Estimation for Nonlinear Dynamical Systems over Packet-Dropping Networks

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 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

The extended Kalman filter (EKF), one of the most popular state estimators for nonlinear uncertain dynamic systems, is considered here in its continuous-discrete (CD) form. The CD version enhances the EKF's accuracy but requires robust and computationally efficient numerical integration methods. The purpose of this article is to present several new efficient integration methods suited to the implementation of the CD-EKF and to compare them to classical implementations such as the Dormand–Prince 4/5 and Euler methods. They are first applied on two proposed nonlinear parameter estimation testbenches and to the stiff Curtiss and Hirschfelder model for state and parameter estimation. Then, they are applied to the estimation of the iron losses of a high-speed permanent-magnet synchronous motor. The results show that for highly nonlinear dynamic systems or for a low to medium sampling frequency, the implicit implementation of the EKF provides a better accuracy and convergence safety. For less nonlinear functions and a higher sampling frequency, classical explicit methods obviously give similar results in a lower computation time.

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 studies three-dimensional multi-robot Cooperative Localization (CL) problem. Most of existing CL strategies adopt Extended Kalman Filter (EKF) or Maximum a Posteriori (MAP). In this paper, a novel approach based on Moving Horizon Estimation (MHE) is proposed. The main contribution of this paper is twofold: 1) MHE is integrated with EKF for three-dimensional CL using single mobile beacon, which can bound localization error, impose various constraints on states and noises, and make use of previous range mea- surements for current estimation. 2) A sufficient condition on observability of multi-robot CL is derived by using Fisher Information Matrix. Simulation is conducted to verify that the proposed MHE based CL algorithm outperforms EKF based method in terms of localization accuracy, and two scenarios where our algorithm is superior to EKF are discussed.

An estimation of the state and the unknown inputs of the reduced nonlinear model of an activated sludge process using the Extended Kalman Filter (EKF) is proposed. First, we present the reduced nonlinear model. This model contained five state variables and four unknown inputs. For satisfying the rank condition for the construction of an EKF, one unknown input has been approximated and the daily mean value of another unknown input has been used. Then, to estimate conjointly the state and the unknown inputs, the reduced nonlinear system is transformed to a nonlinear singular system. High performances of the proposed observer will be shown through the simulation results.

This work presents a polynomial version of the well-known extended Kalman filter (EKF) for the state estimation of nonlinear discrete-time stochastic systems. The proposed filter, denoted polynomial EKF (PEKF), consists in the application of the optimal polynomial filter of a chosen degree /spl mu/ to the Carleman approximation of a nonlinear system. When /spl mu/=1 the PEKF algorithm coincides with the standard EKF. For the filter implementation the moments of the state and output noises up to order 2/spl mu/ are required. Numerical simulations compare the performances of the PEKF with those of some other existing filters, showing significant improvements.

Many interplanetary mission concepts can benefit from autonomous orbit estimation, particularly during critical mission phases. Previous studies have examined the feasibility of optical navigation using nanosatellite class instruments. While promising, these techniques are not without drawbacks. Convergence of the navigation estimates are often sensitive to errors in initial state estimates. This thesis compares various methods to perform nonlinear estimation for autonomous optical navigation. These methods include an extended Kalman filter (EKF), an unscented Kalman filter (UKF), a particle filter (PF), a fixed-lag smoother (FLS), and moving horizon estimation (MHE). The EKF, UKF, and PF can be implemented in real time, while the FLS and MHE implement a delay into the estimation process. To compare the performance of each state estimator three initial reference scenarios around Mars were considered: a hyperbolic flyby, an elliptic orbit and a orbital maneuver using observations of Mars and its moons. Parameter estimation was also explored, where the mass of Mars was to be estimated as a reference parameter in both the hyperbolic and elliptical trajectories. One last reference scenario included a low Earth orbit (LEO) using observations of satellites in a geosynchronous equatorial orbit. In each case, the FLS and MHE showed similar or better performance over each state estimator but at the cost of an increased computation time with respect to the reference EKF. Similarly the UKF was able to provide improved results withe respect to the EKF. While, the PF provided poor estimates in the Mars trajectories but improvements were seen from the UKF and EKF in the LEO scenario.

Accurate crop start date estimation is crucial for crop yield forecasting which is important not only for a government but also for agriculture-based or trading companies. The estimation can be done using the Normalized Difference Vegetation Index (NDVI) computed from radiant energy from the crops of interest. The NDVI collected from the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard the Terra satellite is chosen in this study thanks to its free availability which is suitable for a developing country. In a tropical country as Thailand, the NDVI data is very noisy due to high density of clouds. An appropriate estimation technique must therefore be implemented. In this paper, the NDVI is modelled by a triply modulated cosine function with the mean, the amplitude and the initial phase as state variables. The state and the NDVI of single rice crop in the northeast Thailand are estimated using the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF), the Moving Horizon Estimator (MHE) and the Moving Horizon Estimator with Pre-Estimation (MHE-PE). The MHE-PE, recently proposed in the literature, is an optimization-based estimator using an auxiliary estimator to describe the dynamics of the state over the horizon which has been shown to overcome the classical MHE strategy in terms of accuracy and computation time. The EKF and the MHE-PE provide the smallest start date estimation error compared to the others, which is 0 day in mean and 18 days in standard deviation. However, the EKF fail to detect the NDVI of preplant crops and parasite weeds while the MHE-PE does not.

The main idea presented in this paper is to use interval analysis technique on state estimation of nonlinear dynamic system, in this concrete case the PMSM (Permanent Magnet Synchronous Machine). PMSM drives offers in comparison to other drives several advantages but it is necessary to have knowledge of actual rotor position and actual speed of rotation for precise control. Measurement of these state variables is technically or financially unnecessarily consumptive. These data are usually obtained by state observers, in most cases by extended Kalman filter or his modifications. Unfortunately, in many cases this is insufficient. That is why other methods of state estimation are being researched. One of these methods is interval analysis in which results are not points, but intervals. Advantage of this is that these intervals are guaranteed.

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.

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

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.

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.