Localization; review GPS and sonar sensors

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Localization; reviewLocalization; review GPS GPS and and sona sonar sensorsr sensors

نام استاد: دكتر سعيد شيرينام استاد: دكتر سعيد شيري

نام ارائه دهنده: وحيد حقيقت دوستنام ارائه دهنده: وحيد حقيقت دوست

Amirkabir University of Technology Computer Engineering & Information Technology Department

Robotics:

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Previous presentationsPrevious presentations

Robocup Soni robots

Rescue

RescueRescue

xx

yy

wheeled mobile robot

Motion planning

Robot Motion Planning Under Unertainty

Localization,GPS and sonar

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ContentsContents

►LocalizationLocalization►Sonar sensorsSonar sensors►GPSGPS

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Mobile Robot LocalizationMobile Robot Localization

►Where am I?Where am I?►Given a map, determine the robot’s locationGiven a map, determine the robot’s location

Landmark locations are known, but the robot’s Landmark locations are known, but the robot’s position is notposition is not

From sensor readings, the robot must be able to infer From sensor readings, the robot must be able to infer its most likely position on the fieldits most likely position on the field

Example : where are the AIBOs on the soccer field?Example : where are the AIBOs on the soccer field?

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Mobile Robot MappingMobile Robot Mapping

► What does the world look like?What does the world look like?► Robot is unaware of its environmentRobot is unaware of its environment► The robot must explore the world and determine its The robot must explore the world and determine its

structurestructure Most often, this is combined with localizationMost often, this is combined with localization Robot must update its location according to the landmarksRobot must update its location according to the landmarks Known in the literature as Simultaneous Localization and Known in the literature as Simultaneous Localization and

Mapping, or Concurrent Localization and Mapping : Mapping, or Concurrent Localization and Mapping : SLAM (CLM)SLAM (CLM)

Example : AIBOs are placed in an unknown environment Example : AIBOs are placed in an unknown environment and must learn the locations of the landmarks (An and must learn the locations of the landmarks (An interesting project idea?)interesting project idea?)

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LocalizationLocalization

Initial statedetects nothing:

Moves and detects landmark:

Moves and detects nothing:

Moves and detects landmark:

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What we know…What we know…What we don’t know…What we don’t know…► We know what the control inputs of our process areWe know what the control inputs of our process are

We know what we’ve told the system to do and have a model for what We know what we’ve told the system to do and have a model for what the expected output should be if everything works rightthe expected output should be if everything works right

► We don’t know what the noise in the system truly isWe don’t know what the noise in the system truly is We can only estimate what the noise might be and try to put some sort We can only estimate what the noise might be and try to put some sort

of upper bound on itof upper bound on it

► When estimating the state of a system, we try to find a When estimating the state of a system, we try to find a set of values that comes as close to the truth as possibleset of values that comes as close to the truth as possible There will always be some mismatch between our estimate of the There will always be some mismatch between our estimate of the

system and the true state of the system itself. We just try to figure out system and the true state of the system itself. We just try to figure out how much mismatch there is and try to get the best estimate possiblehow much mismatch there is and try to get the best estimate possible

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Problem One: LocalizationProblem One: Localization

►Given:Given: World map Robot’s initial pose Sensor updates

►Find: Robot’s pose as it moves

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Localization FoundationLocalization Foundation

►At every time step t:At every time step t: UPDATEUPDATE each sample’s new location each sample’s new location

based on movementbased on movement

RESAMPLE RESAMPLE the pose distribution based the pose distribution based on sensor readingson sensor readings

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Problem Two: MappingProblem Two: Mapping

►Given:Given: Robot Sensors

►Find: Map of the environment

(and implicitly, the robot’s location as it moves)

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Simultaneous LocalizationSimultaneous LocalizationAnd Mapping (SLAM)And Mapping (SLAM)

If we have a map:

We can localize!

If we can localize:

We can make a map!

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Circular Error ProblemCircular Error Problem

If we have a map:

We can localize!

If we can localize:

We can make a map!

NOT THAT SIMPLE!

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How do we solve SLAM?How do we solve SLAM?

►Incorporate location/map uncertainties into a single model

► Optimize robot’s exploratory path► Use geometry (especially indoors)

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The Localization ProblemThe Localization Problem

►Ingemar Cox (1991):

“Using sensory information to locate the robot in its environment is the most fundamental problem to provide a mobile robot with autonomous capabilities.” Position tracking (bounded uncertainty) Global localization (unbounded uncertainty) Kidnapping (recovery from failure)

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Localization’s Sidekick: Localization’s Sidekick: GlobalizationGlobalization►Localization without knowledge of start location

►One step further: “kidnapped robot problem”

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Kidnapped RobotKidnapped Robot

Placed into an environment with a map, not knowing its initial position.

“Wake up” – turn on the power

How can the robot find its location?

Recover from a localization failure.

