Modified unscented recursive nonlinear dynamic data reconciliation for constrained state estimation

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.

An improved recursive non-linear dynamic data reconciliation for non-linear state estimation subject to bound constraints

Constrained unscented recursive estimator for nonlinear dynamic systems

This paper investigates the problem of nonlinear state estimation for control moment gyroscope (CMG) inverted pendulum. The dynamics of CMG inverted pendulum result into stiff nonlinearities and are included here. Both Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) algorithms are utilized for state estimation to investigate their effectiveness. The computer simulations are included for comparison of the two algorithms. There are inherent difficulties in state estimation for systems with stiff nonlinearities. In this research, the results show that EKF performs far better than UKF in most cases for this system. However, this is an attempt to explore the nonlinear estimation problem for this challenging system.

State estimation with delayed measurements is essential to the operation of polymer processes due to the limited availability of reliable online sensors and the unavoidable hold‐up time in the acquisition of critical variables data. In this work, a two‐timescale approach is applied to three filters based on the Unscented Transformation, the Unscented Kalman Filter, the Unscented Recursive Nonlinear Dynamic Data Reconciliation and the Reformulated Constrained Unscented Kalman Filter, in order to incorporate delayed measurements into their estimation scheme. A comprehensive comparative analysis is performed, which shows that the three of them have very good accuracy and convergence properties. However, the Unscented Kalman Filter performs better in terms of computational time. magnified image

Nonlinear dynamic state estimation in instrumented structures with conditionally linear Gaussian substructures

The unscented Kalman filter (UKF) has become a popular method for nonlinear state estimation during the last decade. However, the conventional UKF may not be suitable for real-world applications with state constrains that stem from physical definitions, physical laws or model restrictions. A UKF based method with optimized parameters was proposed in this paper to handle state constraints via the projection of sigma points. In the proposed method, the generated sigma points that violate the state constraints were projected onto the constraint boundary first. The three free parameters of the UKF, i.e., α ,β ,κ , were then optimized using a Gaussian process optimization (GPO) method. Simulations indicate that the proposed optimized UKF algorithm with the projection of sigma points can handle constrained state estimation problem effectively and efficiently.

This paper compares state estimation techniques for nonlinear stochastic dynamic systems, which are important for target tracking. Recently, several methods for nonlinear state estimation have appeared utilizing various random-point-based approximations for global filters (e.g., particle filter and ensemble Kalman filter) and local filters (e.g., Monte-Carlo Kalman filter and stochastic integration filters). A special emphasis is placed on derivations, algorithms, and commonalities of these filters. All filters described are put into a common framework, and it is proved that within a single iteration, they provide asymptotically equivalent results. Additionally, some deterministic-point-based filters (e.g., unscented Kalman filter, cubature Kalman filter, and quadrature Kalman filter) are shown to be special cases of a random-point-based filter. The paper demonstrates and compares the filters in three examples, a random variable transformation, re-entry vehicle tracking, and bearings-only tracking. The results show that the stochastic integration filter provides better accuracy than the Monte-Carlo Kalman filter and the ensemble Kalman filter with lower computational costs.

A solution to the state estimation problem of systems with unmeasurable non-zero mean inputs/disturbances, which do not satisfy the disturbance decoupling conditions, is given using the Kalman filtering and Bayesian estimation theory. The proposed estimation algorithm, named Supervisory Kalman Filter (SKF), consists of a Kalman filter with an extra update step which is inspired by the particle filtering technique. The extra step, called supervisory layer, numerically solves the measurement equations for the portion of the state vector that cannot be estimated by the Kalman filter. First, it produces N randomly generated state vectors, the particles, which are distributed based on the Kalman filter’s last updated estimate. Then, the estimated measurement vector associated with each particle is compared to the actual measurement vector to identify the particle’s probability to be a solution. Finally, a so-called resampling stage is implemented to refine the particles with higher likelihoods. The effectiveness of the SKF is demonstrated by comparing its estimation performance with that of the standard Kalman Filter and the particle filter for a vehicle state estimation problem. The estimation results confirm that the SKF precisely estimates those states of the vehicle that cannot be estimated by either the Kalman filter or the particle filter, regardless of the unknown disturbances from the road. The filtering methodology offered in the article has a potential to improve performance of the systems presented in the patents WO2011115960, WO2010024751, US8073528, and US20110299730. Keywords: Bayesian state estimation, disturbance decoupling conditions, inputs/disturbances, particle filtering, state estimation, systems with unknown kalman filtering, unscented kalman filtering

