TABLE OF CONTENTS By now we know how to implement and solve for the differential equations that compute the navigation equations parameters. What remains like for solving any differential equation is initializing these parameters. Traditionally this process is called alignment, a term inherited from the legacy gimbaled systems because it mechanically aligns the stable platform to the navigation frame. Here we have a body-fixed inertial suite that is oriented in some arbitrary direction, not the mechanical frame. To start the solution we need to determine the craft initial attitude and heading as well as its initial position and velocity in the navigation frame. Ideally, we could use the inertial sensor outputs to execute the alignment process. However, we are facing the challenge that the accelerometer and gyro are contaminated with many error sources [1-3]. Even though these data are preprocessed to account for known error sources, the process is not exhaustive. Other error sources are still unaccounted for because some of these errors are random and can't be calibrated against. Nevertheless, some errors can be estimated, chief amongst them are the accelerometer and gyro residual biases that varies from one power-on to another.
The craft's position coordinates longitude, latitude and altitude are initialized manually or by reading stored data from its past trajectory. Its velocity components are initialized with zeros if it is grounded or from an external data source such as GPS if in motion. This leaves us with the craft attitude, accelerometer bias, and gyro...
