Mathematics & Physics 2016, 9(2), 173–179 УДК 519.213 Probability Distribution Functions of the Sum of Squares of Random Variables in the Non-zero Mathematical Expectations Yuri L.Fateev∗ Military Engineering Institute Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Vladimir V. Shaidurov† Institute of Computational Modelling Siberian Branch of the Russian Academy of Sciences Akademgorodok, 50/44, Krasnoyarsk, 660036 Russia Evgeny N. Garin‡ Dmitry D. Dmitriev§ Valeriy N.Tyapkin¶ Military Engineering Institute Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Received 20.11.2015, received in revised form 25.01.2016, accepted 20.02.2016 The article concluded probability distribution functions sum of the squares of the random variables in the non-zero expectations. <...> The resulting distribution function is possible to create an efficient single-step phase ambiguity resolution algorithm in determining the spatial orientation of the signals of satellite radio navigation systems. <...> Obtained thresholds at rejecting false solutions, as well as statistical data of the algorithm. <...> Most problems in designing, research and operation of electronic equipment operate on a random variable having a normal distribution of probabilities. <...> The value of the normal distribution is characterized by two parameters - the expectation of m and variance D. In practice, very often have to deal with the sum of normally distributed variables. <...> Given that the variance is the square of the standard deviation, the resulting dispersion is the sum of squares of the standard variance of the initial terms. ∗fateev_yury@inbox.ru †shaidurov04@mail.ru ‡EGarin@sfu-kras.ru §dmitriev121074@mail.ru ¶tyapkin58@mail.ru ⃝ Siberian Federal University. <...> All rights reserved c – 173 – Yuri L. Fateev, Vladimir V. Shaidurov, Evgeny N. Garin . . . <...> In the analysis of the resulting error is usually assumed that the individual components are independent and have the expectation of zero. <...> On this basis, the resulting error is determined as the sum of squares of the components of the error or the square root of this value. <...> For the statistical analysis used probability distribution of the sum of squares of random variables with expectation of zero. <...> However, in some cases, it may be that error components are the expectation, not equal to zero and a priori unknown. <...> For example, such a situation is encountered in the resolution of phase <...>