scholarly journals Reduced-Rank Sigma-Point Kalman Filter and Its Application in ENSO Model

2014 ◽  
Vol 31 (10) ◽  
pp. 2350-2366 ◽  
Author(s):  
K. K. Manoj ◽  
Youmin Tang ◽  
Ziwang Deng ◽  
Dake Chen ◽  
Yanjie Cheng
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Unscented Kalman Filter ◽  
Southern Oscillation ◽  
Estimation Accuracy ◽  
Dimensional System ◽  
Square Root ◽  
Reduced Rank ◽  
Sigma Point ◽  
Enso Events

Abstract The huge computational expense has been a main challenge while applying the sigma-point unscented Kalman filter (SPUKF) to a high-dimensional system. This study focuses on this issue and presents two methods to construct a reduced-rank sigma-point unscented Kalman filter (RRSPUKF). Both techniques employ the truncated singular value decomposition (TSVD) to factorize the covariance matrix and reduce its rank through truncation. The reduced-rank square root matrix is used to select the most important sigma points that can retain the main statistical features of the original sigma points. In the first technique, TSVD is applied on the covariance matrix constructed in the data space [RRSPUKF(D)], whereas in the second technique TSVD is applied on the covariance matrix constructed in the ensemble space [RRSPUKF(E)]. The two methods are applied to a realistic El Niño–Southern Oscillation (ENSO) prediction model [Lamont-Doherty Earth Observatory model, version 5 (LDEO5)] to assimilate the sea surface temperature (SST) anomalies. The results show that both the methods are more computationally efficient than the full-rank SPUKF, in spite of losing some estimation accuracy. When the truncation reaches a trade-off between cost expense and estimation accuracy, both methods are able to analyze the phase and intensity of all major ENSO events from 1971 to 2001 with comparable estimation accuracy. Furthermore, the RRSPUKF is compared against ensemble square root filter (EnSRF), showing that the overall analysis skill of RRSPUKF and EnSRF are comparable to each other, but the former is more robust than the latter.

scholarly journals State of Charge Estimation for Lithium-Ion Battery by Using Dual Square Root Cubature Kalman Filter

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Luping Chen ◽  
Liangjun Xu ◽  
Ruoyu Wang
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Lithium Ion ◽  
State Of Charge ◽  
Estimation Accuracy ◽  
Square Root ◽  
Battery Management ◽  
Balance Performance ◽  
Soc Estimation ◽  
Cubature Kalman Filter

The state of charge (SOC) plays an important role in battery management systems (BMS). However, SOC cannot be measured directly and an accurate state estimation is difficult to obtain due to the nonlinear battery characteristics. In this paper, a method of SOC estimation with parameter updating by using the dual square root cubature Kalman filter (DSRCKF) is proposed. The proposed method has been validated experimentally and the results are compared with dual extended Kalman filter (DEKF) and dual square root unscented Kalman filter (DSRUKF) methods. Experimental results have shown that the proposed method has the most balance performance among them in terms of the SOC estimation accuracy, execution time, and convergence rate.

A New Adaptive Square-Root Unscented Kalman Filter for Nonlinear Systems

2013 ◽  
Vol 300-301 ◽  
pp. 623-626 ◽  
Author(s):  
Yong Zhou ◽  
Yu Feng Zhang ◽  
Ju Zhong Zhang
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Covariance Matrix ◽  
Unscented Kalman Filter ◽  
Square Root ◽  
Noise Covariance Matrix ◽  
Measurement Noise Covariance ◽  
Noise Covariance ◽  
The Stability ◽  
Stability And Accuracy

This paper describes a new adaptive filtering approach for nonlinear systems with additive noise. Based on Square-Root Unscented Kalman Filter (SRUKF), the traditional Maybeck’s estimator is modified and extended to the nonlinear systems, the estimation of square root of the process noise covariance matrix Q or measurement noise covariance matrix R is obtained straightforwardly. Then the positive semi-definiteness of Q or R is guaranteed, some shortcomings of traditional Maybeck’s algorithm are overcome, so the stability and accuracy of the filter is improved greatly.

Study on SRUKF Applied in Initial Alignment with Large Misalignment Angle on Stationary Base of SINS

2011 ◽  
Vol 383-390 ◽  
pp. 5088-5093 ◽  
Author(s):  
Kai Cheng ◽  
Chun Mei Huang ◽  
Yue Yuan Zhao
Keyword(s):  
Kalman Filter ◽  
Nonlinear System ◽  
Inertial Navigation System ◽  
Unscented Kalman Filter ◽  
Estimation Accuracy ◽  
Alignment Error ◽  
Square Root ◽  
Misalignment Angle ◽  
Initial Alignment ◽  
Better Than

The initial alignment error model of SINS (Strap-down Inertial Navigation System) with large misalignment angle is nonlinear. The traditional EKF (Extended Kalman Filter) was used to linearization a nonlinear system, but its performance is limited. In this paper we use the SRUKF (Square Root Unscented Kalman Filter) to process this nonlinear system and the results indicate that SRUKF is better than EKF in convergence speed and estimation accuracy.

scholarly journals Multi-Sensor Combined Measurement While Drilling Based on the Improved Adaptive Fading Square Root Unscented Kalman Filter

