Unscented Kalman Filters and Particle Filter Methods for Nonlinear State Estimation

AbstractFor nonlinear state space models to resolve the state estimation problem is difficult or these problems usually do not admit analytic solution. The Extended Kalman Filter (EKF) algorithm is the widely used method for solving nonlinear state estimation applications. This method applies the standard linear Kalman filter algorithm with linearization of the nonlinear system. This algorithm requires that the process and observation noises are Gaussian distributed. The Unscented Kalman Filter (UKF) is a derivative-free alternative method, and it is using one statistical linearization technique. The Particle Filter (PF) methods are recursive implementations of Monte-Carlo based statistical signal processing. The PF algorithm does not require either of the noises to be Gaussian and the posterior probabilities are represented by a set of randomly chosen weighted samples

Fractional central difference Kalman filter with unknown prior information

© 2018 In this paper, a generalized fractional central difference Kalman filter for nonlinear discrete fractional dynamic systems is proposed. Based on the Stirling interpolation formula, the presented algorithm can be implemented as no derivatives are needed. Besides, in order to estimate the state with unknown prior information, a maximum a posteriori principle based adaptive fractional central difference Kalman filter is derived. The adaptive algorithm can estimate the noise statistics and system state simultaneously. The unbiasedness of the proposed algorithm is analyzed. Several numerical examples demonstrate the accuracy and effectiveness of the two Kalman filters

Iterative State Estimation in Non-linear Dynamical Systems Using Approximate Expectation Propagation

Bayesian inference in non-linear dynamical systems seeks to find good posterior approximations of a latent state given a sequence of observations. Gaussian filters and smoothers, including the (extended/unscented) Kalman filter/smoother, which are commonly used in engineering applications, yield Gaussian posteriors on the latent state. While they are computationally efficient, they are often criticised for their crude approximation of the posterior state distribution. In this paper, we address this criticism by proposing a message passing scheme for iterative state estimation in non-linear dynamical systems, which yields more informative (Gaussian) posteriors on the latent states. Our message passing scheme is based on expectation propagation (EP). We prove that classical Rauch--Tung--Striebel (RTS) smoothers, such as the extended Kalman smoother (EKS) or the unscented Kalman smoother (UKS), are special cases of our message passing scheme. Running the message passing scheme more than once can lead to significant improvements of the classical RTS smoothers, so that more informative state estimates can be obtained. We address potential convergence issues of EP by generalising our state estimation framework to damped updates and the consideration of general alpha-divergences

Estimation of Radioactivity Release Activity Using Non-Linear Kalman Filter-Based Estimation Techniques

The estimation of radioactivity release following an accident in a nuclear power plant is crucial due to its short and long-term impacts on the surrounding population and the environment. In the case of any accidental release, the activity needs to be estimated quickly and reliably to effectively plan a rapid emergency response and design an appropriate evacuation strategy. The accurate prediction of incurred dose rate during normal or accident scenario is another important aspect. In this article, three different non-linear estimation techniques, extended Kalman filter, unscented Kalman filter, and cubature Kalman filter are proposed in order to estimate release activity and to improve the prediction of dose rates. Radionuclide release rate, average wind speed, and height of release are estimated using the dose rate monitors data collected in proximity of the release point. Further, the estimates are employed to improve the prediction of dose rates. The atmospheric dispersion phenomenon of radioactivity release is modelled using the Gaussian plume model. The Gaussian plume model is then employed for the calculation of dose rates. A variety of atmospheric and accident related scenarios for single source and multiple sources are studied in order to assess the efficacy of the proposed filters. Statistical measures have been used in order to validate the performance of the proposed approaches

Mechanical speed estimation of a DFIG based on the Unscented Kalman Filter (UKF)

This work proposes a new estimation technique for the doubly-fed induction generator (DFIG) variables. Researchers have designed numerous sensorless control strategies for the DFIG used either for mechanical speed, electromagnetic torque, or rotor position estimation. In this paper, an analysis of an Unscented Kalman Filter (UKF) will be presented as an observer for both rotor and stator currents, and mechanical speed, which are key information in DFIG control. The performance of the proposed observer has been validated in a 9 MW wind turbine under MATLAB/Simulink. Based on the results obtained, UKF is safely able to replace mechanically coupled sensors which have many disadvantages such as high cost, maintenance, and cabling requirements

A critical review of online battery remaining useful lifetime prediction methods.

Lithium-ion batteries play an important role in our daily lives. The prediction of the remaining service life of lithium-ion batteries has become an important issue. This article reviews the methods for predicting the remaining service life of lithium-ion batteries from three aspects: machine learning, adaptive filtering, and random processes. The purpose of this study is to review, classify and compare different methods proposed in the literature to predict the remaining service life of lithium-ion batteries. This article first summarizes and classifies various methods for predicting the remaining service life of lithium-ion batteries that have been proposed in recent years. On this basis, by selecting specific criteria to evaluate and compare the accuracy of different models, find the most suitable method. Finally, summarize the development of various methods. According to the research in this article, the average accuracy of machine learning is 32.02% higher than the average of the other two methods, and the prediction cycle is 9.87% shorter than the average of the other two methods

