1,214 research outputs found

    Estimation of airship states and model uncertainties using nonlinear estimators

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    This Airships are lighter than air vehicles and due to their growing number of applications, they are becoming attractive for the research community. Most of the applications require an airship autonomous flight controller which needs an accurate model and state information. Usually, airship states are affected by noise and states information can be lost in the case of sensor's faults, while airship model is affected by model inaccuracies and model uncertainties. This paper presents the application of nonlinear and Bayesian estimators for estimating the states and model uncertainties of neutrally buoyant airship. It is considered that minimum sensor measurements are available, and data is corrupted with process and measurement noise. A novel lumped model uncertainty estimation approach is formulated where airship model is augmented with six extra state variables capturing the model uncertainty of the airship. The designed estimator estimates the airship model uncertainty along with its states. Nonlinear estimators, Extended Kalman Filter and Unscented Kalman Filter are designed for estimating airship attitude, linear velocities, angular velocities and model uncertainties. While Particle filter is designed for the estimation of airship attitude, linear velocities and angular velocities. Simulations have been performed using nonlinear 6-DOF simulation model of experimental airship for assessing the estimator performances. 1− uncertainty bound and error analysis have been performed for the validation. A comparative study of the estimator's performances is also carried out

    The Role of Kalman Gain and Noise Covariance Selection on the Convergence in State Estimation

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    This is the author accepted manuscript. The final version is available from IEEE via the DOI in this recordIn state estimation problems, the Kalman filter (KF) algorithm considers the noise in the measurements and the systems facilitating convergence to the true state. This paper presents the Bayesian derivation of the discrete-time KF algorithm for a simple example known as the random walk model. However, if the KF coefficients are not well-tuned, it can significantly impact the estimation accuracy and may lead to algorithmic inconsistency. The Kalman gain is a quantitative measure which plays a crucial role in achieving the optimum convergence and stability. In this study, we evaluate the importance of the Kalman gain in the KF algorithm across several choices of the error covariance within the context of the random walk model. Furthermore, we demonstrate that the optimal Kalman gain is determined by minimizing the mean squared error (MSE), producing an unbiased and efficient estimate. This adaptive adjustment enables the KF to tune parameters easily. The theoretical and numerical investigations were carried out using the random walk plus noise model

    Composite Disturbance Filtering: A Novel State Estimation Scheme for Systems With Multi-Source, Heterogeneous, and Isomeric Disturbances

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    State estimation has long been a fundamental problem in signal processing and control areas. The main challenge is to design filters with ability to reject or attenuate various disturbances. With the arrival of big data era, the disturbances of complicated systems are physically multi-source, mathematically heterogenous, affecting the system dynamics via isomeric (additive, multiplicative and recessive) channels, and deeply coupled with each other. In traditional filtering schemes, the multi-source heterogenous disturbances are usually simplified as a lumped one so that the "single" disturbance can be either rejected or attenuated. Since the pioneering work in 2012, a novel state estimation methodology called {\it composite disturbance filtering} (CDF) has been proposed, which deals with the multi-source, heterogenous, and isomeric disturbances based on their specific characteristics. With the CDF, enhanced anti-disturbance capability can be achieved via refined quantification, effective separation, and simultaneous rejection and attenuation of the disturbances. In this paper, an overview of the CDF scheme is provided, which includes the basic principle, general design procedure, application scenarios (e.g. alignment, localization and navigation), and future research directions. In summary, it is expected that the CDF offers an effective tool for state estimation, especially in the presence of multi-source heterogeneous disturbances

