Fire control apparatus for a laser weapon

A laser weapon fire control computer apparatus for responding in real time to the escort/threat scenario that confronts the weapon. The first control computer apparatus compares the threat data with stored predicted scenarios to develop a firing strategy menu which takes into account the fact that the laser energy is instantaneously propagated to the target but requires a substantial amount of time to inflict damage. The fire control computer apparatus utilizes the weapon's status, dwell time, slew time and fuel limits to yield a weapon pointing sequence and weapon on-off times.

BACKGROUND OF THE INVENTION 
The present invention relates broadly to a laser weapon system, and in 
particular to a laser weapon fire control apparatus. 
The damage mechanism of a laser weapon differs significantly from that of 
conventional guns and missiles. While bullets have finite flight times to 
their targets and cause damage instantaneously, laser energy propagates 
instantaneously to its target but requires a substantial amount of time to 
inflict damage. This operational difference requires that the fire control 
apparatus which controls a laser weapon utilize the distinctive 
characteristics of the laser weapon. The control apparatus must consider 
the weapon dwell time for each target, which is an aspect of laser fire 
control systems that has been previously ignored. In addition, the laser 
fire control system will have to consider the laser weapon slew times and 
fuel limits, and must be capable of adapting in real time to multiple 
missile threat scenarios which evolve rapidly in fractions of seconds. 
These constraints are considerably more stringent than those which may 
occur during a conventional fire control problem. 
In the prior art, there have not been any systems for a laser weapon fire 
control apparatus or process which have been implemented in real time. 
Although various techniques and approaches have been utilized, they 
generally suffer from two or more of the following deficiencies: 
(1) It has not been implemented and tested in a real time system. 
(2) It does not find a firing strategy which maximizes survivability and is 
globally optimal with respect to a realistic model of the engagement 
scenario. 
(3) It cannot output firing strategies which are always feasible, even if 
they are non-optimal. 
(4) It cannot revise firing strategies at a frequency which is high enough 
to allow the weapon system to adequately respond to a rapidly evolving 
threat scenario. 
(5) It does not present the operator of the weapon system with a firing 
strategy which estimates future weapon activity for a substantial portion 
of the (if not the entire) engagement. 
(6) It does not adequately consider weapon fuel limits and slewing times. 
The present invention which provides a solution to the problems that exist 
in the prior art is the first laser weapon fire control apparatus that 
enhances ownship/escort survivability and is implemented in real time. It 
successfully copes with all of the various constraints mentioned above, 
and maximizes the joint probability of survival for the system being 
defended. The maximization is with respect to a realistic and dynamic 
model of the engagement scenario. 
SUMMARY OF THE INVENTION 
The present invention utlizes a laser weapon fire control apparatus which 
controls a laser weapon to enhance the survivability of the systems which 
are being defended by the laser weapon. The fire control apparatus 
responds in real time to the escort/threat scenario which confronts the 
weapon. The laser weapon fire control apparatus yields a weapon pointing 
sequence and controls the laser weapon on-off times. 
It is one object of the present invention, therefore, to provide an 
improved laser weapon fire control apparatus by shifting a large part of 
the computational burden to the early part of the engagement where real 
time constraints are not as stringent. 
It is another object of the present invention, to provide an improved laser 
weapon fire control apparatus by utilizing a high speed computer, which 
reduces computation times. 
It is a further object of the present invention, therefore, to provide an 
improved laser weapon fire control apparatus by formulating the problem so 
that the global optimum can be found quickly and accurately while 
considering a wide variety of constraints. 
It is yet another object of the present invention, to provide an improved 
laser weapon fire control apparatus by utilizing input data which is 
readily available in a real time system and which enables the control 
process to realistically evaluate the current engagement and predict its 
future development. 
It is still another object of the present invention, to provide an improved 
laser weapon fire control apparatus by characterizing the situation as a 
resource allocation problem, so that the absolute values of data inputs 
which are not available lose much of their importance, and relative values 
which are more easily obtained become the driving factors. 
These and other advantages, objects and features of the invention will 
become more apparent after considering the following description taken in 
conjunction with the illustrative embodiment in the accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring now to FIG. 1, there is shown a fire control apparatus for a 
laser weapon. The present apparatus utilizes conventional sensors 10 which 
may include a radar unit or other such type of electronic device to 
provide data concerning a hostile environment. An example of a hostile 
environment may include enemy aircraft activity in a given sector. The 
input data from the sensors 10 is applied to the fire control computer 20. 
The fire control computer 20 may be implemented by any of the readily 
available general purpose computers of reasonable size and or capacity. An 
example of the type of general purpose computer that may be utilized, is 
the VAX model 11/780 or VAX model 11/750 which are both available from 
Digital Equipment Corporation of Maynard, Mass. The fire control computer 
20 comprises a threat register unit 21 which receives the threat input 
data from sensors 10. The data from the threat register unit 21 is applied 
to the predictions of scenario development unit 22 which may comprise a 
memory unit with a plurality of pre-planned scenarios stored therein. The 
input data is compared to the stored scenarios. When a correlation occurs, 
a predicted scenario is sent to the estimated future scenario time-lines 
unit 23. A time-lines arrangement is established for the predicted 
scenario. The processing engagement for firing strategy unit 24 receives 
the estimated scenario time-lines and establishes a firing strategy for 
the various threat scenarios. The laser weapon 30 provides a weapon status 
signal to the weapon status unit 26 which in turn provides this signal to 
the firing strategy unit 24. The firing strategy unit 24 establishes a 
firing strategy for the various threat scenarios and applies it to the 
weapon pointing sequence and on-off times unit 25. The weapon pointing 
sequence, together with the firing burst of the laser weapon, are applied 
to the operator's console 40 for display and to the laser weapon 30. The 
operator's console 40 is connected to the laser weapon 30 for control of 
the laser weapon. 
