Presentation on theme: "ADJUSTMENT COMPUTATIONS"— Presentation transcript:
1ADJUSTMENT COMPUTATIONS STATISTICS AND LEAST SQUARESIN SURVEYING AND GISPAUL WOLFCHARLES D. GHILANI
2TRAVERSE CLOSURE√ ΔX2 +ΔY2 =Distance Error Distance Error/ Total Distance = Error per foot Or Error Ratio Tan -1 (ΔY / ΔX) = Angular Error (Azimuth)
3ACCURACY VS. PRECISION PRECISE BUT NOT ACCURATE PRECISE AND ACCURATE REPEATABILITY TO CONFORM TO THE STANDARDThe target on the left could be acceptable if proper steps are taken to correct for the presence of systematic errors. (This is equivalent to a marksman realigning the sights after the shots.)PRECISE BUT NOT ACCURATEPRECISE AND ACCURATE
4ACCURACY 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.Accuracy relates to the quality of the result obtained when compared to the standard.The standard used to determine accuracy compared to the true value. Can the true value be determined?No. Error is always present in all measurements. How much is determined by several factors.
5ACCURACY 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.
6ACCURACY VS. PRECISIONSurvey observations can have a high precision, but still be inaccurate.Poorly adjusted instrumentPoor methods and proceduresInstrument set upNot checking workHuman error
7STANDARDS National 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
8READING ERRORS Repetition reading instrument Repetition MethodCircle is zeroedReading errorsσαr = √σo2 + σr2nσσr - Estimated Standard Error in the average angle due to readingσo - estimated error in setting zeroσr - estimated error in the final readingn – number of repetitionsStandard deviation- square root of the sample variance.68% of the time measurement will fall within this standard.Square the Sum of the difference between the measurement and meanDivided by the number of repetitions minus one.
9READING ERRORS Ability to set zero and read the circle equal
10READING ERRORS σαr = ±1.5√2 = ±0.4” 6 Example: Repetition Method Suppose 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
11READING ERRORS Direct Method σαr = σr√2 √ n Backsight and Foresight readingsAngle is difference between to readingsMultiple measurementsσαr = σr√2√ nσσr - Estimated Standard Error in the average angle due to readingσr - estimated error in the final readingn – number of repetitions
12READING ERRORS σαr = ±1.5√2 = ±0.9” √6 Example: Direct Method Suppose 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
13POINTING ERRORS SEVERAL FACTORS AFFECT ACCURACY OPTIC QUALITIESTARGET SIZEOBSERVER’S PERSONAL ABILITY TO PLACE CROSSHAIRS ON THE TARGETWEATHER CONDITIONSPOINTING ERRORS ARE RANDOMTHEY WILL OCCURPOINTING ERRORS NOT DEPENDENT ON INSTRUMENT.Pointing errors occur at each back sight and fore sight, the pointing error will be the mean of the number of repetitions
14POINTING ERRORSAssume for any given instrument and observer the pointing error can be the same for each repetition.σαp = σp√2√ n
15POINTING ERRORS Example: 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
16TOTAL STATIONS DIN NUMBER (DIN 18723) Deutsches Institut fϋr Normung DIN 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”DIN is associated with statements of accuracy of theodolites since the introduction of electronic theodolites. DIN loosely translated German Institute for standards.Least count- with the advent of electronic instruments, reliance on the least count for anything but an estimate of precision achievable (not accuracy) is highly inadvisable.
17What is a mgon? milligon1 grad = 1,000 mgon = 54’ of arc1 mgon = 3.24” of arc= grad
18TRAVERSE BY TOTAL STATION POSSIBLE SOURCES OF ERRORREADING ERRORSSET UP ERRORSINSTRUMENT AND REFLECTORPOINTING ERRORSINSTRUMENT LEVELING ERRORSMEASUREMENT ERRORS BY EDMErrors are always introduced in all instruments measuring distances and angles. Small or large depending on the operator, instrument and conditions at the time of measurement. Each source produce a small amount of random error.
