The Algorithms

					                                                     A.1      Main

Purpose:          To enter area parameters, initialize variables, call computation algorithm and output
                  results


Input: L, C, NMT
Output: MAXSC, NY, P, Percent Clearance, SCDIST, Y

begin main
input number of computation points, NY

/* algodes defaults to NATO-only */
algodes=NO
input YES if US algorithmic description, algodes
if algodes = YES
        /* US-only */
        use initialization algorithm to compute number of computation points
end if

/* compute distance between computation points */
              C
     DY 
           NY  1
/* compute location of computation points */
IY=0
do while IY < NY
       Y IY     IY  DY
                  C
                  2
       increment IY
end do

do for each mine type, I
         input expected deployment/arming1 time relative to start of operation
         input MOORED (yes or no)
         input INFLUENCE (yes or no)
         if INFLUENCE
                  input ship count settings
         end if
         initialize reduced transition matrix
end do
‘-------------------------------------------------------------------------------------------------------
set coverage to 1
do while more coverages
       input coverage parameters algorithm
       do for each mine type, I
               case (mcm technique)

                     influence sweep
                            if INFLUENCE (mine) and Tstart  arming time
                                   input effectiveness parameters
                            else
                                   A=0.0
                                   B=0.0
                            end if
                     mechanical sweep
                            if MOORED (mine)
                                   if Tstart  deployment time
                                             input effectiveness parameters
                                   else
                                             A=0.0
                                             B=0.0
                                   end if
                            else
                                   input effectiveness parameters (mechanical sweep of bottom
                                   mine)
                            end if
                     mine hunting
                            if MOORED
                                   if Tstart  deployment time
                                             input effectiveness parameters based on moored mine
                                   else
                                             input effectiveness parameters based on bottom mine
                                   end if
                            else
                                   input effectiveness parameters based on bottom mine
                            end if
              end case
              compute YHMIN and YHMAX
              IY=0
              do while IY < NY ‘for all computation points
                     compute computation
                     increment IY
              end do

              display percent clearance as a function of ship count and cross-channel position for
              current mine type

              if algodes = YES
                      /* US-only */
                        use Trapezoid rule to compute and then display the average cross-channel
                        percent clearance for each ship count (save for Simple Initial Threat)
               else
                        /* NATO only */
                        compute and then display the average cross-channel percent clearance for each
                        ship count (save for risk)
               end if
               use the distribution of ship counts to compute and then display weighted percent
               clearance for each cross-channel position (save for risk and Simple Initial Threat)
              compute and display a single weighted-average (weighted over ship count and averaged
              over cross channel position) percent clearance (save for risk and Simple Initial Threat)
       end do on mine type

       if algodes = YES
               /* US-only TIME FOR COVERAGE ALGORITHM */
               compute time for non-uniform coverage
               compute running total of runs and times for coverages
               display coverage and total, runs and times
       end if
       increment coverage
end do on coverage
                                        A.2 end main
                                 Ship Count Settings Algorithm

Purpose:       To determine the maximum ship count and the distribution of ship
               counts if the maximum is greater than one


Input: I
Output: MAXSC, SCDIST

begin ship count settings
input MAXSC(I)
if MAXSC(I)>1
       input ship count distribution type (uniform, geometric or user input)
       if ship count is geometric then input the reciprocal average ship count setting, B
       do for each ship count, S
               case on ship count distribution
                       uniform
                                SCDIST S , I  
                                                       1.0
                                                  MAXSC I 
                       geometric
                                SCDIST S , I   B  1  B 
                                                               S 1


                       user input
                               input SCDIST(S,I)
                       end case
       end do
       /* normalize ship count distribution */
                               MAXSC( I )
                  SUM             SCDIST S , I 
                                  S 1

         do for each ship count S
                                            SCDISTS , I 
                  SCDISTS , I  
                                               SUM
         end do
end if
                                     A.3 end ship count settings
                         Initialize Reduced Transition Matrix2 Algorithm

Purpose:          To initialize the reduced transition matrix to indicate that the probability is 1.0 that each
                  mine has received exactly 0 ship counts and the probability is 0.0 for all other ship
                  counts. The reduced transition matrix is a three dimensional matrix whose (S,IY,I)
                  element contains the probability that a mine of type I located at position IY has received
                  exactly S counts. The probabilities that a mine of type I at position IY is not effected by
                  mechanical sweeping and mine hunting (PMSo and PHo respectively) are also
                  initialized.