The fire control apparatus for the laser weapon operates in the following 
manner. The fire control apparatus transforms data inputs which are 
received from one or more of the sensors 10 into a weapon pointing 
sequence and weapon on-off time. This transformation is accomplished with 
the aid of the additional stored data delineating environmental, threat, 
and weapon characteristics, and with information regarding the current 
status of the weapon. The driving force behind the process is an attempt 
to characterize the survivability of those systems being defended by the 
weapon, and to develop a firing strategy which yields the greatest 
increase in the likelihood of that survival. 
The threat register of the fire control apparatus utilizes the data which 
it gathers from on-board sensors 10 to characterize a threat/escort 
scenario in real time. This data resides in the threat/escort register 
unit 21, and is updated at frequencies which typically vary from five to 
twenty-five Hertz. It normally consists of the following items: 
(1) threat/escort identification; 
(2) threat/escort/ownship position vectors; 
(3) threat/escort/ownship velocity vectors; 
(4) ownship pressure altitude. 
The above information is time-tagged and presented in a consistent 
coordinate system. While an automatic identification processor may be 
utilized to identify the various threat scenarios, the present example 
utilizes the threat identification which is provided a priority by the 
operator. 
The predictions of scenario development unit 22 convolves the stored threat 
characteristics with information which is contained in the threat register 
unit 21. The scenario development unit 22 develops a set of time-lines 
which estimate the future positions, velocities, and attitudes of each 
threat. The scenario development unit 22 also uses environmental 
parameters and weapon characteristics to develop a set of flux (time rate 
of delivery of fluence) versus range curves, one such curve for each 
altitude of interest. Finally, the threat time-lines and the flux versus 
range curves are used to form a cumulative fluence versus time table for 
each threat. The tables give the amount of fluence which would be 
delivered to that threat if laser firing were to commence at the time 
corresponding to the beginning of the table and continue up to the 
particular time of interest. 
All of the above tables are calculated early in the scenario, when real 
time constraints are not as stringent as they are late in the scenario. 
This is before actual weapon activity commences. They are updated only as 
necessary. It is necessary to update the tables when the actual real world 
scenario begins to significantly diverge from the estimated time-lines. 
This is checked by comparing the data in the threat register with the 
stored time-lines for equivalent times. 
The estimated future scenario time-lines unit 23 is utilized to generate 
the tables created and stored by the fire control computer during the 
activity described above. These tables for each threat are: 
1. Range from the weapon to that threat, versus time; 
2. The aspect angle of that threat's longitudinal axis with respect to the 
line of sight (LOS) from that threat to the weapon, versus time; 
3. The cumulative fluence versus time table for that threat. 
In addition to the above tables, a set of tables which contain flux versus 
range curves, one table for each altitude of interest, is computed and 
stored. The altitudes of interest form an altitude grid which extends from 
the lowest average altitude between the weapon and any threat or escorted 
aircraft, to the highest average altitude. This set of tables is 
calculated once for a given engagement, and stored for the remainder of 
that engagement. 
The weapon status unit is utilized to monitor the weapon status during the 
fire control process, and is used when processing the engagement to find 
the optimal firing strategy. The items monitored are: 
1. Current weapon pointing angles; 
2. Current weapon track mode (i.e., slewing, coarse track, precision track, 
spiral search, etc.); 
3. Current beam status (on/off); and if on, the time at which firing 
commenced. 
The processing engagement for firing strategy unit 24 utilizes the data 
gathered, generated, and stored by the above steps, and repeatedly 
generates firing strategies. The firing strategies are repeatedly 
generated so that they will quickly reflect new data, actively responding 
to the time-evolution of the engagement. The rate at which strategies are 
generated is typically five to ten Hertz. 
The first step of this stage in the processing is to choose three times for 
each threat. These times are: 
(1) The earliest time at which we can begin to deliver fluence to that 
threat, at or above a minimum rate. 
(2) The latest time at which we can or at which we may wish to deliver 
fluence to that threat at or above a minimum rate. 
(3) The time at which we estimate the rate of delivery of fluence will be 
at a maximum for that threat (lying between the earliest and latest 
times). 
The second step orders threats into three sequences: one according to the 
earliest firing times, one according to the latest firing times, and one 
according to the maximum flux times. 
The third step is repeated for each of the three sequences. It chooses that 
combination of open and cease fire times for all threats which maximizes 
an objective function that is stored in the computer. The key aspects of 
this process are: 
(1) The fluence delivered by a specified shot time to a given threat is 
easily computed from the stored cumulative fluence versus time curve for 
that threat, by subtracting the fluence value at the open fire time from 
the fluence value at the cease fire time. 
(2) The objective function being maximized is the sum of the logs of the 
probability of survival of each defended resource attacked by a threat. 
