scholarly journals Comparison of Several Filtering Approaches on Water Treatment Processes

2021 ◽  
Vol 25 (3) ◽  
pp. 225-248
Author(s):  
António Pedro Aguiar ◽  
◽  
Oussama Hadj-Abdelkader ◽  
Keyword(s):  
Growth Rate ◽  
Kalman Filter ◽  
State Estimation ◽  
Research Work ◽  
The State ◽  
Estimation Problem ◽  
Efficient Estimation ◽  
Multiple Model ◽  
Deterministic Models ◽  
Treatment Processes

This paper addresses the state estimation problem of a bioreactor in wastewater treatment processes. The state variables of this process are the concentrations of the organic pollutants and of the bacteria inside the bioreactor. A specific growth rate function is used to describe the variation of the bacteria concentration when the amount of pollutants increases. This rate can also represent the speed of the biological degradation of the pollutants. Most research work in this field uses only deterministic models that do not conveniently account for uncertainties. These models are often obtained using several simplifications during the modeling procedure such as neglecting the measurement noises. In this paper, we consider stochastic models and study the state estimation problem using three approaches: the Extended Kalman filter, the Unscented Kalman filter and the Particle filter. These methods are adapted to the models in study and compared to understand which is the most adequate for this type of processes considering their slow evolution, discrete time measurements and high-intensity noises. Further, we also apply a Multiple Model Adaptive method which adapts the filters to the correct growth rate type. This method is also used to automatically choose the most efficient estimation method for this type of biological processes.

State estimation problems in PRF-shift magnetic resonance thermometry

2018 ◽  
Vol 28 (2) ◽  
pp. 315-335 ◽  
Author(s):  
César Pacheco ◽  
Helcio R.B. Orlande ◽  
Marcelo Colaco ◽  
George S. Dulikravich
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Magnetic Resonance ◽  
State Estimation ◽  
Real Time ◽  
The State ◽  
Estimation Problem ◽  
Content Type ◽  
Magnetic Resonance Thermometry ◽  
Direct Inversion

Purpose The purpose of this paper is to apply the Steady State Kalman Filter for temperature measurements of tissues via magnetic resonance thermometry. Instead of using classical direct inversion, a methodology is proposed that couples the magnetic resonance thermometry with the bioheat transfer problem and the local temperatures can be identified through the solution of a state estimation problem. Design/methodology/approach Heat transfer in the tissues is given by Pennes’ bioheat transfer model, while the Proton Resonance Frequency (PRF)-Shift technique is used for the magnetic resonance thermometry. The problem of measuring the transient temperature field of tissues is recast as a state estimation problem and is solved through the Steady-State Kalman filter. Noisy synthetic measurements are used for testing the proposed methodology. Findings The proposed approach is more accurate for recovering the local transient temperatures from the noisy PRF-Shift measurements than the direct data inversion. The methodology used here can be applied in real time due to the reduced computational cost. Idealized test cases are examined that include the actual geometry of a forearm. Research limitations/implications The solution of the state estimation problem recovers the temperature variations in the region more accurately than the direct inversion. Besides that, the estimation of the temperature field in the region was possible with the solution of the state estimation problem via the Steady-State Kalman filter, but not with the direct inversion. Practical implications The recursive equations of the Steady-State Kalman filter can be calculated in computational times smaller than the supposed physical times, thus demonstrating that the present approach can be used for real-time applications, such as in control of the heating source in the hyperthermia treatment of cancer. Originality/value The original and novel contributions of the manuscript include: formulation of the PRF-Shift thermometry as a state estimation problem, which results in reduced uncertainties of the temperature variation as compared to the classical direct inversion; estimation of the actual temperature in the region with the solution of the state estimation problem, which is not possible with the direct inversion that is limited to the identification of the temperature variation; solution of the state estimation problem with the Steady-State Kalman filter, which allows for fast computations and real-time calculations.

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.

Set-membership filtering for automatic guided vehicles with unknown-but-bounded noises

2021 ◽  
pp. 014233122110436
Author(s):  
Hao Yang ◽  
Yilian Zhang ◽  
Wei Gu ◽  
Fuwen Yang ◽  
Zhiquan Liu
Keyword(s):  
State Estimation ◽  
Estimation Algorithm ◽  
The State ◽  
Estimation Problem ◽  
Filtering Method ◽  
Automatic Guided Vehicles ◽  
Tracking Process ◽  
Set Membership ◽  
Text Filtering ◽  
System States

This paper is concerned with the state estimation problem for an automatic guided vehicle (AGV). A novel set-membership filtering (SMF) scheme is presented to solve the state estimation problem in the trajectory tracking process of the AGV under the unknown-but-bounded (UBB) process and measurement noises. Different from some existing traditional filtering methods, such as Kalman filtering method and [Formula: see text] filtering method, the proposed SMF scheme is developed to provide state estimation sets rather than state estimation points for the system states to effectively deal with UBB noises and reduce the requirement of the sensor precision. Then, in order to obtain the state estimation ellipsoids containing the true states, a set-membership estimation algorithm is designed based on the AGV physical model and S-procedure technique. Finally, comparison examples are presented to illustrate the effectiveness of the proposed SMF scheme for an AGV state estimation problem in the present of the UBB noises.

