# 20.3 The Sensor Fusion Observational Model

The task is to define the functional dependence for the transformation of the state vector x_{n} into the components of the sensor fusion observation vector z_{n}. If the observation noise is included, this transformation can be written as

(20.2)

where . The observations consist of two separate components, the IMU components and the photogrammetric components, which must be fused together to provide an asynchronous stream of observation data.

## 20.3.1 The Inertial Measurement Unit Component of the Observation Model

The IMU package outputs data from three orthogonal accelerometers and three orthogonal rate gyroscopes. The IMU observation vector at time t_{n} can be written as

(20.3)

where z_{x,n}, z_{y,n}, and z_{z,n} are the accelerations (in G's) measured by the x-forward, y-right, and z-down accelerometers, respectively, and z_{ϕ,n}, z_{θ,n} and z_{ϕ,n} are rotation rates (in degrees) measured by the roll (counterclockwise about the x-axis), pitch (counterclockwise about the y-axis), and yaw (counterclockwise about the z-axis) rate gyroscopes, respectively. Note that since the IMU package is attached to the rigid body, it rotates as the body rotates so that the measurements ...