This is equivalent to maximizing the joint probability of survival. The 
log is taken so that the function is additive for the threats which are 
being lased. The additive property of the objective function is important, 
because it greatly simplifies the optimization process. The probability 
that the threat's target will survive is stored as a function of the 
amount of fluence which has been delivered to the threat. This function is 
converted to a log and tabularized, the table indices being related to the 
fluence delivered. The table is pre-calculated before the engagement 
begins. Thus, calculating the value of the objective function for a given 
amount of fluence is merely a table look-up, interpolated as necessary. 
This reduces the computational time required. 
(3) The slewing constraints and fuel constraints are easily accounted for, 
because they merely restrict the set of firing windows which must be 
considered in the maximization effort. Additional constraints can be 
included as desired. 
(4) The specific optimization technique for two threats, is the use a total 
search over a one-second grid, followed by a steepest gradient approach 
using a Fibonacci search to refine the solution to 0.1 sec. 
The weapon pointing sequency and on-off times unit 25 utilizes the results 
of the fire control process which consists of a firing sequence and the 
begin and cease fire times for each threat. The operator by means of the 
operator's console 40 is presented with a time line display to inform him 
of scenario development. The weapon is controlled in real time by 
commanding pointing and tracking system mode, pointing direction, and 
turn-on/turn-off times in response to the real time inputs of firing 
strategy, threat/escort tracks, weapon status, and pointing and tracking 
system status. The weapon is slaved to the line of sight of the pointing 
and tracking system. The pointing and tracking system requests commands 
from the fire computer regularly (typically at 100 cycles) but 
asynchronously to the fire control computer process of firing strategy 
generation. 
The pointing and tracking system is slewed to the highest priority threat 
by commanding weapon azimuth and elevation obtained through coordinate 
transformation. After weapon turn-on, fluence delivery is monitored until 
an amount of fluence sufficient to demand weapon shifting to succeeding 
threats is delivered. The weapon is commanded to succeeding threats until 
all fuel is exhausted. 
1.0 Introduction 
This section briefly outlines this overall structure of The Battle Plan 
Generator, used to compute the commands which control the laser weapon. 
Turning now to FIG. 2 there is shown the battle plan generator routines for 
the fire control computer. There are seven major subroutines in the battle 
plan generator. The data flow is shown in FIG. 2. The subroutines are: 
(1) Threat Register Update Subroutine 
(2) Threat Identification Processor 
(3) Threat Preassessment Subroutine 
(4) Least Time Trajectory Algorithm 
(5) Fluence Model 
(6) Scheduling Algorithm 
(7) Threat Kill Assessment Subroutine 
The inputs, outputs, and basic functioning for each of the above are 
described in the following paragraph. 
2.0 Threat Register Update Subroutine 
As its title implies, this subroutine updates the threat register. The data 
inputs are from four sources, consisting of the following: 
(1) Operator Inputs--The operator must provide threat identification data 
to the subroutine. Four categories of identification exist: 
(a) Friendly or escorted aircraft, 
(b) Enemy aircraft, 
(c) Enemy ground threats, 
(d) Enemy missiles. 
The distinction between categories (a) and (b) is of prime importance, 
since the system has no other means of ascertaining whether a given target 
A/C is friend or foe. 
The information provided must be tagged with an index which identifies that 
track in the threat register to which the given data applies. 
(2) Radar Outputs--The RDP must provide the following information for each 
track in the threat register: 
(a) Whether the track was established during a mini-search mode about an 
enemy A/C or ground threat. 
(b) Whether the engine sideband processing indicates that the track is a 
missile or A/C. 
(c) The signal amplitude of the returns associated with each track. 
Information provided must be tagged so that it may be associated with the 
proper track. In addition, the radar parameters necessary to convert a 
signal amplitude into a target cross-section must be provided. Those 
values not provided will have assumed nominal values. 
(3) Kalman Filter Outputs--The Kalman filter will supply position, 
velocity, and acceleration vectors for each threat in the register. The 
filter will also supply the time at which this given information was 
generated, and a flag indicating that threat in the register to which the 
given information applies. 
(4) INS Outputs--The INS must provide the position and velocity vectors for 
the HELRATS platform, and its attitude. 
The above four sources provide all of the threat register information 
needed to generate the battle plan and to perform threat identification. 
However, there are additional uses for the register, which will require 
additional data inputs. Their absence from this report is not meant to 
imply that they do not exist. 
Those items required by the battle plan generator from the threat register 
are: 
(1) Threat Number 
(2) Threat Identity as determined from radar and operator inputs 
(3) Threat Identity as determined by the I.D. processor 
(4) Absence or presence of engine sidebands 
(5) Whether or not threat was detected in mini-search or in queued search 
(6) Signal amplitude 
(7) Position vector 
(8) Velocity vector 
(9) Acceleration vector 
(10) Aspect angle 
(11) Ownship parameters (position, velocity, attitude) 
Other items which should probably be incorporated into the threat register 
(but are not needed to generate the battle plan) are: 
(12) Priority flag, to indicate the necessity for mini-search or queued 
search, and the track data rate. 
(13) Extrapolation parameters, supplied by the Kalman filter to enable 
extrapolation of threat state vectors from the time they were generated to 
time now. 
3.0 Threat Identification Processor 
The threat I.D. processor is identical to that described in the HELRATS 
final report. It will perform a threat identification based upon the 
information contained in the threat register. 
Note that the threat identity established by the I.D. processor will not be 
used in the battle plan. The battle plan will regard all tracks 
established in mini-search or identified by the operator as missiles, and 
only those tracks will be considered. 
