Strapdown inertial navigation integration algorithm design part 1: Attitude algorithms

This series of two papers provides a rigorous comprehensive approach to the design of the principal software algorithms utilized in modern-day strapdown inertial navigation systems: integration of angular rate into attitude, acceleration transformation/integration into velocity, and integration of velocity into position, The algorithms are structured utilizing the two-speed updating approach originally developed for attitude updating in which an analytically exact equation is used at moderate speed to update the integration parameter (attitude, velocity, or position) with input provided from a high-speed algorithm measuring dynamic angular rate/acceleration effects within the parameter update time interval [coning for attitude updating, sculling for velocity updating, and scrolling (writer's terminology) for high-resolution position updating], The algorithm design approach accounts for angular rate/specific force acceleration measurements from the strapdown system inertial sensors as well as rotation of the navigation frame used for attitude referencing and velocity integration. This paper, Part 1, defines the overall design requirement for the strapdown inertial navigation integration function and develops direction cosine and quaternion forms for the attitude updating algorithms, Part 2 [Savage, P. G., "Strapdown Inertial Navigation Integration Algorithm Design Part 2: Velocity and Position Algorithms," Journal of Guidance, Control, and Dynamics (to be published)] deals with design of the velocity and position integration algorithms, Although Parts 1 and 2 often cover fundamental inertial navigation concepts, the material presented is intended for use by the practitioner who is already familiar with basic inertial navigation concepts.