Calculating a trajectory between two known points and an IMU

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Question

Query:

I want to estimate the trajectory of a person wearing an IMU between point a and point b. I know the exact location of point a and point b in an x,y,z space and the time it takes the person to walk between the points.

Is it possible to reconstruct the trajectory of the person moving from point a to point b using the data from an IMU and the time?

Answer

This question is too broad for SO. You could write a PhD thesis answering it, and I know people who have.

However, yes, it is theoretically possible.

However, there are a few things you'll have to deal with:

  • Your system is going to discretize time on some level. The result is that your estimate of position will be non-smooth. Increasing sampling rates is one way to address this, but this frequently increases the noise of the measurement.

  • Possible paths are non-unique. Knowing the time it takes to travel from a-b constrains slightly the information from the IMUs, but you are still left with an infinite family of possible routes between the two. Since you mention that you're considering a person walking between two points with z-components, perhaps you can constrain the route using knowledge of topography and roads?

  • IMUs function by integrating accelerations to velocities and velocities to positions. If the accelerations have measurement errors, and they always do, then the error in your estimate of the position will grow over time. The longer you run the system for, the more the results will diverge. However, if you're able to use roads/topography as a constraint, you may be able to restart the integration from known points in space; that is, if you can detect 90 degree turns on a street grid, each turn gives you the opportunity to tie the integrator back to a feasible initial condition.

Given the above, perhaps the most important question you have to ask yourself is how much error you can tolerate in your path reconstruction. Low-error estimates are going to require better (i.e. more expensive) sensors, higher sampling rates, and higher-order integrators.