Main Content

Implement three-axis accelerometer

**Library:**Aerospace Blockset / GNC / Navigation

The Three-Axis Accelerometer block implements an accelerometer on each of the three axes. For more information on the ideal measured accelerations, see Algorithms.

Optionally, to apply discretizations to the Three-Axis Accelerometer block inputs and dynamics along with nonlinearizations of the measured accelerations, use the Saturation block.

The Three-axis Accelerometer block icon displays the input and output
units selected from the **Units** parameter.

Vibropendulous error and hysteresis effects are not accounted for in this block.

This block is not intended to model the internal dynamics of different forms of the instrument.

The ideal measured accelerations ($${\overline{A}}_{imeas}$$) include the acceleration in body axes at the center of gravity ($${\overline{A}}_{b}$$) and lever arm effects due to the accelerometer not being at the center of gravity. Optionally, gravity in body axes can be removed. This is represented by the equation:

$${\overline{A}}_{imeas}={\overline{A}}_{b}+{\overline{\omega}}_{b}\times ({\overline{\omega}}_{b}\times \overline{d})+{\dot{\overline{\omega}}}_{b}\times \overline{d}-\overline{g}$$

where $${\overline{\omega}}_{b}$$ are body-fixed angular rates, $${\dot{\overline{\omega}}}_{b}$$ are body-fixed angular accelerations, and $$\overline{d}$$ is the lever arm. The lever arm ($$\overline{d}$$) is defined as the distances that the accelerometer group is forward, right, and below the center of gravity:

$$\overline{d}=\left[\begin{array}{l}{d}_{x}\\ {d}_{y}\\ {d}_{z}\end{array}\right]=\left[\begin{array}{c}-({x}_{acc}-{x}_{CG})\\ {y}_{acc}-{y}_{CG}\\ -({z}_{acc}-{z}_{CG})\end{array}\right]$$

The orientation of the axes used to determine the location of the accelerometer group
(*x _{acc}*,

Measured accelerations ($${\overline{A}}_{meas}$$) output by this block contain error sources and are defined as

$${\overline{A}}_{meas}={\overline{A}}_{imeas}\times {\overline{A}}_{SFCC}+{\overline{A}}_{bias}+noise,$$

where $${\overline{A}}_{SFCC}$$ is a 3-by-3 matrix of scaling factors on the diagonal and misalignment terms in the nondiagonal, and $${\overline{A}}_{bias}$$ are the biases.

[1] Rogers, R. M.,
*Applied Mathematics in Integrated Navigation Systems*, AIAA
Education Series, 2000.