scholarly journals Extended Fractional Singular Kalman Filter

2021 ◽  
Author(s):  
Komeil Nosrati ◽  
Juri Belikov ◽  
Aleksei Tepljakov ◽  
Eduard Petlenkov
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Space Form ◽  
Complex Dynamics ◽  
Algorithm Design ◽  
Estimation Algorithm ◽  
Data Fitting ◽  
Estimation Methods ◽  
Usual State ◽  
Filter Analysis

Abstract Effective and accurate state estimation is a staple of modern modeling. On the other hand, nonlinear fractional-order singular (FOS) systems are an attractive modeling tool as well since they can provide accurate descriptions of systems with complex dynamics. Consequently, developing accurate state estimation methods for such systems is highly relevant since it provides vital information about the system including related memory effects and long interconnection properties with constraint elements. However, missing features in transforming structures such as violation of constraints in non-singular versions of such systems may affect the performance of the estimation result. This paper proposes the state estimation algorithm design for the original and non-transformed stochastic nonlinear FOS system. We introduce a deterministic data-fitting based framework which helps us to take steps directly towards Kalman filter (KF) derivation of the system, called extended fractional singular KF (EFSKF). Using stochastic reasoning, we demonstrate how to construct recursive form of the filter. Analysis of the filter shows how the proposed algorithm reduces to the nominal nonlinear filters when the system is in its usual state-space form making said algorithm highly flexible. Finally, simulation results verify that the estimation of nonlinear states can be accomplished with the proposed EFSKF algorithm with a reasonable performance.

scholarly journals The New Trend of State Estimation: From Model-Driven to Hybrid-Driven Methods

Sensors ◽  
2021 ◽  
Vol 21 (6) ◽  
pp. 2085
Author(s):  
Xue-Bo Jin ◽  
Ruben Jonhson Robert RobertJeremiah ◽  
Ting-Li Su ◽  
Yu-Ting Bai ◽  
Jian-Lei Kong
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Future Development ◽  
Data Driven ◽  
Estimation Methods ◽  
Multiple Model ◽  
Development Trends ◽  
Research Results ◽  
Model Driven ◽  
Model Based

State estimation is widely used in various automated systems, including IoT systems, unmanned systems, robots, etc. In traditional state estimation, measurement data are instantaneous and processed in real time. With modern systems’ development, sensors can obtain more and more signals and store them. Therefore, how to use these measurement big data to improve the performance of state estimation has become a hot research issue in this field. This paper reviews the development of state estimation and future development trends. First, we review the model-based state estimation methods, including the Kalman filter, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF), cubature Kalman filter (CKF), etc. Particle filters and Gaussian mixture filters that can handle mixed Gaussian noise are discussed, too. These methods have high requirements for models, while it is not easy to obtain accurate system models in practice. The emergence of robust filters, the interacting multiple model (IMM), and adaptive filters are also mentioned here. Secondly, the current research status of data-driven state estimation methods is introduced based on network learning. Finally, the main research results for hybrid filters obtained in recent years are summarized and discussed, which combine model-based methods and data-driven methods. This paper is based on state estimation research results and provides a more detailed overview of model-driven, data-driven, and hybrid-driven approaches. The main algorithm of each method is provided so that beginners can have a clearer understanding. Additionally, it discusses the future development trends for researchers in state estimation.

scholarly journals Robust and Fast State Estimation for Poorly-Observable Low Voltage Distribution Networks Based on the Kalman Filter Algorithm

Energies ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4457 ◽  
Author(s):  
Antončič ◽  
Papič ◽  
Blažič
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Low Voltage ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Measurement Data ◽  
Estimation Algorithm ◽  
Distribution Networks ◽  
Voltage Distribution ◽  
State Estimator

This paper presents a novel approach for the state estimation of poorly-observable low voltage distribution networks, characterized by intermittent and erroneous measurements. The developed state estimation algorithm is based on the Extended Kalman filter, where we have modified the execution of the filtering process. Namely, we have fixed the Kalman gain and Jacobian matrices to constant matrices; their values change only after a larger disturbance in the network. This allows for a fast and robust estimation of the network state. The performance of the proposed state-estimation algorithm is validated by means of simulations of an actual low-voltage network with actual field measurement data. Two different cases are presented. The results of the developed state estimator are compared to a classical estimator based on the weighted least squares method. The comparison shows that the developed state estimator outperforms the classical one in terms of calculation speed and, in case of spurious measurements errors, also in terms of accuracy.

scholarly journals Ship tracking based on the fusion of Kalman filter and particle filter

2021 ◽  
Vol 2113 (1) ◽  
pp. 012017
Author(s):  
Wanjin Xu ◽  
Jiying Li ◽  
Junjie Bai ◽  
Yingying Zhang
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
State Estimation ◽  
Particle Filtering ◽  
Unscented Kalman Filter ◽  
Optimal Estimation ◽  
Estimation Algorithm ◽  
Tracking Accuracy ◽  
Gps Navigation ◽  
Degradation Degree

Abstract Aiming at the problem of low filtering accuracy and even divergence caused by model mismatch when using extended Kalman filter in ship GPS navigation and positioning state estimation, a positioning ship state estimation algorithm based on the fusion of improved unscented Kalman filter and particle filter is proposed. Compared with the traditional particle filtering algorithm, the algorithm has two improvements: first, the algorithm uses untraced Kalman as the main framework, and uses the optimal estimation of particle updating state by particle algorithm; Secondly, in the resampling process, a resampling algorithm based on weight optimization is proposed to increase the diversity of particles. The simulation results show that not only the particle degradation degree of the particle filter is reduced, but also the particle tracking accuracy is improved.

scholarly journals Three-Phase State Estimation of a Low-Voltage Distribution Network with Kalman Filter

Energies ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 7421
Author(s):  
Fabio Napolitano ◽  
Juan Diego Rios Penaloza ◽  
Fabio Tossani ◽  
Alberto Borghetti ◽  
Carlo Alberto Nucci
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Phase State ◽  
Low Voltage ◽  
Distribution Network ◽  
Estimation Algorithm ◽  
The State ◽  
Voltage Distribution ◽  
Smart Meters ◽  
Three Phase

The state estimation of distribution networks has long been considered a challenging task for the reduced availability of real-time measures with respect to the transmission network case. This issue is expected to be improved by the deployment of modern smart meters that can be polled at relatively short time intervals. On the other hand, the management of the information coming from many heterogeneous meters still poses major issues. If low-voltage distribution systems are of interest, a three-phase formulation should be employed for the state estimation due to the typical load imbalance. Moreover, smart meter data may not be perfectly synchronized. This paper presents the implementation of a three-phase state estimation algorithm of a real portion of a low-voltage distribution network with distributed generation equipped with smart meters. The paper compares the typical state estimation algorithm that implements the weighted least squares method with an algorithm based on an iterated Kalman filter. The influence of nonsynchronicity of measurements and of delays in communication and processing is analyzed for both approaches.

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