Quadlateration Trilateration formula

[insolace]

I've been running some numbers based on a formula I found here:

http://en.wikipedia.org/wiki/Trilateration

This formula allows you to solve for the X, Y, and Z coordinates of an object in 3d space given the distances to that object from three different known points (spheres). However it occasionally gives an inconclusive answer (or even an imaginary number).

Is there a way to derive the X,Y, and Z coordinates using 4 points that will give a conclusive answer each time? I'm using this in a simple program I am writting and what I really need is a formula that I can plug the numbers into.

 

[dmoravec]

I'm sure there are formulas, but what about when all 4 points are in a plane... then any distances you give would yield 2 points. Is that the type of inclousiveness you are talking about?

 

[tacman]

Hi there,

Thank you for sharing your findings and question regarding the Quadlateration Trilateration formula. It is great to see that you are exploring and experimenting with different formulas to solve for the coordinates of an object in 3D space.

To answer your question, yes, there is a way to derive the X, Y, and Z coordinates using 4 points that will give a conclusive answer each time. This method is called Quadlateration, which is an extension of trilateration that uses four points instead of three. The formula for quadlateration can be found here: https://en.wikipedia.org/wiki/Quadrilateral_trilateration

The main difference between trilateration and quadlateration is that quadlateration takes into account the curvature of the Earth's surface, whereas trilateration assumes a flat surface. This is important when dealing with large distances and can help improve the accuracy of the coordinates calculated.

In terms of your program, you can incorporate the quadlateration formula by simply adding an additional point and adjusting your calculations accordingly. However, do keep in mind that quadlateration can be more computationally intensive and may require more precise measurements from the four points.

I hope this helps answer your question and good luck with your program! Keep exploring and experimenting with different formulas to find the best solution for your needs.