Input: I, MAXSC, NY
Output: P, PMSo, PHo

begin initialize reduced transition matrix
IY  0
do while IY < NY
        PMSo IY , I   1.0
         PH o IY , I   1.0
         P0, IY , I   1.0
          S 1
         do while S  MAXSC(I)
                 PS , IY , I   0.0
                increment S
         end do
         increment IY
end do
end initialize reduced transition matrix
                                                   A.4
                                    Input Coverage Parameters Algorithm

Purpose:          To set those parameters that define an MCM coverage.


Input: C
Output: , JT, mcm technique, NT, Tstart, Tt, V, YT

begin input coverage parameters
input time that coverage starts relative to start of operation, Tstart
input mcm technique (influence sweep, mechanical sweep or mine hunting)
input standard deviation of navigational error3, 
input tow speed, V
input turn time, Tt
input number of tracks, NT
input coverage type (uniform or non-uniform coverage)
if uniform coverage
        input number of runs on each track, J
        /* compute track location for each track*/
                         C
                 DYT 
                        NT
                 IT  0
        do while IT < NT
                /* compute location of each track */
                        YT IT     DYT  IT  0.5
                                     C
                                     2
                set number of runs on each track to J
                        JT IT   J
                increment IT
        end do
else
         IT  0
        do while IT < NT
                input YT(IT)
                input JT(IT)


                  increment IT
         end do
end if
                               A.5 end input coverage parameters
                            Input Effectiveness Parameters Algorithm

Purpose:          To input the effectiveness parameters for the current coverage and mine
                  type. Note that since this is inside a loop on mine type, mine hunting and mechanical
                  sweeping, as well as influence sweeping, computations are a function of mine type.


Input: none, algodes
Output: A, B, Bc, Bn, MCT, µ

begin input effectiveness parameters
if mine hunting
/* input effectiveness parameters for mine hunting */
        input Multiple Classification Tactic (MCT)
        input characteristic width, A
       if (MCT) then
               input probability of detection and classification, B
       else
               input probability of detection, B
               input probability of classification, Bc
       end if
       input fraction undetectable, µ
       input probability of neutralization, Bn

else
/* input effectiveness parameters for sweeping */
        input characteristic width, A
        input characteristic probability, B
end if
end input effectiveness parameters




                          A.6     YHMIN AND YHMAX Algorithm


Input: A, 
Output: YHMIN, YHMAX

begin yhmin and yhmax
                    A
         YPMIN  
                   2.0
                   A
         YPMAX 
                  2.0
         YGMIN  3.0  
         YGMAX  3.0  
         YHMIN  YPMIN  YGMIN
      YHMAX  YPMAX  YGMAX
end yhmin and yhmax
                                            A.7
                                     Computation Algorithm

Purpose:        To compute the probabilities of clearance and update the reduced transition matrix for a
                particular mine at a particular point based on the parameters of the current coverage.

Input:  A, B, Bn, Bc,  , I, INFLUENCE, IY, JT, NT, MAXSC, mcm technique, P, PHo, PMSo, Y,
        YHMIN, YHMAX, YT, µ
Output: PC


begin computation
IT=0
do while IT < NT                 for all tracks
       YH  Y IY   YT IT    YT = location of each track from center of channel in meters
                                 Y( ) = distance from center of channel in meters
                                 IY = index on computation point mine @position IY
                                 IT = index on each track
                                 YH = distance from intended track to computation point

         if YHMIN  YH  YHMAX
                compute probability of transition, PT
                do for each run
                        case (mcm technique)
                               influence sweep
                                      if INFLUENCE
                                              update reduced transition matrix
                               mechanical sweep
                                      update PMSo
                               mine hunting
                                      update PHo
                        end case
                end do
         end if
         increment IT
end do
compute percent clearance, PC (for mine I at position IY)
                                       A.8    end computation
                                             PT Algorithm
Purpose:               To compute the probability of sweeping, cutting or detecting a mine
                       located at a point YH from the intended track. Since this probability is used to adjust
                       the reduced transition matrix, the probabilities are referred to as the probability of
                       transition, PT. This routine computes H as it is needed (sometimes referred to as
                       computing H "on-the-fly") rather than precomputing H.4