4.0 Threat Preassessment Subroutine 
This subroutine sets up all of the inputs required by the scheduling 
algorithm. To do so, it needs access to threat register items (1), (2), 
and (7)-(11). 
The first step is the selection of those tracks identified as missiles in 
item (2) of the threat register. These are the only targets considered. 
The second step is to call the least time trajectory algorithm. This 
establishes a predicted trajectory for the missile, and a time at which 
the missile reaches the keep out range. 
The third step is to call the fluence model. This model computes a fluence 
versus range curve for that threat, i.e., the rate at which fluence would 
be delivered on a normal surface of that threat if fired on at that range. 
The fourth step is to calculate the fluence vs. time curves for the threat, 
by combining the predicted trajectory with the fluence versus range curve. 
Those portions of the trajectory which are obscured by the ownship 
structure will have the rate of fluence delivery set to zero. (The rate 
will stay at zero for a period of time after the obscuration occurs, to 
allow reacquisition.) 
The fifth step is to establish time constraints on the firing and 
cease-firing times for that threat. The earliest firing time is determined 
by the larger of two times: the first time that the fluence delivery rate 
versus time curve exceeds a threshold value, and the lowest time at which 
precision track could be established. The latest cease-firing time is 
established by the lesser of two times: the last time at which the fluence 
versus time curve yields a threshold fluence delivery rate, and the keep 
out time for that threat. The third time calculated is that time at which 
the fluence delivery rates reaches its maximum value. Finally, the time 
windows throughout which a conical scan acquisition mode will be required 
are specified. These windows are calculated from the predicted trajectory 
range and aspect angle. 
Steps two through five are accomplished for each threat designated by step 
one. 
The final step is specification of the order in which threats should be 
attacked. Three orderings are specified: 
(1) Threats are ordered by the earliest fire times calculated in step five. 
(2) Threats are ordered by the latest cease-firing times generated in step 
five. 
(3) Threats are ordered by the times at which maximum fluence can be 
delivered to the threat. 
The outputs of the threat preassessment routine are: 
(1) The three threat orderings (Step 6) 
(2) The time constraints (Step 5) 
(3) The fluence versus time curves (Step 4) 
5.0 Least Time Trajectory Algorithm 
The inputs required by this algorithm are contained in items (1), (2), and 
(7)-(11). In addition, the time of launch for the missile is needed. 
The least time trajectory algorithm computes a predicted trajectory for the 
missile. To compute this trajectory, the missile's target must be 
identified. Hence, this is the first step. 
Identification of the missile's target is accomplished as follows. The 
missile's velocity vector is extended into space as a straight line. A 
cone is constructed about this straight line, with its apex at the 
missile. That friendly target which is inside the cone and closest to the 
missile is assumed to be the missile's target. 
Once the target is established, the missile is assumed to fly a straight 
line collision course with the target. The thrust generated by the missile 
is varied according to his time of flight. 
Given the predicted trajectory, the range from the HELRATS platform is 
computed as a function of time, along with the aspect of the missile and 
the HELRATS to missile line of sight. Finally, the time at which the 
missile reaches the keep out range with respect to its target is 
calculated. These data items are the output of the least trajectory 
algorithms. 
6.0 Fluence Model 
The fluence model is the simple propagation model developed by AFWL. The 
inputs required are: 
(1) HELRATS altitute above sea level. 
(2) Target altitude above sea level (average during the engagement). 
(3) Power of HELRATS weapon. 
(4) Ownship speed.* 
(5) Wavelength of HELRATS weapon. 
(6) Radius of output optics. 
(7) Average angle between ownship velocity vector and ownship to missile 
line of sight during engagement.* 
(8) Average angular slew velocity during engagement.* 
(9) Minimum and maximum target ranges during engagement. 
(10) Platform jitter due to ownship motion, and tracking and pointing. 
(11) Relative humidity. 
(12) Weather indicator--good or bad. 
FNT * Only needed if blooming is included. 
Given the above inputs, the fluence model calculates a rate of fluence 
delivered versus range curve for each missile, extending from the minimum 
to the maximum ranges. If there is a significant variation in items (2), 
(7), and (8), then several such curves may be needed. However, it is 
currently anticipated that one curve will be sufficient for each threat. 
The output of the fluence model is the set of calculated curves. 
7.0 Threat Kill Assessment Subroutine 
The threat kill assessment routine utilizes data from four sources. 
These are: 
(1) Operator Observation--If the operator decides that a given missile is 
not a threat any longer, he may tell the routine to regard that missile as 
having no capability. 
(2) Threat Register items (1), (2), and (7)-(11). 
(3) The fluence versus range curves for each threat. 
(4) The HELRATS weapon fire and cease-fire times, and the threat fired 
upon. Note that if the weapon is firing, but there is no precision track 
(as in a conical scan acquisition mode), the relevant firing time for the 
kill assessment routine is the time that precision track is established. 
Using items (2), (3), and (4), the routine calculates the amount of fluence 
delivered to the missile. An input from the operator signifying a threat 
kill would be transformed into the artificial deliverance of a large 
amount of energy. 
The routine the modifies a curve which gives the probability that the 
missile will kill its target as a function of the amount of fluence 
delivered to the missile. The modification consists of shifting the origin 
of the curve forward to the amount of fluence delivered. 
The modified curve for each threat is the output of the kill assessment 
subroutine, along with the time that the weapon actually opened fire (for 
fuel constraint purposes). 
