In this paper, we design and evaluate the performance of two inertially-aided (IA) vector matching algorithm (VMA) architectures for estimating the attitude of a spin stabilized spacecraft. More specifically, we design two attitude determination (AD) systems that use inexpensive commercial-off-the-shelf sensors suitable for application on nanosatellites and evaluate the performance of the resulting AD systems. For both architectures, the sensor set consists of rate gyros and a three-axis magnetometer (TAM). The stochastic systems are formulated using combinations of attitude dynamic equations, attitude kinematic equations, and sensor measurement models. We evaluate the performance of the IA VMA architectures by using extended Kalman filters to blend post-processed spaceflight data measured on the Stanford Gravity Probe-B spacecraft. We demonstrate that the stochastic systems developed using this sensor set are observable using a series of TAM measurements spanning several epochs. Furthermore, we conduct trade studies to study the effect of rate gyro grade on the errors of the attitude estimates.