Regularized State Estimation And Parameter Learning Via Augmented Lagrangian Kalman Smoother Method

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

Dynamic response identification based on state estimation and operational modal analysis

This brief is concerned with the joint state and fault estimation problem for a class of multi-rate systems with dynamical bias. To reflect real practice, the multi-rate sampling is considered which allows the sensor sampling rate and the state update rate to be different. The sensor is subject to the sensor fault that changes according to a dynamic equation. Instead of applying the traditional lifting technique, we introduce a time-varying delay into the measurement equation so as to transform the multi-rate systems into single-rate ones. The aim of this brief is to develop a joint state and fault estimation algorithm with minimized estimation error covariance. The recursion of the estimation error covariance is first derived, and appropriate estimator gains are then characterized that minimizes the estimation error covariance. A simulation example on the DC servo system is given to confirm the usefulness of the developed recursive state and fault estimation algorithm.

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

Guest Editorial: Situational awareness of integrated energy systems

SummaryThis paper presents a novel state estimation approach for linear dynamic systems when measurements are corrupted by outliers. Since outliers can degrade the performance of state estimation, outlier accommodation is critical. The standard approach combines outlier detection utilizing Neyman‐Pearson (NP) type tests with a Kalman filter (KF). This approach ignores all residuals greater than a designer‐specified threshold. When measurements with outliers are used (ie, missed detections), both the state estimate and the error covariance matrix become corrupted. This corrupted state and covariance estimate are then the basis for all subsequent outlier decisions. When valid measurements are rejected (ie, false alarms), potentially using the corrupted state estimate and error covariance, measurement information is lost. Either using invalid information or discarding too much valid information can result in divergence of the KF. An alternative approach is moving‐horizon (MH) state estimation, which maintains all recent measurement data within a moving window with a time horizon of length L. In MH approaches, the number of measurements available for state estimation is affected by both the number of measurements per time step and the number of time steps L over which measurements are retained. Risk‐averse performance‐specified (RAPS) state estimation works within an optimization setting to choose a set of measurements that achieves a performance specification with minimum risk of outlier inclusion. This paper derives and formulates the MH‐RAPS solution for outlier accommodation. The paper also presents implementation results. The MH‐RAPS application uses Global Navigation Satellite Systems measurements to estimate the state of a moving platform using a position, velocity, and acceleration model. In this application, MH‐RAPS performance is compared with MH‐NP state estimation.

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

The relationship between the parameters and the states of state-space systems is nonlinear, which makes the identification problems of state-space systems complicated. This paper considers the joint parameter and state estimation issues for a class of state-space systems in the observer canonical form with the process noises and the observation noises. By means of the least squares principle and the Kalman filtering, we derive a Kalman filtering based recursive extended least squares algorithm. For purpose of achieving the higher estimation accuracy, a Kalman filtering based multi-innovation recursive extended least squares algorithm is proposed by utilizing a range of available data and more information at each recursion. Finally, the effectiveness of the proposed algorithms is validated through a simulation example.

Joint state and actuator fault estimation for networked systems under improved accumulation-based event-triggered mechanism

