A Data-Driven Interval Type-2 Fuzzy Kalman Filter of Minimum Realization for Forecasting Spacecraft Formation on Low Earth Orbit

Abstract

This chapter proposes a machine learning methodology for forecasting a spacecraft formation's 3-dimensional relative position and velocity in low Earth orbit. To reduce noise effects, the adopted methodology consists of identifying linear local models recursively. The database was partitioned using the interval type-2 fuzzy maximum likelihood clustering algorithm in order to create linear sub models. Singular spectral analysis was used to divide the measured signal into unobserved components, reducing noise dependence on data set. To each fuzzy set obtained by the clustering algorithm, the Eigensystem Realization Algorithm/Observer Kalman Identification (ERA/OKID) was used to identify a Kalman filter equation of minimum realization. The proposed algorithm performs these operations in two stages: offline and online. In the latter, the singular spectral analysis and realization algorithm is performed recursively. The proposed methodology was applied to forecasting the relative position and velocity of a PRISMA spacecraft formation simulation.