Probabilistic models for data efficient reinforcement learning

Trial-and-error based reinforcement learning (RL) has seen rapid advancements in recent times, especially with the advent of deep neural networks. However, the standard deep learning methods often overlook the progress made in control theory by treating systems as black-box. We propose a model-based RL framework based on probabilistic Model Predictive Control (MPC). In particular, we propose to learn a probabilistic transition model using Gaussian Processes (GPs) to incorporate model uncertainty into long-term predictions, thereby, reducing the impact of model errors. We provide theoretical guarantees for first-order optimality in the GP-based transition models with deterministic approximate inference for long-term planning. We demonstrate that our approach not only achieves the state-of-the-art data efficiency, but also is a principled way for RL in constrained environments. When the true state of the dynamical system cannot be fully observed the standard model based methods cannot be directly applied. For these systems an additional step of state estimation is needed. We propose distributed message passing for state estimation in non-linear dynamical systems. In particular, we propose to use expectation propagation (EP) to iteratively refine the state estimate, i.e., the Gaussian posterior distribution on the latent state. We show two things: (a) Classical Rauch-Tung-Striebel (RTS) smoothers, such as the extended Kalman smoother (EKS) or the unscented Kalman smoother (UKS), are special cases of our message passing scheme; (b) running the message passing scheme more than once can lead to significant improvements over the classical RTS smoothers. We show the explicit connection between message passing with EP and well-known RTS smoothers and provide a practical implementation of the suggested algorithm. Furthermore, we address convergence issues of EP by generalising this framework to damped updates and the consideration of general -divergences. Probabilistic models can also be used to generate synthetic data. In model based RL we use ’synthetic’ data as a proxy to real environments and in order to achieve high data efficiency. The ability to generate high-fidelity synthetic data is crucial when available (real) data is limited as in RL or where privacy and data protection standards allow only for limited use of the given data, e.g., in medical and financial data-sets. Current state-of-the-art methods for synthetic data generation are based on generative models, such as Generative Adversarial Networks (GANs). Even though GANs have achieved remarkable results in synthetic data generation, they are often challenging to interpret. Furthermore, GAN-based methods can suffer when used with mixed real and categorical variables. Moreover, the loss function (discriminator loss) design itself is problem specific, i.e., the generative model may not be useful for tasks it was not explicitly trained for. In this paper, we propose to use a probabilistic model as a synthetic data generator. Learning the probabilistic model for the data is equivalent to estimating the density of the data. Based on the copula theory, we divide the density estimation task into two parts, i.e., estimating univariate marginals and estimating the multivariate copula density over the univariate marginals. We use normalising flows to learn both the copula density and univariate marginals. We benchmark our method on both simulated and real data-sets in terms of density estimation as well as the ability to generate high-fidelity synthetic data.Open Acces

A critical review of improved deep learning methods for the remaining useful life prediction of lithium-ion batteries.

As widely used for secondary energy storage, lithium-ion batteries have become the core component of the power supply system and accurate remaining useful life prediction is the key to ensure its reliability. Because of the complex working characteristics of lithium-ion batteries as well as the model parameter changing along with the aging process, the accuracy of the online remaining useful life prediction is difficult but urgent to be improved for the reliable power supply application. The deep learning algorithm improves the accuracy of the remaining useful life prediction, which also reduces the characteristic testing time requirement, providing the possibility to improve the power profitability of predictive energy management. This article analyzes, reviews, classifies, and compares different adaptive mathematical models on deep learning algorithms for the remaining useful life prediction. The features are identified for the modeling ability, according to which the adaptive prediction methods are classified. The specific criteria are defined to evaluate different modeling accuracy in the deep learning calculation procedure. The key features of effective life prediction are used to draw relevant conclusions and suggestions are provided, in which the high-accuracy deep convolutional neural network — extreme learning machine algorithm is chosen to be utilized for the stable remaining useful life prediction of lithium-ion batteries

Latent state estimation in a class of nonlinear systems

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The problem of estimating latent or unobserved states of a dynamical system from observed data is studied in this thesis. Approximate filtering methods for discrete time series for a class of nonlinear systems are considered, which, in turn, require sampling from a partially specified discrete distribution. A new algorithm is proposed to sample from partially specified discrete distribution, where the specification is in terms of the first few moments of the distribution. This algorithm generates deterministic sigma points and corresponding probability weights, which match exactly a specified mean vector, a specified covariance matrix, the average of specified marginal skewness and the average of specified marginal kurtosis. Both the deterministic particles and the probability weights are given in closed form and no numerical optimization is required. This algorithm is then used in approximate Bayesian filtering for generation of particles and the associated probability weights which propagate higher order moment information about latent states. This method is extended to generate random sigma points (or particles) and corresponding probability weights that match the same moments. The algorithm is also shown to be useful in scenario generation for financial optimization. For a variety of important distributions, the proposed moment-matching algorithm for generating particles is shown to lead to approximation which is very close to maximum entropy approximation. In a separate, but related contribution to the field of nonlinear state estimation, a closed-form linear minimum variance filter is derived for the systems with stochastic parameter uncertainties. The expressions for eigenvalues of the perturbed filter are derived for comparison with eigenvalues of the unperturbed Kalman filter. Moment-matching approximation is proposed for the nonlinear systems with multiplicative stochastic noise