Tracking a moving object

[BigBallerJMan]

Hello all

I've been working on this problem I can't wrap my head around.
I have a certain object H moving through a 2D plane at a constant velocity v, at an unknown angle from two recievers R1 and R2. The distance between H and R1 and H and R2 is h and i respectively. Using Doppler's effect and other math I won't get into, I know [MATH]\frac{\mathrm{d} h}{\mathrm{d} x}[/MATH] and i know [MATH]\frac{\mathrm{d} i}{\mathrm{d} x}[/MATH], while I do not know the actual value of i and h.

Given that H is travelling at a constant velocity in a single direction, I would like to extract some sort of information from the situation for a given [MATH]\frac{\mathrm{d} h}{\mathrm{d} x}[/MATH] and [MATH]\frac{\mathrm{d} i}{\mathrm{d} x}[/MATH]. I imagine I'd be able to extract some sort of relationship between h and i or some parametric equations for the coordinates of H.

For the moment I've tried mapping H as the point of interesction of two circles with changing radius h and i, but it hasn't brought me anywhere.

Any help is greatly appreciated.

 

[Romsek]

do you have bearing to target from the two stations?

Have you looked at using a Kalman filter?

 

[BigBallerJMan]

I do not have the bearings, and the way I understand it a Kalman filter is used when there is uncertainty or fluctuations invovled, whereas here the numbers are certain (this math is not to be used in real life, this is only a model.) Is this correct?

 

[Romsek]

Yes, this is correct, though a Kalman filter could be used with strictly deterministic data.

So basically you have perfect knowledge that your target is on a linear course constant speed
and you have perfect info on the range rates from each station?

 

[Romsek]

Here's a link to a paper that treats the general case. You can see the problem is quite involved.

https://journals.sagepub.com/doi/full/10.1177/1550147718776863

 

[BigBallerJMan]

I'll give a little more context; essentially I'm trying to find the velocity (or a relationship describing the velocity of this object depending on what the actual measurements of h and i are) of this travelling object given the information above. This is only a mathematical and geometrical model, so all values are "certain" in that I'm describing them with variables.

I read into the paper but I'll admit I'm in a little over my head. I think this problem may just not be solvable for my math level.

Either way, thank you for time.