The authors construct a Mortensen-type observer on the Wasserstein space P2(R^d), establish dynamic programming and viscosity solution properties for the associated HJB equation using two formulations, prove uniqueness via comparison, and introduce a convergent semi-Lagrangian scheme.
Maximum-likelihood recursive nonlinear filtering
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A polynomial approximation to the minimum energy estimator is derived from successive differentiations of the value function, reducing to the extended Kalman filter at lowest order and showing local convergence in numerical tests up to order eight.
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The Mortensen observer on the space of probability measures
The authors construct a Mortensen-type observer on the Wasserstein space P2(R^d), establish dynamic programming and viscosity solution properties for the associated HJB equation using two formulations, prove uniqueness via comparison, and introduce a convergent semi-Lagrangian scheme.
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Approximations of the Mortensen observer using higher order extended Kalman filters
A polynomial approximation to the minimum energy estimator is derived from successive differentiations of the value function, reducing to the extended Kalman filter at lowest order and showing local convergence in numerical tests up to order eight.