3d multilateration with unknown, but proportional, distances

I am trying to position a digital unit using a number of receivers by recording the signal strength at each receiver.

However, since not all digital units will emit with the same signal strength I cannot use the traditional approaches to multilateration (that I’ve heard of at least).

Could someone help me, sort of, get over the hump with this?

I’ve tried by considering the signal strengths [RSSI] as proportional to one another and subsequently tried to project them onto a coordinate system [m] – but just can’t seem to get it right.

EDIT:

Essentially I want to reformulate this problem:

FIND coordinates of P

Given:

coordinates of receivers/nodes A,B,C in a 2D-plane : {x_A,y_A,…,y_C} [unit: m]
signal strength received at the nodes from unknown point P: {|RSSI_AP|,…,|RSSI_CP|}
Into this problem (that is easily solved using a trilateration algorithm):

FIND coordinates of P

GIVEN:

coordinates of receivers/nodes A,B,C in a 2D-plane : {x_A,y_A,…,y_C} [unit: m]
distance to point P from the receivers: {d_AP,d_BP,d_CP}