The modified extended Kalman filter based recursive estimation for Wiener nonlinear systems with process noise and measurement noise

2020 ◽  
Vol 34 (10) ◽  
pp. 1321-1340
Author(s):  
Xuehai Wang ◽  
Fang Zhu ◽  
Feng Ding
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Extended Kalman Filter ◽  
Recursive Estimation ◽  
Measurement Noise ◽  
Process Noise

Data Assimilation of River Networks Using Extended Kalman Filter

2014 ◽  
Vol 580-583 ◽  
pp. 1923-1927
Author(s):  
Yi Fan Chen ◽  
Jing Lin Qian
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Real Time ◽  
Extended Kalman Filter ◽  
River Network ◽  
Measurement Noise ◽  
River Networks ◽  
Network System ◽  
Process Noise ◽  
Measurement Noises

In order to improve the accuracy of river network hydraulic model, extended kalman filter was used for real-time updating model states. In a simulation example of a river network composed of 14 channels, it systematically analyzed the effects of process and measurement noises on state correction. The results show that the extended kalman filter is able to effectively carry out data assimilation of non-linear river network system, and big process noise in combination with relatively small measurement noise is recommended for state correction.

scholarly journals A Modified Extended Kalman Filter for a Two-Antenna GPS/INS Vehicular Navigation System

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3809 ◽  
Author(s):  
Yushi Hao ◽  
Aigong Xu ◽  
Xin Sui ◽  
Yulei Wang
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Navigation System ◽  
Adaptive Estimation ◽  
Estimation Method ◽  
Measurement Noise ◽  
Model Errors ◽  
State Process ◽  
Stability And Accuracy ◽  
The Impact

Recently, the integration of an inertial navigation system (INS) and the Global Positioning System (GPS) with a two-antenna GPS receiver has been suggested to improve the stability and accuracy in harsh environments. As is well known, the statistics of state process noise and measurement noise are critical factors to avoid numerical problems and obtain stable and accurate estimates. In this paper, a modified extended Kalman filter (EKF) is proposed by properly adapting the statistics of state process and observation noises through the innovation-based adaptive estimation (IAE) method. The impact of innovation perturbation produced by measurement outliers is found to account for positive feedback and numerical issues. Measurement noise covariance is updated based on a remodification algorithm according to measurement reliability specifications. An experimental field test was performed to demonstrate the robustness of the proposed state estimation method against dynamic model errors and measurement outliers.

scholarly journals Discrete EKF with pairwise Time Correlated Measurement Noise for Image-Aided Inertial Integrated Navigation

2014 ◽  
Vol II-2 ◽  
pp. 61-66 ◽  
Author(s):  
N. S. Gopaul ◽  
J. G. Wang ◽  
B. Hu
Keyword(s):  
Kalman Filter ◽  
Inertial Navigation ◽  
Measurement Noise ◽  
Integrated Navigation ◽  
Process Noise ◽  
Shaping Filter ◽  
Egomotion Estimation ◽  
Simulation Results ◽  
The One ◽  
Better Than

An image-aided inertial navigation implies that the errors of an inertial navigator are estimated via the Kalman filter using the aiding measurements derived from images. The standard Kalman filter runs under the assumption that the process noise vector and measurement noise vector are white, i.e. independent and normally distributed with zero means. However, this does not hold in the image-aided inertial navigation. In the image-aided inertial integrated navigation, the relative positions from optic-flow egomotion estimation or visual odometry are <i>pairwise</i> correlated in terms of time. It is well-known that the solution of the standard Kalman filter becomes suboptimal if the measurements are colored or time-correlated. Usually, a shaping filter is used to model timecorrelated errors. However, the commonly used shaping filter assume that the measurement noise vector at epoch <i>k</i> is not only correlated with the one from epoch <i>k</i> &ndash; 1 but also with the ones before epoch <i>k</i> &ndash; 1 . The shaping filter presented in this paper uses Cholesky factors under the assumption that the measurement noise vector is pairwise time-correlated i.e. the measurement noise are only correlated with the ones from previous epoch. Simulation results show that the new algorithm performs better than the existing algorithms and is optimal.

scholarly journals Tracking: B

2021 ◽  
pp. 193-204
Author(s):  
Jean Walrand
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
Extended Kalman Filter ◽  
Random Variable

AbstractIn Chapter Tracking: A, we explained the estimation of a random variable based on observations. We also described the Kalman filter and we gave a number of examples. In this chapter, we derive the Kalman filter and explain some of its properties. We also discuss the extended Kalman filter.Section 10.1 explains how to update an estimate as one makes additional observations. Section 10.2 derives the Kalman filter. The properties of the Kalman filter are explained in Sect. 10.3. Section 10.4 shows how the Kalman filter is extended to nonlinear systems.

scholarly journals Performance Enhancement of Pedestrian Navigation Systems Based on Low-Cost Foot-Mounted MEMS-IMU/Ultrasonic Sensor

Sensors ◽  
2019 ◽  
Vol 19 (2) ◽  
pp. 364 ◽  
Author(s):  
Ming Xia ◽  
Chundi Xiu ◽  
Dongkai Yang ◽  
Li Wang
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Navigation System ◽  
Low Cost ◽  
Ultrasonic Sensor ◽  
Measurement Unit ◽  
Positioning Error ◽  
Process Noise ◽  
Pedestrian Navigation ◽  
Mems Imu

