This paper deals with one of the most prominent problems in industrial prognostics, namely the estimation of the Remaining Useful Life (RUL) of the most popular industrial battery, viz., the lithium-ion battery. The paper presents a state-space model of the battery, and then estimates the dynamic behavior of seven of its process variables and two of its sensor variables. The estimation is achieved via two well known estimators, the Unscented Kalman Filter (UKF) and the Particle Filter (PF) when noise of various levels and types is injected. Numerical and chart comparisons of these two computing estimators are reported and discussed.