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 1897
Author(s):  
Yi Yang ◽  
Fei Li ◽  
Yi Gao ◽  
Yanhui Mao
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Unscented Kalman Filter ◽  
Computational Method ◽  
Attitude Measurement ◽  
Square Root ◽  
Drilling Tool ◽  
Measurement While Drilling ◽  
Fading Factor ◽  
Filter Divergence

In the process of the attitude measurement for a steering drilling system, the measurement of the attitude parameters may be uncertain and unpredictable due to the influence of server vibration on bits. In order to eliminate the interference caused by vibration on the measurement and quickly obtain the accurate attitude parameters of the steering drilling tool, a new method for multi-sensor dynamic attitude combined measurement is presented. Firstly, by using a triaxial accelerometer and triaxial magnetometer measurement system, the nonlinear model based on the quaternion is established. Then, an improved adaptive fading square root unscented Kalman filter is proposed for eliminating the vibration disturbance signal. In this algorithm, the square root of the state covariance matrix is used to replace the covariance matrix in the classical unscented Kalman filter (UKF) to avoid the filter divergence caused by the negative definite state covariance matrix. The fading factor is introduced into UKF to adjust the filter gain in real-time and improve the adaptive ability of the algorithm to mutation state. Finally, the computational method of the fading factor is optimized to ensure the self-adaptability of the algorithm and reduce the computational complexity. The results of the laboratory test and the field-drilling data show that the proposed method can filter out the interference noise in the attitude measurement sensor effectively, improve the solution accuracy of attitude parameters of drilling tools in the case of abrupt changes in the measuring environment, and thus ensuring the dynamic stability of the well trajectory.

scholarly journals A New Adaptive Square-Root Unscented Kalman Filter for Nonlinear Systems with Additive Noise

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Yong Zhou ◽  
Chao Zhang ◽  
Yufeng Zhang ◽  
Juzhong Zhang
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Covariance Matrix ◽  
Adaptive Filtering ◽  
Additive Noise ◽  
Unscented Kalman Filter ◽  
Square Root ◽  
Noise Covariance Matrix ◽  
Highly Nonlinear ◽  
Noise Covariance

The Kalman filter (KF), extended KF, and unscented KF all lack a self-adaptive capacity to deal with system noise. This paper describes a new adaptive filtering approach for nonlinear systems with additive noise. Based on the square-root unscented KF (SRUKF), traditional Maybeck’s estimator is modified and extended to nonlinear systems. The square root of the process noise covariance matrixQor that of the measurement noise covariance matrixRis estimated straightforwardly. Because positive semidefiniteness ofQorRis guaranteed, several shortcomings of traditional Maybeck’s algorithm are overcome. Thus, the stability and accuracy of the filter are greatly improved. In addition, based on three different nonlinear systems, a new adaptive filtering technique is described in detail. Specifically, simulation results are presented, where the new filter was applied to a highly nonlinear model (i.e., the univariate nonstationary growth model (UNGM)). The UNGM is compared with the standard SRUKF to demonstrate its superior filtering performance. The adaptive SRUKF (ASRUKF) algorithm can complete direct recursion and calculate the square roots of the variance matrixes of the system state and noise, which ensures the symmetry and nonnegative definiteness of the matrixes and greatly improves the accuracy, stability, and self-adaptability of the filter.

scholarly journals A square root unscented Kalman filter for multiple view geometry based stereo cameras/inertial navigation

2016 ◽  
Vol 13 (5) ◽  
pp. 172988141666485 ◽  
Author(s):  
Zhiwen Xian ◽  
Junxiang Lian ◽  
Mao Shan ◽  
Lilian Zhang ◽  
Xiaofeng He ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Inertial Navigation ◽  
Square Root ◽  
Multiple View Geometry ◽  
Multiple View ◽  
Stereo Cameras

Model aided airborne integrated navigation system based on an improved square-root unscented H∞ filter

2018 ◽  
Vol 41 (5) ◽  
pp. 1290-1300
Author(s):  
Jieliang Shen ◽  
Yan Su ◽  
Qing Liang ◽  
Xinhua Zhu
Keyword(s):  
Kalman Filter ◽  
Navigation System ◽  
Unscented Kalman Filter ◽  
Statistical Characteristics ◽  
Small Scale ◽  
Strong Nonlinearity ◽  
Square Root ◽  
Integrated Navigation ◽  
Fusion Algorithm ◽  
Integrated Navigation System

An inertial navigation system (INS) aided with an aircraft dynamic model (ADM) is developed as a novel airborne integrated navigation system, coping with the absence of a global navigation satellite system. To overcome the shortcomings of the conventional linear integration of INS/ADM based on an extended Kalman filter, a nonlinear integration method is proposed. Fast-update ADM makes it possible to utilize a direct filtering method, which employs nonlinear INS mechanics as system equations and a nonlinear ADM as observation equations, substituting the indirect filtering based on linear error equations. The strong nonlinearity generally calls for an unscented Kalman filter to accomplish the fusion process. Dealing with the model uncertainty, the inaccurate statistical characteristics of the noise and the potential nonpositive definiteness of the covariance matrix, an improved square-root unscented H∞ filter (ISRUHF) is derived in the paper, in which the robust factor [Formula: see text] is further expanded into a diagonal matrix [Formula: see text], to improve the accuracy and robustness of the integrated navigation system. Corresponding simulations as well as real flight tests based on a small-scale fixed-wing aircraft are operated and ISRUHF shows superiority compared with the commonly used fusion algorithm.

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