8.0 The Scheduling Algorithm 
The scheduling algorithm is the heart of the battle plan generator. Its 
inputs are: 
(1) The outputs of the threat preassessment subroutine (threat orderings, 
time constraints, fluence versus time curves, and the conical scan 
acquisition windows). 
(2) The modified curves from the kill assessment subroutine, giving the 
probability that the missle will kill its target as a function of the 
fluence which may be delivered to that threat. 
(3) The current status of the APT (current line of sight, and whether or 
not track is established on any given target, and if so, for how long). 
(4) The time at which the weapon actually opened fire. 
Using the above inputs, the scheduling algorithm calculates the optimal 
fire and cease-fire times for the threats, given the order in which the 
threats are attacked. These times are calculated for each of the three 
orderings, and the best of the three is output as the battle plan. 
The criterion used maximization of the probability of survival of the 
missile's target. 
The battle plan gives the firing and cease-firing times for each of the 
threats, and the sequence in which the threats are to be attacked. 
As soon as the first battle plan is generated, the APT should be slewed to 
the first threat in the sequence. When the firing time for the threat is 
reached, the weapon fires. As soon as it ceases firing on that threat, it 
should slew to the next threat in the sequence. 
Note that the battle plan is being updated while the system is executing 
the plan. Thus, the kill assessment will affect the weapon activity. 
DETAILED DESCRIPTIONS OF THE THREAT PREASSESSMENT 
Kill Assessment, and Fluence Models 
1.0 Threat Preassessment Routine 
The Threat Preassessment Routine is largely explained in the previous 
section, The Battle Plan Generator, paragraph 4.0. The following 
information clarifies some fine points. 
1.1 Calculation of TMIN(N) 
TMIN is the earliest time in the future at which HELRATS can begin to 
deliver fluence to the missile. If the acquisition mode for the tracker 
involves a spiral search preceeding a conical scan, TMIN is the time at 
which the conical scan begins. (This of course, assumes that F, the rate 
of fluence deliver, is large enough to be useful). 
The acquisition mode must be specified. Let this be MACQ, with 
MACQ=1: Spiral search acquistion 
MACQ=2: Linear search acquistion 
MACQ=3: Normal acquistion (no search). 
The situation is shown (for a typical set of inputs) in FIG. 3. The 
variables therein are defined as: 
TNOW=Time now 
TSL(N)=time required to slew from the current APT line of sight to the line 
of sight for threat N 
TZLOS=time at which the difference between the threat and the APT LOS is 
less than some small .epsilon.. 
TACQ(N)=time required to achieve precision track after the LOS differential 
is zeroed at TZLOS 
TOPFR=time the weapon is turned on 
TPTRK=time at which the APT achieves precision track 
DELT(MACQ)=waiting time or anticipatory time between TOPFR and TPTRK for 
acquisition mode MACQ. (The value shown in FIG. 3 is &lt;0.) 
TWMUP=time required for warm up, to achieve full power 
TFLPR=time at which the weapon achieves full power 
TSRCH(MACQ)=time spent in spiral (MACQ=1) or linear (MACQ=2) search to 
refine the aim point. For MACQ=3, TSRCH is the settling time after the 
establishment of precision track before the delivery of fluence can begin. 
TMIN(N)=earliest time at which we can begin to deliver fluence to threat N. 
From FIG. 3, the following relationships are clear: 
TPTRK=TNOW+TSL(N)+TACQ(N) 
TOPFR=TPTRK+DELT(MACQ) 
TFLPR=TOPFR+TWMUP 
We define the following additional variables: 
FDMIN=threshold fluence delivery rate 
TI(N)=first time at which F&gt;FDMIN for the current predicted least time 
trajectory of threat N 
NTRK=threat currently acquired (i.e., LOS differential has been zeroed) by 
the APT (coarse or precision track; spiral or linear search; conical 
scan). Set NTRK=0 if no threat is currently acquired 
Depending upon the variables involved, we may have TFLPR&lt;TPTRK or 
TFLPR&gt;TPTRK. The spiral or linear search begins at the larger of these 
times, given that sufficient fluence can be delivered to the target. 
We thus define the beginning of search, for N.noteq.NTRK and MACQ=1 or 2, 
as 
EQU TBSRCH=MAX (TI(N), TFLPR, TPTRK). 
Then, we have 
EQU TMIN(N)=TBSRCH+TSRCH (MACQ) 
for N.noteq.NTRK; MACQ=1 or 2. 
For MACQ=3, we must allow a settling time and the laser must be at full 
power delivering sufficient fluence. Hence, 
EQU TMIN(N)=MAX(T1(N), TFLPR, TPTRK+TSRCH(MACQ)) 
for N.noteq.NTRK; MACQ=3. 
The situation N=NTRK is slightly more complicated. Since N=NTRK, we known 
that the LOS differential has been zeroed. Define the following times, 
which correspond to real world inputs (unlike the previously defined times 
which are estimates of future events, excepting TNOW): 
TZLOSD=time at which a discrete signal, denoting that the APT and threat 
LOS differential is less than some .epsilon., is received (corresponds to 
TZLOS). 
TPTD=time at which the discrete signal denoting beginning of precision 
track is received (corresponds to TPTRK). 
TWPFR=time at which the command to open fire was sent to the weapon 
(corresponds to TOPFR) 
TCONSD=time at which the discrete signal indicating that spiral search ends 
and conical scan begins, or that linear search ends, is received. 
