Ensemble State Estimation for Nonlinear Systems Using Polynomial Expansions in the Innovation

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.

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

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.

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

This manuscript deals with parametric and state estimation problem of discrete-time nonlinear polynomials systems. In this respect, the aim is to design a Recursive State and Parametric Estimation (RSPE) algorithm, based on least square principle, polynomial adjustable models and Kalman filter theory. Our simulation results show the validity of the proposed algorithm.

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.

This paper adresses the problem of simultaneously estimating the state and the fault of nonlinear discrete-time stochastic systems in light of the unknown input filtering framework. The fault and unknown disturbances which may cause great estimate errors and even divergence of conventional filters, affect both the system state and the measurements. Inspired by the robust two stage Kalman filter for linear discrete-time system, a nonlinear robust state and fault estimator is derived. In order to achieve the aim, the nonlinear system with fault and unknown disturbances is first transformed into an equivalent descriptor system. Next, it is shown that the previously proposed robust two stage Kalman filter can be applied to yield a robust state and fault estimation. Simulation results for a robotic manipulator show the effectiveness of the proposed method.

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.

We present a distributed observer for nonlinear systems, which can be used to estimate the state of a central plant with unknown parameters using a network of sensors that measure noisy linear combinations of the state. Our state estimator is based on the unscented Kalman filter and the dual Kalman filter method, which runs two Kalman filters in parallel for both state and parameter estimation. This allows us to improve estimates of the central plants parameters in order to improve state estimates, and vice versa. Furthermore, using results from stochastic stability analysis, we prove that under certain conditions the expected value of the proposed algorithm's estimation error is bounded. This result also shows us that as t goes to infinity, the error bound scales as a function of the largest eigenvalue of the sensor noise covariance matrix. Lastly, we demonstrate the ability of our state estimator to accurately track the state of nonlinear systems through simulations.

Guaranteed methods based on constrained zonotopes for set-valued state estimation of nonlinear discrete-time systems

A generalized performance evaluation method is presented for extended Kalman filter based state estimation of first order nonlinear dynamic systems. The first order nonlinear dynamic systems are placed in three categorizes in terms of the upper bound of the absolute values of the derivatives of the nonlinear functions. According to the proposed theoretical analysis, it is shown that different state estimation performances are achieved by applying the extended Kalman filter to the first order nonlinear systems in these three categorizes. The steady state mean square error performance of the filter is presented explicitly in terms of the bounds on the nonlinearity and noise variance. The advantage of this performance evaluation method is that the convergence property of estimation error variance can be easily concluded from the system nonlinearity before its implementation. This provides insight into what is going to happen in applications, e.g. for dynamic systems used in chaotic synchronization. The simulation of several different nonlinear dynamic systems shows the effectiveness of the proposed performance evaluation criteria.

This paper presents new estimation methods for discrete fractional-order state-space systems with coloured measurement noise. A novel approach is proposed to convert a fractional system with coloured measurement noise to a system with white measurement noise in which the process and measurement noises are correlated with each other. In this paper, two new Kalman filter algorithms for fractional-order linear state-space systems with coloured measurement noise, as well as a new extended Kalman filter algorithm for state estimation in nonlinear fractional-order state-space systems with coloured measurement noise, are proposed. The accuracy of the equations and relations is confirmed in several theorems. The validity and effectiveness of the proposed algorithms are verified by simulation results and compared with previous work. Results show that for linear and nonlinear fractional-order systems with coloured noise, the proposed methods are more accurate than conventional methods regarding estimation error and estimation error covariance. Simulation results demonstrate that the proposed algorithms can accurately perform estimation in fractional-order systems with coloured measurement noise.

This work focuses on filters for nonlinear dynamic systems with nonlinear measurements. The Recursive Nonlinear Least Square Error (RNLS) filter has been recently derived for the state estimation of nonlinear dynamic systems. The RNLS is optimal under the LMSE criterion. Performances of RNLS, EKF and SDDRE-based filters are compared on a common basis. The Pareto formalism is used as a tool for such comparison on a common basis. The comparison is performed for a $6^{\mathrm {t}\mathrm {h}}$ order nonlinear system. This system models a tracking target that performs a coordinated turn/barrel-roll maneuver with unknown turning rate, measured by radar in polar coordinates. It is demonstrated by simulations that the RNLS filter is the optimal filter with respect to the quadratic criterion it is designed for. This places the RNLS filter as a vital candidate estimator of nonlinear systems.

This paper investigates the problem of simultaneous input and state estimation (SISE) for nonlinear dynamic systems. By the augmented state approach, we convert this problem into a standard filtering problem. Then, the split-and-merge technique is utilized for the augmented state estimation. Based on this, a novel split-and-merge based simultaneous input and state filter is developed in order to enhance the ability of dealing with highly nonlinear systems. Simulations demonstrate the effectiveness and efficiency of the proposed filter.