# In FMCW RADAR, how to use signal difference to calculate the position of a new object entered a clutter

FMCW radar with 1 TX and 2 RX both have IQ channel. So a single (stationary) object's range and angle can be calculated.

Problem:

If two objects are at about same distance but different angle, looking at the snapshot spectrum alone, we cannot differentiate these two objects. It will looks like one object at certain angle (as a combine effect of 2 objects)

Potential solution:

If we have a signal snapshot of the scene (containing many objects) at time A, and then another signal snapshot at time B, and we assume there is only one object entered the scene that caused signal changes. Can we use the change of signal to compute the exact location of the new object entered the scene? (even if the new object's location is about the same range of some existing objects). The new object's range and angle would need some calculation:

$$\displaystyle a\sin(x+\theta _{a})-b\sin(x+\theta _{b})=c\sin(x+\varphi )$$

where new object signal's amplitude c and phase φ would be:

$$\displaystyle c=\sqrt{a^{2}+b^{2}-2ab\cos \left(\theta _{a}-\theta _{b}\right)}$$

$$\displaystyle \varphi =\arctan({\frac {a\sin \theta _{a}-b\sin \theta _{b}}{a\cos \theta _{a}-b\cos \theta _{b}})}$$

And then finally, new object's angle will be calculated using phase difference between two RX channels.

Also if an object that was part of the clutter leaves the scene, we can see a change in spectrum and calculate its previous location. (Just switch the snapshot, the problem is rephrased as object enter the scene)

Question:

Is this a well solved problem? Any paper or source code for reference? (I googled, but haven't found anything, maybe I am not using the right keywords as I am new to the field and knows nothing.)