Kalman filter algorithm based on singular value decomposition

2005 ◽  
Author(s):  
L. Wang ◽  
G. Libert ◽  
P. Manneback
Keyword(s):  
Kalman Filter ◽  
Singular Value Decomposition ◽  
Singular Value ◽  
Kalman Filter Algorithm ◽  
Value Decomposition

scholarly journals An Improved Unscented Kalman Filter Algorithm for Radar Azimuth Mutation

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Dazhang You ◽  
Pan Liu ◽  
Wei Shang ◽  
Yepeng Zhang ◽  
Yawei Kang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Singular Value Decomposition ◽  
Unscented Kalman Filter ◽  
Tracking System ◽  
Sudden Change ◽  
Singular Value ◽  
Tracking Accuracy ◽  
Kalman Filter Algorithm ◽  
Value Decomposition ◽  
Accuracy And Stability

An improved UKF (Unscented Kalman Filter) algorithm is proposed to solve the problem of radar azimuth mutation. Since the radar azimuth angle will restart to count after each revolution of the radar, and when the aircraft just passes the abrupt angle change, the radar observation measurement will have a sudden change, which has serious consequences and is solved by the proposed novel UKF based on SVD. In order to improve the tracking accuracy and stability of the radar tracking system further, the SVD-MUKF (Singular Value Decomposition-based Memory Unscented Kalman Filter) based on multiple memory fading is constructed. Furthermore, several simulation results show that the SVD-MUKF algorithm proposed in this paper is better than the SVD-UKF (Singular Value Decomposition of Unscented Kalman Filter) algorithm and classical UKF algorithm in accuracy and stability. Last but not the least, the SVD-MUKF can achieve stable tracking of targets even in the case of angle mutation.

scholarly journals Nonlinear Unknown Input Observer Based on Singular Value Decomposition Aided Reduced Dimension Cubature Kalman Filter

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Wei Zhao ◽  
Huiguang Li ◽  
Liying Zou ◽  
Wenjuan Huang
Keyword(s):  
Kalman Filter ◽  
Singular Value Decomposition ◽  
Integral Form ◽  
Singular Value ◽  
Unknown Input ◽  
Unknown Input Observer ◽  
Proposed Model ◽  
Cubature Kalman Filter ◽  
Reduced Dimension ◽  
Value Decomposition

The paper presents a nonlinear unknown input observer (NUIO) based on singular value decomposition aided reduced dimension Cubature Kalman filter (SVDRDCKF) for a special class of nonlinear systems, the nonlinearity of which is only caused by part of its states. Firstly, the algorithm of general NUIO is discussed and the unknown input observer based on singular value decomposition aided Cubature Kalman filter (SVDCKF) given. Then a special nonlinear system model with unknown input is introduced. Based on the proposed model and the corresponding NUIO, the equivalent integral form with partial sampling and all sampling of the state vector in Cubature Kalman filter is analyzed. Finally the nonlinear unknown input observer based on singular value decomposition aided reduced dimension Cubature Kalman filter is obtained. Simulation results show that the proposed algorithm can meet the requirements of the system and is more important to increase the calculating efficiency a lot, although it has a decline in the accuracy of the filter.

scholarly journals Singular Value Decomposition-based Robust Cubature Kalman Filtering for an Integrated GPS/SINS Navigation System

2014 ◽  
Vol 68 (3) ◽  
pp. 549-562 ◽  
Author(s):  
Qiuzhao Zhang ◽  
Xiaolin Meng ◽  
Shubi Zhang ◽  
Yunjia Wang
Keyword(s):  
Kalman Filter ◽  
Singular Value Decomposition ◽  
Navigation System ◽  
Design Parameter ◽  
Singular Value ◽  
Design Parameters ◽  
Data Sets ◽  
Test Results ◽  
Cubature Kalman Filter ◽  
Value Decomposition