    Probabilistic Inference for Model Based Control

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    Robotic systems are essential for enhancing productivity, automation, and performing hazardous tasks. Addressing the unpredictability of physical systems, this thesis advances robotic planning and control under uncertainty, introducing learning-based methods for managing uncertain parameters and adapting to changing environments in real-time. Our first contribution is a framework using Bayesian statistics for likelihood-free inference of model parameters. This allows employing complex simulators for designing efficient, robust controllers. The method, integrating the unscented transform with a variant of information theoretical model predictive control, shows better performance in trajectory evaluation compared to Monte Carlo sampling, easing the computational load in various control and robotics tasks. Next, we reframe robotic planning and control as a Bayesian inference problem, focusing on the posterior distribution of actions and model parameters. An implicit variational inference algorithm, performing Stein Variational Gradient Descent, estimates distributions over model parameters and control inputs in real-time. This Bayesian approach effectively handles complex multi-modal posterior distributions, vital for dynamic and realistic robot navigation. Finally, we tackle diversity in high-dimensional spaces. Our approach mitigates underestimation of uncertainty in posterior distributions, which leads to locally optimal solutions. Using the theory of rough paths, we develop an algorithm for parallel trajectory optimisation, enhancing solution diversity and avoiding mode collapse. This method extends our variational inference approach for trajectory estimation, employing diversity-enhancing kernels and leveraging path signature representation of trajectories. Empirical tests, ranging from 2-D navigation to robotic manipulators in cluttered environments, affirm our method's efficiency, outperforming existing alternatives

    Moving Horizon Estimation for the Two-tank System

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    This thesis presents the application and evaluation of Moving Horizon Estimation (MHE) for the nonlinear two-tank system. MHE is an iterative optimization-based approach that continuously updates the estimates of the states by solving an optimization problem over a fixed-size, receding horizon. Linear and nonlinear MHE-based estimators are designed and implemented in Matlab for evaluation in simulation environment and Simulink for on-line realization and validation. The linear and nonlinear MHE are evaluated in comparison with the Kalman and Extended Kalman filter through extensive simulations and experimental validation, assessing their accuracy, efficiency, and overall performance. The results of the two-tank state and unmeasured disturbance estimation shows the benefit of the MHE

    Navigation Sensor Stochastic Error Modeling and Nonlinear Estimation for Low-Cost Land Vehicle Navigation

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    The increasing use of low-cost inertial sensors in various mass-market applications necessitates their accurate stochastic modeling. Such task faces challenges due to outliers in the sensor measurements caused by internal and/or external factors. To optimize the navigation performance, robust estimation techniques are required to reduce the influence of outliers to the stochastic modeling process. The Generalized Method of Wavelet Moments (GMWM) and its Multi-signal extensions (MS-GMWM) represent the latest trend in the field of inertial sensor error stochastic analysis, they are capable of efficiently modeling the highly complex random errors displayed by low-cost and consumer-grade inertial sensors and provide very advantageous guarantees for the statistical properties of their estimation products. On the other hand, even though a robust version exists (RGMWM) for the single-signal method in order to protect the estimation process from the influence of outliers, their detection remains a challenging task, while such attribute has not yet been bestowed in the multi-signal approach. Moreover, the current implementation of the GMWM algorithm can be computationally intensive and does not provide the simplest (composite) model. In this work, a simplified implementation of the GMWM-based algorithm is presented along with techniques to reduce the complexity of the derived stochastic model under certain conditions. Also, it is shown via simulations that using the RGMWM every time, without the need for contamination existence confirmation, is a worthwhile trade-off between reducing the outlier effects and decreasing the estimator efficiency. Generally, stochastic modeling techniques, including the GMWM, make use of individual static signals for inference. However, it has been observed that when multiple static signal replicates are collected under the same conditions, they maintain the same model structure but exhibit variations in parameter values, a fact that called for the MS-GMWM. Here, a robust multi-signal method is introduced, based on the established GMWM framework and the Average Wavelet Variance (AWV) estimator, which encompasses two robustness levels: one for protection against outliers in each considered replicate and one to safeguard the estimation against the collection of signal replicates with significantly different behaviour than the majority. From that, two estimators are formulated, the Singly Robust AWV (SR-AWV) and the Doubly Robust (DR-AWV) and their model parameter estimation efficiency is confirmed under different data contamination scenarios in simulation and case studies. Furthermore, a hybrid case study is conducted that establishes a connection between model parameter estimation quality and implied navigation performance in those data contamination settings. Finally, the performance of the new technique is compared to the conventional Allan Variance in a land vehicle navigation experiment, where the inertial information is fused with an auxiliary source and vehicle movement constraints using the Extended and Unscented Kalman Filters (EKF/UKF). Notably, the results indicate that under linear-static conditions, the UKF with the new method provides a 16.8-17.3% improvement in 3D orientation compared to the conventional setting (AV with EKF), while the EKF gives a 7.5-9.7% improvement. Also, in dynamic conditions (i.e., turns), the UKF demonstrates an 14.7-17.8% improvement in horizontal positioning and an 11.9-12.5% in terms of 3D orientation, while the EKF has an 8.3-12.8% and an 11.4-11.7% improvement respectively. Overall, the UKF appears to perform better but has a significantly higher computational load compared to the EKF. Hence, the EKF appears to be a more realistic option for real-time applications such as autonomous vehicle navigation

