Human populations outside of Africa have experienced at least two bouts of introgression from archaic humans, from Neanderthals and Denisovans. In Papuans there is prior evidence of both these introgressions. Here we present a new approach to detect segments of individual genomes of archaic origin without using an archaic reference genome. The approach is based on a hidden Markov model that identifies genomic regions with a high density of single nucleotide variants (SNVs) not seen in unadmixed populations. We show using simulations that this provides a powerful approach to identifying segments of archaic introgression with a low rate of false detection, given data from a suitable outgroup population is available, without the archaic introgression but containing a majority of the variation that arose since initial separation from the archaic lineage. Furthermore our approach is able to infer admixture proportions and the times both of admixture and of initial divergence between the human and archaic populations. We apply the model to detect archaic introgression in 89 Papuans and show how the identified segments can be assigned to likely Neanderthal or Denisovan origin. We report more Denisovan admixture than previous studies and find a shift in size distribution of fragments of Neanderthal and Denisovan origin that is compatible with a difference in admixture time. Furthermore, we identify small amounts of Denisova ancestry in South East Asians and South Asians.