Then, in the same manner as before, we have 
______________________________________ 
MAX(TNOW, TZLOSD + TACQ(NTRK)) 
TPTRK = if TPTD not received 
TPTD if received 
MAX(TNOW, TPTRK + DELT(MACQ)) 
TOPFR = if TWPFR not commanded 
TWPFR is already commanded 
TFLPR = TOPFR + TWMUP 
______________________________________ 
In defining TMIN(NTRK), we wish to insure that TMIN.gtoreq.TNOW, and that 
T1(NTRK) has no influence if TWPFR has already has been commanded. For 
notational ease, we define the following variables: 
TT(1)=T1(NTRK)+TSRCH(MACQ) 
TT(2)=TFLPR+TSRCH(MACQ) 
TT(3)=TPTRK+TSRCH(MACQ) 
Then we have: 
For MACQ=1 or 2, 
______________________________________ 
MAX[TNOW, TT(1), TT(2), TT(3)] 
if TCONSD has not been received and 
TWPRF has not been commanded 
TMIN(NTRK) = MAX[TNOW, TT(2), TT(3)] if 
TCONSD has not been received and 
TWPFR has been commanded 
TNOW if TCONSD has been received 
For MACQ = 3, 
MAX[TNOW, T1(NTRK), TFLPR, 
TT(3)] if TWPFR 
has not been commanded 
TMIN(NTRK) = MAX[TNOW, TFLPR, TT(3)] if 
TWPFR has already 
been commanded 
______________________________________ 
Note that when TMIN(N) depends upon T1(N), which in turn depends upon the 
rate of fluence delivery, a two step calculation will be required. First 
we set T1(N)=TNOW-TSRCH(MACQ), calculating TMIN(N) for this value of 
T1(N). Then, starting with this value of TMIN(N), the rate of fluence 
delivery for threat N is calculated for times TMIN(N)+K.DELTA.T 
(.DELTA.T=0.1 sec), K=0, 1, 2 . . . . The first time at which the rate of 
fluence delivery exceeds FDMIN is the correct value for TMIN(N). This two 
step calculation step calculation will be required unless we are 
calculating TMIN(NTRK) and we have already opened fire 
(TWPRF.ltoreq.TNOW), in which case T1(NTRK) has no impact on TMIN(NTRK). 
1.2 Calculation of TMAX(N) 
TMAX is the latest time at which HELRATS is interested in firing upon a 
missile threat. For a system intended to operate in a "real world" 
environment, TMAX(N) would be the minimum of two times: 
TI=latest time at which F&gt;FDMIN for threat N 
TKO=time at which threat N reaches the keep-out range with respect to its 
intended target. 
In the test situation for which the current algorithm must be designed, 
there is further constaint on TMAX. This reflects the fact that the system 
must fire on threat N even if it does not reach its intended target. We 
express this constraint as a restriction that firing must cease within a 
specified time of the launch time for threat N. Defining the elapsed time 
after launch by which countering must have occurred as TCFTST (TCF test) 
we have (TL=time of launch). 
EQU TMAX(N)=MIN (T1, TK0, TL+TCFTST) 
1.3 Calculation of Fluence vs. Time curves 
Calculation of the cumulative versus time curve is done for each threat, 
each time its predicted trajectory changes. 
The curve is calculated for T in the interval (TMIN(N), TMAX(N)). 
From the least time trajectory calculation, we have the functions: 
PRNG(N,T)=predicted range to threat N at time T 
PASPCT(N,T)=predicted aspect angle of threat N with respect to the HELRATS 
to threat LOS at time T 
PA(N,T)=predicted average pressure altitude between threat N and HELRATS at 
time T. 
On an apriori basis, the operator must type in a value of NTYP which 
denotes the threat type and remains constant for the day. The values are: 
NTYP=1: Sidewinder air-to-air missile 
NTYP=2: Falcon air-to-air missile 
NTYP=3: Hawk ground-to-air missile 
We assume that a forward aspect angle with a spiral search acquistion mode 
connotes, a nose acquistion, while a linear search connotes a side aspect 
body acquistion. 
To specify the type of surface we are aiming at, we calculate an aim point 
index MAIM. The values of this index are: 
MAIM=1: Nose shot with an ogive nose 
MAIM=2: Body shot 
MAIM=3: Nose shot with a hemispherical nose which is significantly larger 
than the weapon spot size. 
For a sidewinder of Falcon, we have MAIM=3 for a nose shot. For a Hawk, 
MAIM=1 for a nose shot. The proper values of MAIM are shown in Table 1-1. 
The aspect angles at which a spiral search acquisition is regarded as a 
body shot are those exceeding 90.degree.. Those aspect angles at which a 
linear search acquistion is regarded as a nose shot are those less than 
.theta., where 
TABLE 1-1 
______________________________________ 
Determination of the aim point MAIM. 
##STR1## 
NTYP MACQ PASPCT(N,T) MAIM 
______________________________________ 
3 1 &lt;90.degree. 1 
3 2,3 &lt;4.1.degree. 
1,2,3 1 .gtoreq.90.degree. 
2 
1 2,3 .gtoreq.2.3.degree. 
2 2,3 .gtoreq.4.4.degree. 
3 2,3 .gtoreq.4.1.degree. 
1,2 1 &lt;90.degree. 3 
1 2,3 &lt;2.3.degree. 
