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Licensed Unlicensed Requires Authentication Published by De Gruyter May 17, 2019

A State Estimation Method Based on Integration of Linear and Extended Kalman Filters

M. Farsi and M. Dehghan Manshadi

Abstract

The Linear Kalman Filter (LKF) and Extended Kalman Filter (EKF) as correction-prediction observers are two common model-based filters, which are widely used to estimate the unmeasurable states and parameters in the chemical processes. The main disadvantages of LKF and EKF are low accuracy and reliability of estimation and high computational time, respectively. The main object of this work is the modification of conventional Kalman filter to cover the disadvantages of LKF and EKF. The proposed method is planned based on the systematic updating the Jacobian matrix of estimator applied on the nonlinear systems. In this regard, a linearity index is defined based on the characteristics of outputs to determine switching time between LKF and EKF to avoid unnecessary updating the Jacobian matrix. The performance of the proposed method is compared with the LKF and EKF considering four chemical benchmarks as the nonlinear state space models. Altought EKF and proposed filter present similar precision to estimate unmeasurable states, the proposed method has a lower computational time.

Nomenclature

aicm2

Outlet cross-sectional area of tanks

Aim2

Cross section area of ith reactor

C

Linearized matrix of measurements function

CAmol lit1

Concentration of A in the reactor

CBmol lit1

Concentration of B in the reactor

CPJ kg1K1

Specific Heat capacity of mixture

CpjJ kg1K1

Specific Heat capacity of coolant

d

Disturbance in the system

EJ mol1

Activation energy of reaction

Flits1

Flowrate

Fjlits1

Flowrate of jacket

gms2

The acceleration due to gravity

kicm3s1

Pump constants

K

Kalman gain matrix

Kilit mol1s1

Reaction pre-exponential factor

Kxn.i

Recurrence relationship of fourth-order Runge-Kutta

Licm

Level

P

Adaptation gain matrix

Q

Covariance matrix of model noise

R

Covariance matrix of measurement noise

RJ mol1K1

Universal gas constant

S

Slope of the state variations

t (sec)

Time

TK

Temperature

u

Input of the system

UWm2K1

Heat transfer coefficient

υi

Percent of maximum speed in pump i

Vm3

Volume

x

States of the system

y

Measured states of the system (outputs)

Greek letter
α

The threshold for second derivative

ω

Process-noise vector

v

Measurement-noise vector

ΔHJ mol1

Heat of reaction

ρkgm3

Density

Abbreviations

ANNs

Artificial Neural Networks

EKF

Extended Kalman Filter

LKF

Linear Kalman Filter

NEKF

Neuro Extended Kalman Filter

NHGO

Neuro High Gain Observer

UKF

Unscented Kalman Filters

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Received: 2018-09-03
Revised: 2019-04-29
Accepted: 2019-04-30
Published Online: 2019-05-17

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