IN SURVEYING AND GIS PAUL WOLF CHARLES D GHILANI TRAVERSE CLOSURE ΔX 2 Δ Y 2 Distance Error Distance Error Total Distance Error per foot Or Error Ratio Tan 1 Δ ID: 1019154
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1. ADJUSTMENT COMPUTATIONSSTATISTICS AND LEAST SQUARES IN SURVEYING AND GISPAUL WOLFCHARLES D. GHILANI
2. TRAVERSE CLOSURE√ ΔX2 +ΔY2 =Distance ErrorDistance Error/ Total Distance = Error per footOr Error Ratio Tan -1 (ΔY / ΔX) = Angular Error (Azimuth)
3. ACCURACY VS. PRECISIONPRECISE BUT NOT ACCURATEPRECISE AND ACCURATE
4. ACCURACY VS. PRECISIONACCURACY-the degree of conformity with a standard or measure of closeness to a true value.An exact value, such as the sum of three angles of a triangle equals 180°A value of a conventional unit by physical representation, such as U.S. Survey foot.A survey or map deemed sufficiently near the ideal or true value to be held constant for the control of dependent operations.
5. ACCURACY VS. PRECISIONPrecision – the degree of refinement in the performance of an operation (procedures and instrumentation) or in the statement of a result.Applied to methods and instruments used to attain a high order of accuracy.The more precise the survey method, the higher the probability that the results can be repeated.
6. ACCURACY VS. PRECISIONSurvey observations can have a high precision, but still be inaccurate.Poorly adjusted instrumentPoor methods and proceduresInstrument set upNot checking workHuman error
7. STANDARDSNational Geodetic Control Networks are based on accuracy.Consistent with the network not just a particular surveyNot the mathematical closure but the ability to duplicate established control values
8. READING ERRORSRepetition reading instrumentRepetition MethodCircle is zeroedReading errorsσαr = √σo2 + σr2 nσσr - Estimated Standard Error in the average angle due to reading σo - estimated error in setting zeroσr - estimated error in the final readingn – number of repetitions
9. READING ERRORSAbility to set zero and read the circle equalσαr = σr√2n
10. READING ERRORSExample: Repetition MethodSuppose an angle is read six times using the repetition method. An operator having a personal reading error of ±1.5”, what is the estimated error in the angle due to circle reading?σαr = ±1.5√2 = ±0.4” 6
11. READING ERRORSDirect MethodBacksight and Foresight readingsAngle is difference between to readingsMultiple measurementsσαr = σr√2 √ nσσr - Estimated Standard Error in the average angle due to reading σr - estimated error in the final readingn – number of repetitions
12. READING ERRORSExample: Direct MethodSuppose an angle is read six times using the direct method. An operator having a personal reading error of ±1.5”, what is the estimated error in the angle due to circle reading?σαr = ±1.5√2 = ±0.9” √6
13. POINTING ERRORSSEVERAL FACTORS AFFECT ACCURACYOPTIC QUALITIESTARGET SIZEOBSERVER’S PERSONAL ABILITY TO PLACE CROSSHAIRS ON THE TARGETWEATHER CONDITIONSPOINTING ERRORS ARE RANDOMTHEY WILL OCCUR
14. POINTING ERRORSAssume for any given instrument and observer the pointing error can be the same for each repetition.σαp = σp√2 √ n
15. POINTING ERRORSExample:Suppose an angle is read six times by an operator whose ability to point on a well-defined target is estimated to be ±1.8”, what is the estimated error in the angle due to pointing?σαp = ±1.8√2 = ±1.0” √6
16. TOTAL STATIONSDIN NUMBER (DIN 18723)Deutsches Institut fϋr NormungDIN accuracy is not inferred from the least countExample of DIN useAccuracy according to DIN of 5” in a face 1 and face 2 directionStandard Deviation of a Face 1 and Face 2 reading is ±5”Standard Deviation of an angleσ =√2 * 5” = 7”
17. What is a mgon? milligon1 grad = 1,000 mgon = 54’ of arc1 mgon = 3.24” of arc= 0.001 grad
18. TRAVERSE BY TOTAL STATIONPOSSIBLE SOURCES OF ERRORREADING ERRORSSET UP ERRORSINSTRUMENT AND REFLECTORPOINTING ERRORSINSTRUMENT LEVELING ERRORSMEASUREMENT ERRORS BY EDM
19. TOTAL STATIONESTIMATED POINTING AND READING ERRORσαpr = 2σDIN √n
20. Example:An angle is read six times (3 direct and 3 reverse) using a total station having a published DIN 18723 value for pointing and reading of ± 5” . What is the estimated error in the angle due to pointing and reading?σαpr = 2 * 5” = ± 4.1” √6
21. TARGET CENTERING ERRORSSetting a target over a pointWeather conditionsOptical plummetQuality of optical plummetPlumb bob centeringPersonal abilitiesOthers?Usually set up within 0.001’ to 0.01’
22. TARGET CENTERING ERRORSPossible variations in centering targetVariation (d) maximum error
23. TARGET CENTERING ERRORSMaximum error in an individual direction due to target decentering e = ± σd (RAD) De = uncertainty σd= the amount of centering error at the time of pointingD= distance from the instrument center to the target.
