Maximum Likelihood Type-2 Fuzzy Kalman Filter Recursive State Space Identification with Time-Varying Order
摘要
This paper proposes a recursive, refined, and interval type-2 fuzzy algorithm for Kalman filter identification with system order temporal variation based on singular spectral analysis. The adopted methodology entails partitioning and pre-processing the database, which consists of the input and output time series of a dynamic system, in order to create simpler submodels with low noise interference. The database was divided into simpler subsets using the interval type-2 maximum likelihood fuzzy clustering algorithm, resulting in an uncertain region on the database. The singular spectral analysis was employed to extract the unobserved components of measurements, culminating in a database with a lower noise dependence. To identify state-space models for each fuzzy set obtained by the fuzzy clustering algorithm, the eigensystem realization algorithm and observer/Kalman filter identification (ERA/OKID) was used. The proposed algorithm was used in tracking and forecasting of relative position and velocity measurements of the PRISMA spacecraft formation. The results demonstrate the effectiveness of the proposed methodology in complex situations with noisy and multivariable dataset.