19TOTAL STATIONESTIMATED POINTING AND READING ERRORσαpr = 2σDIN√n
20Example:An angle is read six times (3 direct and 3 reverse) using a total station having a published DIN 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
21TARGET CENTERING ERRORS Setting a target over a pointWeather conditionsOptical plummetQuality of optical plummetPlumb bob centeringPersonal abilitiesOthers?Usually set up within 0.001’ to 0.01’Whenever a target is set over a station, there will be some error due to faulty centering.This type of error will appear as a random in the adjustment of a network involving many stations.
22TARGET CENTERING ERRORS Possible variations in centering targetVariation (d) maximum error
23TARGET CENTERING ERRORS Maximum error in an individual direction due to target decenteringe = ± σd (RAD)De = uncertaintyσd= the amount of centering error at the time of pointingD= distance from the instrument center to the target.e = uncertainty in the direction due to target decentering
24TARGET CENTERING ERRORS Two directions are required for an angular measurementσσt = σd σd2D D2 σσt = angular error due to target centeringσd1 & σd2 = target center errors at sta. 1 & 222
25TARGET CENTERING ERRORS σσt = ± (D1) (D2) σt ρD1D2ρ= 206,264.8”/radianAssumes ability to center the target is independent of the particular direction.This makes σ1 = σ2 = σt
27TARGET CENTERING ERRORS If a hand-held range pole were used in this example with an estimated centering error of +/- 0.01’, the estimated error due to target centering would be almost 10”.This is why a range pole makes for a poor control point measuring tool.
28INSTRUMENT CENTERING ERRORS Set-up location vs. True LocationDependenton quality of instrumentState of adjustment of optical plummetSkill of observerCan be compensatingError is maximized when the individual setup is on the angle bisector.
29INSTRUMENT CENTERING ERRORS Bisector angle error maximized at b and c.
33EFFECTS OF LEVELING ERROR If 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 randomRandom error- If the bubble of a theodolite were to remain off center by the same amount during the entire angle-measuring process at a station, the resulting error would be systematic. However, because an operator normally carefully monitors the bubble and attempts to keep it centered while turning angles, the amount and direction by which the instrument is out of level become random, and hence the resulting errors tend to be random.
34EFFECTS OF LEVELING ERROR σαl = ± fdμ tan (vb) 2 + fdμ tan (vf) 2√ n
35EFFECTS OF LEVELING ERROR σαl = ± fdμ tan (vb) 2 + fdμ tan (vf) 2√ nFd = the fractional division the instrument is off levelVb and vf = vertical angles to the BS and FS respectivelyn = the number of repetitions
36EFFECTS OF LEVELING ERROR This error is generally small for traditional surveying when normal care in leveling the instrument is taken. Thus is can be ignored except for precise work.
48PARALLAXA 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.Parallax occurs when the focal point of the eyepiece does not coincide with the plane of the cross hairs. Depending on the shape of each observer’s eyeball, the focal length may vary.This is also a major concern in the optical plummet.To check for parallax in the telescope, focus on some well-defined distant object. Slowly move the head back and forth, about an inch from the eyepiece, while watching the relationship of the object to the cross hairs. If the object appears to move, parallax exists.The optical plummet can be checked by rotating the knurled eyepiece until the cross hairs are the thickest and blackest, refocus and check for parallax.
49HUMAN ERRORS Measuring 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.Do not stamp on the tripod feet. Pressure should be parallel to each leg.Legs- In windy conditions, additional stability can be achieved if one leg is set downwind.On hillsides- one leg uphill and two legs downhillIf the ground in soft or muddy, drive hubs in the ground to support the tripod legs.
50HUMAN ERRORSCheck the optical plummet after the instrument is set up and just before moving to another point.Recheck the instrument levelIf the instrument has moved, check the angle just measured.The bubble should remain within one graduation when the instrument is smoothly turned through one circle (if the instrument is shaded).
51ACCURACY OF A GPS SURVEY ACCURACY 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
52ACCURACY OF A GPS SURVEY Satellite 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.
53OPERATIONAL PROCEDURES IDENTIFY 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
54OPERATIONAL PROCEDURES ENSURE 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.