This paper presents an extension of the recently presented genetic algorithm-embedded quaternion particle filter (GA-QPF). Belonging to the class of Monte Carlo sequential methods, the GA-QPF is an estimator that uses approximate numerical representation techniques for performing the otherwise exact time propagation and measurement update of potentially non-Gaussian probability density functions in the inherently nonlinear attitude estimation problem. The spacecraft attitude is represented via the quaternion of rotation, and a genetic algorithm is used to estimate the gyro biases, allowing to estimate just the quaternion via the particle filter. An adaptive version of the GA-QPF is presented herein, that extends the applicability of this filter to problems with highly uncertain measurement noise distributions. The adaptive algorithm estimates the measurement noise distribution on the fly, along with the estimation of the spacecraft attitude and gyro biases. A simulation study is used to demonstrate the performance of the adaptive algorithm using real data obtained from the Technion's TechSAT satellite, whose three-axis magnetometer's data is non-Gaussian. The simulation, which compares the performance of the filter to two alternative algorithms that are aware of the true statistical nature of the measurement noise, demonstrates the viability of the new algorithm.