Since the 1940s, population projections have in most cases been pro- duced using the deterministic cohort component method. However, in 2015, for the first time, in a major advance, the United Nations issued official probabilistic population projections for all countries based on Bayesian hi- erarchical models for total fertility and life expectancy. The estimates of these models and the resulting projections are conditional on the UN’s of- ficial estimates of past values. However, these past values are themselves uncertain, particularly for the majority of the world’s countries that do not have longstanding high-quality vital registration systems, when they rely on surveys and censuses with their own biases and measurement errors. This paper is a first attempt to remedy this for total fertility rates, by extending the UN model for the future to take account of uncertainty about past val- ues. This is done by adding an additional level to the hierarchical model to represent the multiple data sources, in each case estimating their bias and measurement error variance. We assess the method by out-of-sample pre- dictive validation. While the prediction intervals produced by the current method have somewhat less than nominal coverage, we find that our pro- posed method achieves close to nominal coverage. The prediction intervals become wider for countries for which the estimates of past total fertility rates rely heavily on surveys rather than on vital registration data.   Keywords: Bayesian hierarchical model, Markov chain Monte Carlo, Measurement error, Population projection, Total fertility rate, Vital registration