I'm using an array of ultrasonic receivers to estimate the location of an object, but the total length of the array is about 1 meter (all of them are on the same line).
By using the distance obtained, I tried using trilateration to see if I could estimate the position.
The problem starts here: While the y-axis component of the position is reasonably close to the actual position, the x-axis component of the position is about half the actual position. In other words, if the actual position is (5,10)m, the obtained position is about (2.5,9.8)m. The equation I used is
x = (r1^2 - r2^2 - x1^2 + x2^2) / (2*(x2-x1))
where r1 and r2 are the distances obtained for receiver 1 and receiver 2, and x1 and x2 are the x-coordinates of the receiver position.
I'm wondering if this is due to the small baseline, or if there's something about the math that I'm missing. Also, how should I go about fixing this problem? I thought about just multiplying the x-component by 2, but it may just be a coincidence that it's about half the actual x-component right now.