Explicit Fractional Model Order Estimation Using Unscented and Ensemble Kalman Filters

2011 ◽  
Author(s):  
Michailas Romanovas ◽  
Lasse Klingbeil ◽  
Martin Traechtler ◽  
Yiannos Manoli
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Estimation Method ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Computationally Efficient ◽  
Ensemble Kalman Filters ◽  
Model Order ◽  
Order Estimation ◽  
Augmented State

The article presents an approach for combining methods of recursive Bayesian estimation with models of dynamical systems with varying differentiation order. The work addresses the problem of explicit fractional order estimation and tracking by constructing an efficient Unscented Kalman filter, where the model order is directly estimated within an augmented state along with the variables of interest. The feasibility of the estimation method is assessed using a benchmark problem based on a simplified fractional neuron firing rate model and time-dependent differentiation order. The proposed technique is compared to an implicit method based on Interacting Multiple Model filtering and a computationally efficient method using a modification of the Ensemble Kalman filter. The performance with respect to different parameters and filter settings is analyzed and a corresponding discussion is provided.

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.

State Observers for Suspension Systems with Interacting Multiple Model Unscented Kalman Filter Subject to Markovian Switching

2021 ◽  
Vol 22 (6) ◽  
pp. 1459-1473
Author(s):  
Zipeng Zhang ◽  
Nan Xu ◽  
Hong Chen ◽  
Zhenfeng Wang ◽  
Fei Li ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Markovian Switching ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Suspension Systems ◽  
State Observers

scholarly journals A Grey Model and Mixture Gaussian Residual Analysis-Based Position Estimator in an Indoor Environment

Sensors ◽  
2020 ◽  
Vol 20 (14) ◽  
pp. 3941
Author(s):  
Yan Wang ◽  
Wenjia Ren ◽  
Long Cheng ◽  
Jijun Zou
Keyword(s):  
Kalman Filter ◽  
Measurement Errors ◽  
Unscented Kalman Filter ◽  
Grey Model ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Localization Accuracy ◽  
Gaussian Fitting ◽  
Degree Of Membership ◽  
Measured Distance

As the progress of electronics and information processing technology continues, indoor localization has become a research hotspot in wireless sensor networks (WSN). The adverse non-line of sight (NLOS) propagation usually causes large measurement errors in complex indoor environments. It could decrease the localization accuracy seriously. A traditional grey model considers the motion characteristics but does not take the NLOS propagation into account. A robust interacting multiple model (R-IMM) could effectively mitigate NLOS errors but the clipping point is hard to choose. In order to easily cope with NLOS errors, we present a novel filter framework: mixture Gaussian fitting-based grey Kalman filter structure (MGF-GKFS). Firstly, grey Kalman filter (GKF) is proposed to pre-process the measured distance, which can mitigate the process noise and alleviate NLOS errors. Secondly, we calculate the residual which is the difference between the filtered distance of GKF and the measured distance. Thirdly, a soft decision method based on mixture Gaussian fitting (MGF) is proposed to identify the propagation condition through residual value and give the degree of membership. Fourthly, weak NLOS noise is further processed by unscented Kalman filter (UKF). The filtered results of GKF and UKF are weighted using the degree of membership. Finally, a maximum likelihood (ML) algorithm is applied to get the coordinate of the target. MGF-GKFS is not supported by any of the priori knowledge. Full-scale simulations and an experiment are conducted to compare the localization accuracy and robustness with the state-of-the-art algorithms, including robust interacting multiple model (R-IMM), unscented Kalman filter (UKF) and interacting multiple model (IMM). The results show that MGF-GKFS could achieve significant improvement compared to R-IMM, UKF and IMM algorithms.

IMM-UKF-TFS Model-based Approach for Intelligent Navigation

2013 ◽  
Vol 66 (6) ◽  
pp. 859-877 ◽  
Author(s):  
M. Malleswaran ◽  
V. Vaidehi ◽  
S. Irwin ◽  
B. Robin
Keyword(s):  
Kalman Filter ◽  
Constant Velocity ◽  
Unscented Kalman Filter ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
State Variables ◽  
Constant Acceleration ◽  
Positional Accuracy ◽  
Model Based ◽  
Novel Approach

This paper aims to introduce a novel approach named IMM-UKF-TFS (Interacting Multiple Model-Unscented Kalman Filter-Two Filter Smoother) to attain positional accuracy in the intelligent navigation of a manoeuvring vehicle. Here, the navigation filter is designed with an Unscented Kalman Filter (UKF), together with an Interacting Multiple Model algorithm (IMM), which estimates the state variables and handles the noise uncertainty of the manoeuvring vehicle. A model-based estimator named Two Filter Smoothing (TFS) is implemented along with the UKF-based IMM to improve positional accuracy. The performance of the proposed IMM-UKF-TFS method is verified by modelling the vehicle motion into Constant Velocity-Coordinated Turn (CV-CT), Constant Velocity – Constant Acceleration (CV-CA) and Constant Acceleration-Coordinated Turn (CA-CT) models. The simulation results proved that the proposed IMM-UKF-TFS gives better positional accuracy than the existing conventional estimators such as UKF and IMM-UKF.

