An improved fuzzy Kalman filter for state estimation of nonlinear systems

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.

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.

The development of a Kalman filter for state and parameter estimation of a biotechnical process is discussed. Because of the large complexity of biotechnical processes, mathematical models for online estimation are based on extensive simplifications. Therefore model errors in the structure and parameters cannot be avoided. In such situations, simulations of the process in combination with the estimator are very helpful during the design phase: these permit fast examinations of the different behaviour of linear filters compared to nonlinear algorithms and also investigations of the influence of sampling interval and initial values of state and filter variables on the estimation. By the use of such simulations, the suitability of process models with various degrees of simplifications can also be easily tested. Based on the simulations, an extended Kalman filter with iteration of the output equations was chosen. Besides the states, two parameters of a third order process model are estimated online. The filter algorithm was tested during batch processes and worked well after a slight modification. The filter behaviour observed in the experiments was very similar to the simulations.

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.

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

Three-stage unscented Kalman filter for state and fault estimation of nonlinear system with unknown input

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

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.

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

This paper proposes a composite state observer structure that combines the sliding mode and cubic observers for state estimation of linear time-invariant and nonlinear Lipschitz systems. The proposed observer generalises the aforementioned ones and can be reduced by the proper assignment of parameters. Convergence criteria and performance advantages are given for the proposed observer structure. The paper also provides a simple structural parameter selection framework for the design of the sliding mode and sliding mode cubic observers. Simulation examples show the superiority of the proposed observer to the existing ones.

Extended Kalman filter (EKF) has been widely accepted as an important tool in the state estimation of nonlinear systems. However, defects of EKF such as biased estimation, computational complexity and inefficacy when analytical derivatives (Jacobians or Hessians) can not be calculated also affect its application in many fields. In this paper, unscented Kalman filter (UKF) was employed as an alternative to estimate the vehicle velocity and wheel angular speed of the anti-lock braking system (ABS). Simulation results show that the UKF can provide more accurate and efficient performance than the EKF for the state estimation.

The effectiveness of the stationary form of the discrete Kalman filter for state estimation in noisy process systems was demonstrated by simulated and experimental tests on a pilot plant evaporator. The filter was incorporated into a multivariable, computer control system and resulted in good control despite process and/or measurement noise levels of 10%. The results were significantly better than those obtained when the Kalman filter was omitted or replaced by conventional exponential filters. In this application the standard Kalman filter was reasonably insensitive to incorrect estimates of initial conditions or noise statistics and to errors in model parameters. The filter estimates were sensitive to unmeasured process disturbances. However this sensitivity could be reduced by treating the noise covariance matrices R and Q as design parameters rather than noise statistics and selecting values which result in increased weighting of the process measurements relative to the calculated model states.

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.

This paper investigates the application of multisensor data fusion (MSDF) technique to enhance the state estimation of a nonlinear plant. The proposed method is based on Kalman filters approach to improve the state estimation obtained by the novel adaptive unscented Kalman filter (AUKF). The common trend for the KF implementation assumes pre-specified fixed distribution matrices for both process and measurement noises. Here, however, the variance matrices for both process and measurement noise signals are assumed unknown a priori and thus incrementally estimated and updated using a sliding time window paradigm within which an estimation of the noise variance is calculated and adaptively updated each time the window is shifted forward. The proposed methodology is tested on a simulated continuous stirred tank reactor (CSTR) problem to estimate 4 states of this nonlinear plant. The simulation results demonstrate the superiority of the suggested method in state estimation compared with a previously reported approach.

Image reconstruction algorithm of electromagnetic tomography based on fractional Kalman filter