I.(Haran) Arasaratnam, PhD

Finding a solution to nonlinear Bayesian state-estimation problems is intractable and has engaged many researchers since Kalman’s seminal paper was published in 1960. The selection of suitable sub-optimal approximate solutions to the recursive Bayesian estimation problem represents a trade-off between global optimality on one hand and computational tractability (and robustness) on the other hand.

I derived a new approximate Bayesian filter for solving discrete-time non- linear filtering problems efficiently and named the cubature Kalman filter. Here, the term "Cubature" refers to numerical integration in multi-dimensions. Under the assumption that all the conditional densities are Gaussian, the optimal Bayesian filter reduces to the problem of how to compute multi-dimensional Gaussian-weighted moment integrals present in the time and measurement update steps. To compute these integrals numerically, a couple of transformations are required: (i) Transform Non-standarad Gaussian weighted integrals to standard Gaussian-weighted integrals using the change of varaiables. (ii) Transform these integrals in the Cartesian coordinate to the spherical-radial coordinate. Subsequently, a a third-degree spherical-radial cubature rule was prescribed to compute them numerically. The resulting cubature rule entails a set of 2n cubature points, where n is the state-vector dimension. The cubature Kalman filter is the closest known approximate filter in the sense of preserving second-order information due to the maximum entropy principle. A detailed derivation can be found in IEEE Transactions on Automatic Control published in 2009.

Please see below a complete list of my scholary articles published during the course of my PhD:

PhD Dissertation
Patent
Journals
Book Chapters
Conference Papers
Poster Presentations
Misc.