NOTE: i wanted to tag the question with TDOA precision multilateration but i dont have the reputation needed, but these are the appropriate tags :/
I am working on a college project with LoRa. I want to place transmitters (without gps) on animals and using three receivers calculate/estimate the location of the animal.
My current approach is using hyperbolas:
constant = $\sqrt{(x - x_1)^2 + (y - y_1)^2} - \sqrt{(x - x_2)^2 + (y - y_2)^2}$
with:
constant = delta_arrival_time * speed_of_light
$(x_i, y_i)$ = the positions of the receivers
$(x, y)$ = the transmitter's position to be estimated
note: removed absolute value from hyperbola expression assuming the left hand side sqrt is the furthest receiver, so its always positive the subtraction, and i keep one branch of the hyperbolas to have one intersection point.
note: receivers have gps so times are synchronized to apply this method.
Taking combinations of two, i have three hyperbolas, and i do an average of the hyperbolas intersections. Currently, im having error margins from 30m to 250m due to the time precision which is microseconds and given the speed of light great value.
The question is: if i increase amount of receivers, and apply this same exact method with more intersection points. Will the error margin decrease? Also i have being reading about different methods getting to read
the first answer suggests using least squares techniques. For this use case, is there a better method? Will least squares be better than my approach? and same question, will increasing amount of receivers do better? Or im stuck with time precision which will not do better than microseconds due to the amount of metres traveled because the huge value of speed of light.