Sherborne Missile Fire Frequency with Unconstraint Parameters

For the modeling problem of shipborne missile fire frequency, the fire frequency models with unconstant parameters were proposed, including maximum fire frequency models with unconstant parameters, and actual fire frequency models with unconstant parameters, which can be used to calculate the missile fire frequency with unconstant parameters.


Introduction
Ship borne missile fire frequency is an important impact indicator of target kill probability. Kenan Teng 1 and Fei Li etc 2 proposed ship borne missile fire frequency models by not considering parameters of both sides. In this paper, ship borne missile fire frequency models with unconstraint parameters are proposed, including maximum fire frequency models with unconstraint parameters, and actual fire frequency models with unconstraint parameters.

Maximum fire frequency models with unconstraint parameters
Assume that trh be the moment when the target is detected by warning radar of ship borne missile system, rh  be the reciprocal of the average time required for the target detected by the radar.
Assume that trh1 and trh2 be the moments when the target reached the far boundary and near boundary of the missile launch area respectively, trh2≥trh1. Assume that tfy be the required time for the missile system to execute the target detection, the target threat evaluation, fire control computing and so on, trhs be the missile system reaction time between pressing the first missile launch button and the missile taking off, △tg be the missile launch interval, trhy be the time between the missile taking off and flying at collision point on the far boundary. The time for the target being initially intercepted by the missile system is trh+tfy.

Case one
When trh+tfy≤trh1, the target can be detected by the radar before the target reached the far boundary of the missile launch area, the target can be intercepted by the missile system.
Assume that g t  be a constant, trh1 follows a normal distribution with a mean of trh10 and a standard deviation of 1 t  , trh2 follows a normal distribution with a mean of trh20 and a standard deviation of 2 and a standard deviation of Assume that   2 rh P C be the probability that the fire frequency is Crh2, it can be calculated by Assume that Pmc2 be the target kill probability when the fire frequency is Crh2, Pmdh be the target kill probability with single fire, and Pmc2 can be calculated by The maximum fire frequency with unconstraint parameters in case two is the Crh2 value corresponding to the maximum value of Pmc2   2 rh P C .

Case two
Assume that t rh follows a normal distribution with a mean of t rh0 and a standard deviation of t  , t fy follows a normal distribution with a mean of t fy0 and a standard deviation of tfy  . Based on Eq.(6), C rh3 follows a normal distribution with a mean of C rh30 =( 20 Assume that   3 rh P C be the probability that the fire frequency is Crh3, it can be calculated by Assume that Pmc3 be the target kill probability when the fire frequency is Crh3, it can be calculated by The maximum fire frequency with unconstraint parameters in case three is the Crh3 value corresponding to the maximum value of Pmc3  

Actual Fire Frequency Models with Unconstraint Parameters under Single Shot
Assume that t pd is a constant.

Case one. D rh1 follows a normal distribution with a mean of D rh10 = (
Assume that Pmd1 be the target kill probability when the fire frequency is Drh1, it can be calculated by Assume that   2 rh P D be the probability that the fire frequency is Drh2, it can be calculated by Assume that Pmd2 be the target kill probability when the fire frequency is Drh2, it can be calculated by

Conclusion
Ship borne missile fire frequency is an important impact indicator, target kill probability is affected by it. For the fire frequency models with unconstraint parameters, the maximum fire frequency values with unconstraint parameters can be obtained through the maximum fire frequency models with unconstraint parameters in case one and case two, the actual fire frequency values with unconstraint parameters under single shot can be obtained through the actual fire frequency models with unconstraint parameters under single shot in case one and case two, the actual fire frequency values with unconstraint parameters under salvo can be obtained through the actual fire frequency models with unconstraint parameters under salvo in case one and case two.