Abstract
A novel modelbased approach to design a fullorder state observer for estimating the states of a threetank process has been attempted in this research study. State estimation has been a methodology that integrates the prediction from exact models pertaining to the system and achieves consistent estimation of the nonmeasurable variables. This study has attempted to develop a fullorder observer for estimation of nonmeasurable variables of the considered threetank process control system. Neural observer is designed with the nonlinear state update equation that is structured as the neural network employing radial basis function (RBF) model. Also, nonlinear fullorder state observer is designed based on a new recursive likelihood synthesizer (RLS) of the extended Kalman filter (EKF) and classic unscented Kalman filter (UKF) and finally the states are estimated. The likelihood synthesizer determines the covariance and Kalman gains so as to match the realtime process measurements. Threetank process system (TTPS) is represented by its mathematical model and the developed state estimation techniques are applied for estimating the nonmeasurable variables. Likelihood synthesizer tends to evaluate the covariance of the initial states and simulation tests confirm the attainment of better results using the new nonlinear filtering techniques. RBF neural observer has resulted in an ARMSE of 4.1629 × 10^{–3}, 0.3963 × 10^{–3} and 0.1085 × 10^{–3} for the measured heights h_{1}, h_{2} and h_{3}, respectively. The new RLSEKF observer with its recursive determination of the maximum likelihood has attained ARMSE of 2.1982 × 10^{–6}, 0.1512 × 10^{–6} and 0.0261 × 10^{–7} for the measured heights h_{1}, h_{2} and h_{3}, respectively. This novel RLSEKF has proved to be highly robust and has higher precision than the RBF neural observer and UKF technique as applied for the TTPS model.
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Appendix
Appendix
Abbreviations
 RBF :

Radial basis function
 RLS :

Recursive likelihood synthesizer
 EKF :

Extended Kalman filter
 UKF :

Unscented Kalman filter
 TTPS :

Threetank process system
 UI :

Unknown inputs
 IAUKF :

Intelligent adaptive unscented Kalman filter
 EM :

Expected maximum
 ARMSE :

Average root mean square error
List of symbols
 h :

Height of liquid/fluid level in the tank
 fw :

Flow rate within and from the three tanks
 R :

Resistance of the flow
 g :

Gravitational force
 a :

Area of connecting pipes
 A :

Area of cylindrical tanks
 D :

Inner diameter of the tanks
 h _{1} :

Steadystate fluid level of tank 1
 h _{2} :

Steadystate fluid level of tank 2
 h _{3} :

Steadystate fluid level of tank 3
 C _{1} :

Discharge of inlet orifice
 C _{2} :

Discharge of interconnecting orifice—coupler
 C _{3} :

Discharge of outlet orifice
 x(q):

System’s unobserved state
 y(q):

Observed state
 u(q):

Input signal
 v(q) and z(q):

Gaussian white noise
 L and M:

Covariance matrices
 G and H:

Functional vectors
 δ(q):

Past and present observations
 ψ _{ RBF } :

Nonlinear function
 α _{ y } :

Number of past output corresponding to the measured state
 α _{ e } :

Number of past output corresponding to the observed state
 e(q):

Error term used in RBF fullorder neural observer
 χ _{ 0 } :

Initial covariance
 x _{ q } Q :

Smoothing estimate state value
 J _{ q } :

Jacobian matrix of the measured vector
 C _{ q } :

Conditional covariance of x_{q}
 C _{ qQ } :

Covariance estimate
 w :

Dimensions
 V(j):

Linked weights
 σ :

Spread of the mean of the sigma point
 Q :

Secondary scaling coefficient
 ζ :

Prior knowledge of the probability distribution
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Suguna, A., Ranganayaki, V. & Deepa, S.N. Design of FullOrder Neural Observer with Nonlinear Filter Techniques for State Estimation of a ThreeTank Process Control System. Iran J Sci Technol Trans Electr Eng (2022). https://doi.org/10.1007/s4099802200528y
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DOI: https://doi.org/10.1007/s4099802200528y
Keywords
 Neural observer
 State estimator
 Likelihood synthesizer
 Threetank process system
 Extended Kalman filter
 Unscented Kalman filter
 Observer design