## 1 Introduction  
For some guided spinning projectiles, it is essential to measure the roll angle and rotational speed in real time when it is in the air, because the control surfaces must be correctly actuated to maintain a right trajectory to the target. There are various sensors to detect the roll angle of a spinning projectile in which magnetic and inertial sensors are widely applied, but with some defects. The French-German Research Institute of Saint-Louis have attempted to correct the path of an air-defense projectile using two embedded magnetometers. However, the distortions caused by a ferromagnetic body and changeable geomagnetic environment cannot be modeled and figured out easily to improve the precision of angular information [1]. [PERSON] and [PERSON] [2] presented a roll angle estimation algorithm using pitch and yaw rate gyroscopes as well as the Extended Kalman Filter (EKF), which works only under low spinning speed. Moreover, it is difficult to estimate rotational information with a low-cost MEMS (Micro-electromechanical Systems) gyroscope which has a low-dynamic range, because ordinary inertial sensors cannot work properly under the harsh conditions of gun-lunching projectiles [3]. In addition to magnetometers and inertial sensors, roll information can also be determined by GPS [4; 5; 6]. There are several kinds of GPS-based attitude determining methods, such as the carrier phase-based [7; 8], amplitude-based [9; 10], and SNR (Signal-to-noise ratio)-based methods, for coarse attitude determination [11]. GPS receivers on guided projectiles normally provide the guidance computer with information of position and velocity. However, it is difficult to obtain position and velocity using receivers with a side-mounted single antenna. [PERSON] and [PERSON] [12] proposed a method to track the discontinuous signal received by a single-patch antenna mounted on the side of a spinning vehicle and got the real-time position of it, which enables a GPS receiver to locate and get both the roll angle and roll rate of a spinning vehicle, at the same time. Therefore, the functions of location and roll angle detection can be realized by the study of GPS-based roll angle measurement with only a receiver, which is of great significance in practice for the miniaturization and low cost of projectiles. Some institutions and corporations have carried out in-depth research, such as Interstate Electronics Corporation [13], May Flower [14], and Honeywell [15]. There is a technology called Advanced Spinning Vehicle Navigation (ASVN), developed by Rockwell Collins, which utilizes the amplitude and phase modulation of GPS signals caused by vehicle rotation to obtain the roll angle of a spinning vehicle. The received signals are used to detect a projectile's spinning parameters by adding a rotation-demodulating module prior to the correlation of the GPS signals [16; 17; 18]. [PERSON] and [PERSON] [13] proposed a method for determining the rotational attitude of a spinning vehicle by the value of one-millisecond accumulation results in the tracking process of the receiver. However, all of these works lack profound analysis in theory, and do not give a set of specific parameters to be realized, as well as not mentioning the parameter optimization method. Based on the existing research, we explain and analyze the mechanism of drawing the angular information from the satellite signals received by a single side-mounted antenna, seeking a way to improve the precision of roll angle and rotational speed by means of the signal communication processing method, namely, the phase-locked loops. Firstly, the formation mechanism and extraction method of roll modulation signals, which are amplitude modulated signals encoded with rotation information, are analyzed. Then the roll angle detection method based on Frequency-Locked Loop (FLL)-assisted Phase-Locked Loop (PLL) is described and the specific parameters are studied and optimized. Lastly, experiments are carried out to verify the proposed method.