# A Comprehensive Review of GNSS/INS Integration Techniques for Land and Air Vehicle Applications
## 3 GNSS Solution. Strapdown INS Approach. Strapdown INS Mechanization. Inertial Error Propagation  
Extended KF is commonly used to process GNSS receiver measurements in integrated systems. For this purpose, it is necessary to compose the equations of the state of the object, which are integrated to predict the state vector of the object. It is also necessary to construct a measurement model to determine the pseudorange prediction. After receiving the measurements, the deviations between the real measurements and the measurement model are calculated. These deviations are then used in EKF to correct the state vector of the object and obtain its estimate. At the next stage, the obtained estimate of the state vector of the object is used as initial data to obtain a predictive estimate of the state vector. Thus, the complexity and scale of the algorithm depend on the model of the state vector of the object, namely on the dynamics of the object. Several types of models of the state vector of an object are distinguished in the literature, in particular a model of an object at rest when the velocity is zero (P model), a model of an object with weak dynamics when the velocity is described by a random walk model (PV model) and a model of an object with accelerated motion when the state vector contains not only coordinates and velocities but also accelerations, which are modeled as Markov processes (PVA model) [8]. In most cases, the PV model is sufficient, but the PVA model is considered the most appropriate for air transport applications. This model was applied in [41; 68; 69]. In view of the peculiarities of the functioning of the GNSS receiver together with the model of the state vector of the object, the clock bias model, which is the integral of the receiver clock frequency error, is used. As mentioned above, INS are usually gyroscopically stabilized using mechanical devices, which are a special platform on which the integrated system is installed. INS rigidly attached directly to the body of the object; the so-called strapdown INS (SINS) have recently been used to simplify the structure. This imposes certain conditions on the sensors and computing devices of SINS. They must be able to measure high speeds of turns and perform computational operations to handle coordinate systems and calculate the position, velocity, attitude and angular velocity of an object in the required coordinate system based on measurements of INS sensors. As is known, a classical INS includes a gyro sensor that measures the angular velocity of an object relative to the inertial coordinate system and an accelerometer that measures the acceleration of the object due to the influence of gravity relative to the inertial coordinate system. This value measured by an accelerometer is often called the specific force [60]. The basic equation of inertial navigation, as is known, has the form [60]:  
\[\frac{d^{2}\mathbf{r}}{dt^{2}}=\mathbf{f}+\mathbf{g} \tag{8}\]  
where \(\mathbf{r}\) is the position of the object in the inertial coordinate system, \(\mathbf{g}\) is the gravitational acceleration and \(\mathbf{f}\) is the specific force. Equation (8) can be resolved in different coordinate systems; in other words, the INS can operate in different coordinate systems. There are many possible implementations of Equation (8) called mechanization equations in coordinate systems associated with the Earth. Typically, these equations contain additional forces that are functions of the parameters of motion associated with the SINS coordinate system relative to the inertial coordinate system, for example, Coriolis forces.