1. A spectrum sensing system, the system comprising: an antenna configured to receive electromagnetic signals in one or more frequency spectrums; one or more data storage devices storing an observation window of a plurality of primary user state observations corresponding to a frequency spectrum and one or more primary user spectrum use parameters comprising already determined hidden markov model parameters; and one or more hardware processors in communication with the antenna and the one or more data storage devices, the one or more hardware processors configured to execute modules comprising at least a sensing module configured to, after having accessed the already determined hidden markov model parameters, periodically cause the one or more hardware processors to perform the following: receive, via the antenna, one or more primary user observations corresponding to the frequency spectrum; update the observation window to incorporate the one or more primary user observations into the plurality of primary user state observations, the observation window having a starting observation point and an ending observation point, the ending observation point corresponding to the most recent primary user state observation; determine one or more forward state probabilities based on the one or more primary user spectrum use parameters and the plurality of primary user state observations in the observation window; determine one or more backward state probabilities based on the one or more primary user spectrum use parameters and a portion of the plurality of primary user state observations in the observation window, the portion comprising at least the ending point, the portion comprising less primary user state observations than the plurality of primary user state observations; determine one or more posterior state probabilities for one or more observations in the observation window, wherein the one more posterior state probabilities are based on the one or more forward state probabilities and the one or more backward state probabilities; determine a risk of a sensing error for each potential primary user state corresponding to an observation period about which a sensing decision is being made based on one or more cost factors and the one or more posterior state probabilities; select a potential primary user state having a minimum amount of risk of sensing error for each observation corresponding to a time period about which a sensing decision is being made; send the one or more selected potential primary user states to a sensing decision consumer.