In this paper, we propose a robust Kalman filtering framework for systems with probabilistic unce... more In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The uncertainty, characterized by mean and variance of the states, is propagated using conditional expectations and polynomial chaos expansion framework. The results obtained using the proposed filter are compared with existing robust filters in the literature. The proposed filter demonstrates better performance in terms of estimation error and rate of convergence. Index Terms-Robust Kalman filter, estimation of uncertain systems, probabilistic uncertainty, polynomial chaos.
Among algorithms used for sensor fusion for attitude estimation in unmanned aerial vehicles, the ... more Among algorithms used for sensor fusion for attitude estimation in unmanned aerial vehicles, the Extended Kalman Filter (EKF) is the most commonly used for estimation. In this paper, we propose a new version of H2 estimation called extended H2 estimation that can overcome the limitations of the extended Kalman Filter, specifically with respect to computational speed, memory usage, and root mean squared error. We formulate a new attitude-estimation algorithm, where the filter gain is designed offline about a nominal operating point, but the filter dynamics is implemented using the nonlinear system dynamics. We refer to this implementation of the H2 optimal estimator as the extended H2 estimator. The solution presented is tested on two cases, corresponding to slow and rapid motions, and compared against the EKF in the performance metrics mentioned above.
I. Introduction Accurate state estimation using low-cost MEMS (Micro Electro-Mechanical Systems) ... more I. Introduction Accurate state estimation using low-cost MEMS (Micro Electro-Mechanical Systems) sensors present on Commercialoff-the-shelf (COTS) drones has been reported to be a challenging problem [1-4]. Most UAV systems use a combination of a gyroscope, an accelerometer, and a magnetometer to obtain measurements and estimate attitude. Since measurements from these sensors are subjected to noise, bias, as well as magnetic disturbances, a filtering framework that incorporates sensor fusion is essential to obtaining a reliably accurate estimate of the vehicle's attitude [5-7]. Under the sensor fusion paradigm, the Extended Kalman Filter (EKF) is the most popular algorithm for attitude estimation in UAVs [8-10]. EKF estimation is very accurate and widely used in practical scenarios, particularly on open-source autopilot softwares like Ardupilot and PX4. However, the Extended Kalman filter has a few limitations of its own. Firstly, it can be complicated to implement, which is reflected by the numerous proposed methods to improve efficiency [11, 12]. Secondly, determining Kalman gain after every time interval requires two steps: prediction and update, thus requiring more computations to calculate mean and covariance, and larger memory to store the results. Finally, the EKF scheme also assumes Gaussian uncertainty in its modeling, which is reasonable for uncertainty propagation over short intervals of time, but requires the algorithm to run at a higher rate resulting in larger processor usage. These aspects make it difficult to implement EKF in low power microprocessors. In this work, we propose a novel estimation technique called extended H 2 filter that can overcome the limitations of the EKF, specifically with respect to computational speed, memory usage, and root mean squared error. Since we have previously demonstrated the technique using Euler angles [13], we focus exclusively on the quaternion representation in this paper. The unique nature of the quaternion vector prohibits a direct application of the general estimation algorithm. An error dynamics model of sensors is derived to estimate the error quaternion. The H 2 optimal filter gain is * Graduate Student and AIAA Student Member † Graduate Student and AIAA Student Member ‡ Associate Professor, and AIAA Associate Fellow
In this paper, we propose a robust Kalman filtering framework for systems with probabilistic unce... more In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The uncertainty, characterized by mean and variance of the states, is propagated using conditional expectations and polynomial chaos expansion framework. The results obtained using the proposed filter are compared with existing robust filters in the literature. The proposed filter demonstrates better performance in terms of root mean squared error and rate of convergence.
In this paper, we propose a robust Kalman filtering framework for systems with probabilistic unce... more In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The uncertainty, characterized by mean and variance of the states, is propagated using conditional expectations and polynomial chaos expansion framework. The results obtained using the proposed filter are compared with existing robust filters in the literature. The proposed filter demonstrates better performance in terms of estimation error and rate of convergence. Index Terms-Robust Kalman filter, estimation of uncertain systems, probabilistic uncertainty, polynomial chaos.
Among algorithms used for sensor fusion for attitude estimation in unmanned aerial vehicles, the ... more Among algorithms used for sensor fusion for attitude estimation in unmanned aerial vehicles, the Extended Kalman Filter (EKF) is the most commonly used for estimation. In this paper, we propose a new version of H2 estimation called extended H2 estimation that can overcome the limitations of the extended Kalman Filter, specifically with respect to computational speed, memory usage, and root mean squared error. We formulate a new attitude-estimation algorithm, where the filter gain is designed offline about a nominal operating point, but the filter dynamics is implemented using the nonlinear system dynamics. We refer to this implementation of the H2 optimal estimator as the extended H2 estimator. The solution presented is tested on two cases, corresponding to slow and rapid motions, and compared against the EKF in the performance metrics mentioned above.
I. Introduction Accurate state estimation using low-cost MEMS (Micro Electro-Mechanical Systems) ... more I. Introduction Accurate state estimation using low-cost MEMS (Micro Electro-Mechanical Systems) sensors present on Commercialoff-the-shelf (COTS) drones has been reported to be a challenging problem [1-4]. Most UAV systems use a combination of a gyroscope, an accelerometer, and a magnetometer to obtain measurements and estimate attitude. Since measurements from these sensors are subjected to noise, bias, as well as magnetic disturbances, a filtering framework that incorporates sensor fusion is essential to obtaining a reliably accurate estimate of the vehicle's attitude [5-7]. Under the sensor fusion paradigm, the Extended Kalman Filter (EKF) is the most popular algorithm for attitude estimation in UAVs [8-10]. EKF estimation is very accurate and widely used in practical scenarios, particularly on open-source autopilot softwares like Ardupilot and PX4. However, the Extended Kalman filter has a few limitations of its own. Firstly, it can be complicated to implement, which is reflected by the numerous proposed methods to improve efficiency [11, 12]. Secondly, determining Kalman gain after every time interval requires two steps: prediction and update, thus requiring more computations to calculate mean and covariance, and larger memory to store the results. Finally, the EKF scheme also assumes Gaussian uncertainty in its modeling, which is reasonable for uncertainty propagation over short intervals of time, but requires the algorithm to run at a higher rate resulting in larger processor usage. These aspects make it difficult to implement EKF in low power microprocessors. In this work, we propose a novel estimation technique called extended H 2 filter that can overcome the limitations of the EKF, specifically with respect to computational speed, memory usage, and root mean squared error. Since we have previously demonstrated the technique using Euler angles [13], we focus exclusively on the quaternion representation in this paper. The unique nature of the quaternion vector prohibits a direct application of the general estimation algorithm. An error dynamics model of sensors is derived to estimate the error quaternion. The H 2 optimal filter gain is * Graduate Student and AIAA Student Member † Graduate Student and AIAA Student Member ‡ Associate Professor, and AIAA Associate Fellow
In this paper, we propose a robust Kalman filtering framework for systems with probabilistic unce... more In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The uncertainty, characterized by mean and variance of the states, is propagated using conditional expectations and polynomial chaos expansion framework. The results obtained using the proposed filter are compared with existing robust filters in the literature. The proposed filter demonstrates better performance in terms of root mean squared error and rate of convergence.
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