1. A speech-to-speech translation system comprising: one or more processors; and memory storing instructions that are executable by the one or more processors, the memory including: an automated speech recognition (ASR) engine to convert audio input in a source language into text output in the source language; a machine translation (MT) engine to receive the text output in the source language from the ASR engine and translate the text output in the source language into text output in a target language that is different than the source language; and a MT training module configured to: model ASR errors of the ASR engine based at least in part on the text output of the ASR engine to create an ASR simulation model; train a phoneme-to-word MT engine with the ASR simulation model to create a trained phoneme-to-word MT engine; convert, using the trained phoneme-to-word MT engine, phoneme sequences into output text, the output text matching the text output of the ASR engine given the phoneme sequences as input; store the output text in association with the phoneme sequences as training data; and train the MT engine using the training data.