A new framework for data reconciliation and measurement bias identification in generalized linear dynamic systems

Sequential data reconciliation algorithms have been developed for input-output models in linear dynamic systems. Existing filtering methods do not treat the case where there are measurement errors in the input variables. In our approach, the measurement errors in the input variables are optimally handled by the least squares method. This method shows good performance for input-output models.

Determining a dynamic model for flotation circuits using plant data to implement a Kalman filter for data reconciliation

For linear dynamic systems with white process and measurement noise, the Kalman filter is known to be the minimum variance linear state estimator. In the case that the random quantities are Gaussian, then the Kalman filter is the minimim variance state estimator. However, in the application of Kalman filters 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 optimal filter. Previous work by the authors demonstrated an analytic method of incorporating deterministic state equality constraints in the Kalman filter. This paper extends that work to develop the properties of Kalman filters in the presence of statistical state constraints. That is, given a linear system such that the expected values of the state variables satisfy some linear equality, we can constrain the Kalman filter estimates to satisfy those constraints. This results in a family of constrained filters with each member parameterized by a weighting matrix. This paper derives several interesting properties of the constrained Kalman filters.

A variational Bayesian robust linear dynamic system approach for dynamic process modelling and fault detection

Since measurements of process variables are subject to measurements errors as well as process variability, data reconciliation is the procedure of optimally adjusting measured date so that the adjusted values obey the conservation laws and constraints. Thus, data reconciliation for dynamic systems is fundamental and important for control, fault detection, and system optimization. Attempts to successfully implement estimators are often hindered by serve process nonlinearities, complicated state constraints, and un-measurable perturbations. As a constrained minimization problem, the dynamic data reconciliation is dynamically carried out to product smoothed estimates with variances from the original data. Many algorithms are proposed to solve such state estimation such as the extended Kalman filter (EKF), the unscented Kalman filter, and the cubature Kalman filter (CKF). In this paper, we investigate the use of CKF algorithm in comparative with the EKF to solve the nonlinear dynamic data reconciliation problem. First we give a broad overview of the recursive nonlinear data dynamic reconciliation (RNDDR) scheme, then present an extension to the CKF algorithm, and finally address the issue of how to solve the constraints in the CKF approach. The CCRNDDR method is proposed by applying the RNDDR in the CKF algorithm to handle nonlinearity and algebraic constraints and bounds. As the sampling idea is incorporated into the RNDDR framework, more accurate estimates can obtained via the recursive nature of the estimation procedure. The performance of the CKF approach is compared with EKF and RNDDR on nonlinear process systems with constraints. The conclusion is that with an error optimization solution of the correction step, the reformulated CKF shows high performance on the selection of nonlinear constrained process systems. Simulation results show the CCRNDDR is an efficient, accurate and stable method for real-time state estimation for nonlinear dynamic processes.

Linear dynamical systems over finite rings

Measurement bias invariant moving horizon estimation in the presence of outliers for data reconciliation of nonlinear dynamic systems

The network oriented representation of the 3-D electromagnetic structures is based on two types of linear systems. The former one is a dynamic linear system which describes the interaction of electric and magnetic fields inside the structure while the latter one is a linear system consisting of delay lines meant for the reflection and propagation. The system identification of the linear dynamic system needs the estimation of the poles positions and the maximum duration of the delays of complementary linear system. The improved system identification scheme based on poles set stability criterion is introduced. This scheme offers to divide the restored impulse response into the finite duration entire part and the infinite pole part which pertain to the each linear system correspondingly. The simulation results of the model parameter estimation for the two-port coplanar resonator are demonstrated.

P.253 Individual differences in striatal dopamine at steady state influence L-DOPA effects on delay discounting behaviour

An expanded form of the third-order Markov undulation model is developed which includes undulation of the geoid, vertical deflections, gravity anomaly, and the anomalous gravity gradients. First, the complete set of autocorrelation and cross-correlation functions, as specified by the autocorrelation of undulation, is obtained. Then, a time-domain approach is used to synthesize the corresponding linear system driven by white noise that represents the anomalous gravity field behavior along a straight horizontal track. The resulting nine-state Markov model provides a shaping filter for applying covariance analysis and optimal estimation techniques to inertial navigation and gravity gradiometry systems analysis. ONTINUED mechanical refinement has brought inertial navigation technology to the stage where unmodeled variations in the Earth's gravity field have become significant and sometimes dominant error sources.1 At the same time, inertial navigation system analysts have been facing the task of developing error models to evaluate the impact of gravity uncertainties on navigation system performance. Ad- ditionally, the development of gravity gradiometers has made it necessary to model gravity-gradient signals to specify sensor requirements and analyze gradiometer-aided inertial navigation or gradiometry survey performance. To apply the powerful tools of linear system theory and Kalman filtering, it has become common to consider gravity uncertainties random variables, and to model them as Markov processes. Following the first treatment of vertical deflections as a first-order Markov process,2 a succession of higher order Markov models was proposed culminating with the third- order Markov undulation model3'4 which is fully self- consistent; that is, the auto- and cross-correlation functions of undulation, vertical deflections, and gravity anomaly obey and are derived according to the mathematical relationships of physical geodesy. The motivation for using Markov models for gravity un- certainties is that they can be cast in the form of linear dif- ferential equations driven by white noise. This allows use of the model as a shaping filter in covariance analysis of linear dynamic systems, Kalman filters, and optimal smoothing algorithms. The expanded third-order Markov undulation model described in this paper is derived from the original version, but it has three differences. First, it was found that the original model could easily be extended to include all the anomalous gravity gradients by continued differentiation of auto- and cross-correlation functions. Second, the exact cross-correlation function between undulation and gravity anomaly contains modified Bessel functions.4 Modified Bessel functions are solutions to a class of differential equations whose coefficients are functions of the independent variable. To obtain a Markov shaping filter, it is necessary to substitute an approximate function which is the solution to a linear differential equation with constant coefficients. While the chosen exponential form did not approximate the exact Bessel function as well as at first hoped possible, it provides a suitable representation of the un- dulation-gravity anomaly cross-correlation.

