Real-Time Estimation for Roll Angle of Spinning Projectile Based on Phase-Locked Loop on Signals from Single-Axis Magnetometer

Abstract

As roll angle measurement is essential for two-dimensional course correction fuze (2-D CCF) technology, a real-time estimation of roll angle of spinning projectile by single-axis magnetometer is studied. Based on the measurement model, a second-order frequency-locked loop (FLL)-assisted third-order phase-locked loop (PLL) is designed to obtain rolling information from magnetic signals, which is less dependent on the amplitude and able to reduce effect from geomagnetic blind area. Method of parameters optimization of tracking loop is discussed in the circumstance of different speed and it is verified by six degrees of freedom (six degrees of freedom (DoF)) trajectory. Also, the measurement error is analyzed to improve the accuracy of designed system. At last, experiments on rotary table are carried out to validate the proposed method indicating the designed system is able to track both phase and speed accurately and stably. The standard deviation (SD) of phase error is no more than 3°.

Keywords: 2-D CCF; FLL-assisted PLL; magnetic sensor; roll angle measurement; spinning projectile.

Figure 1

Description of geomagnetic field.

Figure 2

Here are figures to describe projectile body based on a model of 155 mm artillery projectile launched by howitzer: (a) Description of body coordinate system and (b) description of the cross-section.

Figure 3

Description of compensation angle.

Figure 4

Process of obtaining roll angle.

Figure 5

Block diagram of phase-locked loop in frequency domain (Laplace transform).

Figure 6

Block diagram of discrete time system of combined loop filter.

Figure 7

Designed tracking system.

Figure 8

(a) Descriptions of amplitude–frequency characteristic. (b) Descriptions of step response of third-order PLL.

Figure 9

(a) Description of amplitude–frequency characteristic. (b) Description of step response of second-order FLL.

Figure 10

Model of 6-degrees of freedom (DoF) trajectory: (a) Trajectory of projectile and (b) information of the speed, pitch and yaw from 6-DoF.

Figure 11

Amplitude of $B_{\mathrm{Z}}$ changing in flight: (a) Description of the amplitude of $B_{\mathrm{Z}}$. (b) Description of part of the amplitude of $B_{\mathrm{Z}}$ (within 0.03 second).

Figure 12

Tracking results. (a) Description of $B_{\mathrm{Z}}$ and local replicas (amplitude of local replicas is amplified 8 times for the convenience of comparison). (b) Description of phase of local replicas. (c) Description of the output of phase discriminator. (d) Description of error of phase tracking.

Figure 13

Tracking results: (a) Description of the contrast of speed and (b) description of error of speed tracking.

Figure 14

Comparison of compensation angle based on different geomagnetic information in north direction (a), east (b) direction, south (c) direction, and west (d) direction.

Figure 15

Deviation of compensation angle caused by different geomagnetic information in north direction (a), east (b) direction, south (c) direction, and west (d) direction.

Figure 16

SD and mean of deviation of compensation angle caused by the noise.

Figure 17

Compensation angle and deviation when yaw is 0° and 180°: (a,c) Description of compensation angle in the north and south direction and (b,d) description deviation of compensation angle.

Figure 18

Cross-section and geomagnetic vector.

Figure 19

Experiments on rotary table.

Figure 20

Design of integrated circuit.

Figure 21

Results of group 1: (a) Description of digital amplitude of $B_Z;$ (b) Comparison of pulses produced by hall sensor and controller and (c) is part of (b); (d) Description of speed figured out from controller; (e) Description of speed error and phase error.

Figure 21

Results of group 1: (a) Description of digital amplitude of $B_Z;$ (b) Comparison of pulses produced by hall sensor and controller and (c) is part of (b); (d) Description of speed figured out from controller; (e) Description of speed error and phase error.

Figure 22

Results of group 2: (a) Description of digital amplitude of $B_Z;$ (b) Comparison of pulses produced by hall sensor and controller; (d) Description of speed figured out from controller; (e) Description of speed error and phase error.

Figure 23

Results of group 3: (a) Description of digital amplitude of $B_Z;$ (b) Comparison of pulses produced by hall sensor and controller; (d) Description of speed figured out from controller; (e) Description of speed error and phase error.