1. A gas concentration estimation method for a coal-burning boiler, adapted to estimate a concentration of a gas component emitted from a coal-burning boiler using a neural network comprising: (a) storing process data of the coal-burning boiler; (b) performing filtering processing for extracting data suitable for learning of a neural network, from the process data stored; (c) performing learning processing of the neural network based on the data which is extracted in (b) and suitable for learning of the neural network; and (d) performing estimation processing of one of the CO concentration and the NOx concentration in an exhaust gas emitted from the coal-burning boiler, based on the learning processing of the neural-network; wherein (b) includes: (b1) specifying error data within the data, which includes a substantial error with respect to the data used for learning of the neural network, based on a trend of a variation to signals used as input signals of the neural network, and (b2) filtering the specified error data to eliminate the error data from the data used in the learning processing of the neural network; (b3) extracting the process data having input signals including one reference input signal and the other input signals, where each of the other input signals having a value within a predetermined threshold value range and each of the values are close to each other, to make a group, with respect to the process data used for learning of the neural network and having signals used as input signals of the neural network, (b4) obtaining a function of fitting the relationship between the reference input signal and a gas concentration signal value as the estimation object, both included in the process data belonging to the same group, and (b5) specifying the data to be eliminated based on the difference between the value of the function thus fitted and the signal value of one of the CO concentration and the NOx concentration as the estimation object.