The SWOT satellite mission is the first to conduct a global survey of the Earth’s surface waters, measuring water surface height, river width, and water surface slope, based on which river discharge is estimated. At mid-latitudes, the repeat orbit design of SWOT only allows a sampling of twice per repeat cycle, which is considered too low for most hydrological applications. We develop a linear dynamic system that ingests SWOT observations for daily discharge estimation over continuous reaches in a single-branch river network to overcome this limitation. The linear dynamic system includes a process model based on a physically-based spatiotemporal discharge correlation model and observation equations utilizing SWOT products. We solve this dynamic system through a Kalman filter, which is executed in the time domain to obtain daily discharge. Building on the strong performance of the method with synthetic data, we apply this algorithm using SWOT measurements in the Rhine River, where we validate its performance by comparing the estimates against gauge discharge data. These efforts aim to unlock the potential of SWOT data for daily discharge estimation in diverse river networks globally.

In this paper, we study the Poincare recurrence phenomenon in linear dynamical systems, that is, dynamical systems whose trajectories return infinitely often to neighborhoods of their initial condition. Specifically, we provide several equivalent notions of Poincare recurrence and review sufficient conditions for nonlinear dynamical systems that ensure that the system exhibits Poincare recurrence. Furthermore, we establish necessary and sufficient conditions for Poincare recurrence in linear dynamical systems. Finally, we show that in the case of linear systems the absence of volume-preservation is equivalent to the absence of Poincare recurrence implying irreversibility of a dynamical system

This paper presents uncented Kalman filter technique for identification of non linear dynamic systems. A novel unscented Kalman filter (UKF) has been proposed that has the advantage over EKF since it does not use linearization for state prediction and covariance's and costly calculations of derivatives. This leads to an accurate computation of Kalman gain and error covariance matrices which ultimately leads to an accurate identification of the system. The approach is shown to exhibit robustness characteristics and fast convergence property. A simulation example dealing with applications of the proposed algorithm is given.

The presence of measurement bias and random noise significantly deteriorates the information quality of plant data. Data reconciliation techniques for steady‐state processes have been widely applied to processing industries to improve the accuracy and precision of the raw measurements. This paper develops an algorithm for simultaneous bias correction and data reconciliation for dynamic processes. The algorithm considers process model error as an important contributing factor in the estimation of the measurement bias and process state variables. It employs black‐box models for the process as would be done when phenomenological models are difficult or impractical to obtain. Simulation results of a distillation column demonstrated that this algorithm effectively compensates constant and non‐constant measurement biases yielding much improved reconciled values of process variables. It has computational advantages over previously proposed algorithms based on non‐linear dynamic data reconciliation because an analytical solution is available when using linear process models to approximate the process.

This article presents a method of analyzing mixed logic/dynamic systems. The article describes the development of a computational tool for the analysis of piecewise linear (PL) dynamical systems. Unfortunately, many PL controllers are developed from ad hoc "intelligent systems" ideas which do not aim or allow the associated dynamic behavior to be predicted. An example of such a system is the anti-skid braking system in a car, where the controller is rule-based and designed using the engineer's knowledge of the system. The only current viable approach to testing such a system is by using extensive simulation and prototype testing, which must be repeated for each of the different car models on which it is installed. Anything that provides insight into the logic and dynamic interaction of such a system would be useful: hence the development of the work in this article. Similarly, systems with programmable logic controllers and gain schedulers also fall into the class of piecewise linear systems. The authors take ideas and known results from linear systems, convex set theory, and computational geometry and synthesize them to create an analysis tool for studying a class of systems that mix logic and dynamics. We choose to develop a computational analysis tool primarily because the traditional theoretical analysis of piecewise linear processes is intractable, except, that is, for certain local dynamic behavior.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>