4,307 research outputs found
Flight Dynamics-based Recovery of a UAV Trajectory using Ground Cameras
We propose a new method to estimate the 6-dof trajectory of a flying object
such as a quadrotor UAV within a 3D airspace monitored using multiple fixed
ground cameras. It is based on a new structure from motion formulation for the
3D reconstruction of a single moving point with known motion dynamics. Our main
contribution is a new bundle adjustment procedure which in addition to
optimizing the camera poses, regularizes the point trajectory using a prior
based on motion dynamics (or specifically flight dynamics). Furthermore, we can
infer the underlying control input sent to the UAV's autopilot that determined
its flight trajectory.
Our method requires neither perfect single-view tracking nor appearance
matching across views. For robustness, we allow the tracker to generate
multiple detections per frame in each video. The true detections and the data
association across videos is estimated using robust multi-view triangulation
and subsequently refined during our bundle adjustment procedure. Quantitative
evaluation on simulated data and experiments on real videos from indoor and
outdoor scenes demonstrates the effectiveness of our method
Balanced data assimilation for highly-oscillatory mechanical systems
Data assimilation algorithms are used to estimate the states of a dynamical
system using partial and noisy observations. The ensemble Kalman filter has
become a popular data assimilation scheme due to its simplicity and robustness
for a wide range of application areas. Nevertheless, the ensemble Kalman filter
also has limitations due to its inherent Gaussian and linearity assumptions.
These limitations can manifest themselves in dynamically inconsistent state
estimates. We investigate this issue in this paper for highly oscillatory
Hamiltonian systems with a dynamical behavior which satisfies certain balance
relations. We first demonstrate that the standard ensemble Kalman filter can
lead to estimates which do not satisfy those balance relations, ultimately
leading to filter divergence. We also propose two remedies for this phenomenon
in terms of blended time-stepping schemes and ensemble-based penalty methods.
The effect of these modifications to the standard ensemble Kalman filter are
discussed and demonstrated numerically for two model scenarios. First, we
consider balanced motion for highly oscillatory Hamiltonian systems and,
second, we investigate thermally embedded highly oscillatory Hamiltonian
systems. The first scenario is relevant for applications from meteorology while
the second scenario is relevant for applications of data assimilation to
molecular dynamics
Kalman Filtering With State Constraints: A Survey of Linear and Nonlinear Algorithms
The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results
Kalman Filtering With State Constraints: A Survey of Linear and Nonlinear Algorithms
The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results
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