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.

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.

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.

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.

Bayesian monthly index for building activity based on mixed frequencies: the case of Chile

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Byron J. Idrovo-Aguirre ◽  
Javier E. Contreras-Reyes
Keyword(s):  
Kalman Filter ◽  
Bayesian Inference ◽  
State Space ◽  
State Space Model ◽  
Natural Extension ◽  
The State ◽  
Likelihood Method ◽  
Content Type ◽  
Space Model ◽  
Construction Activity

PurposeThis paper combines the objective information of six mixed-frequency partial-activity indicators with assumptions or beliefs (called priors) regarding the distribution of the parameters that approximate the state of the construction activity cycle. Thus, this paper uses Bayesian inference with Gibbs simulations and the Kalman filter to estimate the parameters of the state-space model, used to design the Imacon.Design/methodology/approachUnlike other economic sectors of similar importance in aggregate gross domestic product, such as mining and industry, the construction sector lacked a short-term measure that helps to identify its most recent performance.FindingsIndeed, because these priors are susceptible to changes, they provide flexibility to the original Imacon model, allowing for the assessment of risk scenarios and adaption to the greater relative volatility that characterizes the sector's activity.Originality/valueThe classic maximum likelihood method of estimating the monthly construction activity index (Imacon) is rigid to the incorporation of new measures of uncertainty, expectations or different volatility (risks) levels in the state of construction activity. In this context, this paper uses Bayesian inference with 10,000 Gibbs simulations and the Kalman filter to estimate the parameters of the state-space model, used to design the Imacon, inspired by the original works of Mariano and Murasawa (2003) and Kim and Nelson (1998). Thus, this paper consists of a natural extension of the classic method used by Tejada (2006) in the estimation of the old Imacon.

Plant-Input-Mapping Discretization Method for a Feedback System in the State-Space Form

2021 ◽  
Author(s):  
Keisuke Yagi ◽  
Hiroaki Muto ◽  
Yoshikazu Mori
Keyword(s):  
Transfer Function ◽  
State Space ◽  
State Feedback ◽  
Closed Loop ◽  
Space Form ◽  
Feedback System ◽  
The State ◽  
Loop System ◽  
Closed Loop System ◽  
Digital Redesign

Abstract The paper proposes the digital redesign technique called plant-input-mapping (PIM) method for a feedback system described in the state-space form. The PIM method, which was originally presented in the transfer function form, focuses on the plant input signal via the plant input transfer function and discretizes it so as to satisfy the control zero principle in the resulting discrete-time closed-loop system, which leads to guaranteeing the closed-loop stability for any non-pathological sampling interval. In accordance with this approach, the proposed PIM method focuses on the control zeros included in the plant input signal. The paper proves that the matched-pole-zero discrete-time model of the plant input state-equation satisfies the control zero principle with the step-invariant model of the plant. Then, when the matched-pole-zero model is set as the target of model matching, the parameters of the state-space PIM controller employing the observer-based dynamic state-feedback can systematically be determined from the underlying continuous-time closed-loop system with guaranteed stability. This discretization process can immediately be applied to a state-feedback system and a class of multi-input multi-output systems without any modification, which cannot be discretized by the conventional PIM methods. The discretization performance of the proposed PIM method is evaluated through illustrative examples with comparable digital redesign methods, which reveal that the proposed method performs a good reproduction of the characteristics of the underlying closed-loop system.

InSAR Adaptive Extended Kalman Filter Phase Unwrapping Algorithm

2013 ◽  
Vol 798-799 ◽  
pp. 493-496
Author(s):  
Hua Dong Hao ◽  
Ting Yi Bai ◽  
Guo Lin Liu
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Extended Kalman Filter ◽  
State Space Model ◽  
Model Error ◽  
Phase Unwrapping ◽  
The State ◽  
Observation Equation ◽  
Space Model ◽  
The One

Phase Unwrapping (PU) is the key step in the image processing for Interferometric Synthetic Aperture Radar (InSAR). In the Extended Kalman Filter (EKF) model of PU, due to the state space model is not taken into account the terrain factors, it is often resulted in unwrapping error delivery as the pixel to the next when the state changes rapidly in steep terrain. The observation equation is nonlinear and usually applied in PU through linear processing, requiring the system model and noise statistics known. But in fact the mathematical model or statistical noise is completely or partially unknown; the results have been inevitably lead to the declining of valuation accuracy and filter divergence. If directly applied in phase unwrapping, it is made impossible to retrieve surface deformation. In order to solve this problem and fully consider the terrain effect and model error, an adaptive EKF PU algorithm (AEKFPU) for InSAR is presented. On the one hand, it is achieved local adaptive estimation of image fringe frequency through 2D FFT and Chirp-Z Transform (CZT) joint method, by considering the impact of terrain factors on unwrapping results; On the one hand, the fading factor is calculated by innovation covariance and adaptively adjusted with the error covariance so as to suppress the memory length of the filter, compensating the effect of incomplete information on unwrapping. The experimental results are proved the proposed method is effective, it can be dealt with phase unwrapping and filtering simultaneously, and can be adaptively considered terrain factors in state space model and compensated for model error in observation equation model, ultimately improving the accuracy of phase unwrapping.

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