Model prediction of spatial non-cooperative target measurement information based on the Koopman operator

Abstract

This paper proposes a prediction method for spatial non-cooperative measurement information based on the Koopman operator, aiming at the problem of incomplete or missing measurement information in optical relative navigation. Combining the global linear representation theory of the Koopman operator, the paper first projects the nonlinear measurement model into a Hilbert space using a dimensionality expansion function, and constructs a global linear optical measurement model based on the Koopman operator. Secondly, by using a linear combination of Koopman modes, eigenvalues, and feature functions, the paper achieves global linearization of the measurement model, reducing the loss of nonlinear information. Furthermore, a model algorithm based on the Dynamic Mode Decomposition (DMD) method is designed to approximate the Koopman operator, and the main modes of the operator are used to obtain the phase space topology structure of the model, realizing high-precision prediction of measurement information. Finally, Monte Carlo simulation results show that compared with existing methods, the proposed method improves the accuracy of measurement information prediction by 52.07%, providing an effective solution for high-precision prediction of measurement information for subsequent optical relative navigation targets.