Extending GTSAM to ECEF coordinates

[Mike]

Hello, I am interested in extending GTSAM to optimizing across ECEF coordinates. 

The main issue I see how we can incorporate a gravity vector that is position dependent. You can make the assumption(at first anyway) that during the IMU pre integration interval the gravity vector is a fixed direction, I believe this simplifies things but the IMU pre integration term will still need to be modified to account for global position changing it.

It's not obvious to me what the best approach to add this would be, any suggestions? We have a(differentiable) formula that takes ECEF position to gravity but I'm not sure to start in terms of plugging it in to the IMU factor.

- Michael

[Dellaert, Frank]

It would be interesting to see a sensitivity analysis of how much this matters. Gut feeling, if you know where you are up to a few you should be able to initialize a PIM with a gravity vector that's essentially correct. For long-term missions, this can gradually change over time.

If you have zero idea where you are at the beginning, so no GPS measurements. That's a different case. 

As for supporting cartesian ECEF coordinates, I think only the PIM needs to be changed, if it cannot already do this.

Frank

--
You received this message because you are subscribed to the Google Groups "gtsam users" group.
To unsubscribe from this group and stop receiving emails from it, send an email to gtsam-users...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/gtsam-users/c9cb609f-3546-4258-b8c4-16dcc8a98ba5n%40googlegroups.com.

[Mike]

Hi Frank, thanks for the info.

What would the process look like to integrate a gravitational acceleration vector that changes with respect to position into the PIM? A possible application is something that covers a significant distance so it's important to be able to optimize it too. 

[Davide]

Dear Mike 

We've made a paper long ago about how to do IMU pre-integration in ECEF, accounting for Earth rotation and a gravity model. You can find it here:

https://isprs-annals.copernicus.org/articles/IV-2-W5/549/2019/

There may be more up-to-date references, and I believe the IMU preintegration technique is slightly different from the one implemented in GTSAM, but maybe it gives you some inspiration.

best

Davide

To view this discussion visit https://groups.google.com/d/msgid/gtsam-users/3c5e1c70-20d3-4c92-bd9f-00e6fafaa64cn%40googlegroups.com.

[Michael Lowell]

Thanks, I will take a look.

For systems with high accuracy sensors that go over large distances this is an important feature.