2 2,3 &lt;4.4.degree. 
______________________________________ 
As a fixed set of data inputs, we have (MAIM.ltoreq.2) 
SURF(NTYP,MAIM)=angle between the longitudinal axis of the missile and the 
normal of the surface being fired upon, for threat type NTYP and aim point 
MAIM. Thus, MAIM=1 implies the normal for the nose, while MAIM=2 implies 
the normal for the body. 
For MAIM=3, we set 
SURF(NYTP,3)=PASPCT (N,T) 
The threat is assumed to be symmetric about its longitudinal axis. 
FIG. 4 shows the assumed situation at time T. The angle between the surface 
normal and the HELRATS to threat LOS is NORM (N,T) for threat N at time T. 
This angle is a function of the threat type, the aim point, and the aspect 
angle. Using Table 1-1 to calculate MAIM, we have 
EQU NORM(N,T)=ABS(PASPCT(N,T)-SURF(NTYP,MAIM)) 
From the fluence model, we have 
FDOT(A,R)=rate of fluence delivery on a normal surface at a range R and an 
altitude A, where A is the average altitude between the weapon and its 
target. 
We now have the means to compute the desired curve. Define 
FLNCE(N,T)=the cumulative fluence which could be delivered on threat N in 
the interval (TMIN(N),T). 
We initialize: 
EQU FLNCE(N,TMIN)N))=0 
and sequentially calculate 
EQU FLNCE(N,T+.DELTA.T)=FLNCE(N,T)+FDOT (PA(N,T) PRNG(N,T))*.DELTA.T* COS (NORM 
(N,T)). 
In the above equation, if the cosine is less than zero, it should be set to 
zero. It is suggested that .DELTA.T=0.1 sec. When T exceeds TMAX, we 
terminate the calculation. When FLNCE(N,T) is accessed with a value 
T&gt;TMAX(N), set FLNCE(N,T)=FLNCE(N,TMAX(N)). 
Note that as the above table is being constructed, the incremental increase 
in FLNCE(N,T) should be compared against the largest increase which has 
occurred prior to time T. If it is greater than the largest increase, set 
TMXFL(N)=T. This is the time at which the rate of influence delivery is 
the greatest. (TMXFL(N) is initialized as TMIN(N).) 
1.4 Data Inputs 
The data inputs which are required as external inputs to the Battle Plan 
Generator in order to accomplish the above calculations are: 
(1) TNOW 
(2) APT inputs are necessary to calculate TSL(N) 
(3) TACQ(N) 
(4) DELT (MACQ) 
(5) TWMUP 
(6) TSRCH(MACQ) 
(7) FDMIN 
(8) NTRK 
(9) TZLOSD 
(10) TPTD 
(11) TCONSD 
(12) TL 
(13) TCFTST 
(14) NTYP 
(15) MACQ 
(16) SURF(NTYP, MAIM) for MAIM.ltoreq.2 
2. Threat Kill Assessment Routine 
The threat kill assessment routine has two functions. Before the engagement 
begins, it initializes a table which gives the return for firing on a 
given threat and delivering a specified amount of fluence. 
During the engagement, this routine calculates the fluence actually 
delivered to a given threat up to time now. 
2.1 Initialization of the Function R(N,F) 
As a data input, the following pair of values will be supplied for NTYP=1,2 
and MAIM=1,2,3: 
EQU (PKD (NTYP, MAIM, I), FD (NTYP, MAIM, I) I=1,4) 
PKD represents the data input for the probability that a threat of type 
NTYP will kill its target given that a fluence FD has been delivered to 
aim point MAIM. 
Given NTYP and MAIM, the kill assessment routine sets 
______________________________________ 
PK(I) = PKD(NTYP, MAIM, I 
I = 1,4 
F(I) = FD (NTYP, MAIM, I 
______________________________________ 
This function is represented in FIG. 5. These four pairs completely specify 
the form of a piecewise linear function of the probability that the 
missile will kill its target (PK) versus the amount of fluence delivered 
on the missile (F). (Clearly, PK (4)=F(1)=0). 
This curve must be transformed into a table from which the return R (N,FL) 
obtained by delivering a fluence FL on threat N is ascertained. This 
return is repeatedly calculated for use in the scheduling algorithm. The 
values N and FL are supplied by the scheduling algorithm. FL as supplied 
already includes the fluence delivered prior to time now, so that no 
adjustment is required. The value of N is not required in the current 
version of the battle plan because all threats are assumed to be of the 
same type, NTYP. 
The table contains the values 
EQU TR(J)=ln [1-PK1(F1(J))], J=1, JMAX 
where 
EQU F1(J)=(J+0.5)*F(4)/JMAX=(J+0.5)/CONST 
and PK1(F) is a linear interpolation on the four data points (PK(I), F(I)), 
as shown in FIG. 5. 
Thus, to evaluate the function R(N, FL), we calculate (truncate the RHS) 
EQU J=FL*CONST. 
If J.gtoreq.JMAX, R(N, FL)=0. If J=0, set J=1. Then, 
EQU R(N,FL)=TR(J). 
Note that the calculation of J involves a multiplication. Since this is 
done a large number of times, any alternative method of obtaining J from 
FL which would be quicker should be utilized. (e.g., a bit shift). The 
test for J=0 may be avoided by incorporating a dummy location in front of 
the table TR(J), with the value of TR(1). 
