5,666 research outputs found
Incremental least squares methods and the extended Kalman filter
Caption titleIncludes bibliographical references (leaves 16-18).Supported by the NSF. 9300494-DMIby Dimitri P. Bertsekas
Robust State Space Filtering under Incremental Model Perturbations Subject to a Relative Entropy Tolerance
This paper considers robust filtering for a nominal Gaussian state-space
model, when a relative entropy tolerance is applied to each time increment of a
dynamical model. The problem is formulated as a dynamic minimax game where the
maximizer adopts a myopic strategy. This game is shown to admit a saddle point
whose structure is characterized by applying and extending results presented
earlier in [1] for static least-squares estimation. The resulting minimax
filter takes the form of a risk-sensitive filter with a time varying risk
sensitivity parameter, which depends on the tolerance bound applied to the
model dynamics and observations at the corresponding time index. The
least-favorable model is constructed and used to evaluate the performance of
alternative filters. Simulations comparing the proposed risk-sensitive filter
to a standard Kalman filter show a significant performance advantage when
applied to the least-favorable model, and only a small performance loss for the
nominal model
Digital adaptive flight controller development
A design study of adaptive control logic suitable for implementation in modern airborne digital flight computers was conducted. Two designs are described for an example aircraft. Each of these designs uses a weighted least squares procedure to identify parameters defining the dynamics of the aircraft. The two designs differ in the way in which control law parameters are determined. One uses the solution of an optimal linear regulator problem to determine these parameters while the other uses a procedure called single stage optimization. Extensive simulation results and analysis leading to the designs are presented
Revision of TR-09-25: A Hybrid Variational/Ensemble Filter Approach to Data Assimilation
Two families of methods are widely used in data assimilation: the
four dimensional variational (4D-Var) approach, and the ensemble Kalman filter
(EnKF) approach. The two families have been developed largely through parallel
research efforts. Each method has its advantages and disadvantages. It is of
interest to develop hybrid data assimilation
algorithms that can combine the relative strengths of the two approaches.
This paper proposes a subspace approach to investigate the theoretical equivalence between the suboptimal
4D-Var method (where only a small number of optimization iterations are
performed) and the practical EnKF method (where only a small number of ensemble
members are used) in a linear Gaussian setting. The analysis motivates a new
hybrid algorithm: the optimization directions obtained from a short window
4D-Var run are used to construct the EnKF initial ensemble.
The proposed hybrid method is computationally less expensive than a full
4D-Var, as only short assimilation windows are considered. The hybrid method has the potential to
perform better than the regular EnKF due to its look-ahead property.
Numerical results
show that the proposed hybrid ensemble filter method performs better than the
regular EnKF method for both linear and nonlinear test problems
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