scholarly journals The State Space Subdivision Filter for Estimation on SE(2)

Sensors ◽  
2021 ◽  
Vol 21 (18) ◽  
pp. 6314
Author(s):  
Florian Pfaff ◽  
Kailai Li ◽  
Uwe D. Hanebeck
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Unscented Kalman Filter ◽  
Linear Part ◽  
The State ◽  
Conditional Density ◽  
Periodic Part ◽  
Order Of Magnitude ◽  
Circular Domains ◽  
Position And Orientation

The SE(2) domain can be used to describe the position and orientation of objects in planar scenarios and is inherently nonlinear due to the periodicity of the angle. We present a novel filter that involves splitting up the joint density into a (marginalized) density for the periodic part and a conditional density for the linear part. We subdivide the state space along the periodic dimension and describe each part of the state space using the parameters of a Gaussian and a grid value, which is the function value of the marginalized density for the periodic part at the center of the respective area. By using the grid values as weighting factors for the Gaussians along the linear dimensions, we can approximate functions on the SE(2) domain with correlated position and orientation. Based on this representation, we interweave a grid filter with a Kalman filter to obtain a filter that can take different numbers of parameters and is in the same complexity class as a grid filter for circular domains. We thoroughly compared the filters with other state-of-the-art filters in a simulated tracking scenario. With only little run time, our filter outperformed an unscented Kalman filter for manifolds and a progressive filter based on dual quaternions. Our filter also yielded more accurate results than a particle filter using one million particles while being faster by over an order of magnitude.

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.

scholarly journals Experience Rating of ARIMA Processes by the Kalman Filter

1986 ◽  
Vol 16 (1) ◽  
pp. 19-31 ◽  
Author(s):  
Jukka Rantala
Keyword(s):  
Kalman Filter ◽  
Time Delay ◽  
State Space ◽  
Theoretical Approach ◽  
Space Form ◽  
The State ◽  
Experience Rating ◽  
Filter Technique ◽  
Main Emphasis ◽  
Arima Processes

AbstractThis paper deals with experience rating of claims processes of ARIMA structures. By experience rating we mean that future premiums should be only a function of past values of the claims process. The main emphasis is on demonstrating the usefulness of the control-theoretical approach in the search for optimal rating rules. Optimality is here defined to mean as smooth a flow of premiums as possible when the variation in the accumulated profit is restricted to a certain amount. First it is shown how the underlying model in its simplest form can be transformed into the state-space form. Then the Kalman filter technique is used to find the optimal rules. Also a time delay in information is taken into account. The optimal rules are illustrated by examples.

Identification of Stochastic System and Controller via Projection Filters

1996 ◽  
Vol 118 (2) ◽  
pp. 169-176 ◽  
Author(s):  
Hyun Chang Lee ◽  
Min-Hung Hsiao ◽  
Jen-Kuang Huang ◽  
Chung-Wen Chen
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Stochastic System ◽  
State Space Model ◽  
Open Loop ◽  
The State ◽  
Loop System ◽  
Test Facility ◽  
System Response ◽  
Space Model

A method based on projection filters is presented for identifying an open-loop stochastic system with an existing feedback controller. The projection filters are derived from the relationship between the state-space model and the AutoRegressive with eXogeneous input (ARX) model including the system, Kalman filter and controller. Two ARX models are identified from the control input, closed-loop system response and feedback signal using least-squares method. Markov parameters of the open-loop system, Kalman filter and controller are then calculated from the coefficients of the identified ARX models. Finally, the state-space model of the open-loop stochastic system and the gain matrices for the Kalman filter and controller are realized. The method is validated by simulations and test data from an unstable large-angle magnetic suspension test facility.

scholarly journals Research on the State of Charge of Lithium-Ion Battery Based on the Fractional Order Model

Energies ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 6307
Author(s):  
Lin Su ◽  
Guangxu Zhou ◽  
Dairong Hu ◽  
Yuan Liu ◽  
Yunhai Zhu
Keyword(s):  
Kalman Filter ◽  
Fractional Order ◽  
Colored Noise ◽  
Unscented Kalman Filter ◽  
The State ◽  
State Of Charge ◽  
Accurate Estimation ◽  
Order Model ◽  
Discrete State ◽  
Fractional Order Model

Accurate estimation of the state of charge (SOC) of lithium batteries is paramount to ensuring consistent battery pack operation. To improve SOC estimation accuracy and suppress colored noise in the system, a fractional order model based on an unscented Kalman filter and an H-infinity filter (FOUHIF) estimation algorithm was proposed. Firstly, the discrete state equation of a lithium battery was derived, as per the theory of fractional calculus. Then, the HPPC experiment and the PSO algorithm were used to identify the internal parameters of the second order RC and fractional order models, respectively. As discovered during working tests, the parameters identified via the fractional order model proved to be more accurate. Furthermore, the feasibility of using the FOUHIF algorithm was evaluated under the conditions of NEDC and UDDS, with obvious colored noise. Compared with the fractional order unscented Kalman filter (FOUKF) and integer order unscented Kalman filter (UKF) algorithms, the FOUHIF algorithm showed significant improvement in both the accuracy and robustness of the estimation, with maximum errors of 1.86% and 1.61% under the two working conditions, and a terminal voltage prediction error of no more than 5.29 mV.

