This paper reports a method for the simultaneous estimation of unwrapped phase and higher order phase derivatives from a single phase fringe pattern recorded in an optical interferometric setup, thereby overcoming substantial barriers to achieving such measurements. The proposed method considers the interference phase as a weighted linear combination of Gaussian radial basis functions defined along a given row or column at a time. The Gaussian radial basis functions are defined with a constant standard deviation and equally spaced centers. Unscented Kalman filter is employed for the accurate estimation of the weights of the basis functions using the state space representation of the spatial evolution of the interferogram. The estimated weights along with the numerically computed gradients of the basis functions also provide the estimations of phase derivatives of arbitrary order. The proposed representation of interference phase along with the unscented Kalman filter provides high robustness against the speckle noise. Simulation study is preformed to evaluate the dependence of the phase and phase derivative estimation accuracy on the selection of basis dimension and the noise level. Experimental results demonstrate the practical applicability of the proposed method.