State and Parameter Estimation in Distributed Constrained Systems. 1. Extended Kalman Filtering of a Special Class of Differential-Algebraic Equation Systems

Abstract

State and parameter estimation plays an important role in many different engineering fields. Estimation of systems described by linear and nonlinear differential equations has been very well studied in the literature. Work in the past decade has been geared toward efficiently extending these algorithms to constrained systems. Of recent interest is the evaluation of state estimation techniques for differential-algebraic equation (DAE) systems. The algebraic equations in these studies are exact, an example being the mole fractions adding to unity. However, there are situations where algebraic equations can be of both certain and uncertain types. In this paper, we propose a modified extended Kalman filter (EKF) approach that can handle uncertainties in both differential and algebraic equations, and equality constraints. We also show the importance of this work in estimation of mole fraction, temperature, and pressure profiles in a water gas shift reactor. The impact of location and type of measurements on the estimation accuracy is also studied.

Identification of Non-Linear Differential-Algebraic Equation Models with Process Disturbances

“…Methods for ensuring the existence of well-defined solutions in these cases are discussed in [9], together with an approximate implementation of a particle filter for state estimation. A modified extended Kalman filter that can handle both uncertainty in the differential constraints as well as continuoustime white noise in algebraic constraints of index 1 DAEs is presented in [10], while [11] presents conditions for wellposed estimation problems for linear DAEs with process disturbances.…”

“…The basic idea relies on the use of predictors that are simpler to compute than the optimal mean-square error one-step ahead predictor, which is known to be intractable for most nonlinear stochastic systems. One of the predictors proposed in [10] is the mean of the model's output. It is well known that among constant predictors the mean minimizes the mean-squared error and from this property one can derive consistency of a parameter estimator based on this predictor.…”

Quantitative Kinetic Models from Intravital Microscopy: A Case Study Using Hepatic Transport

“…38 We highlight here that the method of cascades is an important, fast, and general alternative to extended Kalman filters or other Kalman filter variants. 60–62 Kalman filters may solve similar problems to that above but may suffer in the case of pronounced non-linearities in the dynamics, that is, eq 1. This is especially relevant to us here as we would like our method to hold for a broad range of non-linear dynamics.…”

Dynamic Data Reconciliation to Decrease the Effect of Measurement Noise on Controller Performance Assessment

“…A trade‐off between the amount of noise attenuation and the time delay after filtering is required to improve the performance of the exponential filter . Kalman filtering methods are also widely used in practice . However, Kalman filter is limited to dynamic linear and stochastic state‐space models and cannot be directly used in the ARMAX models.…”