1. A gas concentration estimation device of a coal-burning boiler adapted to estimate the concentration of the gas component included in an exhaust gas emitted from a coal-burning boiler using a neural network, comprising: a process database section adapted to store process data of a coal-burning boiler; a filtering processing section adapted to perform filtering processing for extracting data suitable for learning of a neural network from the process data stored in the process database section; a neural-network learning processing section adapted to perform learning processing of the neural network based on the data extracted by the filtering processing section and suitable for learning of the neural network; and a neural-network estimation processing section adapted to perform estimation processing of the CO concentration or the NOx concentration in the exhaust gas emitted from the coal-burning boiler based on the learning processing of the neural-network learning processing section.