Explicit Exact Solution of Damage Probability for Multiple Weapons against a Unitary Target

Abstract We study the damage probability when M weapons are used against a unitary target. We use the Carleton damage function to model the distribution of damage probability caused by each weapon. The deviation of the impact point from the aimpoint is attributed to both the dependent error and independent errors. The dependent error is one random variable affecting M weapons the same way while independent errors are associated with individual weapons and are independent of each other. We consider the case where the dependent error is significant, non-negligible relative to independent errors. We first derive an explicit exact solution for the damage probability caused by M weapons for any M. Based on the exact solution, we find the optimal aimpoint distribution of M weapons to maximize the damage probability in several cases where the aimpoint distribution is constrained geometrically with a few free parameters, including uniform distributions around a circle or around an ellipse. Then, we perform unconstrained optimization to obtain the overall optimal aimpoint distribution and the overall maximum damage probability, which is carried out for different values of M, up to 20 weapons. Finally, we derive a phenomenological approximate expression for the damage probability vs. M, the number of weapons, for the parameters studied here.

INS stochastic error detection during kinematic tests and impacts on INS/GNSS performance

Inertial Navigation System(INS)and Global Navigation Satellite System(GNSS)integration requires accurate modelling of both INS deterministic and stochastic errors.The Allan Variance(AV)analysis on INS static data is one method of determining INS stochastic errors.However,it is known that INS errors can vary depending on a vehicle’s motion and environment,and application of AV results from static data in kinematic operations typically results in an over-confident estimation of stochastic.In order to overcome this limitation,this paper proposes the use of Dynamic Allan Variance(DAV).The paper compares the resulting performance of the INS/GNSS integrated system by varying the stochastic coefficients obtained from the AV and DAV.The results show that the performance improved when utilizing the stochastic coefficients obtained from the DAV,applied on a kinematic dataset compared to the AV,applied on a static laboratory dataset.