• Dr. Mark Psiaki
  • Cornell University
  • Holden Auditorium (Room 112)
  • 4:00 p.m.
  • Faculty Host: Dr. Joseph Schetz

Solutions of model-based estimation problems can be used to enhance scientific and engineering endeavors that range from spacecraft attitude and orbit determination to remote sensing of the Earth's atmosphere.  The common threads in these problems are the existence of hidden internal states, the availability of sensor data, and an ability to model the dependence of the data on the states.  An estimation practitioner must invert the forward model in order to infer the states from the data.  One must also estimate the potential inaccuracies caused by model and measurement uncertainties.  Standard solutions include a batch filter for static problems, Kalman filters for systems with dynamically varying states, and Ensemble Kalman filters (EnKF) for systems with enormous numbers of states.   A good solution involves the development of an accurate system model and the use of an appropriate inversion algorithm.  An important aspect is the art of appropriately simplifying and tuning models when needed.

Recent theoretical contributions to estimation include a new Gaussian mixture filter and a new EnKF.  The new Gaussian mixture filter provides a powerful tool for solving difficult nonlinear estimation problems, problems that cannot be solved by the “usual suspects”: Extended Kalman filters (EKFs), Unscented Kalman filters (UKFs), or Particle Filters.  The contribution to Gaussian mixture filtering is a new mixture re-sampling algorithm that limits mixand covariance, thereby enabling the use of EKF or UKF calculations for the individual mixands within a static multiple model filtering framework.  Comparisons of this algorithm with other nonlinear filters are presented for the 7-state Blind Tricyclist benchmark problem.  Current efforts to apply this filter to Space Situational Awareness problems are also discussed.

The new EnKF provides a tool for solving estimation problems with very large numbers of states, on the order of 105-108.  Such problems are too large to store and update the filter’s full estimation error covariance matrix.  A traditional EnKF stores and updates only a low-rank approximation of the covariance square-root.  The new filter works instead with a low-rank approximation of an increment to the filter’s square-root information matrix.  Its execution speed is on the order of traditional EnKFs, but it removes the two traditional ad hoc fixes: localization of measurements during the measurement update and covariance inflation as a substitute for process noise during the dynamic propagation.  Instead, it uses an assumed a priori covariance, one that would exist if there had never been any measurement updates.  A diagonal approximation or some other sparse approximation of this a priori covariance can be used, thereby avoiding large computation costs associated with its inversion.  Initial comparisons on a simulated “toy” problem will be used to demonstrate the benefits of this new EnKF when using measurements that are like GPS radio-occultations applied to an upper atmosphere model.

Two recent applications of estimation theory will also be discussed, GPS spoofing detection and remote sensing of the local ionosphere.  One spoofing detection method exploits direction-of-arrival information as deduced from a small 2-antenna array.  It has been tested against live-signal spoofing attacks during a cruise around Italy in late June 2014.

The remote sensing work fuses GPS TEC data and ionosonde data in order to deduce a local ionosphere model above the HAARP array on Gakona, AK.  This effort constitutes the initial step of a project that aims to develop global real-time corrections to the International Reference Ionosphere model.