GPS Accuracy Improvement via Mathematical Optimization

Hi!
I am a chemical engineer that recently has been involved with drone activity. In the last few days I have been thinking of GPS accuracy and how it could be possibly improved without investing on RTK.
One technique to minimize these errors is named Data Reconciliation. It is basically an optimization problem taking into account an objective function that aims to minimize the differences between measured sensors values and corrected values (reconciled ones). The second one, in theory, closer to the “real” value. All that driven from the optimization math point of view, constrained by first principles equation, in this particular case, mass and energy balances, to mention the two main equations in process engineering.
Drone sensors are not 100% accurate, GPS, barometer, compass, as well as in chemical industries (process sensors). On the other hand, one can also derive equations to calculate latitude and longitude formulas from compass and velocity (pitot tube) and compare them with GPS data. That is exactly what is behind data reconciling in chemical process. Base on that, I derived an optimization problem that could be solved with nonlinear optimization algorithms and deliver reconciled values (superior accuracy compared to sensors readings like in chemical process). Theoretically …
I tested it.
The optimization problem converged! The results are exactly those ideally generated before random error have been introduced

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Seems as interesting approach, do you have any documentation or a git repo where you did the solving of the optimization problem, and regarding the solving how heavy the calculation, can they be implemented in the embedded system?

Note that the drone’s position eatimation is already based on sensor fusion of all available sensors, and not just GPS alone. I assume you’re aware of that?

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