A novel technique is proposed for obtaining unwrapped phase estimation from a highly noisy exponential phase field. In this technique, the interference phase is represented as a linear combination of linearly independent and pre-defined basis functions along each row/column of the phase field at a time. Consequently, the problem of phase estimation is converted into the problem of the estimation of the weights of the basis functions. The extended Kalman filter formulation allows for the accurate estimation of these weights. The simulation results indicate that the formulation offers a strong noise robustness in the phase estimation. Experimental results obtained using digital holographic interferometry and digital speckle pattern interferometry setups are provided to demonstrate the practical applicability of the proposed method.