# EKF AlgorithmsΒΆ

This section develops the equations that form the basis of an Extended Kalman Filter (EKF) used to calculate position, velocity, and orientation of a body in space[1]. In a VG, AHRS, or INS[2], inertial sensors are used to form high data-rate (DR) estimates of the system states while less frequent or noisier measurements (GPS and inertial sensors, which act as references) aid in correcting errors in the system.

In addition to deriving the equations used in the EKF, this paper describes a measurement model based on Euler angles resulting from accelerometers, magnetometers, and GPS readings. Then it describes implementations that result in improved solutions under both static and dynamic conditions.

Finally, a series of examples for implementing existing algorithm for VG, AHRS, and INS are presented.

The algorithm development description is broken up into a series of sections that build upon one another, as follows:

[1] | This discussion presupposes a certain amount of knowledge. Details related to differential equations, linear algebra, multi-variable calculus, stochastic processes, etc. are not described. |

[2] | A VG uses rate-sensors and accelerometers to estimate roll and pitch. An AHRS adds magnetometers to the VG to estimate heading. An INS adds GPS messages to the VG or AHRS to estimate position and velocity or provide a way to estimate heading without magnetometers. |