In this paper we develop and test algorithmic techniques to estimate genotypes fitnesses by analysis of observed daily frequency data monitoring the long-term evolution of bacterial populations. In particular, we develop a non-linear least squares approach to estimate selective advantages of emerging new mutant strains in locked-box stochastic models describing bacterial genetic evolution similar to the celebrated Lenski experiment on Escherichia Coli. Our algorithm first analyses emergence of new mutant strains for each individual trajectory. For each trajectory our analysis is progressive in time, and successively focuses on the first mutation event before analyzing the second mutation event. The basic principle applied here is to minimize (for each trajectory) the mean squared errors of prediction w(t) - W(t) where the observed white cell frequencies w(t) are predicted by W(t), which is computed as the conditional expectation of w(t) given the available information at time (t-1). The pooling of all selective advantages estimates across all trajectories provides histograms on which we perform a precise peak analysis to compute final estimates of selective advantages. We validate our approach using ensembles of simulated trajectories.