Detecting subsystem faults quickly is critical to the accuracy and reliability of integrated navigation systems. This paper, therefore, proposes an effective approach based on the novel test statistic to detect faults. Machine learning is introduced to estimate the innovation and its variance of local filter. The estimates combined with the actual ones are used to construct the test statistic, which is then proved to obey chi-square distribution. Thus fault detection can be realized by chi-square test. However, the special structure of the test statistic makes it sensitive to faults, even to the gradual faults. The experimental results demonstrate that the approach can detect faults quickly. Especially for gradual fault detection, the proposed test statistic has a marked superiority compared with the traditional test statistic of residual chi-square test.