Bifurcating autoregressive (BAR) processes are an adaptation of autoregressive processes to binary tree structured data. They were first introduced by Cowan and Staudte for cell lineage data. We have carried out a sharp analysis of the asymptotic properties of the least squares (LS) estimators of the unknown parameters of first-order BAR processes and improved the previous results of Guyon via a martingale approach, based on the generation-wise filtration. Namely, we have established the almost sure convergence of our LS estimators with a sharp rate of convergence, together with the quadratic strong law and the central limit theorem.