Abstract In this thesis, a new approach based on the bank of Kalman filters is proposed to reduce the fault detection time and the incorrect exclusion rate. The dynamic behavior of the failure vector can be described as P-V (position-velocity) model。By applying the bank of the Kalman filters, the updated fault value can be obtained. Furthermore, the test statistic can be constructed from the fault value. By hypothesis testing, the detection threshold under a given false alarm rate can be calculated directly. Simulation results show that in comparison with the parity-space method, the best improvement of percentage for average detection time is 84.3% and the best improvement of percentage for incorrect exclusion rate is 100% under the step-type failure Also the best improvement of percentage for average detection time is 45.6% and the best improvement of percentage for incorrect exclusion rate is 100% under the ramp-type failure.. The method of the bank of the Kalman filters is better than the method of the parity-space method both in average detection time and incorrect exclusion rate when the fault value is small. Both methods are almost the same in detection time when the fault value is big. Therefore by use of the bank of Kalman filters can monitor the small fault value to keep GPS working continuously. At the end of thesis the concept of the modified bank of Kalman filters is proposed to reduce the number of Kalman filters. From the observerbility analysis, the upper bound of the number of satellites to be monitored by one Kalman filter is obtained.