Would you happen the memory complexity of this algorithm? I maintain an online machine learning library written in Python, called creme, where we implement online statistics. We have a generic onine algorithm for estimating quantiles, and so a specific algorithm for estimating medians would be welcome. I'm always on the lookout for such online algorithms.
The P^2 algorithm used in creme is interesting. For the median it would give a 2 sided median deviation. Maybe this could be changed slightly to be symmetric and give Median and MAD. I'll look into.