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.

Computational development of a practical educational tool for state estimation of power systems using the MATLAB optimization toolbox

2018 ◽  
Vol 56 (2) ◽  
pp. 105-123 ◽  
Author(s):  
EA Zamora-Cárdenas ◽  
A Pizano-Martínez ◽  
JM Lozano-García ◽  
VJ Gutiérrez-Martínez ◽  
R Cisneros-Magaña
Keyword(s):  
Power Systems ◽  
State Estimation ◽  
Electric Power ◽  
Smart Grids ◽  
Weighted Least Squares ◽  
Electric Power Systems ◽  
The State ◽  
Estimation Problem ◽  
Educational Tool ◽  
And Control

State estimation is one of the most important processes to perform a reliable monitoring and control of the steady-state operating condition of modern electric power systems; thus, it is currently a fundamental part in the development of research to enhance the monitoring and security of the smart grids operation. This important topic is taught in advanced courses of operation and control of power systems, for graduate and undergraduate power engineering students. However, the most used software packages for simulation and analysis of power systems by researchers, students, and educators have put little attention on the state estimation module. Due to this fact, this paper proposes an approach to develop the computational implementation of a practical educational tool for state estimation of electric power systems using the MATLAB optimization toolbox. In this proposal, the formulation of the state estimation problem consists of developing a general digital code to implement an objective function based on the weighted least squares method. While the lsqnonlin function of the MATLAB optimization toolbox solves the formulated state estimation problem. Simplifying both research and educational processes, this tool helps graduate and undergraduate students to improve learning, understanding, and the times of implementation and development of research in state estimation. Simulations of an equivalent model of the Mexican interconnected power system consisting of 190 buses and 46 machines are used to test and validate the proposal performance.

scholarly journals A Strong Tracking Mixed-Degree Cubature Kalman Filter Method and Its Application in a Quadruped Robot

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2251 ◽  
Author(s):  
Jikai Liu ◽  
Pengfei Wang ◽  
Fusheng Zha ◽  
Wei Guo ◽  
Zhenyu Jiang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Real Time ◽  
Quadruped Robot ◽  
The State ◽  
Estimation Accuracy ◽  
Robot System ◽  
Calculation Time ◽  
Motion State ◽  
Cubature Kalman Filter

The motion state of a quadruped robot in operation changes constantly. Due to the drift caused by the accumulative error, the function of the inertial measurement unit (IMU) will be limited. Even though multi-sensor fusion technology is adopted, the quadruped robot will lose its ability to respond to state changes after a while because the gain tends to be constant. To solve this problem, this paper proposes a strong tracking mixed-degree cubature Kalman filter (STMCKF) method. According to system characteristics of the quadruped robot, this method makes fusion estimation of forward kinematics and IMU track. The combination mode of traditional strong tracking cubature Kalman filter (TSTCKF) and strong tracking is improved through demonstration. A new method for calculating fading factor matrix is proposed, which reduces sampling times from three to one, saving significantly calculation time. At the same time, the state estimation accuracy is improved from the third-degree accuracy of Taylor series expansion to fifth-degree accuracy. The proposed algorithm can automatically switch the working mode according to real-time supervision of the motion state and greatly improve the state estimation performance of quadruped robot system, exhibiting strong robustness and excellent real-time performance. Finally, a comparative study of STMCKF and the extended Kalman filter (EKF) that is commonly used in quadruped robot system is carried out. Results show that the method of STMCKF has high estimation accuracy and reliable ability to cope with sudden changes, without significantly increasing the calculation time, indicating the correctness of the algorithm and its great application value in quadruped robot system.

scholarly journals Ellipsoidal and Gaussian Kalman Filter Model for Discrete-Time Nonlinear Systems

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1168 ◽  
Author(s):  
Ligang Sun ◽  
Hamza Alkhatib ◽  
Boris Kargoll ◽  
Vladik Kreinovich ◽  
Ingo Neumann
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
State Estimation ◽  
Discrete Time ◽  
Probability Distributions ◽  
Nonlinear Problems ◽  
The State ◽  
Filter Model ◽  
Highly Nonlinear ◽  
Correction Step

In this paper, we propose a new technique—called Ellipsoidal and Gaussian Kalman filter—for state estimation of discrete-time nonlinear systems in situations when for some parts of uncertainty, we know the probability distributions, while for other parts of uncertainty, we only know the bounds (but we do not know the corresponding probabilities). Similarly to the usual Kalman filter, our algorithm is iterative: on each iteration, we first predict the state at the next moment of time, and then we use measurement results to correct the corresponding estimates. On each correction step, we solve a convex optimization problem to find the optimal estimate for the system’s state (and the optimal ellipsoid for describing the systems’s uncertainty). Testing our algorithm on several highly nonlinear problems has shown that the new algorithm performs the extended Kalman filter technique better—the state estimation technique usually applied to such nonlinear problems.

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