24. TARGET CENTERING ERRORSTwo directions are required for an angular measurement σσt = σd1 + σd2 D1 D2 σσt = angular error due to target centering σd1 & σd2 = target center errors at sta. 1 & 222
25. TARGET CENTERING ERRORSσσt = ± (D1)2 + (D2)2 σt ρ D1D2 ρ= 206,264.8”/radianAssumes ability to center the target is independent of the particular direction.This makes σ1 = σ2 = σt
26. TARGET CENTERING ERRORS
27. TARGET CENTERING ERRORS
28. INSTRUMENT CENTERING ERRORSSet-up location vs. True LocationDependent on quality of instrumentState of adjustment of optical plummetSkill of observerCan be compensatingError is maximized when the individual setup is on the angle bisector.
29. INSTRUMENT CENTERING ERRORS
30. INSTRUMENT CENTERING ERRORS
31. INSTRUMENT CENTERING ERRORSσαi2 = ± D3 σi ρ D1D2 √2 ρ = 206,264.8”/radian
32. INSTRUMENT CENTERING ERRORS
33. EFFECTS OF LEVELING ERRORIf instrument is not level, then its vertical axis is not vertical and the horizontal circle is not horizontalErrors are most severe when backsight and or foresight is steeply inclined.Error tends to be random
34. EFFECTS OF LEVELING ERRORσαl = ± fdμ tan (vb) 2 + fdμ tan (vf) 2 √ n
35. EFFECTS OF LEVELING ERROR σαl = ± fdμ tan (vb) 2 + fdμ tan (vf) 2 √ n Fd = the fractional division the instrument is off levelVb and vf = vertical angles to the BS and FS respectivelyn = the number of repetitions
36. EFFECTS OF LEVELING ERROR
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44. TRAVERSING BY GPSPOSSIBLE SOURCES OF ERRORSREFERENCE POSITION ERRORSANTENNA POSITION ERRORSTIMING ERRORSSIGNAL PATH ERRORSHUMAN ERRORSCOMPUTING ERRORSSATELLITE CONSTELLATION ERRORSNOISE CAUSING ERRORS
45. TOTAL STATIONPOSSIBLE SOURCES OF ERRORCOLLIMATION-TO ADJUST THE LINE OF SIGHT OR LENS AXIS OF AN OPTICAL INTRUMENT SO THAT IT IS IN ITS PROPER POSITION RELATIVE TO OTHER PARTS OF THE INSTRUMENT.
46. COLLIMATIONINSTRUMENTEYE PIECEMAIN MIRROR
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48. PARALLAXA change in the apparent position of an object with respect to the reference marks of an instrument which is due to imperfect adjustment of the instrument, to a change in the position of the observer, or both.
49. HUMAN ERRORSMeasuring the height of the instrument and reflector. Setting up the instrument and reflectorPush the tripod shoes firmly into the groundPlace the legs in positions that will require minimum walking around the setup.Ensure the instrument is set properly over the point.
50. HUMAN ERRORSCheck the optical plummet after the instrument is set up and just before moving to another point. Recheck the instrument level
51. ACCURACY OF A GPS SURVEYACCURACY DEPENDENT UPON MANY COMPLEX, INTERACTIVE FACTORS, INCLUDINGOBSERVATION TECHNIQUE USED, e.g., static vs. kinematic, code vs. phase, etc.Amount and quality of data acquiredGPS signal strength and continuityIonosphere and troposphere conditionsStation site stability, obstructions, and multipath
52. ACCURACY OF A GPS SURVEYSatellite orbit used, e.g., predicted vs. precise orbitsSatellite geometry, described by the dilution of precision (DOP)Network design, e.g., baseline length and orientationProcessing methods used, e.g., double vs. triple differencing, etc.
53. OPERATIONAL PROCEDURESIDENTIFY AND MINIMIZE ALL ERRORS BY REDUNDANCY, ANALYSIS, AND CAREFUL OPERATIONAL PROCEDURES, INCLUDING:REPETITION OF MEASUREMENTS UNDER INDEPENDENT CONDITIONSREDUNDANT TIES TO MULTIPLE, HIGH-ACCURACY CONTROL STATIONSGEODETIC GRADE INSTRUMENTATION, FIELD AND OFFICE PROCEDURES
54. OPERATIONAL PROCEDURESENSURE PROCESSING WITH THE MOST ACCURATE STATION COORDINATES, SATELLITE EPHEMERIDES, AND ATMOSPHERIC AND ANTENNA MODELS AVAILABLE.CAUTION: BE AWARE THAT THESE PROCEDURES CANNOT DISCLOSE ALL PROBLEMS.
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