Parallel Optimal Kalman Filtering for Stochastic Systems in Multimodeling Form

1999 ◽  
Vol 122 (3) ◽  
pp. 542-550 ◽  
Author(s):  
Cyril Coumarbatch ◽  
Zoran Gajic
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Kalman Filters ◽  
Stochastic Systems ◽  
State Variables ◽  
State Transformation ◽  
Eighth Order ◽  
Reduced Order ◽  
Filtering Technique ◽  
Ill Conditioning

In this paper we show how to completely and exactly decompose the optimal Kalman filter of stochastic systems in multimodeling form in terms of one pure-slow and two pure-fast, reduced-order, independent, Kalman filters. The reduced-order Kalman filters are all driven by the system measurements. This leads to a parallel Kalman filtering scheme and removes ill-conditioning of the original full-order singularly perturbed Kalman filter. The results obtained are valid for steady state. In that direction, the corresponding algebraic filter Riccati equation is completely decoupled and solved in terms of one pure-slow and two pure fast, reduced-order, independent, algebraic Riccati equations. A nonsingular state transformation that exactly relates the state variables in the original and new coordinates (in which the required decomposition is achieved) is also established. The eighth order model of a passenger car under road disturbances is used to demonstrate efficiency of the proposed filtering technique. [S0022-0434(00)01703-2]

scholarly journals Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering

2003 ◽  
Author(s):  
Dan Simon ◽  
Donald L. Simon
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Kalman Filters ◽  
Inequality Constraints ◽  
Computational Effort ◽  
Estimation Accuracy ◽  
State Variables ◽  
Turbofan Engine ◽  
State Variable ◽  
State Variable Constraints

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results obtained from application to a turbofan engine model. This model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.

scholarly journals Aircraft Turbofan Engine Health Estimation Using Constrained Kalman Filtering

2005 ◽  
Vol 127 (2) ◽  
pp. 323-328 ◽  
Author(s):  
Dan Simon ◽  
Donald L. Simon
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Kalman Filters ◽  
Inequality Constraints ◽  
Computational Effort ◽  
Estimation Accuracy ◽  
State Variables ◽  
Turbofan Engine ◽  
State Variable ◽  
State Variable Constraints

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state-variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state-variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state-variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results obtained from application to a turbofan engine model. This model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.

Does the brain implement the Kalman filter?

2004 ◽  
Vol 27 (3) ◽  
pp. 404-405 ◽  
Author(s):  
Valeri Goussev
Keyword(s):  
Kalman Filter ◽  
Data Processing ◽  
Kalman Filtering ◽  
Brain Structures ◽  
Parameter Evaluation ◽  
Filtering Technique ◽  
Processing Techniques ◽  
The Brain

The Kalman filtering technique is considered as a part of concurrent data-processing techniques also related to detection, parameter evaluation, and identification. The adaptive properties of the filter are discussed as being related to symmetrical brain structures.

scholarly journals Kalman Filtering Applied to Induction Motor State Estimation

2020 ◽  
Author(s):  
Yassine Zahraoui ◽  
Mohamed Akherraz
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Induction Motor ◽  
Kalman Filtering ◽  
Speed Estimation ◽  
Stochastic Algorithm ◽  
State Variables ◽  
Extended Kalman Filtering ◽  
Filtering Theory ◽  
State Observation

This chapter presents a full definition and explanation of Kalman filtering theory, precisely the filter stochastic algorithm. After the definition, a concrete example of application is explained. The simulated example concerns an extended Kalman filter applied to machine state and speed estimation. A full observation of an induction motor state variables and mechanical speed will be presented and discussed in details. A comparison between extended Kalman filtering and adaptive Luenberger state observation will be highlighted and discussed in detail with many figures. In conclusion, the chapter is ended by listing the Kalman filtering main advantages and recent advances in the scientific literature.

