Chennai Mathematical Institute


3.30 p.m., Lecture Hall 6
The Kushner filter and its quantum generalizations due to V.P.Belavkin

Harish Parthasarathy
Netaji Subhash Institute of Technology, University of Delhi, New Delhi.


I shall introduce the derivation of the Kushner filter as a real time estimator of a classical observable for a system of stoch astic differential equations based on noisy measurements. Its approximations especially the extended Kalman filter and its applications to robotics shall also be discussed. The stochastic Lyapunov method for proving stability of parametric estimation and trajectory tracking in a simple two link robot shall be introduced using the classical Ito formula.

Finally, I shall conclude by discussing the more recent work of the Late V.P.Belavkin on filtering of quantum stochastic processes based on non-demolition measurements. This formula hinges around the well known quantum Ito formula for operator valued processes due to R.L.Hudson and K.R.Parthasarathy and the quantum Kallianpur-Striebel formula presented in a paper by Gough Prior to discussing Belavkin's work, I shall introduce the audience to the construction of creation, annihilation and conservation processes in Boson Fock space. The possibility of applying quantum stochastic calculus as a model for noise in nano-robots shall be indicated.