Kalman Filter (KF) is widely used in process industries as state estimator to diagnose the faults either in the sensor, actuator or in the plant because of its recursive nature. But, due to increase in non-linearity and exogenous perturbations in the monitored plant, it is often difficult to use a simple KF as state estimator for nonlinear process monitoring purposes. Thus, the first objective of this paper is to design an Adaptive Linear H∞ Filter ( ALH∞F) using gain scheduling algorithm to estimate nonlinear process states in the presence of unknown noise statistics and unmodeled dynamics. Next the designed ALH∞F is used to detect sensor and actuator faults which may occur either sequentially or simultaneously using Multi Model ALH∞F (MMALH∞F). The proposed estimator is demonstrated on Continuously Stirred Tank Reactor (CSTR) process to show the efficacy. And the performance of MMALH∞F is compared with MMALKF. The proposed MMALH∞F is detecting and isolating the faults exactly in the presence of unknown noise statistics and unmodeled dynamics.