On-Line Performance Monitoring and Engine Diagnostic Using Robust Kalman Filtering Techniques

2003 ◽  
Author(s):  
Pierre Dewallef ◽  
Olivier Le´onard
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Kalman Filters ◽  
Performance Monitoring ◽  
Stochastic Methods ◽  
Inlet Temperature ◽  
State Variables ◽  
Present Contribution ◽  
Regression Problem ◽  
On Line

In this contribution, an on-line engine performance monitoring is carried out through an engine health parameter estimation based on several gas path measurements. This health parameter estimation makes use of the analytical redundancy of an engine model and therefore implies the knowledge of the engine state. As the latter is a priori not known the second task is therefore an engine state variable estimation. State variables here designate working conditions such as inlet temperature, pressure, Mach number, rotational speeds, … Estimation of the state variables constitutes a general application of the Extended Kalman Filter theory, while the health parameter estimation is a classical recurrent regression problem. Recent advances in stochastic methods [1] show that both problems can be solved by two Kalman filters working jointly. Such filters are usually named Dual Kalman Filters. The present contribution aims at using a dual Kalman filter modified to provide robustness. This procedure should be able to cope with as much as 20 to 30% of faulty data. The resulting online method is applied to a turbofan model developed in the frame of the OBIDICOTE 1 project. Several tests are carried out to check the performance monitoring capability and the robustness that can be achieved.

Improving the accuracy of a vibratory sensor using Kalman filtering

Robotica ◽  
1993 ◽  
Vol 11 (2) ◽  
pp. 129-138 ◽  
Author(s):  
D.T. Pham ◽  
K. Hafeez
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Natural Frequencies ◽  
Industrial Robot ◽  
Sensor System ◽  
Location Information ◽  
Location Determination ◽  
Sensor Signals ◽  
Filtering Technique ◽  
Position And Orientation

SUMMARYThis paper presents a Kalman filtering technique for reducing errors in locating 3-D objects using a sensor system. The location information is employed to control the motion of an industrial robot to pick up the objects. The sensor consists of a rigid platform mounted on a flexible column. Each object to be located is placed on the sensor. The static deflections and natural frequencies of vibrations of the sensor are measured and processed to determine the position and orientation of the object. In practice, the sensor signals obtained are corrupted with noise leading to errors in location determination. A Kalman filter is used to reduce the noise present in the sensor system.

Measurement of Step Responses of Flowrate in a Pipe Using a Kalman-Filtering Laminar Flowmeter

2021 ◽  
Author(s):  
Kazushi Sanada
Keyword(s):  
Kalman Filter ◽  
Laminar Flow ◽  
Response Time ◽  
Kalman Filtering ◽  
The State ◽  
Step Response ◽  
Working Fluid ◽  
State Variables ◽  
Turbulent Friction ◽  
Experimental Calibration

Abstract The aim of our research project is to develop a Kalman filter system which estimates unsteady flowrate of a pipe using a laminar flowmeter. In this study, incompressible flow is assumed as working fluid. When the flow becomes turbulent, it is difficult to establish flow model for turbulent friction. In this study, a laminar flowmeter is constructed in which thirty-two narrow pipes of 1mm in inner diameter are bundled and inserted in main flow path. When fluid flow in the narrow pipe is laminar flow, the Kalman filter theory can be applied to the flow of the narrow pipe. Kalman filter is applied to one of narrow pipes of laminar flowmeter. Both upstream and downstream pressure signals of the targeted narrow pipe are input to the Kalman filter. Midpoint pressure measured by a pressure sensor is compared with midpoint pressure signal which is estimated by the Kalman filter. When flow is laminar flow or the system has linear characteristics, an error signal between estimated pressure and measured pressure decreases according to Kalman filter principle. As a result, because the state variables of the Kalman filter converge to real variables, unsteady flowrate is estimated from the state variables of the Kalman filter. Experimental calibration of the Kalman-filtering laminar flowmeter under steady-state flow condition has been performed. In this study, experiments of step response of flowrate in a pipe are conducted by constructing an experimental circuit using solenoid valves. The purpose of experiment is confirmation of a response time of the Kalman-filtering laminar flowmeter. As a result of experiments, it was shown that the response time is 0.05s.

