The Modified Optimum Discrete Kalman Filter with Inertial Navigation System (INS) error compensation is developed in this study. The proposed filter is designed for the case of correlated system and measurement noise and it is based on the measurement differencing approach. Measurement differences are used in the filter for the solution of the state estimation problem. The proposed measurement differencing approach based Kalman filter is applied to multi-input multi-output model of an aircraft. A conventional and proposed Kalman Filters have been applied for flight dynamics estimation of an aircraft in the case of biased INS measurements. The comparison of the estimates obtained via conventional and proposed filters is fulfilled. This approach can provide autonomous navigation for realtime applications without using a global positioning system. (C) 2016, IFAC (International Federation Automatic (Control) Hosting by Elsevier Ltd. All rights reserved.