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It is crucially important to estimate unknown parameters in process-based models by integrating observation and numerical simulation. For many applications in earth system sciences, a parameter estimation method which allows parameters to temporally change is required. In the present paper, an efficient and practical method to estimate time-varying parameters of relatively low dimensional models is presented. In the newly proposed method, called Hybrid Offline Online Parameter Estimation with Particle Filtering (HOOPE-PF), an inflation method to maintain the spread of ensemble members in a Sampling-Importance-Resampling Particle Filter (SIRPF) is improved using a non-parametric posterior probabilistic distribution of time-invariant parameters obtained by comparing simulated and observed climatology. HOOPE-PF outperforms the original SIRPF in synthetic experiments with toy models and a real-data experiment with a conceptual hydrological model when an ensemble size is small. The advantage of HOOPE-PF is that its performance is not greatly affected by the size of perturbation to be added to ensemble members to maintain their spread while it is important to get the optimal performance in the original particle filter. Since HOOPE-PF is the extension of the existing particle filter which has been extensively applied to many models in earth system sciences such as land, ecosystem, hydrology, and paleoclimate reconstruction, HOOPE-PF can be applied to improve the simulation of these process-based models by considering time-varying model parameters. Plain Language Summary Computer simulation is widely used to understand earth systems such as atmosphere, ocean, land, ecosystem, and society. Many computer simulation models in earth system sciences inevitably have unknown coefficients of equations, which are called model parameters. It is important for accurate simulation of earth systems to tune these model parameters by comparing the results of computer simulation with observation. Although many previous works assumed that model parameters do not change over time, it is necessary to allow them to change over time in some applications, which makes it more difficult to estimate model parameters. In this study, a new method to estimate time-varying model parameters is proposed. The key idea of this paper is to combine two existing methods which integrate observations into computer simulation models. It is found that the proposed method works better than the existing method in three case studies. The proposed method can contribute to improving many simulations in earth system sciences by efficiently tuning time-varying model parameters. [ABSTRACT FROM AUTHOR]

In this paper, a fractional nonlinear control strategy based on the nested saturations technique and the Caputo-Fabrizio derivative for a quadrotor aircraft, to maintain desired position and orientation in stationary flight and trajectory tracking tasks, is proposed and developed. In addition, the dynamic model is obtained by using the Euler–Lagrange formulation, and then it is generalized to an arbitrary order through the Caputo-Fabrizio derivative. The traditional nonlinear control based on the nested saturation technique is also developed and implemented on the quadrotor for comparison purposes between both control schemes. Numerical simulations demonstrated the superiority of the proposed control strategy for stabilizing the quadrotor at hover and reaching the desired position and orientation, over its integer-order counterpart. In addition, three additional desired trajectories are considered, keeping the same gains and orders, to demonstrate the robustness of the proposed control scheme under different operating conditions. In this sense, our controller presents significant performance improvements, which were validated through system simulations. Our proposed control system and its traditional counterpart were tuned experimentally using the response of the system to a desired trajectory. [ABSTRACT FROM AUTHOR]