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IntroductionIntroduction

►Localization:Localization: Given sensory input, the agent Given sensory input, the agent must be able to infer its position and orientation must be able to infer its position and orientation relative to the global map. Knowledge of current relative to the global map. Knowledge of current position and orientation are crucial to:position and orientation are crucial to: Path-fowloing (and hence to Path-fowloing (and hence to navigationnavigation)) Correct placement of newly-discovered landmarks in Correct placement of newly-discovered landmarks in

the enviroment (and hence to the enviroment (and hence to map-buildingmap-building)) Registeration of multiple fields of view (and hence to Registeration of multiple fields of view (and hence to

explorationexploration).).

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IntroductionIntroduction (continue)(continue)

►Navigation:Navigation: Given a map of the Given a map of the enviroment, the agent should be able to enviroment, the agent should be able to plane a pathplane a path from its current location to from its current location to

another location within the global map, another location within the global map, and then and then follow its pathfollow its path, , possibly possibly updating the pathupdating the path if obstacles are if obstacles are

found.found.

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IntroductionIntroduction (continue)(continue)

►Map-Bulding:Map-Bulding: Upon detection of features and Upon detection of features and landmaks landmaks which do not yet appearwhich do not yet appear in the agent’s in the agent’s internal representationinternal representation of enviroment, the agent of enviroment, the agent should update that representation.should update that representation.

►Exploration:Exploration: Upon discovery of a new object Upon discovery of a new object (not yet in world map)(not yet in world map) The agent should have strategy wich allow the object The agent should have strategy wich allow the object

to be viewed from multiple points, and by multiple to be viewed from multiple points, and by multiple sensing modalitiessensing modalities

The agent should be able to register these multiple The agent should be able to register these multiple views to produce a unified description of the objectviews to produce a unified description of the object

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The problem of localizationThe problem of localization

►The process of navigation can be seen as The process of navigation can be seen as iteration through the loop depicted in figure.iteration through the loop depicted in figure.

Compare to Intended position

Obtain Corrective Maneuver

Execute UnderDead reckoning

Where Am I?

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The problem of localization The problem of localization (continue)(continue)

►““Where am I?”Where am I?” phase constitutes phase constitutes localizationlocalization►There are different types of localization:There are different types of localization:

Dead-reckoningDead-reckoning localization localization Beacon-basedBeacon-based localization localization Feature-basedFeature-based localization localization Landmark-basedLandmark-based localization localization

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Dead-reckoning localization: Dead-reckoning localization:

►base on internal sensing, usually in form of base on internal sensing, usually in form of wheel encoders or some internal navigation wheel encoders or some internal navigation systemsystem

►No sensing of the external environment is No sensing of the external environment is performrdperformrd

►Fast and simpleFast and simple►Prone to error accumulation since no feedback Prone to error accumulation since no feedback

is obtained from the environmentis obtained from the environment► it is usually supplemented with some other form it is usually supplemented with some other form

of loclizationof loclization

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Dead-ReckoningDead-Reckoning

(0,0)

Dead-Reckoning

Accumulated error can be quite big for a period time.

(x, y, α)

α(x+∆x, y+∆y, β)

β

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Dead-ReckoningDead-Reckoning

[ S. Thrun, Robotic Mapping: A Survey ]

A robot’s path as obtained by its odometry, relative to a given map.

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Major Issues with AutonomyMajor Issues with Autonomy

► Movement Movement

InaccuracyInaccuracy Sensor

Inaccuracy

Environmental

Uncertainty

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Beacon-based localization: Beacon-based localization:

► Relies on the Relies on the prior deploymentprior deployment of easily of easily detectable, detectable, recognizable and distinguishable beaconsrecognizable and distinguishable beacons in known in known locations in the environmentlocations in the environment

► The The identity of passive beaconsidentity of passive beacons must be established by must be established by the sensors of mobile agentthe sensors of mobile agent

► Location of the beaconsLocation of the beacons is then accessed from a global is then accessed from a global mapmap

► Active beacons may transmit their identity and current Active beacons may transmit their identity and current location => location => less sensing and signal processingless sensing and signal processing on the on the part of the agentpart of the agent

► Global Position SystemGlobal Position System (GPS) is an example of active (GPS) is an example of active beacon systembeacon system

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Feature-based localization: Feature-based localization:

► Does not rely on modification of the environment.Does not rely on modification of the environment.► Instead, “naturally” occurring features are extracted Instead, “naturally” occurring features are extracted

from the data flowing into the sensors on the agent.from the data flowing into the sensors on the agent.► Correspondence must then be established between Correspondence must then be established between

the detected feature and the features stored in the the detected feature and the features stored in the map.map.

► Correspondence is then established by finding a Correspondence is then established by finding a transformation which brings the local coordinate transformation which brings the local coordinate frame of the agent into the global coordinate frame frame of the agent into the global coordinate frame of the mapof the map

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Feature-based localization: Feature-based localization: (continue)(continue)

►This process is confound by the “phantom” This process is confound by the “phantom” features, failure to detect some features, features, failure to detect some features, uncertainty and noise…uncertainty and noise…

►The correspondence problem is the chief reason The correspondence problem is the chief reason why feature-based localization is much more why feature-based localization is much more difficult than beacon-based localizationdifficult than beacon-based localization

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landmark-based localization:landmark-based localization:

►Relies on the detection of Relies on the detection of uniquely identifiableuniquely identifiable features.features.

