where n is the number of test positions, [i.sub.yj], j = 1,2,..., n, represent the currents in the torque coils, [[omega].sub.xi], i =1, 2 , ..., n, represent the earth rate components of each test position, and [a.sub.xi], [a.sub.yi], [a.sub.zi], i = 1,2,..., n, represent the gravitational acceleration components of each test position.
The gravitational acceleration components and the earth rate components can be expressed as follows:
As a result, there are deviations between the actual earth rate components and the ideal earth rate components, as well as the gravitational acceleration components.
The actual earth rate components and gravitational acceleration components can be calculated as follows:
After removing the Earth rate, the navigator integrates the angular rate measured by gyros to continuously calculate the attitude of IMU with respect to local level navigation frame.
Generally, the Earth rate [[omega].sub.ie], gravity acceleration g, and input angular rate of inertial turntable [OMEGA] are regarded as references, which are compared with outputs of accelerometers and gyros of IMU.
It is well known that the Earth rate [[omega].sub.ie] and local gravity vector g could be sensed by gyros and accelerometers of IMU in the body frame.