State and parameter estimation of nonlinear stochastic systems by evolution strategies based particle filter

This paper presents a Hybrid Particle Filter based RNN method for state estimation of non-linear dynamical system with knowledge of its input and output measurements. Particle filters are sequential Monte Carlo methods based on point mass (or particle) representations of probability densities, which is used to train Recurrent Neural Networks for estimation problems. The performance this method is compared with EKF based estimation and RNN based estimation. An Induction motor is considered as typical non-linear system and is implemented in MATLAB environment.

This paper investigated the problem of state and fault estimation for nonlinear discrete time systems in presence of unknown disturbances. A novel unbiased minimum variance filter (UMVF) is derived by reconstructing the non linear version of NUMV filter. In this work we assume that no prior knowledge about the dynamic of the disturbance and the fault are known. In this paper we considers that the fault affects both the system state and measurement equations, but the disturbance affects only the system state. The NUMV filter presented in this paper is an extension of the filter presented in [11]. The efficacy of the proposed filter is demonstrated by two simulation examples.

Recent massive increase of the computational power has allowed to rebirth of Monte Carlo integration and its application of Bayesian filtering, or particle filters. Particle filters evaluate a posterior probability distribution of the state variable based on observations in Monte Carlo simulation using so-called importance sampling. However, the filter performance is deteriorated by degeneracy phenomena in the importance weights. Recognizing the similarities and the difference of the processes between the particle filters and evolution strategies, an evolutionary computation approaches, a novel filter called the evolution strategies based particle filter (ESP) has been proposed to circumvent this difficulty and to improve the performance. Here, the ESP filter is applied to fault detection of nonlinear stochastic state space models. Its applicability is exemplified by numerical simulation studies

Motivated by state estimation problems in power distribution networks (PDN), the paper proposes a fusion based, reduced order, distributed implementation of the particle filter (FR/DPF) for large scale, nonlinear dynamical systems with localized sensor observations. Direct application of the centralized particle filter is computationally challenging due to the high dimensions of the state-space dynamics. Based on partitioning the overall system into N localized but mathematically coupled subsystems, the near-optimal FR/DPF provides computational savings of a factor of N over the centralized particle filter implementation. By introducing distributed state and observation fusion steps, the proposed FR/DPF does not require a fusion centre and maintains consistency between the local sub-systems. In our Monte Carlo simulations of a simplified PDN, the performance of the FR/DPF is consistently close to that of the centralized implementation.

This paper proposes a Bayesian unscented Kalman filter with simplified Gaussian mixtures (BUKF-SGM) for dynamic state space estimation of nonlinear and non-Gaussian systems. In the BUKF-SGM, the state and noise densities are approximated as finite Gaussian mixtures, in which the mean and covariance for each component are recursively estimated using the UKF. To avoid the exponential growth of mixture components, a Gaussian mixture simplification algorithm is employed to reduce the number of mixture components, which leads to lower complexity in comparing with conventional resampling and clustering techniques. Experimental results show that the proposed BUKF-SGM can achieve better performance compared with the particle filter (PF)-based algorithms. This provides an attractive alternative for nonlinear state estimation problem.

Robust unscented Kalman filter with adaptation of process and measurement noise covariances

Particle filtering has been proved effective for the state estimation of nonlinear and non-Gaussian systems. To solve the problems of sample degradation and depletion in standard particle filtering tracking algorithm, a novel immune particle filtering target tracking method is proposed in Passive Millimeter Wave (PMMW) imaging. Particle filtering provides a framework in which the posterior density of PMMW target state is represented by a weighted sample set. By using the artificial immune algorithm combined with the Mean Shift algorithm, the samples are optimized during the evolution process. To achieve robust description of the PMMW targets, both gray and gradient orientation distributions are taken into account. Besides, the observation density is established by computing the Bhattacharyya distance between the distribution of the target model and that of the candidate. Experimental results demonstrate that the proposed algorithm is superior to traditional ones when tracking scale changing PMMW targets.

An Improved Gaussian Sum Unscented Kalman Filter

A Quick Identification Method of Continuous-Time Nonlinear Systems and Its Application to Power Plant Control

Parameter estimation for uncertain systems based on fault diagnosis using Takagi–Sugeno model

A moving horizon state and parameter estimation scheme with guaranteed robust convergence

A new framework is presented for understanding how a nonnormal probability density function (pdf) may affect a state estimate and how one might usefully exploit the nonnormal properties of the pdf when constructing a state estimate. A Bayesian framework is constructed that naturally leads to an expansion of the expected forecast error in a polynomial series consisting of powers of the innovation vector. This polynomial expansion in the innovation reveals a new view of the geometric nature of the state estimation problem. It is shown that this expansion in powers of the innovation provides a direct relationship between a nonnormal pdf describing the likely distribution of states and a normal pdf determined by powers of the forecast error. One implication of this perspective is that when state estimation is performed on a nonnormal pdf it leads to state estimates based on the mean to be nonlinear functions of the innovation. A direct relationship is shown between the degree to which the state estimate varies with the innovation and the moments of the distribution. These and other implications of this new view of ensemble state estimation in nonlinear systems are illustrated in simple scalar systems as well as on the Lorenz attractor.

An extended model-based observer for state estimation in nonlinear hysteretic structural systems

The article presents an innovative approach to simultaneously estimate states and unknown inputs (UIs) in nonlinear systems using a particle filter (PF) based recursive expectation‐maximization (EM) algorithm. This method is distinct from traditional iterative EM algorithms. During the E‐step, it calculates the Q‐function recursively within the maximum likelihood framework, while the PF estimates the system states. The M‐step involves local maximization of the recursive Q‐function to online estimate the UIs. The effectiveness of the PF‐based recursive EM algorithm is demonstrated with a numerical example, and comparisons with the augmented state PF are made to highlight its advantages. Finally, the proposed algorithm is implemented in a real application for the estimation of the continuous fermentation process.

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.