Multivariate Regression Analysis and Error Estimation in Formation Satellite

In this work, we aim to develop a non-linear multivariate regression model, which predicts the initial condition for periodic orbits of deputy satellite. The used parameters in developing regression model are eccentricity of the chief satellite's orbit, initial true anomaly and initial velocity of deputy satellite's orbit. The analysis is performed for single-loop to five-loops periodic orbit. The proposed regression models are multivariate quadratic polynomials, which are best fitted models. Error analysis is also studied by implementing regression models. Maximum error and minimum error for all the regression models are estimated. It shows that all regression models are best predictor for the initial condition of periodic orbit of deputy satellite. It is remarkable that initial true anomaly of deputy satellite's orbit is also obtained as a function of eccentricity of chief satellite's orbit. This function is obtained using non-linear single variable regression model.