This paper presents the pseudo-linear estimation approach to the high-rate spinning small spacecraft attitude estimation problem. The sensor suit utilised in the presented approach uses gyro, magnetometer and sun-sensor measurements. The presented estimation technique has been designed particularly for the problem of attitude determination during the Aalto-1 nanosatellite's Plasma Brake Experiment (PBE). The design of the PBE demands the satellite to be spun up to 200 deg/s for deploying the tether by the use of centrifugal force resulting from the spin motion. The spinning up of the satellite is achieved only through the magnetic actuation. The used spin controller has been proven to be very robust for different initial conditions and operating scenarios. However, it demands accurate attitude estimates in order to efficiently and successfully spin the satellite up to the required angular velocity. Magnetometers are the most important sensors amongst the available onboard for the presented setup. The reason for this is that the system has the inputs only from the magnetometers and gyros during the eclipse period. It is necessary to estimate the magnetometer biases because the systems are very closely integrated and there is a higher risk of electromagnetic interference in them. A pseudo-linear Kalman Filter (PSLKF) has been studied. The two cases of integrated and separate attitude estimation and magnetometer calibration algorithms have been studied and analyzed in the perspective of their use onboard a nanosatellite.