Mathematical model of the sensor unit for processing on-board algorithms of navigation systems

Recently, strapdown gyro navigation systems have become widely used. In such systems, sensors, gyros, and accelerometers are placed directly aboard the object and an imaginary analytic trihedral is used instead of a stabilized gyroplatform. The object orientation with respect to the analytic trihedral is calculated by numerically solving the Poisson equations taking into account the readings of gyro sensors measuring the object angular velocities. The mutual orientation parameters permit recalculating the apparent acceleration measured by the accelerometers on the object axes for the axes of the analytic trihedral. In the analytic trihedral, the navigation problem is solved in the same way as it is solved in platform systems but, in the whole, the functions of the onboard algorithms of strapdown systems are significantly more complicated than those of platform systems. The possibility of detailed processing of on-board algorithms is of great importance for ensuring the accuracy of the entire navigation system.In the present paper, we state algorithms for reproducing the exact readings of ideal gyro sensors and the exact readings of ideal accelerometers under bench operating conditions of the system under an angular motion imitating the object orientation evolution and the possible angular vibration. Simultaneously, we calculate the exact position and orientation parameters, which can be compared with the results produced by the on-board algorithm.