It is becoming increasingly evident that the analysis of genotype data from recently admixed populations is providing important insights into medical genetics and population history. Such analyses have been used to identify novel disease loci, to understand recombination rate variation and to detect recent selection events. The utility of such studies crucially depends on accurate and unbiased estimation of the ancestry at every genomic locus in recently admixed populations. Although various methods have been proposed and shown to be extremely accurate in two-way admixtures (e.g. African Americans), only a few approaches have been proposed and thoroughly benchmarked on multi-way admixtures (e.g. Latino populations of the Americas). To address these challenges we introduce here methods for local ancestry inference which leverage the structure of linkage disequilibrium in the ancestral population (LAMP-LD), and incorporate the constraint of Mendelian segregation when inferring local ancestry in nuclear family trios (LAMP-HAP). Our algorithms uniquely combine hidden Markov models (HMMs) of haplotype diversity within a novel window-based framework to achieve superior accuracy as compared with published methods. Further, unlike previous methods, the structure of our HMM does not depend on the number of reference haplotypes but on a fixed constant, and it is thereby capable of utilizing large datasets while remaining highly efficient and robust to over-fitting. Through simulations and analysis of real data from 489 nuclear trio families from the mainland US, Puerto Rico and Mexico, we demonstrate that our methods achieve superior accuracy compared with published methods for local ancestry inference in Latinos.