# Innovation / Measurement Error¶

## Innovation Overview¶

The innovation (measurement error) is formed from the sensor measurements and the predicted states. As the measurements and the system states are often not the same, one or the other needs to be transformed into the measurement. In the case of this algorithm, the state consists of an attitude quaternion, NED-velocity, and NED-position. The measurement come from accelerometer readings, GPS latitude/longitude/altitude measurements, and horizontal/vertical velocities along with ground-track. In this case either the states need to be converted to match the measurements or vice-versa.

Once the measurements vectors are formed, the innovation (measurement error), $$\vec{\nu}_{k}$$, is computed:

$\vec{\nu}_{k} = \vec{z}_{k} - \vec{h}_{k}$

This result is used in the update stage of the EKF to generate the state error, $${\Delta\vec{x}}_{k}$$, given the Kalman gain matrix.

The available sensor information is used as follows:

1. Accelerometers “level” the system (used to compute $${^{\perp}}{\phi}{_{meas}^{B}}$$ and $${^{\perp}}{\theta}{_{meas}^{B}}$$) FN
2. Magnetometers and/or GPS heading information align the perp-frame with true or magnetic north ($${^{N}}{\psi}{^{\perp}}$$)
3. GPS position and velocity measurements update the position and velocity estimates ($$\vec{r}^{N}$$ and $$\vec{v}^{N}$$)

Measurement Details To Be Provided