In recent years, the utilization of low-cost observations (e.g., low-fidelity data) and prior knowledge (e.g., established physical laws) has played a greater role in aerodynamic analysis and design. Previously, aerodynamic optimization has widely utilized Bayesian optimization based on Gaussian processes (GPs) and has been applied in areas such as aircraft design. In this research, a new model designed to reduce computational costs, which is itself a variant of GP, was developed and refined. This model aims to enable more efficient aerodynamic design optimization by actively leveraging the aforementioned low-fidelity data and physical laws within the Bayesian optimization framework. Such models have been extensively developed in recent years. For example, multi-fidelity GP models that evaluate the target function with fewer sample points by assisting with low-fidelity data have been widely used [1]. Similarly common are models that incorporate deterministic information into the trend function of a GP [2]. This paper introduces a model that integrates the aforementioned information, such as low-fidelity data and physical laws while unifying the above-mentioned existing approaches. This integration facilitates sequential sampling in Bayesian optimization through the application of uncertainty analysis of the target function to be optimized, expressed in the form of a linear Gaussian model with analytical solutions. In this model, discrete data (typically observational, such as low-fidelity data) are rigorously treated as stochastic functions, while functional data, such as physical laws, are handled as deterministic functions unless other information exists. The resulting uncertainty of the target function is expressed in a form that possesses analytical solutions. As a previous work, [3] summarized data-driven hierarchical multi-fidelity GP models within the framework of linear Gaussian models. Building upon this, the present study introduces an extension to Bayesian optimization, including its practical application to aerodynamic design optimization using a 2D airfoil.