Synthetic data for validation of navigation systems

Sensability and Excitability Metrics Applied to Navigation Systems Assessment

“…The analysis is performed by first synthesising a deterministic trajectory with corresponding measurements signals (inertial and exteroceptive). The method, proposed by Giribet et al (2007), produces the smooth B-spline exactly satisfying the kinematics Equations (1) that best fits the flight data in the a mean square sense. The measurements are calculated with Equation (2) assuming perfect instruments, that is: ξ μ = 0, , and also in Equation (6).…”

“…A new “excitability measure” is proposed here to quantify the information, relative to the initial state, conveyed by the innovations during any given trajectory stretch. This is done based on a synthetic trajectory (Giribet et al, 2007) determined from actual flight data. Linearized models of state deviations and innovations are determined by referring to this synthetic trajectory.…”

Reconstructibilidad y observabilidad por subespacios: Aplicación a la navegación

“…La Observabilidad Determinista por Subespacios se mide en tramos de trayectorias deterministas sintetizadas a partir de datos adquiridos en vuelo [7]. De este modo se evalúa, tramo a tramo, la calidad intrínseca de la información inherente a la dinámica de la trayectoria y a la configuración instrumental.…”

“…A partir de los datos de vuelo se generó una trayectoria sintética solución exacta de las ecuaciones diferenciales cinemáticas de navegación [3] según el método expuesto en [7]. El gráfico en la Fig.…”

Abstract splines in Krein spaces

“…Schoenberg introduced the spline functions [1], they have became an important notion in several branches of mathematics such us approximation theory, statistics, numerical analysis and partial differential equations, among others. Moreover, they have been useful to solve some practical issues in signal and image processing [2][3][4][5], computer graphics [6][7][8], learning theory [9,10] and other applications.…”