> What if we can only carry one sensor?

> That is what happened exactly in the Apollo rocket, back in the 60s the IMUs were veeery heavy and they could only carry one.

The first and most famous application of a Kalman filter in the Apollo program was for the problem of midcourse navigation. In this application, the Apollo PGNCS used the Kalman filter to combine the calculated trajectory based on vehicle dynamics with the sextant measurements (optical starsighting). The IMU was not used for midcourse navigation.

See e.g. Figures 1-6 and 5-5 in http://klabs.org/history/history_docs/mit_docs/1697.pdf.

It was all very simple and concise (thank you) until the extended kalman part where it appears you sped up by 100x and just dismissed the whole non-linear predictor saying we taylor it and create a jacobian for every instance of t.

Thank you. I appreciate your conciseness.

The presentation is similar to the (nice yet more verbose) notebook "01-g-h-filter.ipynb" in github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/