Plunger lift state estimation and optimization using acoustic data

A method of probabilistically estimating a velocity of a plunger of a beam pump may comprise continuously monitoring well acoustics using a plurality of passive acoustic sensors attached to external structures of the beam pump; digitizing outputs of the plurality of passive acoustic sensors and sending the digitized outputs to a computing device for storage and processing; and using the digitized outputs of the plurality of passive acoustic sensors, estimating a probability of the velocity of the plunger using a hidden Markov model (HMM) to represent a probability of a position and the probability of the velocity of the plunger, the HMM comprising a state space model and an observational model.