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Description
In this work the flight characteristics and aircraft geometry required to produce a certain sonic boom signature are estimated using the Unscented Kalman filter (UKF). The Kalman filter is an algorithm that estimates state spaces by combining model predictions and observational data. The UKF extends the Kalman filter to nonlinear systems. Instead of linearizing the system, it uses sampling points (sigma points) to capture the mean and covariance of the state distribution. For the calculations the UKF requires a state vector xk , a measurement vector zk, and a mathematical model. Initially, sigma points are calculated by the mean of the state vector and its covariance. Next a prediction is made using the mathematical model. After that the UKF updates the prediction using the Kalman gain and measurements. The work is organized in two phases. First, UKF is validated by using it to estimate the flight parameters, Mach number and altitude, required by a certain aircraft geometry to achieve measured sonic boom overpressure and duration. Second, UKF is used to solve the inverse design problem where the flight parameters and aircraft shape are estimated so that a target low-boom signature is produced. For the first phase the state vector includes flight parameters. For the second phase the shape and lift of the aircraft are included. The measurement vector includes sonic boom overpressure and duration in both phases. Rise time is added for the second phase. Two mathematical models are employed: the Carlson empirical formula and a non-linear propagation model.