A new nonlinear robust filter is proposed in this paper to deal with the outliers of an integrated Global Positioning System/Strapdown Inertial Navigation System (GPS/SINS) navigation system. The influence of different design parameters for an H∞ cubature Kalman filter is analysed. It is found that when the design parameter is small, the robustness of the filter is stronger. However, the design parameter is easily out of step in the Riccati equation and the filter easily diverges. In this respect, a singular value decomposition algorithm is employed to replace the Cholesky decomposition in the robust cubature Kalman filter. With large conditions for the design parameter, the new filter is more robust. The test results demonstrate that the proposed filter algorithm is more reliable and effective in dealing with the outliers in the data sets produced by the integrated GPS/SINS system.

scholarly journals Engineering Applications of Adaptive Kalman Filtering Based on Singular Value Decomposition (SVD)

2020 ◽  
Vol 10 (15) ◽  
pp. 5168
Author(s):  
Juan Carlos Bermúdez Ordoñez ◽  
Rosa María Arnaldo Valdés ◽  
Victor Fernando Gómez Comendador
Keyword(s):  
Kalman Filter ◽  
Singular Value Decomposition ◽  
Riccati Equation ◽  
Dynamic Models ◽  
Triangular Matrix ◽  
Singular Value ◽  
Estimation Accuracy ◽  
Dual Frequency ◽  
Sensitivity Matrix ◽  
Value Decomposition

This paper presents the results of applying the new mechanization of the Kalman filter (KF) algorithm using singular value decomposition (SVD). The proposed algorithm is useful in applications where the influence of round-off errors reduces the accuracy of the numerical solution of the associated Riccati equation. When the Riccati equation does not remain symmetric and positive definite, the fidelity of the solution can degrade to the point where it corrupts the Kalman gain, and it can corrupt the estimate. In this research, we design an adaptive KF implementation based on SVD, provide its derivation, and discuss the stability issues numerically. The filter is derived by substituting the SVD of the covariance matrix into the conventional discrete KF equations after its initial propagation, and an adaptive estimation of the covariance measurement matrix Rk is introduced. The results show that the algorithm is equivalent to current methods in terms of robustness, and it outperforms the estimation accuracy of the conventional Kalman filter, square root, and unit triangular matrix diagonal (UD) factorization methods under ill-conditioned and dynamic applications, and is applicable to most nonlinear systems. Four sample problems from different areas are presented for comparative study from an ill-conditioned sensitivity matrix, navigation with a dual-frequency Global Positioning System (GPS) receiver, host vehicle dynamic models, and distance measuring equipment (DME) using simultaneous slant range measurements, performed with a conventional KF and SVD-based (K-SVD) filter.

scholarly journals A dynamic adaptive AHRS algorithm for UAV based on SVDCKF

2021 ◽  
Vol 39 (2) ◽  
pp. 350-358
Author(s):  
Yue Yang ◽  
Xiaoxiong Liu ◽  
Weiguo Zhang ◽  
Xuhang Liu ◽  
Yicong Guo
Keyword(s):  
Kalman Filter ◽  
Singular Value Decomposition ◽  
Adaptive Filtering ◽  
Low Cost ◽  
Singular Value ◽  
Noise Variance ◽  
Cubature Kalman Filter ◽  
Value Decomposition ◽  
Solution Accuracy ◽  
Attitude Sensor

Aiming at the attitude solution accuracy and robustness for small UAVs in complex flight conditions, this paper proposes a dynamic adaptive attitude and heading systems(AHRS) estimator with singular value decomposition Cubature Kalman filter(SVDCKF). Considering the problem of random bias for the low-cost attitude sensor, this paper designs a method that the sensor random bias is used as the state vector to eliminate the effect of the sensor random bias. Due to the non-linearity of small UAVs AHRS model and the non-positive definite phenomenon of the covariance matrix, a nonlinear AHRS filter combined with the Cubature Kalman filter and singular value decomposition is designed to improve the attitude solution accuracy. In addition, when the UAV flies in the different flight conditions, the three-axis acceleration of the attitude sensor will affect the attitude solution. Thus, a dynamic adaptive factor based on adaptive filtering is used to adjust continuously the acceleration noise variance to improve the robustness of the AHRS. The experimental results show that the method and algorithm proposed not only improve the attitude solution accuracy, and satisfy the flight requirements of small UAVs, but also eliminate the influence of the attitude sensor random bias and three-axis acceleration for the attitude solution to improve the proposed algorithm robustness and anti-interference.

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