scholarly journals A Novel FEM Based T-S Fuzzy Particle Filtering for Bearings-Only Maneuvering Target Tracking

Sensors ◽  
2019 ◽  
Vol 19 (9) ◽  
pp. 2208 ◽  
Author(s):  
Xiaoli Wang ◽  
Liangqun Li ◽  
Weixin Xie
Keyword(s):  
Kalman Filter ◽  
Particle Filtering ◽  
Unscented Kalman Filter ◽  
Fuzzy Model ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Maneuvering Target Tracking ◽  
Model Probability ◽  
Fuzzy Parameter ◽  
Takagi Sugeno

In this paper, we propose a novel fuzzy expectation maximization (FEM) based Takagi-Sugeno (T-S) fuzzy particle filtering (FEMTS-PF) algorithm for a passive sensor system. In order to incorporate target spatial-temporal information into particle filtering, we introduce a T-S fuzzy modeling algorithm, in which an improved FEM approach is proposed to adaptively identify the premise parameters, and the model probability is adjusted by the premise membership functions. In the proposed FEM, the fuzzy parameter is derived by the fuzzy C-regressive model clustering method based on entropy and spatial-temporal characteristics, which can avoid the subjective influence caused by the artificial setting of the initial value when compared to the traditional FEM. Furthermore, using the proposed T-S fuzzy model, the algorithm samples particles, which can effectively reduce the particle degradation phenomenon and the parallel filtering, can realize the real-time performance of the algorithm. Finally, the results of the proposed algorithm are evaluated and compared to several existing filtering algorithms through a series of Monte Carlo simulations. The simulation results demonstrate that the proposed algorithm is more precise, robust and that it even has a faster convergence rate than the interacting multiple model unscented Kalman filter (IMMUKF), interacting multiple model extended Kalman filter (IMMEKF) and interacting multiple model Rao-Blackwellized particle filter (IMMRBPF).

Implicit Fractional Model Order Estimation Using Interacting Multiple Model Kalman Filters

2011 ◽  
Vol 44 (1) ◽  
pp. 7767-7772 ◽  
Author(s):  
Michailas Romanovas ◽  
Ahmed Al-Jawad ◽  
Lasse Klingbeil ◽  
Martin Traechtler ◽  
Yiannos Manoli
Keyword(s):  
Kalman Filters ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Model Order ◽  
Fractional Model ◽  
Order Estimation ◽  
Model Order Estimation

Comparison of Unscented and Extended Kalman Filters with Application in Vehicle Navigation

2016 ◽  
Vol 70 (2) ◽  
pp. 411-431 ◽  
Author(s):  
Cheng Yang ◽  
Wenzhong Shi ◽  
Wu Chen
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Estimation Method ◽  
Field Tests ◽  
Superior Performance ◽  
Vehicle Navigation ◽  
Prototype Model ◽  
Computationally Efficient ◽  
Theoretical Formulation ◽  
Nonlinear State Estimation

The Unscented Kalman Filter (UKF) is a well-known nonlinear state estimation method. It shows superior performance at nonlinear estimation compared to the Extended Kalman Filter (EKF). This paper is devoted to an investigation between UKF and EKF with different feedback control modes in vehicle navigation. Theoretical formulation, simulation and field tests have been carried out to compare the performance of UKF and EKF. The simulation and test results demonstrate that the estimated state of a UKF relies on the measurements and is less sensitive to historical model information. The results also indicate that UKF has benefits for prototype model design due to avoidance of calculation of a Jacobian matrix. EKF, however, is more computationally efficient and more stable.

scholarly journals Design of an Interacting Multiple Model-Cubature Kalman Filter Approach for Vehicle Sideslip Angle and Tire Forces Estimation

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
SuoJun Hou ◽  
Wenbo Xu ◽  
Gang Liu
Keyword(s):  
Kalman Filter ◽  
Estimation Method ◽  
Lateral Acceleration ◽  
Accurate Estimation ◽  
Interacting Multiple Model ◽  
Tire Model ◽  
Multiple Model ◽  
Vehicle Model ◽  
Sideslip Angle ◽  
Cubature Kalman Filter

Vehicle states estimation (e.g., vehicle sideslip angle and tire force) is a key factor for vehicle stability control. However, the accurate values of these parameters could not be obtained directly. In this paper, an interacting multiple model-cubature Kalman filter (IMM-CKF) is used to estimate the vehicle state parameters. And improvements about estimation method are achieved in this paper. Firstly, the accuracy of the reference model is improved by building two different models: one is 7-degree-of-freedom (7 DOF) vehicle model with linear tire model, and the other is 7 DOF vehicle model with nonlinear Dugoff tire model. Secondly, the different models are switched by IMM-CKF to match different driving condition. Thirdly, the lateral acceleration correction for sideslip angle estimation is considered, because the sensor of lateral acceleration is easy to be influenced by the gravity on banked road. Then, to compare cubature Kalman filter (CKF) estimation method and IMM-CKF estimation method Hardware-In-Loop (HIL) tests are carried out in the paper. And simulation results show that IMM-CKF methodology can provide accurate estimation values of vehicle states parameters.

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