    Personalised parameter estimation of the cardiovascular system: Leveraging data assimilation and sensitivity analysis of the cardiovascular system: Leveraging data assimilation and sensitivity analysis of the cardiovascular system: Leveraging data assimilation and sensitivity analysis

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    Detailed models of dynamical systems used in the life sciences may include hundreds of state variables and many input parameters, often with physical meanings. Therefore, efficient and unique input parameter identification, from experimental data, is an essential but challenging task for this class of models. This study presents a comprehensive analysis of a nine-dimensional single ventricle lumped-parameter model, representing the systemic circulation. This model is formulated in terms of differential algebraic equations, often found in other areas of the life sciences. We introduce a novel computational algorithm designed to incorporate patient-specific beat-to-beat variability into model investigations, utilising the Unscented Kalman Filter (UKF) for efficient parameter estimation. Our findings demonstrate the exceptional adaptability of the UKF to severe parameter perturbations, representing significant physiological changes. Furthermore, we provide novel insights into the continuous sensitivity of model input parameters, illustrating the robustness and efficacy of UKF. The monitoring of a patient’s physiological state, with minimal delay, becomes feasible, by incorporating patient-specific measurements and leveraging the UKF. The workflow presented in this paper enables prompt identification of pathophysiological conditions and will improve patient care

    Set-based state estimation and fault diagnosis using constrained zonotopes and applications

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    This doctoral thesis develops new methods for set-based state estimation and active fault diagnosis (AFD) of (i) nonlinear discrete-time systems, (ii) discrete-time nonlinear systems whose trajectories satisfy nonlinear equality constraints (called invariants), (iii) linear descriptor systems, and (iv) joint state and parameter estimation of nonlinear descriptor systems. Set-based estimation aims to compute tight enclosures of the possible system states in each time step subject to unknown-but-bounded uncertainties. To address this issue, the present doctoral thesis proposes new methods for efficiently propagating constrained zonotopes (CZs) through nonlinear mappings. Besides, this thesis improves the standard prediction-update framework for systems with invariants using new algorithms for refining CZs based on nonlinear constraints. In addition, this thesis introduces a new approach for set-based AFD of a class of nonlinear discrete-time systems. An affine parametrization of the reachable sets is obtained for the design of an optimal input for set-based AFD. In addition, this thesis presents new methods based on CZs for set-valued state estimation and AFD of linear descriptor systems. Linear static constraints on the state variables can be directly incorporated into CZs. Moreover, this thesis proposes a new representation for unbounded sets based on zonotopes, which allows to develop methods for state estimation and AFD also of unstable linear descriptor systems, without the knowledge of an enclosure of all the trajectories of the system. This thesis also develops a new method for set-based joint state and parameter estimation of nonlinear descriptor systems using CZs in a unified framework. Lastly, this manuscript applies the proposed set-based state estimation and AFD methods using CZs to unmanned aerial vehicles, water distribution networks, and a lithium-ion cell.Comment: My PhD Thesis from Federal University of Minas Gerais, Brazil. Most of the research work has already been published in DOIs 10.1109/CDC.2018.8618678, 10.23919/ECC.2018.8550353, 10.1016/j.automatica.2019.108614, 10.1016/j.ifacol.2020.12.2484, 10.1016/j.ifacol.2021.08.308, 10.1016/j.automatica.2021.109638, 10.1109/TCST.2021.3130534, 10.1016/j.automatica.2022.11042
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