Rata Suwantong

Stability of a nonlinear Moving Horizon Estimator with pre-estimation

In this paper, a Moving Horizon Estimator with pre-estimation (MHE-PE) is proposed for discrete-time nonlinear systems under bounded noise. While the classical Moving Horizon Estimator (MHE) compensates for model errors by estimating the process noise sequence over the horizon via optimization, the MHE-PE does it using an auxiliary estimator. The MHE-PE is shown to require significantly less computation time compared to the MHE, while providing the same order of magnitude of estimation errors. The stability of the estimation errors of the MHE-PE is also proven and an upper bound on its estimation errors is derived. Performances of the MHE-PE is illustrated via a simulation example of pressure estimation in a gas-phase reversible reaction.

Robustness analysis of a Moving Horizon Estimator for space debris tracking during atmospheric reentry

Trajectory estimation during atmospheric reentry of ballistic objects such as space debris is a very complex problem due to high variations of their ballistic coefficients. In general, the characteristics of the tracked object are not accurately known and an assumption on the dynamics of the ballistic coefficient has to be made in the estimation model. The designed estimator must hence prove to be robust enough to such model uncertainties, and to bad initialization if no good prior information on the initial position, velocity, and the characteristics of the object is available. Robustness of a Moving Horizon Estimator (MHE) is studied in this paper and compared to several other filters: Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Regularized Particle Filter (RPF). The performances of the filters are analysed in terms of convergence percentage, accuracy, robustness to bad initialization, and computation time, via Monte Carlo simulations of trajectories of several space debris. Contrary to the classical tracking problem of supersonic ballistic objects for which RPF has been proven to be efficient in the literature, it is shown that its performance are overcome by MHE for the space debris tracking problem considered in this paper.

Space debris trajectory estimation during atmospheric reentry using moving horizon estimator

Space debris trajectory estimation during atmospheric reentry is a complex problem. For such an object the ballistic coefficient, which characterizes the response of the object to aerodynamics braking, is usually a highly nonlinear function of time. This function may be unknown if no a priori information on the object type is available. It is therefore interesting to design a robust estimator that would provide accurate estimates of the state of the tracked object, from available measurements. In this paper, a Moving Horizon Estimator (MHE) is implemented for trajectory estimation of a space debris during atmospheric reentry, from radar measurements. Its performances in terms of convergence and accuracy are analysed and compared with that of an Extended Kalman Filter (EKF), traditionally applied to this type of problem.

Moving Horizon Estimation with Pre-Estimation (MHE-PE) for 3D space debris tracking during atmospheric re-entry

Space debris tracking during atmospheric re-entry is a very complex problem due to high variations with time of the ballistic coefficient. The nature of these variations is generally unknown and an assumption has to be made in the estimation model which can result in high model errors. An estimator which is robust against model errors is therefore required. In previous work done by the authors, Moving Horizon Estimation (MHE) has been shown to outperform other classical nonlinear estimators in terms of accuracy and robustness against poor initialization for a simplified 1D case of space debris tracking during the re-entry. However, the large computation time of the MHE prevents its implementation for the 3D cases. Recently, the Moving Horizon Estimation with Pre-Estimation (MHE-PE) which requires much less computation time than the classical MHE while keeping its accuracy and robustness has been proposed. This paper therefore implements the MHE-PE to solve the 3D space debris tracking problem during the re-entry. Its performances are compared to some classical nonlinear estimators in terms of non-divergence percentage, accuracy and computation time through Monte Carlo simulations.

Moving Horizon Estimator with Pre-Estimation for crop start date estimation in tropical area

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.

Stability analysis and robustness assessment of deterministic and stochastic nonlinear moving horizon estimators

This paper proposes a discussion on the classification of the formulations of nonlinear Moving Horizon Estimators (MHE) of the literature into two categories: deterministic and stochastic. The stability of the dynamics of the estimation error is discussed for the MHEs in both frameworks. This paper also provides full explicit formulation of the stability conditions for the MHE in the deterministic framework, which were not given in the literature. Furthermore, robustness of MHE in both frameworks with respect to model errors is investigated through a simulation example of space object tracking. Comparison with other more classical estimators such as EKF, UKF and particle filter is also achieved.