scholarly journals APPLICATION OF FRACTIONAL SENSOR FUSION ALGORITHMS FOR INERTIAL MEMS SENSING

2009 ◽  
Vol 14 (2) ◽  
pp. 199-209 ◽  
Author(s):  
Michailas Romanovas ◽  
Lasse Klingbeil ◽  
Martin Traechtler ◽  
Yiannos Manoli
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Kalman Filters ◽  
Head Motion ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Data Set ◽  
Motion Data ◽  
Definition Of ◽  
The Given

The work presents an extension of the conventional Kalman filtering concept for systems of fractional order (FOS). Modifications are introduced using the Grünwald‐Letnikov (GL) definition of the fractional derivative (FD) and corresponding truncation of the history length. Two versions of the fractional Kalman filter (FKF) are shown, where the FD is calculated directly or by augmenting the state vector with the estimate of the FD. The filters are compared to conventional integer order (IO) Position (P‐KF) and Position‐Velocity (PV‐KF) Kalman filters as well as to an adaptive Interacting Multiple‐Model Kalman Filter (IMM‐KF). The performance of the filters is assessed based on a hand and a head motion data set. The feasibility of the given approach is shown.

Filtering for Linear Stochastic Systems With Small Measurement Noise

1995 ◽  
Vol 117 (3) ◽  
pp. 425-429 ◽  
Author(s):  
Z. Aganovic ◽  
Z. Gajic ◽  
X. Shen
Keyword(s):  
Kalman Filter ◽  
Riccati Equation ◽  
Stochastic Systems ◽  
Measurement Noise ◽  
Algebraic Riccati Equation ◽  
Reduced Order ◽  
Complete Decomposition ◽  
Algebraic Riccati Equations ◽  
Optimal Filters ◽  
Linear Stochastic Systems

In this paper we present a method which produces complete decomposition of the optimal global Kalman filter for linear stochastic systems with small measurement noise into exact pure-slow and pure-fast reduced-order optimal filters both driven by the system measurements. The method is based on the exact decomposition of the global small measurement noise algebraic Riccati equation into exact pure-slow and pure-fast algebraic Riccati equations. An example is included in order to demonstrate the proposed method.

scholarly journals Modeling and Control Design of the Symmetrical Interleaved Coupled-Inductor-Based Boost DC-DC Converter with Clamp Circuits

Energies ◽  
2019 ◽  
Vol 12 (18) ◽  
pp. 3432 ◽  
Author(s):  
Márcio Rodrigo Santos de Carvalho ◽  
Fabrício Bradaschia ◽  
Leonardo Rodrigues Limongi ◽  
Gustavo Medeiros de Souza Azevedo
Keyword(s):  
Mathematical Model ◽  
High Gain ◽  
Reduced Order Model ◽  
State Variables ◽  
Order Model ◽  
Eighth Order ◽  
Loop Control ◽  
Modeling And Control ◽  
Reduced Order ◽  
Point Tracking

The symmetrical input-interleaved high-gain DC-DC converters are suitable candidates to be used as the first stage in PV microinverters and as parallel-connected power optimizers. In both applications, they are responsible for boosting the PV module DC voltage to a higher value and executing the maximum power point tracking control. However, such converters have many state variables, some of them discontinuous, and many operation stages, which make the development of the small-signal model a challenging task. Therefore, the aim of this paper is to propose a reduced-order improved average method (ROIAM) to model the family member of converters that present characteristics such as symmetry, interleaved operation, and discontinuous state-space variables. ROIAM is applied to model for the first time in the literature the symmetrically-interleaved coupled inductor-based boost (SICIBB), leading to a fourth-order mathematical model (reduced-order model). The complete eighth-order mathematical model is developed as well to prove that the reduced-order model represents correctly the dynamic behavior of the SICIBB converter by employing only four state variables, reducing considerably the effort of the modeling. Based on the reduced-order proposed model, a closed-loop control is designed and tested in a 300-W prototype of the SICIBB converter.

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