On kalman filter for linear system with colored measurement noise

Abstract The strapdown inertial navigation system (SINS) with integrated Doppler velocity log (DVL) is widely utilised in underwater navigation. In the complex underwater environment, however, the DVL information may be corrupted, and as a result the accuracy of the Kalman filter in the SINS/DVL integrated system degrades. To solve this, an adaptive Kalman filter (AKF) with measurement noise estimator to provide noise statistical characteristics is generally applied. However, existing methods like moving windows (MW) and exponential weighted moving average (EWMA) cannot adapt to a dynamic environment, which results in unsatisfactory noise estimation performance. Moreover, the forgetting factor has to be determined empirically. Therefore, this paper proposes an improved EWMA (IEWMA) method with adaptive forgetting factor for measurement noise estimation. First, the model for a SINS/DVL integrated system is established, then the MW and EWMA based measurement noise estimators are illustrated. Subsequently, the proposed IEWMA method which is adaptive to the various environments without experience is introduced. Finally, simulation and vehicle tests are conducted to evaluate the effectiveness of the proposed method. Results show that the proposed method outperforms the MW and EWMA methods in terms of measurement noise estimation and navigation accuracy.

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A Novel Robust Kalman Filter With Non-stationary Heavy-tailed Measurement Noise

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2020.12.188 ◽

2020 ◽

Vol 53 (2) ◽

pp. 368-373

Author(s):

Guangle Jia ◽

Yulong Huang ◽

Mingming B. Bai ◽

Yonggang zhang

Keyword(s):

Kalman Filter ◽

Measurement Noise ◽

Robust Kalman Filter ◽

Heavy Tailed

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

Sensors ◽

10.3390/s18113809 ◽

2018 ◽

Vol 18 (11) ◽

pp. 3809 ◽

Cited By ~ 6

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.

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

ISPRS Annals of Photogrammetry Remote Sensing and Spatial Information Sciences ◽

10.5194/isprsannals-ii-2-61-2014 ◽

2014 ◽

Vol II-2 ◽

pp. 61-66 ◽

Cited By ~ 2

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 pairwise 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 k is not only correlated with the one from epoch k – 1 but also with the ones before epoch k – 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.

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Drag Coefficient Identification from Flight Data via Optimal Observer

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.687-691.787 ◽

2014 ◽

Vol 687-691 ◽

pp. 787-790

Author(s):

Rong Jun Yang ◽

Yao Ye

Keyword(s):

Parameter Estimation ◽

Kalman Filter ◽

Drag Coefficient ◽

Dynamic Equation ◽

Unscented Kalman Filter ◽

Flight Test ◽

Measurement Noise ◽

Estimation Technique ◽

Flight Data ◽

Coefficient Identification

. For effectively using flight test data to extract drag coefficient, an optimal observer based on parameter estimation technique is proposed. The point mass dynamic equation is used to form the Unscented Kalman Filter (UKF) and the smoother (URTSS) for the estimation of a projectile’s flight states. The projectile flight states are then solved and utilized to extract the drag coefficient information using the observer techniques. The simulation verifies the feasibility of the method: with measurement noise, the accurate drag coefficient is obtained by using the smoother.

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A normal‐gamma‐based adaptive dual unscented Kalman filter for battery parameters and state‐of‐charge estimation with heavy‐tailed measurement noise

International Journal of Energy Research ◽

10.1002/er.5042 ◽

2020 ◽

Vol 44 (5) ◽

pp. 3510-3525 ◽

Cited By ~ 2

Author(s):

Jing Hou ◽

Yan Yang ◽

Tian Gao

Keyword(s):

Kalman Filter ◽

Unscented Kalman Filter ◽

State Of Charge ◽

Measurement Noise ◽

Heavy Tailed ◽

State Of Charge Estimation

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Volterra filter modelling of non-linear system using Artificial Electric Field algorithm assisted Kalman filter and its experimental evaluation

ISA Transactions ◽

10.1016/j.isatra.2020.09.010 ◽

2020 ◽

Author(s):

L. Janjanam ◽

S.K. Saha ◽

R. Kar ◽

D. Mandal

Keyword(s):

Kalman Filter ◽

Linear System ◽

Electric Field ◽

Experimental Evaluation ◽

Volterra Filter ◽

Non Linear ◽

Non Linear System

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

Complexity ◽

10.1155/2020/4361812 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11 ◽

Cited By ~ 1

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.

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

Applied Sciences ◽

10.3390/app9091726 ◽

2019 ◽

Vol 9 (9) ◽

pp. 1726 ◽

Cited By ~ 8

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.

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