Input: A, B, , YH
Output: PT

begin PT
       PT  H YH 
end PT
                                                       A.9
                                                    H Algorithm

Purpose:               To compute the value of the vector, H (the probability of success versus lateral range
                       curve) at a distance YH from the intended track. This curve is actually the convolution
                       of the probability of actuation (or detection or cutting) curve, Py, and the navigational
                       error curve, g(y).5 The current algorithm assumes that probability of actuation curve is
                       a rectangle (i.e., cookie cutter) A wide and B high and the navigational error curve is
                       Gaussian with a standard deviation of .


Input: A, B, , YH
Output: H

begin H
/* compute probability of success at lateral range of YH */

                             A          A 
                        YH  2      YH  
              H  B                 2 
                                       
                                            
                       
                                           




                                                   A.10
                                  Update Reduced Transition Matrix Algorithm




              
    H y     P y  y' g  y'dy'
5
              
Purpose:          To update the reduced transition matrix which is used to account for influence
                  sweeping based on current run.


Input: I, IY, MAXSC, P, PT
Output: P

begin update reduced transition matrix
S  MAXSC I 
do while S  1
         PS , IY , I   1  PT   PS , IY , I   PT  PS  1, IY , I 
        decrement S
end do
P0, IY , I   P0, IY , I   1  PT 
end update reduced transition matrix




A.11
                                            Update PMSo Algorithm

Purpose:          To update the probability that a mine of type I and at location IY has not been
                  mechanically swept.


Input: I, IY, PMSo, PT
Output: PMSo

begin update PMSo
       PMS o IY , I   1  PT   PMS o IY , I 
end update PMSo
                                                          A.12



                                                                                           Update PHo
                                                       Algorithm

Purpose:          To update the probability that a mine of type I and at location IY has not been
                  detected/classified.


Input: I, IY, PHo, PT
Output: PHo
begin update PHo
       PH o IY , I   1  PT   PH o IY , I 
end update PHo
                                                            A.13



                                 Compute Percent Clearance6 Algorithm
Purpose:                    To compute the percent clearance for a mine of type I at cross-
                            channel position IY.


Input: Bc, Bn, I, IY, MAXSC, MCT, P, PHo, PMSo, µ
Output: PC

begin compute percent clearance
 Po  PH o IY , I 
/* compute probability of clearance by mine hunting */
        if (MCT)
                    PH  1  Po   1     B n
        else
                    PH  1  Po   1     B c  B n
        end if
/* compute probability of clearance by influence sweeping */
 PC1, IY , I   1  P0, IY , I 
 S 2
do while S  MAXSC(I)
         PC S , IY , I   PC S  1, IY , I   PS  1, IY , I 
        increment S
end do
/* compute combined probability of clearance from all techniques */
        S=1
        do while S  MAXSC(I)
                    PC S , IY , I   1  1  PC S , IY , I   PMS o IY , I   1  PH 
                   increment S
        end do
end compute percent clearance




    PC(s, IY, i) = 1 - (1 - PC(s, IY, i)) * PMSo(IY, i) * (1 - PH)
                APPENDIX B.    US ONLY ALGORITHMS
                    B.1 Initialization Algorithm (US Only)
Purpose:              If US algorithmic description, compute the location of the computation points.


Input: C, algodes, NY
Output: NY, Y

begin initialization
/* US-only Algorithm */

   if NY >501
       NY=501
       alert user that NY was set to 501
   end if

   modNY=mod(NY,2)
   if modNY=0
        /* if NY is even, increment NY by 1 to make it odd */
       NY=NY+1
   end if
end initialization
                      B.2      Time for Coverage Algorithm (US Only)
Purpose:                If US algorithmic description, compute the time spent on track and making turns
                        during a coverage. This algorithm is only meaningful in the pre-mission
                        analysis of a plan. When evaluating an actual operation, the actual time is
                        known. Other time such as classification and neutralization are not considered.


