Nonlinear state estimation for three tank experimental setup: A comparative evaluation

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

Two approaches, extended Kalman filter (EKF) and moving horizon estimation (MHE), are discussed for state estimation for nonlinear dynamical systems over packet-dropping networks. For EKF, we provide sufficient conditions that guarantee a bounded EKF error covariance. For MHE, a natural scheme on organizing the finite horizon window is proposed to handle intermittent observations. A nonlinear programming software package, SNOPT, is employed in MHE and the formulation for constraints is discussed in detail. Examples and simulation results are presented.

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.

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

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.

This paper investigates the problem of nonlinear state estimation for control moment gyroscope (CMG) inverted pendulum. The dynamics of CMG inverted pendulum result into stiff nonlinearities and are included here. Both Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) algorithms are utilized for state estimation to investigate their effectiveness. The computer simulations are included for comparison of the two algorithms. There are inherent difficulties in state estimation for systems with stiff nonlinearities. In this research, the results show that EKF performs far better than UKF in most cases for this system. However, this is an attempt to explore the nonlinear estimation problem for this challenging system.

This paper addresses the problem of state estimation for nonlinear systems by means of the unscented Kalman filter (UKF). Compared to the traditional extended Kalman filter, the UKF does not require the local linearization of the system equations used in the propagation stage. Important results using the UKF have been reported recently but in every case the system equations used by the filter were considered known. Not only that, such models are usually considered to be differential equations, which requires that numerical integration be performed during the propagation phase of the filter. In this paper the dynamical equations of the system are taken to be difference equations--thus avoiding numerical integration--and are built from data without prior knowledge. The identified models are subsequently implemented in the filter in order to accomplish state estimation. The paper discusses the impact of not knowing the exact equations and using data-driven models in the context of state and joint state-and-parameter estimation. The procedure is illustrated by means of examples that use simulated and measured data.

MHE Based State and Parameter Estimation for Systems subjected to Non-Gaussian Disturbances

Industrial process monitoring tools require robust and efficient estimation techniques that maintain a high service factor by remaining online during abnormal operating conditions, such as during loss of measurements, changes in control status, or maintenance. Constraints incorporate additional process knowledge into estimation by bounding estimated disturbances within feasibility limits thereby providing robustness to faulty measurements or conditions that violate process models. Moving horizon estimation (MHE) and unscented Kalman filtering (UKF) are two estimation techniques that permit incorporation of constraints prior to evaluating the a priori estimate. This paper evaluates both constrained nonlinear estimators versus the extended Kalman filter (EKF) using industrial process data provided by ExxonMobil Chemical Company. Results provide short-term insight into the fouling process, and parameter estimates produced by UKF and MHE are shown to be more accurate than EKF.

This paper presents the efficient Unscented Kalman filter (UKF) based estimation and control of a 3-DOF Omni bundle robot. The angular trajectory tracking becomes more difficult under highly non-linear measurement noise and process noise. A rapidly converging Unscented Kalman Filter (UKF) is presented in the paper. The extended Kalman filter (EKF) provides less accurate results in the highly non-linear system and sometime may become unstable because of convergence related issues, whereas in UKF the results in the non-linear system are better than EKF. UKF is more accurate in state and noise estimation. The computed torque technique is taken as a model to apply UKF. After, estimation the noise is removed. The experiment is conducted on Omni bundle with process and measurement noise. The results prove the superiority of presented UKF over conventional UKF and EKF.

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.

Angular glint noise is a kind of correlated and non-gaussian noise. When dealing with tracking problem in correlated and non-gaussian noise environment, the performance of traditional Unscented Kalman Filter(UKF) will degrade significantly. In order to solve the target tracking problem under the angular glint, this paper raises a new UKF algorithm based on the measurement equations linearization, and it is compared with traditional UKF. The simulation result shows that the new method can effectively get the nonlinear system state estimation in the colored noise environment. Because the linearization is proceeded during the process of solving the new measurement equations' error, so the accuracy of this method is influenced smaller, and this method has extensive adaptability.

On the use of shape constraints for state estimation in reaction systems

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.

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.