Functional iterative integration-based method and system for inertial navigation solution

A navigation system based on an inertial navigation solution, comprising:

• a fitting module, wherein the fitting module is configured to fit a Chebyshev polynomial function of an angular velocity and a Chebyshev polynomial function of a specific force according to gyroscope-measured values and accelerometer-measured values on a time interval to obtain Chebyshev polynomial coefficients of the angular velocity and Chebyshev polynomial coefficients of the specific force;
• an attitude iterative solution module, wherein the attitude iterative solution module is configured to iteratively calculate Chebyshev polynomial coefficients of an attitude quaternion by using the Chebyshev polynomial coefficients of the angular velocity and an integral equation of the attitude quaternion, and perform polynomial truncation on a result obtained from each iterative calculation of the Chebyshev polynomial coefficients of the attitude quaternion according to a first preset order;
• a velocity/position iterative solution module, wherein the velocity/position iterative solution module is configured to iteratively calculate Chebyshev polynomial coefficients of a velocity/position by using the Chebyshev polynomial coefficients of the specific force, the Chebyshev polynomial coefficients of the attitude quaternion and an integral equation of the velocity/position, and perform polynomial truncation on a result obtained from each iterative calculation of the Chebyshev polynomial coefficients of the velocity/position according to a second preset order;
• an attitude/velocity/position acquisition module, wherein the attitude/velocity/position acquisition module is configured to obtain attitude/velocity/position information on the time interval according to the Chebyshev polynomial coefficients of the velocity/position, the Chebyshev polynomial coefficients of the attitude quaternion and a Chebyshev polynomial corresponding to the velocity/position and the attitude quaternion;
• and
• a navigation module, wherein the navigation module is configured to perform a navigation according to the attitude/velocitv/position information on the time interval.