Input: JT, NT, L, Tt, V
Output: Tcov

begin time for coverage
/* US-only Algorithm */
    input tow speed, V
    input turn time, Tt
    input number of tracks, NT
    Tcov = 0.0
    n=1

   do while n≤NT
          input number of runs on nth track, JT(n)
          input length of nth track, L(n)
          /* compute time for JT runs on nth track*/

                                  L ( n) 
           Tcov  Tcov   JT (n)           JT (n)  1 Tt
                                   V    
           increment n
   end do
end time for coverage
                                            C.1        Data Dictionary

Modification History:
Version      Date             Responsible Individual                           Modification
 0.1.0      06 Dec 1991 F.P. Sutter, US                     (a) Original US release
  1.0           Sep 1994     F.P. Sutter, US                (a) Original NATO release
  1.2           Jan 1997     F.P. Sutter, US                (a) Replaced term mode with technique
                                                            (a) Converted Modification History to
                                                                table format
                                                            (b) Added US-only parameters (algodes,
  1.4       14 June 2011 L.G. Wazlavek, US                      PROS, PHo, PMSo, Tcov and Tt)
                                                            (c) Moved data dictionary to Appendix
                                                                C
                                                            (d) Modified NY footnote
                                                            (a) Deleted PROS parameter from mine
                                                                hunting coverages (US-only
  1.5       23 June 2011 L.G. Wazlavek, US                      parameter)
                                                            (b) Modified NY footnote


         Name                            Definition                                Type          Min.       Max.
                                                                        enumerated
                                                                        (inf. sweep,
                    mcm technique
                                                                        mech. sweep,
                                                                        or hunt)
                   standard deviation of navigational error in meters real                      0+     999
  µ                 undetectable fraction of mines                      real                     0      1
  A                 characteristic width in meters                      real                     0      9999
  algodes           type of algorithmic description                     enumerated (yes or no)
                    characteristic probability of actuation, cutting or
  B                                                                     real                     0      1
                    search
  Bc                probability of classification                       real                     0      1
  Bn                probability of neutralization                       real                     0      1
  C                 channel width in meters                             real                     0+     99999
  DY                distance between computation points in meters       real                     10     9999
  DYT               distance between tracks in meters                   real                     0+     9999
  I                 index on mine type                                  integer                  0      99
  IHMAX             maximum number of points on H curve                 integer                  2      1000
  INFLUENCE         influence mine indicator                            enumerated (yes or no)
  IL                index of first point on H curve below YH            integer
  IY                index on computation point                          integer                  3      100
  JT                runs per track                                      real                     1      999
  L                 channel length in nautical miles                    real                     0+     999
  MAXSC             maximum ship count                                  integer                  1      32
         Name                         Definition                                Type        Min.       Max.
MCT             multiple classification tactic                        enumerated (yes/no)
MOORED          moored mine indicator                                 enumerated (yes/no)
NMT             number of mine types                                  integer               1      10
NT              number of tracks                                      integer               0      999
NY              number of computation points                          integer               3      1017
P               transition matrix                                     real                  0      1
PC              percent clearance as a fraction                       real                  0      1
                probability that mine has not been
PHo                                                                   real                  0      1
                detected/classified
                probability that mine has not been mechanically
PMSo                                                                  real                  0      1
                swept
Po              probability of mine not being effected                real                  0      1
PT              probability of transition                             real                  0      1
SCDIST          ship count distribution vector                        real                  0      1
Tcov            total coverage time                                   real                  0
                time of coverage start (hours, relative to start of
Tstart                                                                real                  0      9999
                operation)
Tt              turn time in hours                                    real                  0      9
V               velocity in knots                                     real                  0+     99
Y               distance from center of channel in meters             real                  0      99999
                distance from intended track to computation
YH                                                                    real                  0      99999
                point in meters
YHMAX           maximum y for which H>0                               real                  0      99999
YHMIN           minimum y for which H>0                               real                  -99999 0
                location of each track from center of channel in
YT                                                                    real                  0
                meters

				
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posted:12/1/2011
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