I try to find a solution to the navigation problem. There is a navigation system consists of three navigation positions, forming two bases (one position belongs two bases) and emitting three different signals. It provides us the opportunity to get two navigation parameters - two Time Differences of Arrival. So we have two surfaces - hyperboloids. But I need to complement my system with another navigation parameter, like Time of Arrival to find the 3d coordinates of my position.

What should I use as the third parameter to get the simplest equations, expressing my coordinates?

It could be Time of Arrival only from one position; Time of Arrival between two positions. But it could be two Times of Arrival which provide me the opportunity of having more information.

How can I find the equations, expressing my 3d coordinates in this navigation system?

I have a system of equations:

x1 = a*cosh(m1)*cos(n1)

y1 = a*sinh(m1)*sin(n1)

x2 = b*cosh(m2)*cos(n2)

y2 = b*sinh(m2)*sin(n2)

alpha - the angle between the bases.

I can suppose that the bases are equivalent and m1=m2. Then I obtain the problem of intersection of tho circles. It is the right way?

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