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 SCDISTS , I SCDISTS , 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 P0, IY , I 1.0 S 1 do while S MAXSC(I) PS , 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 PS , IY , I 1 PT PS , IY , I PT PS 1, IY , I decrement S end do P0, IY , I P0, 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 */ PC1, IY , I 1 P0, IY , I S 2 do while S MAXSC(I) PC S , IY , I PC S 1, IY , I PS 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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