This paper describes the derivation, analysis and evaluation of a new sequential integrity monitoring for Kalman filter (KF) applications. The monitor uses innovation sequence obtained from a single Kalman filter for fault detection. Unlike multiple hypothesis solution separation monitors, it does not require running sub-filters to detect and exclude the fault. The main contributions of this paper is an analytical recursive expression of the worst case failure mode slopes, which is direct means of computing protection levels in real-time. The performance of the monitor is evaluated and verified against single satellite faults through a tightly-coupled INS/GNSS integrated navigation systems in aircraft approach and en route operations. However, the methodology developed in this paper is not limited to INS/GNSS systems but applicable to any other multi-sensor systems using KF estimators.