Synchronization of perturbed non-linear Hamiltonians

We propose a new method based on Lie transformations for simplifying perturbed Hamiltonians in one degree of freedom. The method is most useful when the unperturbed part has solutions in non-elementary functions. A non-canonical Lie transformation is used to eliminate terms from the perturbation that are not of the same form as those in the main part. The system is thus transformed into a modified version of the principal part. In conjunction with a time transformation, the procedure synchronizes the motions of the perturbed system onto those of the unperturbed part.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42559/1/10569_2004_Article_BF00692993.pd

Data and Program Structure for a Modular Extended Kalman Filter

The paper presents a data and program structure that makes it easier to implement a nonlinear process or measurement model when using the extended Kalman filter. This is achieved by a composite data type containing both the estimated value and covariance information. The basic operators ( +, -, *, /) and common functions are implemented for this data type. These enable a model for the extended Kalman filter to be implemented as easily as a discrete-time simulation model