Development and validation of linear covariance analysis tool for atmospheric entry

Entry guidance is a fundamental element of atmospheric entry missions. However, during the atmospheric entry, there are many uncertainties that cannot be predicted and ultimately lead to trajectory dispersions. Linear covariance analysis, widely used for navigation system design and analysis, is a technique that can also be used to assess guidance, navigation, and control (GN&C) system performance. In this paper, linear covariance analysis is used to predict and analyze the 3 − σ dispersions and dispersion error budgets for atmospheric entry. Uncertainties, including atmospheric density, aerodynamic axial and normal force coefficients, sensor measurement errors, and winds, are modeled as exponentially correlated random variables. The closed-loop dispersion covariance propagation and update equations of an augmented system are formulated using linear covariance theory, and a series of simulations are carried out to show that linear covariance analysis can be used for trajectory dispersion analysis for a closed-loop GN&C atmospheric entry system. It is shown that the linear covariance analysis can provide accurate Monte Carlo-like results in a fraction of the time to predict trajectory dispersions and produce dispersion budgets to assess the effects of individual uncertainties.