Noting the fact that the phase and phase derivatives carry the information on the mechanical deformation in optical interferometric measurements techniques, we propose a noise robust fringe analysis technique for the simultaneous estimation of unwrapped phase and arbitrary order phase derivative from a phase fringe pattern. The continuous phase along row or column of the phase fringe pattern is approximated as a weighted linear combination of linearly independent basis functions such as Fourier basis. The weights are accurately estimated based on a state space analysis using the linear Kalman filter. Simulation and experimental results are provided to substantiate the applicability of the proposed method.