Fast Trajectory Deviation Prediction Algorithm with Arbitrary Degree/Order Gravitational Potential

Progress on error propagation and correction of long-range rockets in disturbing gravity field

“…Zheng 46 then expanded it to J 4 , and named this kind of method the state space perturbation method (SSPM). In recent years, by combining the local representation model of disturbing gravitational field, Wang 47 deduced an analytical solution of trajectory considering the influence of arbitrary degree and order disturbing gravitational force based on the SSPM.…”

“…In recent years, the authors 13,14 systematically studied the same problem and proposed a relatively complete navigation error propagation model due to the deflection of the vertical, which mainly contains two parts, that iswhere the first part of the right side of equation (14) is called geometric error term, the second one is called initial error term. Φ(t, t0) represents the state transformation matrix, which is obtained based on small-disturbance theory by Chen in 1980s 15 According to this model, Wang 16 analyzed the influence of the deflection of the vertical on rocket, found that the geometric error term and initial error term have the same magnitude of effect on the trajectory of rocket, and proved that the accuracy of this model is higher than Gore’s one.…”

“…Wang made a careful distinction of this problem, respectively named them by navigation error propagation model and dynamic-based error propagation model, and analyzed the characteristics and application scope of these two models. 16…”

“…Comparatively speaking, Li’s method and Zhang’s method have enough efficiency for real-time computation, and none of extra work needs to be done before launching of rockets, but only the J 2 term is considered in their methods. To improve this, Wang 16,47 derived a closed-form formula to predict the impact deviation caused by higher order non-spherical gravitational force, as introduced above, and then adopted the strategies proposed by Li and Zhang, respectively, to verify the correction efficiency and accuracy. The simulation results show that both of these correction strategies are effective and robust even though the trajectory in the boost phase has greatly deviated from the standard one.…”

Target trajectory detection of multi-UAVs based on arrival time

“…Such protection measures enable the obstacle-target encounter section out of the facility's security boundary for further damage reductions [10][11][12]. Consequently, understanding the target's flight path requires trajectory detection system which is usually a key component in the low altitude protection, playing a significant role particularly in the high-speed ballistic target [13][14][15]. As a prevailing methodology, visual technology is utilized when searching target located in small-scale [16].…”