The pedestrian navigation system (PNS) based on inertial navigation system-extended Kalman filter-zero velocity update (INS-EKF-ZUPT or IEZ) is widely used in complex environments without external infrastructure owing to its characteristics of autonomy and continuity. IEZ, however, suffers from performance degradation caused by the dynamic change of process noise statistics and heading estimation errors. The main goal of this study is to effectively improve the accuracy and robustness of pedestrian localization based on the integration of the low-cost foot-mounted microelectromechanical system inertial measurement unit (MEMS-IMU) and ultrasonic sensor. The proposed solution has two main components: (1) the fuzzy inference system (FIS) is exploited to generate the adaptive factor for extended Kalman filter (EKF) after addressing the mismatch between statistical sample covariance of innovation and the theoretical one, and the fuzzy adaptive EKF (FAEKF) based on the MEMS-IMU/ultrasonic sensor for pedestrians was proposed. Accordingly, the adaptive factor is applied to correct process noise covariance that accurately reflects previous state estimations. (2) A straight motion heading update (SMHU) algorithm is developed to detect whether a straight walk happens and to revise errors in heading if the ultrasonic sensor detects the distance between the foot and reflection point of the wall. The experimental results show that horizontal positioning error is less than 2% of the total travelled distance (TTD) in different environments, which is the same order of positioning error compared with other works using high-end MEMS-IMU. It is concluded that the proposed approach can achieve high performance for PNS in terms of accuracy and robustness.

scholarly journals Improved Pedestrian Positioning with Inertial Sensor Based on Adaptive Gradient Descent and Double-Constrained Extended Kalman Filter

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Miaoxin Ji ◽  
Jinhao Liu ◽  
Xiangbo Xu ◽  
Yuyang Guo ◽  
Zhenchun Lu
Keyword(s):  
Kalman Filter ◽  
Angular Velocity ◽  
Extended Kalman Filter ◽  
Gradient Descent ◽  
Measurement Noise ◽  
Measurement Unit ◽  
Alignment Algorithm ◽  
Extended Kalman Filtering ◽  
Attitude Error ◽  
Gradient Descent Algorithm

The Foot-mounted Inertial Pedestrian-Positioning System (FIPPS) based on the Micro-Inertial Measurement Unit (MIMU) is a good choice for the forest fire fighters when the Global Navigation Satellite System is unavailable. Zero Velocity Update (ZUPT) provides a solution for reducing cumulative positioning errors caused by the integral calculation of the inertial navigation. However, the performance of ZUPT is highly affected by the low accuracy and high noise of the MIMU. The accuracy of conventional ZUPT for attitude alignment is reduced by the zero offset of acceleration and the drift of a gyroscope during the standing phase. An initial alignment algorithm based on Adaptive Gradient Descent Algorithm (AGDA) is proposed. In the stepping phase, the extended Kalman filter (EKF) is often used to correct attitude and position in track estimation. However, the measurement noise of the EKF is influenced by the high-frequency acceleration and angular velocity. Thus, the accuracy of the attitude and position will decrease. A double-constrained extended Kalman filtering (DEKF) is proposed. An adaptive parameter positively correlated with the acceleration and angular velocity is set, and the measurement noise in the DEKF is adaptively adjusted. The performance of the proposed method is verified by implementing the pedestrian test trajectory using MPU-9150 MIMU manufactured by InvenSense. The results show that the attitude error of the AGDA is 33.82% less than that of the conventional GDA. The attitude error of DEKF is 21.70% less than that of the conventional EKF. The experimental results verify the effectiveness and applicability of the proposed method.

scholarly journals Adaptive Dual Extended Kalman Filter Based on Variational Bayesian Approximation for Joint Estimation of Lithium-Ion Battery State of Charge and Model Parameters

2019 ◽  
Vol 9 (9) ◽  
pp. 1726 ◽  
Author(s):  
Jing Hou ◽  
Yan Yang ◽  
He He ◽  
Tian Gao
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Lithium Ion ◽  
Measurement Noise ◽  
Estimation Accuracy ◽  
Variational Bayesian ◽  
Soc Estimation ◽  
Bayesian Approximation ◽  
Noise Statistics ◽  
Discharge Test

An accurate state of charge (SOC) estimation is vital for the safe operation and efficient management of lithium-ion batteries. At present, the extended Kalman filter (EKF) can accurately estimate the SOC under the condition of a precise battery model and deterministic noise statistics. However, in practical applications, the battery characteristics change with different operating conditions and the measurement noise statistics may vary with time, resulting in nonoptimal and even unreliable estimation of SOC by EKF. To improve the SOC estimation accuracy under uncertain measurement noise statistics, a variational Bayesian approximation-based adaptive dual extended Kalman filter (VB-ADEKF) is proposed in this paper. The variational Bayesian inference is integrated with the dual EKF (DEKF) to jointly estimate the lithium-ion battery parameters and SOC. Meanwhile, the measurement noise variances are simultaneously estimated in the SOC estimation process to compensate for the model uncertainties, so that the adaptability of the proposed algorithm to dynamic changes in battery characteristics is greatly improved. A constant current discharge test, a pulse current discharge test, and an urban dynamometer driving schedule (UDDS) test are performed to verify the effectiveness and superiority of the proposed algorithm by comparison with the DEKF algorithm. The experimental results show that the proposed VB-ADEKF algorithm outperforms the traditional DEKF algorithm in terms of SOC estimation accuracy, convergence rate, and robustness.

Sign in / Sign up

Export Citation Format

Share Document