The term, "Waveform inversion" (WFI), refers to a collection of techniques that use the information from seismic data to derive high-fidelity earth models for seismic imaging. The attractiveness of WFI lies mainly in its lack of approximations, at least in a theoretical sense, in contrast to other model determination techniques such as semblance or tomography. However, a whole raft of approximations must be made to make the technique viable with today'scomputing technology and restrictions of seismic acquisition. These are collectively referred to as "waveform inversion strategies" and in this paper we mainly discuss regularization and preconditioning strategies. Because the wavefields need to be accurately modeled to represent the kinematics of all the waves during WFI iterations, the effects of anisotropy often help to improve WFI results. In this paper, forward modeling and its adjoint computation are based on acoustic wave equations in vertical transversely isotropic (VTI)media. We introduce a multi-parameter inversion for P-wave velocity and anisotropy parameters. WFI is a highly nonlinear, ill-posed problem. We introduce additional information and turn the unconstrained optimization problem into a constrained optimization problem in order to reduce the ill-posedness. The geophysics of the problem leads to appropriate constraints, such as restriction of model parameters, or information from well logs. In this paper, we use well logs as constraints and solve the problem using the augmented Lagrangian method (ALM), a mathematical method that replaces a constrained optimization problem by a series of unconstrained problems. The ALM with well constraints aims at preserving velocity characteristics from welllogs and providing us with more reliable velocity updates. This paper presents the acoustic anisotropic WFI implementation using ALM with well constraints. It also discusses practical strategies for regularization and preconditioning and their influences on the models that are obtained from WFI. We illustrate these approaches on a 2D synthetic Marmousi example and another application to 3D VSOOBC data from the Green Canyon area of the Gulf of Mexico. From the results, we show that multi-parameter VTI WFI with ALM provides us with more useful and reliable model updates. To further evaluate our WFI results, we also compare offset gathers and RTM images and illustrate their significant improvement susing updated models generated from WFI.

Input and state estimation for linear systems with a rank-deficient direct feedthrough matrix

State estimation is the basic problem in every area of science and engineering. For the state estimation problem, Kalman filter is the generally used technique when the system is linear. Various derivatives of Kalman filter are proposed earlier for non-linear systems, i.e. Extended Kalman Filter and Unscented Kalman Filter. But, there is a need of tuning in these estimation techniques and therefore the tuning of process and measurement noise covariance matrices is required. Earlier, the different optimization techniques are used for the tuning of Extended Kalman Filter like Genetic Algorithm, Human Opinion Dynamics based Optimization and Particle Swarm Optimization. In this paper, Hybrid HOD-GSA has been proposed for the tuning of Extended Kalman Filter and also to solve the trapping problem of GSA. Then, the results taken from Hybrid HOD-GSA are compared with the results taken from Human Opinion Dynamics and Particle Swarm Optimization in terms of accuracy, error rate, standard deviation and convergence.

On the use of shape constraints for state estimation in reaction systems

In this paper, we propose a novel categorization framework to recognize tactile sequences based on two particular properties of the tactile data. For the first one, tactile sequences are spatio-temporal data which is sequential and dynamic, depicting the process of grasping an object in different grasping stages; therefore, it is reasonable to discover the dynamical pattern by modeling tactile data as integral sequences rather than individual frames. For the second one, a tactile sequence contains various dynamical patterns in different stages of the grasping process; therefore, we decompose the whole sequence into multiple mini-sequences so as to enhance feature resolution. To address both properties in our framework, we take advantage of a Bag-of-System model using parameters of the Linear Dynamic System (LDS) as feature descriptors. Moreover, we employ the LDS with Symmetric Transition matrix (LDSST) rather than the original LDS as the building-block in order to obtain accurate codewords of the codebook of the Bag-of-System. The performance of our framework is evaluated on six real-world databases of three groups. Our experiments show that classification using LDSST is better than the original LDS, and the decomposition of tactile sequences does improve the accuracy of classification. The experiment results also show the superiority of our framework in comparison with other state-of-the-art sequence classifiers.

The primary objective of this study is to develop a mathematical framework for failure prognostics and uncertainty management based on a state-space degradation model, where unknown parameters are present in the model. Joint state and parameter estimation is carried out by the Sequential Monte Carlo methods. Then, a degradation prediction with uncertainty limits is made. Sequential Monte Carlo methods for joint state and parameter estimation are reviewed, and the effectiveness of the techniques for the prognostics task is assessed. A performance comparison of these algorithms is made based on a numerical study. The results presented in this study show that the state-of-art SMC techniques can provide satisfactory results of joint state and parameter estimation for the prognostics task. The Particle Markov Chain Monte Carlo method provides relatively more accurate estimation results compared with other SMC methods while demanding more computing resources.