Hi smart people of StackExchange!
I have a question regarding the combination of two position estimates (X and Y coordinates) where each position estimate has a different certainty/accuracy.
Example
I want to combine the following two position estimates into one position estimate:
X1 = 53m +- 96m // Y1 = 28m +- 96m
X2 = 58m +- 50m // Y2 = 23m +- 50m
Note that the accuracies (the values after the +- sign) can change per position estimate measurement I take, so a formula that merges these two position estimates should be able to handle varying accuracies.
How can I combine these two position estimates? And is it also possible to determine the accuracy (+- value) of the combined position estimate?
I've looked around and found weighted averages/means, but I don't understand how to apply that method here (if it applies at all).
Hopefully you guys and gals can help me with this one ;)
If you need clarification on the question, please let me know.
Edit for clarification
I have a robot of which I want to determine its position. There are two algorithms that are capable of calculating the robot's position, but they have different accuracies.
The first algorithm determines the position of the robot is: X1 = 53 meter +- 96 meters --> this is the estimate X-coordinate with the accuracy of the algorithm Y1 = 58 meter +- 50 meters --> this is the estimate Y-coordinate with the accuracy of the algorithm
Now the second algorithm determines a different position (X2 and Y2), but it has a different accuracy (i.e., a different range that the true X and Y coordinates can lie in).
How can I combine the two position estimates to determine the most likely true X and Y coordinate, taking into account the different accuracies.
Edit 2: I've removed the word "average" as this is not necessarily what I want. Thanks for the comment :)