Decentralized estimation of overflow losses in a hopper dredger

Due to the uncertainty of the Radio Frequency Identification (RFID) measurements and limit of the placement of the readers, it's necessary to use the estimation method to obtain more accurate trajectory in RFID indoor tracking system. The traditional recursive estimation from K to K+1 sampling point may fail, because the measurement of RFID system is irregular sampling due to the data-driven measurement mechanism. This paper develops the tracking method for indoor RFID system, including estimation dynamic model based on the estimated states and nonlinear fusion estimation algorithm for variable-irregular sampling measurements. Two estimation methods are given based on the Extended Kalman filter (EKF) and Unscented Kalman filter (UKF), respectively. The tracking performances are compared and the simulation results show that the performance of UKF can get better performance for indoor RFID tracking, especially in the low detection rate area.

State estimation with a destination constraint using pseudo-measurements

Nonlinear state estimation is a pre-requisite for advanced process control and fault diagnosis tasks. In literature, various recursive nonlinear filtering techniques have been proposed and used for state estimation of nonlinear systems. Over the last few years, Moving Horizon Estimation (MHE) is increasingly being used for state estimation of nonlinear systems. Moving horizon estimation works with a window of data and hence requires additional online computation compared to recursive nonlinear filters. However, MHE performs both smoothing and filtering and thus has the potential to obtain more accurate state estimates as compared to the recursive filters. Most of the available comparisons of MHE with recursive filters are based on simulation case studies where the true states and parameters, as well as noise processes are exactly known. In this work, we apply MHE to a three-tank experimental setup and compare its performance with various nonlinear filters available in literature such as Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Gaussian Sum EKF (GSEKF). We present some of the challenges in experimental implementation of state estimation approaches. These include presence of unknown disturbances, non-whiteness of noise signals as well as lack of accurate measurements. We then discuss the approach followed for obtaining model parameters and noise characterization to make the models amenable for filter implementation. It is found that EKF, GSEKF and UKF perform as well as MHE as far as accuracy is concerned, but require significantly lower computational efforts.

State estimation of induction machines may be a difficult problem, due to the non-linear behavior of theirs. For non-linear state estimation, the unscented Kalman filter (UKF) is a well-known extension of the linear Kalman filter. Operation of the UKF algorithm strongly depends on the process and measurement noise covariance parameters of the estimator. Determination of these parameters is not straightforward and can be difficult, especially if the number of state variables and hence the system complexity is relatively high. In this paper, the UKF algorithm is applied for speed sensorless state estimation of induction machines in such a way that seven state variables are estimated from the measured stator currents and from the known excitation voltages. In order to tune the noise parameters of the UKF, a new, optimization-based method is presented. This tuning method provides adequate behavior for the observer beside difficult operating conditions as it has been shown by simulation experiment.

The normal unscented Kalman filter (UKF) suffers from performance degradation and even divergence while mismatch between the noise distribution assumed to be known as a priori by UKF and the true ones in a real system. In this paper, a novel adaptive UKF (AUKF) is developed and applied to nonlinear joint estimation of both time-varying states and parameters. A cost function is built based on the error between the covariance matrices of innovation and their corresponding estimations. An adaptive algorithm is then designed to online update the covariance of the process noise by minimizing the cost function. The updated covariance is further fed back into the normal UKF. As a result of using such an adaptive mechanism, the robustness of conventional UKF is substantially improved with respect to the uncertain and time-varying noise covariance in the real system. To illustrate this mechanism, simulations are conducted on the dynamics of an unmanned helicopter by jointly estimating both the states and model errors. The improvements of the proposed AUKF are demonstrated by comparing the results with and without the adaptive mechanism.