computing method of the simplex cubature quadrature points and the corresponding weights are obtained. Then, under the nonlinear Kalman filtering framework, the spherical simplex Gauss–Laguerre quadrature cubature Kalman filter is derived. A high-dimensional nonlinear state estimation problem and a target tracking problem are utilized to demonstrate the effectiveness of the proposed spherical simplex Gauss–Laguerre cubature quadrature rule to improve the performance.

Spherical Simplex Unscented Kalman Filter-Based Jumping and Static Interacting Multiple Model

2017 ◽  
Vol 32 (04) ◽  
pp. 1850010
Author(s):  
Yi Pan ◽  
Hui Ye ◽  
Keke He
Keyword(s):  
Kalman Filter ◽  
Nonlinear Filtering ◽  
System Parameter ◽  
Unscented Kalman Filter ◽  
Continuous System ◽  
The State ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Real Time System ◽  
Spherical Simplex

A modified interacting multiple model (IMM) method called spherical simplex unscented Kalman filter-based jumping and static IMM (SSUKF-JSIMM) is proposed to solve the problem of nonlinear filtering with unknown continuous system parameter. SSUKF-JSIMM regards the continuous system parameter space as a union of disjoint regions, and each region is assigned to a model. For each model, under the assumption that the parameter belongs to the corresponding region, one sub-filter is used to estimate the parameter and the state when the parameter is presumed to be jumping, and another sub-filter is used to estimate the parameter and the state when the parameter is presumed to be static. Considering that spherical simplex unscented Kalman filter (SSUKF) is more suitable for a real-time system than the unscented Kalman filter (UKF), SSUKFs are adopted as the sub-filters of SSUKF-JSIMM. Results of the two SSUKFs are fused as the estimation output of the model. Experimental results show that SSUKF-JSIMM achieves higher performance than IMM, SIR, and UKF in bearings-only tracking problem.

A New Nonlinear Filter Method for Ballistic Target Tracking

2011 ◽  
Vol 135-136 ◽  
pp. 99-105
Author(s):  
Chun Ling Wu ◽  
Yong Feng Ju
Keyword(s):  
Kalman Filter ◽  
Target Tracking ◽  
Nonlinear Filtering ◽  
Quadrature Rule ◽  
Filter Method ◽  
Square Root ◽  
Numerical Accuracy ◽  
Filtering Algorithm ◽  
The Mean ◽  
Gauss Hermite Quadrature

In order to track the ballistic re-entry target, a new kind of ballistic target tracking algorithm, square-root quadrature Kalman filter (SRQKF) algorithm, was proposed. The proposed algorithm is the square-root implementation of the quadrature Kalman filter (QKF). The quadrature Kalman filter is a recursive, nonlinear filtering algorithm developed in the Kalman filtering framework and computes the mean and covariance of all conditional densities using the Gauss-Hermite quadrature rule. The square-root quadrature Kalman filter propagates the mean and the square root of the covariance. It guarantees the symmetry and positive semi-definiteness of the covariance matrix, improved numerical stability and the numerical accuracy, but at the expense of increased computational complexity slightly.

scholarly journals Application of Spherical-Radial Cubature Bayesian Filtering and Smoothing in Bearings Only Passive Target Tracking

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1088 ◽  
Author(s):  
Wasiq Ali ◽  
Yaan Li ◽  
Zhe Chen ◽  
Muhammad Asif Zahoor Raja ◽  
Nauman Ahmed ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Target Tracking ◽  
Nonlinear Filtering ◽  
Unscented Kalman Filter ◽  
State Space Model ◽  
Moving Target ◽  
Bayesian Filtering ◽  
Tracking Problem ◽  
Cubature Kalman Filter ◽  
Passive Target Tracking

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.

scholarly journals Simplex Cubature Kalman-Consensus Filter for Distributed Space Target Tracking

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Zhaoming Li ◽  
Wenge Yang ◽  
Dan Ding ◽  
Yurong Liao
Keyword(s):  
Target Tracking ◽  
Quadrature Rule ◽  
Measurement Model ◽  
Linear Regression Method ◽  
Tracking Accuracy ◽  
Cubature Rule ◽  
Weighted Integral ◽  
Spherical Simplex ◽  
Consensus Filter ◽  
Space Target

