This paper presents a novel method for identifying in real-time the sprung mass of a 2-DOF quarter-car suspension model. It does so by uniquely combining the base-excitation concept with polynomial chaos estimation. This unique combination of the two methods provides two important benefits. First, the base-excitation concept makes it possible to estimate the sprung mass without explicitly measuring or knowing the terrain profile prior to estimation. Second, the polynomial chaos estimation strategy makes it possible to perform such mass estimation using sprung and unsprung acceleration measurements without pseudo-integration filters that can be difficult to tune. This paper derives the proposed method in detail and presents computer simulations to evaluate its convergence speed and accuracy. The simulation results consistently converge to within 10% of the true mass value typically within 120 seconds.