The paper proposes an observability analysis and estimation schemes for specific growth rates and biomass concentrations of the anaerobic digestion process. A 3-stage model of 5 dynamic states is assumed, describing the hydrolysis, acidogenesis and methanogenesis of two different populations of microorganisms (acidogenic and methanogenic). The main result is that the specific growth rates of the two populations of bacteria can be stability estimated only from easily measured quantities -- the dilution rate and the flow rates of methane and carbon dioxide in the biogas. The estimation schemes thus obtained have quite interesting features one of which is their freeness of most yield coefficients often hard to identify. The analysis rests on the differential algebraic approach of observation problems. The results are currently being confronted to experimental data from a 100m3 pilot bioreactor fed with cattle dung. Realistic simulations are presented in this paper as illustrations of the estimator performance.