The new method is proposed to monitor the level of currently accumulated fatigue and estimate it by the several statistical methods. The experimental software application was developed and used to get data from sensors (accelerometer, GPS, gyroscope, magnetometer, and camera), conducted experiments, collected data, calculated parameters of their distributions (mean, standard deviation, skewness, kurtosis), and analyzed them by statistical methods (moment analysis, cluster analysis, bootstrapping, periodogram and spectrogram analyses). The hypothesis 1 (physical activity can be estimated and classified by moment and cluster analysis) and hypothesis 2 (fatigue can be estimated by moment analysis, bootstrapping analysis, periodogram, and spectrogram) were proposed and proved. Several "fatigue metrics" were proposed: location, size, shape of clouds of points on bootstrapping plot. The most promising fatigue metrics is the distance from the "rest" state point to the "fatigue" state point (sum of 3 squared non-normal distribution of non-correlated acceleration values) on the skewness-kurtosis plot. These hypotheses were verified on several persons of various age, gender, fitness level and improved standard statistical methods in similar researches. The method can be used in practice for ordinary people in everyday situations (to estimate their fatigue, give tips about it and advice on context-related information).