Nonlinear Observers via Regularized Dynamic Inversion

We propose a nonlinear observer framework in which the state estimate xk of a discrete time dynamical system is chosen to simultaneously minimize the final output residual y_k - h(x_k,u_k,t) while at the same time remaining close to the predicted apriori estimate x_k. This latter constraint regularizes the problem of trying to instantaneously invert an overdetermined system with more states than outputs by putting a cost on the difference between the predicted and final state estimates. As the the apriori estimates used to regularize the inversion process are obtained from the modelled system dynamics, we refer to this approach as regularized dynamic inversion. We discuss a class of nonlinearities for which this style observer yields a computationally feasible filtering algorithm with significantly superior performance compared with its Luenberger style counterparts (EKF) in two scenarios.