Detecting Unstable Fixed Points Using Kalman Filters With Constraints

We introduce a novel application of the extended Kalman filter for detecting unstable periodic orbits of dynamical systems from experimental time series. The unknown dynamics are approximated using local polynomial functions, and the fixed-point constraint conditions are regarded as additional observation functions in the filter framework. Candidate fixed-point values are considered as parameters to be estimated. We demonstrate the application of this method to test systems and use surrogate time series data to test the statistical significance of the results