A simplex cubature Kalman-consensus filter, which is suitable for distributed space target tracking using multiple radars, is proposed to improve the target tracking accuracy. The detailed orbital dynamics model and radar measurement model are given as the system filtering models. The intractable nonlinear Gaussian weighted integral in the filter is decomposed into the spherical integral and radial integral, which are calculated using the spherical simplex rule and the second-order Gauss-Laguerre quadrature rule, respectively. In this way, a new simplex cubature rule is derived. By means of the statistical linear regression method, the posterior mean, covariance, and the transmitted messages in the extended Kalman-consensus filter are approximated using the deduced simplex cubature rule, which results in the proposed simplex cubature Kalman-consensus filter. No data fusion center exists in the filter, and each radar only needs to exchange the information with its neighbors to reach a consensus estimate. The simulation results show that the proposed filter can achieve more accurate results compared with the cubature Kalman-consensus filter.

TWO-SCROLL ATTRACTOR IN A DELAY DYNAMICAL SYSTEM

2007 ◽  
Vol 17 (10) ◽  
pp. 3455-3460 ◽  
Author(s):  
ARŪNAS TAMAŠEVIČIUS ◽  
TATJANA PYRAGIENĖ ◽  
MANTAS MEŠKAUSKAS
Keyword(s):  
Dynamical System ◽  
Time Delay ◽  
Nonlinear Function ◽  
Delay System ◽  
The Novel ◽  
Type Function ◽  
Delay Dynamical System ◽  
Glass Type ◽  
Electronic Oscillator

Nonvanishing 𐑍-shaped nonlinear function has been introduced in delay dynamical system instead of commonly used Mackey–Glass type function. Depending on time delay the system exhibits not only mono-scroll, but also more complex two-scroll hyperchaotic attractors. Delay system with the novel nonlinear function can be implemented as an analogue electronic oscillator.

scholarly journals Tracking of pendulum using particle filter with residual resampling

2018 ◽  
Vol 7 (2.7) ◽  
pp. 12
Author(s):  
Penumarty Hiranmayi ◽  
Kola Sai Gowtham ◽  
S Koteswara Rao ◽  
V Gopi Tilak
Keyword(s):  
Monte Carlo ◽  
Kalman Filter ◽  
Particle Filter ◽  
Extended Kalman Filter ◽  
Horizontal Direction ◽  
Bayesian Filtering ◽  
Discrete State ◽  
Harmonic Motion ◽  
Simple Pendulum ◽  
Importance Resampling

The phenomenon of simple harmonic motion is more vigilantly explained using a simple pendulum. The angular motion of a pendulum is linear in nature. But the analysis of the motion along the horizontal direction is non-linear. To estimate this, several algorithms like the Kalman filter, Extended Kalman Filter etc. are adopted. Here in this paper, Particle filter is chosen which is a method to form Monte Carlo approximations to the solutions of Bayesian filtering equations. Sequential importance resampling based Particle filters are used where the filtering distributions are multi-nodal or consist of discrete state components since under these circumstances the Bayesian approximations do not always work well.

An Implicit Algorithm of Solving Nonlinear Filtering Problems

2014 ◽  
Vol 16 (2) ◽  
pp. 382-402
Author(s):  
Feng Bao ◽  
Yanzhao Cao ◽  
Xiaoying Han
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
Nonlinear Filtering ◽  
State Equation ◽  
Nonlinear Filter ◽  
Filter Method ◽  
Simulation Methods ◽  
Current State ◽  
Numerical Simulation Methods ◽  
Kalman Filter Method

AbstractNonlinear filter problems arise in many applications such as communications and signal processing. Commonly used numerical simulation methods include Kalman filter method, particle filter method, etc. In this paper a novel numerical algorithm is constructed based on samples of the current state obtained by solving the state equation implicitly. Numerical experiments demonstrate that our algorithm is more accurate than the Kalman filter and more stable than the particle filter.

scholarly journals A New Linear Regression Kalman Filter with Symmetric Samples

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2139
Author(s):  
Xiuqiong Chen ◽  
Jiayi Kang ◽  
Mina Teicher ◽  
Stephen S.-T. Yau
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Particle Filter ◽  
Normal Distribution ◽  
Extended Kalman Filter ◽  
Nonlinear Filtering ◽  
Unscented Kalman Filter ◽  
Standard Normal Distribution ◽  
Leibler Divergence ◽  
Standard Normal

Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.

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