How to find circle faster than by Hough Transform

I’m trying to make Hough Transform find a circle faster or find another function that can do it faster.
My use case:
I have a square picture in grayscale, 4 aruco markers in the corners(detected earlier), and a black circle approximately in the middle. Rest of the picture is quite uniformly white-isch/gray
Picture size is 1600x1600
I know the approximate center position and radius of the circle
I use:
cv2.HoughCircles(image, cv2.HOUGH_GRADIENT, 1, 100, 100, 30, 200,250)

This takes about 35-40ms. I would love to get it down to about 15ms