Lumped Parameter Estimation of a Stochastic Process of Second Order Using the Second Moment and Recursiveness Romeo Urbieta Parrazales 1 , José de Jesús Medel Juárez 1 , Karen Alicia Aguilar Cruz 1 , Rosaura Palma Orozco 2 1 Centro de Investigación en Computación - Instituto Politécnico Nacional, CDMX, Mexico 2 Escuela Superior de Cómputo - Instituto Politécnico Nacional, CDMX, Mexico rurbieta700@gmail.com, jjmedelj@yahoo.com.mx, karen_ali320@hotmail.com, rpalma@ipn.mx Abstract. In this article, a stochastic algorithm is briefly presented based on the one of second moment applied to a stochastic process model of second order. The design initially consisted in formulating the state equation model and the stochastic outputs, in order to apply the second moment using the internal prod- uct of Martingale and the stochastic operators of the expectation, variance and covariance. The design results generated the formulas on: the covariances and the internal product variances to calculate the lumped estimation parameters, the error functional based on the mean quadratic error, the output variable as a function of the estimation parameters obtained. Furthermore, the recursive form was formulated in this design starting from the premise of the obtained results using the second stochastic moment. The main interest lays on the recursive form, because this is the one capable of being implemented in a digital system. In order to observe the precision and the convergence of the estimation parame- ters and the output variables, Matlab-based figures are shown. Keywords: Linear stochastic systems, parameter estimation, second moment. 1 Introduction The random input and output variables of a noisy process can be modeled by means of experimental data obtained from measurements carried out during time intervals T. These models are called Black Box Models (Fig. 1) [1, 2]. The Black Box Models are called this way, because their internal states are not known. One method to determine these unknown states starting from observable states are the so called methods of identified states based on the mean quadratic er- ror [3]. 79 ISSN 1870-4069 Research in Computing Science 138 (2017) pp. 79–88; rec. 2017-09-21; acc. 2017-10-23