Formulation and analysis of inertial navigation equations for terrestrial navigation systems.

摘要

The primary objective of this thesis work is to develop and apply a practical means of precisely determining the position of fixed guideway systems (moving rail and rubber-tire vehicles) by sensing and interpreting the various motions of these vehicles with respect to an inertial reference frame. For strapdown navigation systems, the inertial navigation equations (also called the navigator) play the role of interpreting the input signals from accelerometer and gyro sensors to predict the velocity and position of these vehicles.; This work focused on existing navigators and the development of new navigators to match the goal of low cost IMU instruments. In total, six navigators were derived. Specifically, they are the earth-centered frame, local-level frame, reduced earth-centered frame, earth-surface frame, tangent and normal frame, and speed tangent and normal frame navigators. For each of these navigators, the following issues were also investigated: the error model for each navigator, navigator performance, determination and sensitivity of initial conditions, the error effect of the Earth's angular rate, and numerical integration methods for attitude calculation.; From the study of arithmetic operations, we have shown that a nine-parameter scheme is less effective than a three-parameter (Euler angles) scheme. The computational load for the (reduced) earth-centered frame navigator is slightly less than the local-level frame navigator. Also, the speed tangent normal frame navigator is the best navigator among these navigators in terms of the number of arithmetic operations.; The numerical integration methods provided by SIMULINK (from Math Work Inc.) show that a fifth order Runge-Kutta-Fehlberg method is the best among several numerical integration methods (including a third order Runge-Kutta-Fehlberg, the Adams, and the Gear methods). We have also shown that the time step size of 1/75 second is appropriate for terrestrial navigation systems.; A coarse alignment procedure is introduced in this thesis, and the sensitivity of initialization is analyzed. Through the sensitivity of initialization study, a bounded attitude error formula is presented.; The error propagation for the Earth's angular rate is also studied. The study has identified a position error range in terms of velocity, the Earth's angular rate, and the navigation time when modeling ignores the Earth's angular rate. This study provides the information needed for using high-grade sensors in a navigator which does not model the Earth's angular rate.; The study of stability and performance for each navigator shows that most of the navigators exhibit unstable behavior, except the local-level frame navigator. For the navigators which model the Earth's angular rate, they still show the Schuler effect in the error states. We have also compared the position errors produced from each navigator under the same error sources. From this investigation, we found that the speed tangent and normal frame navigator is the best candidate for terrestrial navigation systems. The tangent and normal frame navigator and the earth-surface frame navigator are the next best candidates. However, if high-grade sensors which measure the Earth's angular rate are used, then the earth-centered frame and/or the local-level frame navigator are the best navigators to be used.