## 1 Introduction  
The research on smart ammunitions has long been a popular subject for the conventional uncontrolled projectiles cannot satisfy the requirements of modern warfare, high efficiency, accuracy, as well as low cost and collateral damage [1; 2]. Thus, recent decades have witnessed the emergence of various intelligent weapons, such as terminal sensitive projectile [3], precision-guided munition [4], loitering munition [5], networked munition [6], intelligent munitions system [7], and trajectory correction projectile [8]. Among these developed technologies, the trajectory correction projectile is based on the transformation of conventional spinning projectiles through trajectory correction fuze (CCF). It can not only improve the precision but also be of great significance for destocking of dumb ones. There are two types of CCF: one-dimension CCF (1-D CCF) [9] and two-dimension CCF (2-D CCF) [10]. The technology of 1D-CCF (omnidirectional antenna is applied in the Global Navigation Satellite System (GNSS) receivers of 1-D CCF to obtain the position and velocity) is now mature enough to be equipped in the army force worldwide, but has limited precision for correcting the course in the longitudinal direction only. 2-D CCF minimizes impact point dispersion better than 1-D CCF because it is able to correct both longitudinal and lateral errors by fixed canard; the real-time estimation of the spinning projectile roll angle is key to control the fixed canards to provide deflection command. However, under the firing circumstance of high-g (\(\geq\) 12,000 g) and high spin (\(\geq\) 10 Hz), it is a challenge for sensors to measure the spinning information, roll angle, and rotational speed. There are several researches focusing on this daunting task for a long time. [PERSON] and [PERSON] [11] and [PERSON] and [PERSON] [12] attempted to solve this problem by inertial instruments such as gyroscopes but results showed it works properly only within low-dynamic range. The GNSS and magnetoresistive sensor seem now the best choice to determine the roll information for they can resist the harsh gun-launching environment. Some corporations and institutes have focused on the technology on single-patch antennas mounted on the side of a spinning vehicle to get both location and rotary information. [PERSON], [PERSON], and [PERSON] studied a method to reach that by tracking discontinuous signals from their designed antenna [13; 14], however it was not mature and stable enough resulting in occasional bad measurements in location and velocity and the tracking loop, first-order FLL-assisted second-order PLL designed by [PERSON] and [PERSON] limits in tracking signals phase of which changing in the form of ramp function. On the other hand, the magnetometer owns the advantages of passive sensing, high sensitivity, as well as low power and cost. Thus, the research on measurement based on magnetic sensor has always prospered. The French-German Research Institute of Saint-Louis (ISL) studied on obtaining rolling information of an air defense projectile by two embedded magnetometers [15] and attitude estimation of projectiles using magnetometers and accelerometers [16]. U.S. Army Research Laboratory (ARL) put forward kinds of integrated navigation based on magnetometers. POINTER system [17] is the combination of SOLARSONDE and MAGSONDE consisting of solar sensors and magnetic sensor. Another attitude determination system [18] used three magnetometers aligned with body coordinate system assisted by angular rate sensors to figure out all three Euler angles. ARL achieved accuracy within \(5^{\circ}\) in roll angle measurement and ISL even did better in experimental validation [19] after compensation. However, in all these research above, the precision is affected by conventional algorithm of magnetic measurement, more than one magnetic sensor and based on the amplitude of magnetic sensors' output. ARL has toiled and moiled in lab experimental validation to make precision better for years by extended Kalman filter (EKF).