An estimation of efficiency of filtering algorithms of state vector of small-sized observed object with non-Markovian approximation of trajectory

The article discusses the possibilities of estimating the states vectors of observation objects with the nonMarkovian approximation of the trajectories. The introduction discusses the problem consisting in the fact that the use of the approximation of the trajectory of the observed object by Markov processes in some cases can lead to a discrepancy between theory and practice. In the first section, we simulate the trajectories of observed objects when approximated by a Markovian process and indicate the limitations of this approach. It is proposed to use a multidimensional Gaussian distribution law for generating the trajectory of the observed object. In the second section, a study of the accuracy characteristics of a single-position angular-rangefinder radar and a three-position rangefinder radar are considered. Algorithms α-β, Kalman and nonlinear estimation are used in the modeling as estimation algorithms in these systems. The parameters and characteristics of the simulation are given. In the third part, the results of modeling the process of estimating the location of objects of observation with trajectories of movement approximated by non-Markov processes are presented. Modeling confirms the possibility of using submitted algorithms to estimate the trajectory of a smallsized object of observation, a trajectory model of which uses a multidimensional normal distribution law. It is pointed out that in several cases the filtering errors exceed the errors of a single measurement. This leads to the conclusion that further modification of the algorithms is necessary. In the final part, a recommendation is given on how to further reduce the estimation errors when using Kalman algorithms and nonlinear estimation.

Análisis de Componentes Principales en presencia de datos faltantes: el principio de datos disponibles

En este trabajo proponemos utilizar el principio de datos disponibles derivado del algoritmo NIPALS (Nonlinear estimation by Iterative Partial Least Square) para trabajar el Análisis de Componentes Principales (ACP) en presencia de datos faltantes. Esta propuesta es importante puesto que no realiza imputación de datos, ni se descartan individuos de la base datos, el método propuesto trabaja con los elementos pares disponibles para conformar las matrices de cuasicorrelación en y en la descomposición espectral de estas matrices permite a través de las relaciones de transición realizar un ACP convencional. Del estudio de simulación realizado se encontró que a medida que aumenta el porcentaje de datos faltantes disminuye la inercia explicada en el primer plano factorial. Se desarrolló el algoritmo de solución bajo el entorno de programación R y se anexa el código para uso libre.