# What is strapdown integration?

... First, we consider hinge (or pin) joints. There are several ways to estimate the joint angle of a hinge joint from the measured accelerations and angular velocities. Many of them use strap-down integration and some coordinate transformation.

I'm not sure if this term is used widely, but since it's about integration and kinematics, I thought it would have been a good idea to ask it here.

What's exactly strap-down integration? How is it different from "normal" integration?

Note: the context may not help much if you don't know anything about kinematics and the study of human body analysis. Feel free to migrate this question to a more appropriate Stack Exchange's website, if you think this belongs to another website.

• Have a look at his paper: Quaternion-based strap-down integration method for applications of inertial sensing to gait analysis. DOI: 10.1007/BF02345128 – user_na Mar 7 '17 at 18:57
• I suspect it has more to do with utilization of a strap down sensor rather than integration in a mathematical sense. One of the articles I found "To solve this, a good modeling of the strapdown inertial integration needs to be given. The core of the strapdown inertial integration is acceleration rotation from body frame to navigation frame, which is a nonlinear mapping" xsens.com/wp-content/uploads/2014/01/… – scrappedcola Mar 7 '17 at 19:11

There are essentially two ways to mount accelerometers for the purpose of navigation:

1. Stabilized platform: an intertially stabilized platform is mechanized using either passive mechanical elements or active controls using gyro feedback and mounted within the body of the vehicle. This maintains a local level reference frame and from this frame one can integrate the accelerometers with respect to the intertial frame.
2. Strap down navigation: By this method the accelerometers are fastened rigidly to the body frame of the vehicle. By this method, the signals together with the gyro signals must be processed and rotated on a moment by moment basis to account for the attitude changes in the vehicle to obtain principle axis, intertial accelelerations, velocity and displacement. This requires 3 axis measurements and either Euler or quaternion transformation mathematics.
• A lot of concepts! What's the relationship between these two ways of mounting an accelerometer and "strapdown inertial integration"? – nbro Mar 7 '17 at 22:06

Note: I've still not fully understood the concept of "strapdown inertial integration", and eventually I will edit (or you can edit) this answer to add more details, but here's at least an initial attempt to answer my own question based on the definition given in a paper. The paper contains other details, which for now I've not gone through since I have not too much time, but if you want to help to improve this answer, feel free to do it!

According to this paper Second Order Nonlinear Uncertainty Modeling in Strapdown Integration Using MEMS IM (section $2$), strapdown inertial integration is defined as follows.

Strapdown inertial integration (or dead reckoning) calculates the current position from an initial position using measurements of angular velocity and specific force obtained by the inertial sensors, as shown in Figure 2.

First of all, let's try to clarify the meaning of this paragraph by explaining what's a specific force. According to this Wiki's article regarding specific force:

Accelerometers measure specific force (proper acceleration), which is the acceleration relative to free-fall, not the "standard" acceleration that is relative to a coordinate system.

Now, still according to the paper I'm linking you to above, and related to Figure $2$:

The orientation $q^{nb}$ is calculated by integrating the angular velocity, $\omega^b_{nb}$, measured by gyroscopes. Then the global acceleration ($a^n$?) is obtained by rotating the specific force measured from accelerometers, $f^b$, and correcting the gravity.

Finally the velocity and position relative to an initial point, $v^n$ and $p^n$, are determined by the integration of the acceleration, $a^n$.

Note: I've omitted some details and explanations that the authors of the paper give to simplify things (for now).

### Conclusion

Note: this is only my conclusion based on my limited knowledge, so it could not be completely correct or accurate.

Roughly speaking, "strapdown inertial integration" seems to be a procedure where mathematical integration is used in multiple phases of the same procedure.

Somehow the context is when using inertial measurement units (IMUs), which consist of accelerometers and gyroscopes (and maybe also magnetometers). Accelerometers measure specific force (proper acceleration) whereas gyroscopes measure angular velocity.

So the procedure seems to take the angular velocity given by a gyroscope and integrates it to somehow obtain the orientation (a vector) (of what?). Now, somehow we need to rotate the specific force (a vector?) measured by the accelerometer to obtain a "global acceleration" (what is this? why do we need to rotate?). Then, once we have $a^n$ (which is the global acceleration without the cause of gravity?), we can integrate it once and twice to obtain respectively the velocity and position (of what?)