Amplitude phase shift keying (APSK) modulation signals are of low peak average power ratio and are generated to fight against the potentially non-linear high power amplifier in satellite communication. The benchmark maximum log-likelihood maximum a posteriori probability (max-log-MAP) detector requires to compute the distance squared between the received signal and each APSK constellation point for the extrinsic bit log-likelihood ratio (LLR) information. To overcome this major challenge of high detection complexity, we propose in this paper to partition and order all the APSK constellation points into rings of ordered phase shift keying (PSK) constellation points. We also propose to apply and tailor the iterative search strategies, originally used to detect multiple input multiple output (MIMO) quadrature amplitude modulation (QAM) signals, to search over the ordered irregular PSK constellation points. Compared with previously reported APSK detectors, our proposed detector achieves exactly the max-log-MAP detection, requires very low computational complexity, and is able to detect APSK signals modulated from the APSK constellation with arbitrary number of constellation points, arbitrary phase offsets, and arbitrary ring radii.