Multiple Robust High-degree Cubature Kalman Filter for Relative Position and Attitude Estimation of Satellite Formation

2019 ◽  
Vol 72 (5) ◽  
pp. 1254-1274 ◽  
Author(s):  
Ning Li ◽  
Wentao Ma ◽  
Weishi Man ◽  
Liu Cao ◽  
Hui Zhang
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
High Dimension ◽  
Relative Position ◽  
Attitude Estimation ◽  
The State ◽  
Robust Performance ◽  
Cubature Kalman Filter ◽  
Estimation System ◽  
High Degree

The High-degree Cubature Kalman Filter (HCKF) is proposed as a novel methodology based on the arbitrary degree spherical rule, which can achieve better performance than the traditional Kalman filter. However, it also has a large calculation burden when used in a high-dimension and high-degree of accuracy estimation system. The number of sampling points of an HCKF increases polynomially with increasing state-space dimensions, which further increases the calculation burden. The reduction of the number of the state-space dimensions is the main contribution of this study. A strategy for HCKF based on the partitioning of the state-space and orthogonal principle is introduced, referred to as the Multiple Robust HCKF (MRHCKF). It is shown that this technique can effectively reduce the calculation burden for the high-dimension system with robust performance. Numerical simulations are performed for the example of high-dimension relative position and attitude estimation to show that the proposed method can obtain nearly the same performance as the HCKF, while drastically reducing computational complexity.

A novel trigger mechanism for a dual-filter to improve the state-of-charge estimation of lithium-ion batteries

2021 ◽  
pp. 1-12
Author(s):  
Chuanxiang Yu ◽  
Rui Huang ◽  
Zhaoyu Sang ◽  
Shiya Yang
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Equivalent Circuit Model ◽  
Lithium Ion ◽  
Open Loop ◽  
The State ◽  
State Of Charge ◽  
Loop Model ◽  
Trigger Mechanism ◽  
Soc Estimation

Abstract State-of-charge (SOC) estimation is essential in the energy management of electric vehicles. In the context of SOC estimation, a dual-filter based on the equivalent circuit model represents an important research direction. The trigger for parameter filter in a dual filter has a significant influence on the algorithm, despite which it has been studied scarcely. The present paper, therefore, discusses the types and characteristics of triggers reported in the literature and proposes a novel trigger mechanism for improving the accuracy and robustness of SOC estimation. The proposed mechanism is based on an open-loop model, which determines whether to trigger the parameter filter based on the model voltage error. In the present work, particle filter (PF) is used as the state filter and Kalman filter (KF) as the parameter filter. This dual filter is used as a carrier to compare the proposed trigger with three other triggers and single filter algorithms, including PF and unscented Kalman filter (UKF). According to the results, under different dynamic cycles, initial SOC values, and temperatures, the root-mean-square error of the SOC estimated using the proposed algorithm is at least 34.07% lower than the value estimated using other approaches. In terms of computation time, the value is 4.67%. Therefore, the superiority of the proposed mechanism is demonstrated.

Using an Extended Kalman Filter for Rigid Body Pose Estimation

2004 ◽  
Vol 127 (3) ◽  
pp. 475-483 ◽  
Author(s):  
Kjartan Halvorsen ◽  
Torsten Söderström ◽  
Virgil Stokes ◽  
Håkan Lanshammar
Keyword(s):  
Kalman Filter ◽  
Rigid Body ◽  
State Space ◽  
Pose Estimation ◽  
Measurement Errors ◽  
The State ◽  
State Space Models ◽  
Marker Data ◽  
Measurement Function ◽  
Body Pose Estimation

Rigid body pose is commonly represented as the rigid body transformation from one (often reference) pose to another. This is usually computed for each frame of data without any assumptions or restrictions on the temporal change of the pose. The most common algorithm was proposed by Söderkvist and Wedin (1993, “Determining the Movements of the Skeleton Using Well-configured Markers,” J. Biomech., 26, pp. 1473–1477), and implies the assumption that measurement errors are isotropic and homogenous. This paper describes an alternative method based on a state space formulation and the application of an extended Kalman filter (EKF). State space models are formulated, which describe the kinematics of the rigid body. The state vector consists of six generalized coordinates (corresponding to the 6 degrees of freedom), and their first time derivatives. The state space models have linear dynamics, while the measurement function is a nonlinear relation between the state vector and the observations (marker positions). An analytical expression for the linearized measurement function is derived. Tracking the rigid body motion using an EKF enables the use of a priori information on the measurement noise and type of motion to tune the filter. The EKF is time variant, which allows for a natural way of handling temporarily missing marker data. State updates are based on all the information available at each time step, even when data from fewer than three markers are available. Comparison with the method of Söderkvist and Wedin on simulated data showed a considerable improvement in accuracy with the proposed EKF method when marker data was temporarily missing. The proposed method offers an improvement in accuracy of rigid body pose estimation by incorporating knowledge of the characteristics of the movement and the measurement errors. Analytical expressions for the linearized system equations are provided, which eliminate the need for approximate discrete differentiation and which facilitate a fast implementation.

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