Publication: Localización de múltiples blancos mediante interpolación con funciones de base radial
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2015-06
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2015-06-19
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Abstract
En este proyecto se estudiará e implementará una técnica de estimación de la posición de uno o más blancos a partir de observaciones recogidas por un conjunto de sensores desplegados aleatoriamente por un terreno. Para ello emplearemos una técnica de localización basada en interpolación de funciones con base radial (RBFs).
Para ello, se parte de la hipótesis de que la función que estamos aproximando presenta máximos en las posiciones de los blancos a localizar. Por tanto, si la calidad de la función interpolada es lo suficientemente buena, sus máximos coincidirán también con los de la función original, por lo que la determinación de dichos máximos proporcionará una estima de las posiciones de los blancos.
Para reducir la complejidad del método, las RBFs se distribuirán sobre una rejilla predefinida, por lo que, sólo será necesario calcular el ancho y peso asociados. Como las RBFs son funciones de base local (sólo toman valores significativos en torno a su centro), el peso asociado estará relacionado con el valor de la función a interpolar en su entorno, de forma similar a la que tendría un “sensor virtual” ubicado en su misma posición.
El despliegue de las RBFs sobre la rejilla tiene el inconveniente de que su número aumenta de forma exponencial cuando aumenta el tamaño de la región a controlar. Para mantener controlado el número de RBFs que participan en la interpolación, en este PFC se empleará el método de optimización LASSO. Con este método, se puede optimizar un vector de parámetros (los pesos de las RBFs), de forma que se minimice una determinada función de coste, reduciendo así el número de elementos no nulos en dicho vector.
En este PFC, se ha aplicado el método RBF+Lasso a problemas de localización. Mediante una serie de simulaciones, se han podido ajustar los parámetros del método RBF+Lasso (ancho y número de funciones RBFs activas) y se han obtenido medidas de la calidad de las posiciones estimadas.
In this PFC we’re going to study and implement a technique for estimating the position of a target from observations collected by a group of sensors deployed randomly. To do this we use a technique based on location interpolation with radial basis functions (RBFs). To do this, we begin whit the assumption that the function we are approaching, exhibits maximum at the positions of the targets to locate. Therefore, if the quality of the interpolated function is good, their maximums will coincide with the maximums of the original function, so that the determination of those maximums provides an estimate of the positions of the targets. With the aim to reduce the complexity of the method, the RBFs will be distributed on a predefined grid, so it will only be necessary to calculate the width and weight associated. As the RBFs are functions that only take significant values around of its center, the weight associated is related to the value of the function to interpolate in their environment, simulating a "virtual sensor" located in the same position. The deployment of RBFs on the grid has the disadvantage that their number increases exponentially when increase the size of the control region. To have controlled the number of RBFs involved in the interpolation, in this PFC we use the optimization method called LASSO. This method can optimize a vector of parameters (the weights of the RBFs) so that the cost function is minimized, minimizing the number of nonzero elements in this vector. This PFC was applied RBF + Lasso method for localization issues. Through several simulations, we’ve established the method parameters of RBF + Lasso (width and number of functions RBFs active) and we’ve obtained quality measures of estimated positions.
In this PFC we’re going to study and implement a technique for estimating the position of a target from observations collected by a group of sensors deployed randomly. To do this we use a technique based on location interpolation with radial basis functions (RBFs). To do this, we begin whit the assumption that the function we are approaching, exhibits maximum at the positions of the targets to locate. Therefore, if the quality of the interpolated function is good, their maximums will coincide with the maximums of the original function, so that the determination of those maximums provides an estimate of the positions of the targets. With the aim to reduce the complexity of the method, the RBFs will be distributed on a predefined grid, so it will only be necessary to calculate the width and weight associated. As the RBFs are functions that only take significant values around of its center, the weight associated is related to the value of the function to interpolate in their environment, simulating a "virtual sensor" located in the same position. The deployment of RBFs on the grid has the disadvantage that their number increases exponentially when increase the size of the control region. To have controlled the number of RBFs involved in the interpolation, in this PFC we use the optimization method called LASSO. This method can optimize a vector of parameters (the weights of the RBFs) so that the cost function is minimized, minimizing the number of nonzero elements in this vector. This PFC was applied RBF + Lasso method for localization issues. Through several simulations, we’ve established the method parameters of RBF + Lasso (width and number of functions RBFs active) and we’ve obtained quality measures of estimated positions.
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Redes de comunicación, Radiocomunicación, Funciones de Base Radial (RBFs), Método de optimización LASSO