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Probabilities of recognition of direction of point shift on a plane on a random rotations background
Abstract. The complex motion of a point on a plane has been considered. The observed point and the center of point rotation carry out a parallel shift with the probability p in one of m equidistant on an angle of directions at each discrete time moment and, simultaneously, the observed point rotates relatively to this center on a random angle. The decision rule for determining the direction of shift has been justified. Expressions for conditional probability densities distribution of sample means of coordinates of the observed point have been derived. Formulas for the probabilities of correct recognition of the shift direction have been derived by two ways. One way uses the resulting conditional probability density functions. The second way is realized by averaging over random parameters of motion.
Keywords: random motion on a plane, the statistical pattern recognition theory, statistical hypothesis testing, the probability of correct recognition
Printed reference: Zharkikh A.A., Bychkova S.M. Probabilities of recognition of direction of point shift on a plane on a random rotations background // Vestnik of MSTU. 2013. V. 16, No 1. P. 81-92.
Electronic reference: Zharkikh A.A., Bychkova S.M. Probabilities of recognition of direction of point shift on a plane on a random rotations background // Vestnik of MSTU. 2013. V. 16, No 1. P. 81-92. URL: http://vestnik.mstu.edu.ru/v16_1_n51/81_92_zharki.pdf.
