Recursive state estimation in nonlinear processes

Vachhani, Pramod; Narasimhan, Sriram; Rengaswamy, Raghunathan

doi:10.23919/acc.2004.1383604

Cited by 7 publications

(7 citation statements)

References 2 publications

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“…The filter might then learn the wrong state too well and diverge . The importance of choosing a consistent pair of x̂ 0 and P 0 is also emphasized by other authors …”

Section: Defining the Design Parameters Of The Ekfmentioning

confidence: 97%

“…As a benchmark problem, we consider the popular batch reactor example which was originally published by Haseltine and Rawlings and later used in a number of other publications for estimator performance comparison. ,, The model describes the following reversible gas-phase reactions that take place in an isothermal, well-mixed batch reactor with constant volume: left rightauto fittrue100% A ⇌ k 2 k 1 B + C (13) 2 B ⇌ k 4 k 3 C (14) The true reaction rate constants are given as k = [ k 1 , k 2 , k 3 , k 4 ] T = [0.5, 0.05, 0.2, 0.01] T .…”

Section: Benchmark Problem: Batch Reactormentioning

confidence: 99%

“…14 The importance of choosing a consistent pair of x0 and P 0 is also emphasized by other authors. 15 To that end, some authors, e.g. Jazwinski 14 or Valappil and Georgakis, 5 propose to initialize P 0 as follows:…”

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confidence: 99%

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How To NOT Make the Extended Kalman Filter Fail

Schneider

Georgakis

2013

Ind. Eng. Chem. Res.

100

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In an effort to assess the performance of newer estimation algorithms, many prior publications have presented comparative studies where the Extended Kalman Filter (EKF) failed. This is because the EKF's design parameters were sometimes chosen arbitrarily and with little consideration of their role and impact on filter performance. This paper demonstrates in a tutorial way that EKF failure can often be avoided by a systematic design of its parameters, i.e. its covariance matrices. Particular focus is on the systematic selection of proper initial state and process noise covariance matrices. As in practice, model parameters are first identified from plant measurements. The covariance of these model parameters is subsequently required to calculate the proposed time-varying process noise covariance matrix for the EKF. Finally, the proposed EKF design is evaluated on a popular reactor example process from the literature and converges in all simulation runs. From this extensive set of simulations and by comparison with several out-of-the-box versions of the constrained Unscented Kalman Filter (UKF), we conclude that there exists a systematic way to design the EKF for a very satisfactory performance. Therefore, the EKF's design parameters need not be tuned ad hoc by trial and error.

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“…The filter might then learn the wrong state too well and diverge . The importance of choosing a consistent pair of x̂ 0 and P 0 is also emphasized by other authors …”

Section: Defining the Design Parameters Of The Ekfmentioning

confidence: 97%

Section: Benchmark Problem: Batch Reactormentioning

confidence: 99%

See 1 more Smart Citation

How To NOT Make the Extended Kalman Filter Fail

Schneider

Georgakis

2013

Ind. Eng. Chem. Res.

100

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“…The importance of choosing a consistent pair of an initial state estimate guess and initial state estimate covariance matrix is also emphasized by other authors (Valappil and Georgakis, 2000). For instance, Vachhani et al (2004) emphasized the role of a consistent choice of initial state estimate covariance matrix and consequently the use of alternate initial state information for their simulations. Similarly, Prakash et al (2010) silently adapt their initial state estimate to be more consistent with the original initial state estimate covariance matrix.…”

Section: Introductionmentioning

confidence: 93%

State estimation of chemical engineering systems tending to multiple solutions

Salau

Trierweiler

Secchi

2014

Braz. J. Chem. Eng.

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-A well-evaluated state covariance matrix avoids error propagation due to divergence issues and, thereby, it is crucial for a successful state estimator design. In this paper we investigate the performance of the state covariance matrices used in three unconstrained Extended Kalman Filter (EKF) formulations and one constrained EKF formulation (CEKF). As benchmark case studies we have chosen: a) a batch chemical reactor with reversible reactions whose system model and measurement are such that multiple states satisfy the equilibrium condition and b) a CSTR with exothermic irreversible reactions and cooling jacket energy balance whose nonlinear behavior includes multiple steady-states and limit cycles. The results have shown that CEKF is in general the best choice of EKF formulations (even if they are constrained with an ad hoc clipping strategy which avoids undesired states) for such case studies. Contrary to a clipped EKF formulation, CEKF incorporates constraints into an optimization problem, which minimizes the noise in a least square sense preventing a bad noise distribution. It is also shown that, although the Moving Horizon Estimation (MHE) provides greater robustness to a poor guess of the initial state, converging in less steps to the actual states, it is not justified for our examples due to the high additional computational effort.

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“…Furthermore, even if the filters do not diverge, convergence may be slow if the initial state covariance matrices do not account for the initial state estimates being far from the true values. 17,18 The method based on Maximum Likelihood Estimation presented in [5] is used to obtain initial estimates of the parameters of interest. Although the estimation will be biased in the presence of high remnant power, the initial estimates obtained are sufficiently accurate to initialize the DEKF with.…”

Section: Initializationmentioning

confidence: 99%

Dual Extended Kalman Filter for the Identification of Time-Varying Human Manual Control Behavior

Popovici

Zaal

Pool

2017

AIAA Modeling and Simulation Technologies Conference

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A Dual Extended Kalman Filter was implemented for the identification of time-varying human manual control behavior. Two filters that run concurrently were used, a state filter that estimates the equalization dynamics, and a parameter filter that estimates the neuromuscular parameters and time delay. Time-varying parameters were modeled as a random walk. The filter successfully estimated time-varying human control behavior in both simulated and experimental data. Simple guidelines are proposed for the tuning of the process and measurement covariance matrices and the initial parameter estimates. The tuning was performed on simulation data, and when applied on experimental data, only an increase in measurement process noise power was required in order for the filter to converge and estimate all parameters. A sensitivity analysis to initial parameter estimates showed that the filter is more sensitive to poor initial choices of neuromuscular parameters than equalization parameters, and bad choices for initial parameters can result in divergence, slow convergence, or parameter estimates that do not have a real physical interpretation. The promising results when applied to experimental data, together with its simple tuning and low dimension of the state-space, make the use of the Dual Extended Kalman Filter a viable option for identifying time-varying human control parameters in manual tracking tasks, which could be used in real-time human state monitoring and adaptive human-vehicle haptic interfaces.

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Recursive state estimation in nonlinear processes

Cited by 7 publications

References 2 publications

How To NOT Make the Extended Kalman Filter Fail

How To NOT Make the Extended Kalman Filter Fail

State estimation of chemical engineering systems tending to multiple solutions

Dual Extended Kalman Filter for the Identification of Time-Varying Human Manual Control Behavior

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