Searching for convergence points of the continuous time extended Kalman filter used as a parameter estimator

The authors deal with estimation of two stable pole parameters for a two-dimensional continuous-time linear stochastic system with known process noise covariance, using the extended Kalman filter. Averaging theory permits algebraic computation of a vector field whose stable stationary points are the estimator´s only possible convergence points. Specialized partitioned matrix computations allow the numerical computation of the vector field and graphical computer search for spurious convergence points not corresponding to the true parameter values, with negative results. This supports the conjecture that none exist, a result known from theory in the one-dimensional case