# Altitude Data Reduction

**E.1 Sample Program**

0010 REM TRACK.BAS by Geoff Landis 0020 REM from the 9 / 83 "Model Rocketeer" page 11 0030 REM NAR Tracking Data Reduction by various methods 0040 REM Refer to that issue for full details 0050 REM 0060 REM Tracking Data Reduction Program 0070 REM Program Copyright (C) 1983 0080 REM by Geoffrey A. Landis 0090 REM may be freely used but not sold 0100 REM 0110 REM Minor Edits and Renumbering Copyright (C) 1985 Robert G. Kaplow 0150 REM 0200 REM data input 0210 REM Change the next line as appropriate for your baseline 0220 B = 300. 0240 R1 = .0174532925199433 0500 PRINT 0510 PRINT "Tracker One Azimuth, Elevation: " 0520 INPUT A1, E1 0530 PRINT "Tracker Two Azimuth, Elevation: " 0540 INPUT A2, E2 0550 IF E1 < 0. THEN 9998 0560 IF E2 < 0. THEN 9998 0570 A1 = A1 * R1 0580 E1 = E1 * R1 0590 A2 = A2 * R1 0600 E2 = E2 * R1 1000 REM 1010 REM Geodesic Data Reduction 1020 REM 1030 F = SIN(E1) * SIN(E2) - COS(E1) * COS(E2) * ( COS(A1) * COS(A2) - SIN(A1) * SIN(A2) ) 1040 D = 1. - F ^ 2 1050 T = ( COS(E2) * SIN(E1) * SIN(A2) - COS(E1) * SIN(E2) * SIN(A1)) / SQR(D) 1060 D1 = ( COS(E1) * COS(A1) + F * COS(E2) * COS(A2) ) / D 1070 D2 = ( COS(E2) * COS(A2) + F * COS(E1) * COS(A1) ) / D 1080 A = B * ( SIN(E1) + SIN(E2) ) * ( D1 * D2 ) / ( D1 + D2 ) 1090 C = ABS ( T * B / A ) * 100. 1100 PRINT 1110 PRINT "Geodesic" 1120 GOSUB 9000 2000 REM 2010 REM Vertical Midpoint Data Reduction 2020 REM 2030 S = SIN(A1 + A2) 2040 H1 = SIN(A2) * SIN(E1) / ( S * COS(E1) ) 2050 H2 = SIN(A1) * SIN(E2) / ( S * COS(E2) ) 2060 A = B * ( H1 + H2 ) / 2. 2070 C = ABS ( ( H1 - H2 ) / ( H1 + H2 ) ) * 100. 2080 PRINT 2090 PRINT "Vertical Midpoint" 2100 GOSUB 9000 2110 REM 8999 GO TO 500 9000 REM 9010 REM Display Altitude and Closure 9020 REM 9030 PRINT "Altitude: "; A 9040 IF C > 10. THEN GO TO 9080 9050 IF A < 1. THEN GO TO 9080 9060 PRINT "Track Closed: "; C; "%" 9070 RETURN 9080 PRINT "Track Not Closed: "; C; "%" 9090 RETURN 9998 STOP 9999 END

**E.2 Sample Test Data**

East | West | Geodesic | Vertical Midpoint | ||||
---|---|---|---|---|---|---|---|

Azimuth | Elevation | Azimuth | Elevation | Altitude | Closure | Altitude | Closure |

90 | 45 | 50 | 40 | 380.0 | 6.3% | 374.6 | 4.6% |

30 | 45 | 60 | 45 | 203.3 | 31.2% | 204.9 | 26.8% |

120 | 75 | 25 | 55 | 596.3 | 6.2% | 735.9 | 12.1% |

30 | 80 | 40 | 85 | 1337.8 | 3.2% | 1494.2 | 22.1% |

All altitudes in meters. Test cases assume 300-meter baseline.

**E.3 Symbols used in Equations**

B is the length of the tracking baseline.

A1 and E1 are the azimuth and elevation angles reported by tracking east.

A2 and E2 are the azimuth and elevation angles reported by tracking west.

A is the final, reduced altitude.

C is the closure, expressed as a fraction of the altitude. Closure <= 0.1 denotes a closed track.

Other symbols denote common subexpressions, and are used solely for purposes of clarity.

**E.4 Vertical Midpoint Method**

**E.5 Geodesic Method**