2.2 Calculation of Fluence Delivered 
During the engagement, the scheduling algorithm uses the variable FLDL(N), 
which is the fluence delivered prior to time now on threat N. This 
variable must be computed by the kill assessment routine. 
Define the following variables: 
TNOW=time now 
TLST=time that this routine was last called 
TSTART(N)=time at which HELRATS began to deliver fluence on threat N. For a 
normal acquisition, this is TPTD+TSRCH(N). For a spiral or linear search, 
this is TCONSD (see Section 1.1) 
TSTOP(N)=time at which HELRATS ceased firing on threat N 
NTRK=threat currently being tracked by APT 
AVALT(N)=average of current pressure altitudes of threat N and HELRATS 
RNG(N)=current range to threat N 
FDOT(A,R)=rate of delivery of fluence on a normal surface at range R and 
average altitude A 
ASPCT(N)=aspect angle of longitudinal axis of threat N with respect to the 
line of sight from HELRATS to threat N 
MAIM=aim point index 
The values of TLST and NTRK are initialized to zero at the beginning of the 
flight. The values TSTART(N), TSTOP(N), and FLDL(N) are set to zero when a 
track on threat N is first established by the APT. The values TNOW, NTRK, 
AVALT(N), RNG(N), and ASPCT(N) are provided by HELRATS. FDOT(A,R) is 
provided by the fluence model. The value of MAIM is calculated from Table 
1-1 as before, but using ASPCT(N) in place of PASPCT(N,T). We set 
EQU SURF(NTYP,3)=ASPCT(N) 
as before. 
When called, the routine calculates the amount of fluence delivered since 
the last time the routine was called. The flow chart in FIG. 6 illustrates 
this calculation. During firing, the calculation should be performed every 
0.1 sec, at least. 
2.3 Data Inputs 
The data inputs required as external inputs to the Battle Plan Generator, 
in order to accomplish the above calculations, are: 
(1) NTYP 
(2) PKD(NTYP, MAIM I) 
(3) FD(NTYP, MAIM, I) 
(4) TNOW 
(5) TSTART(N) 
(6) TSTOP(N) 
(7) NTRK 
(8) AVALT(N) 
(9) RNG(N) 
(10) ASPCT(N) 
(11) MACQ 
(12) SURF(NTYP, MAIM), MAIM.ltoreq.2 
3. The fluence Model 
The fluence model is used to provide a value for FDOT(A,R) when requested. 
It should be tabularized in altitude and range. In range, the table should 
extend from 0 to the maximum range of interest, in increments of 150 
meters. 
To establish the altitudes of interest, we calculate the following pressure 
altitudes: 
HT.sub.i =average altitude between HELRATS and the i.sup.th escorted 
friendly A/C 
HM.sub.n =average altiltude between HELRATS and the n.sup.th missile threat 
H=current HELRATS altitude 
Then, the minimum altitude of interest is 
##EQU1## 
The maximum altitude of interest is 
##EQU2## 
Therefore, we define 
##EQU3## 
where AGRID is the grid size for altitude. If the altitudes are in meters, 
AGRID=1500 meters. 
The altitudes for which FDOT(A,R) is calculated are 
EQU A=H+K*AGRID, KMIN.ltoreq.K.ltoreq.KMAX. 
If the above yields A 0, use A=0. 
The model used is identical to that described in the Laser System 
Effectiveness Model, Vol. I, Pg. 109-110. (AFWL-TR-74-17, Vol. I). 
We define the following constants, which are supplied as inputs to the 
model. (All units are in joules, meters, and seconds) 
P.sub.o =nominal laser power 
K=ratio of nominal to useful power exiting the aperture 
K.sub.BS =beam shape factor which describes the angle to the first dark 
ring of the diffraction pattern 
K.sub.BQ =beam quality factor or ratio of actual operating angle to ideal 
spreading angle 
.lambda.=laser wavelength 
D=aperture diameter 
R.sub.min =minimum focal range of the system 
.theta..sub.J =spreading half-angle due to mechanical jitter 
Given the above constants, we can calculate the following beam spreading 
half-angles 
.theta..sub.D =spreading half-angle due to diffraction 
##EQU4## 
.theta..sub.T =spreading half-angle due to atmospheric turbulence 
EQU .theta..sub.T =1.7[(C.sub.n.sup.2 R).sup.3 /.lambda.].sup.1/5 
where C.sub.n.sup.2 =A.sup.-1.075 .times.10.sup.-13 
.theta..sub.MF =spreading half-angle due to out of focus condition 
##EQU5## 
There is one additional input required, the extinction coefficient. This 
will be input as a table .alpha.(A), which may depend upon ambient 
conditions and which must be interpolated for a given value of A, the 
average pressure altitude. 
The equation which gives the flux is: 
##EQU6## 
Note that the exponential term can be calculated without repeated use of 
exponentiation as the range R is stepped through. We have 
EQU e.sup.-.alpha.(R+.DELTA.R) =e.sup.-.alpha.R e.sup.-.alpha..DELTA.R. 
Calculating the constant C=e.sup.-.alpha..DELTA.R, we have 
EQU e.sup.-.alpha.(R+.DELTA.R) =C e.sup.-.alpha.R, 
Which can be used to sequentially calculate the exponential. 
Although the invention has been described with reference to a particular 
embodiment, it will be understood to those skilled in the art that the 
invention is capable of a variety of alternative embodiments within the 
spirit and scope of the appended claims.