Recursive maximum likelihood estimation of complex autoregressive processes

The recursive maximum likelihood estimation (RMLE) algorithm conceived by Kay (see ibid., vol.ASSP-31, p.56, 1983) is extended to complex data sets. The complex version requires the same level of computation as that for real data. The original development was restricted to the case of realm data. The purpose is to extend RMLE to the more universal realm of complex data. The derivation is discussed. It is argued, without direct proof, that the algorithm is stable in the sense that the magnitude of the reflection coefficient at each step is less than unity