►The correspondence problem is alleviated since The correspondence problem is alleviated since the set of possible matches for each detected the set of possible matches for each detected landmark is very small.landmark is very small.

►The detection and identification of a landmark The detection and identification of a landmark generally requires significantly more intensive generally requires significantly more intensive signal processing and higher-level reasoning signal processing and higher-level reasoning than feature-detection.than feature-detection.

►The onus is shifted from establishing The onus is shifted from establishing correspondence to recognition of landmarkscorrespondence to recognition of landmarks

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Update periodUpdate period

► For a system involving a For a system involving a combination of dead combination of dead reckoning with some reckoning with some other localization, the other localization, the accumulation of position accumulation of position and orientation error and orientation error follows the pattern follows the pattern delineated in figure.delineated in figure.

The goal of the localization system is to keep the The goal of the localization system is to keep the accumulated error within tolerable limits.accumulated error within tolerable limits.

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Update period depends on…Update period depends on…

►The sensor modalities selectedThe sensor modalities selected►The types and densities of beacons, features or The types and densities of beacons, features or

landmarks in the environmentlandmarks in the environment►The computational complexity of the algorithms The computational complexity of the algorithms

used for beacon, feature or landmark detectionused for beacon, feature or landmark detection

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Continuous localization verse relocationContinuous localization verse relocation

►One of the most computationally intensive One of the most computationally intensive aspect of feature based localization is aspect of feature based localization is correspondence matching.correspondence matching.

►It is possible to compare It is possible to compare actualactual against against predictedpredicted measurements which are deemed to match, no measurements which are deemed to match, no further correspondence need be established; further correspondence need be established; previous correspondences have been preservedprevious correspondences have been preserved . . If sufficient matches are found to allow position If sufficient matches are found to allow position and orientation estimation, localization is greatly and orientation estimation, localization is greatly facilitated. This method calls facilitated. This method calls continuous continuous localizationlocalization..

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Continuous localization verse relocation Continuous localization verse relocation (continue)(continue)

►When an insufficient number of matches When an insufficient number of matches between actual and predicted measurements between actual and predicted measurements occurs, the agent is considered to be occurs, the agent is considered to be “lost”“lost”. In . In this case, correspondence between extracted and this case, correspondence between extracted and map features must be re-established. Such a map features must be re-established. Such a process is more computationally intensive, and process is more computationally intensive, and is named is named relocationrelocation..

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Continuous localization verse relocation Continuous localization verse relocation (continue)(continue)

►The incorporation of continuous localization The incorporation of continuous localization allows the basic navigatin loop modified.allows the basic navigatin loop modified.




Where Am I?

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Continuouslocalization

CorrespondencePreserved?

Relocation

NO

Where Am I?

YES

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The central role of localizationThe central role of localization

►Localization competency is central not only Localization competency is central not only for for navigationnavigation, but also for , but also for explorationexploration and and map-buildingmap-building by a mobile agent. by a mobile agent.

►If we don’t have reliable localization:If we don’t have reliable localization: RegisterationRegisteration of multiple views of the same object of multiple views of the same object

become more difficultbecome more difficult Feature landmark and obstacle discovered during Feature landmark and obstacle discovered during

an an exploratoryexploratory phase cannot be placed in their phase cannot be placed in their correct positions in a mapcorrect positions in a map

No feedback loops can be implemented for path-No feedback loops can be implemented for path-folloewing during navigation.folloewing during navigation.

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Localization

explorationnavigation

map-building

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Navigation algorithms Navigation algorithms

►Approaches to Approaches to obstacle avoidanceobstacle avoidance, such as the , such as the method of method of potential fieldspotential fields, are typically of , are typically of no no use for localizationuse for localization..

►Algorithms for Algorithms for globally referenced positionglobally referenced position estimation, rely on estimation, rely on prioripriori map, but do not map, but do not address the construction of such a mapaddress the construction of such a map

►Many algorithms for Many algorithms for map buildingmap building don't address don't address the issue of localization while the map is being the issue of localization while the map is being constructed, relying instead on constructed, relying instead on odometryodometry or or hand-measuringhand-measuring of sensing locations. of sensing locations.

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Sensing modalities: Sensing modalities:

Three modalities:Three modalities: UltrasoundUltrasound Patterned-lightPatterned-light Stereo modalitiesStereo modalities

Have been used extensively over the past Have been used extensively over the past three decadesthree decades

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UltrasoundUltrasound

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UltrasoundUltrasound

►IntroductionIntroduction►Physics of sonarsPhysics of sonars►What can be inferred from a single sonar?What can be inferred from a single sonar?►What can be expected from multiple What can be expected from multiple

measurements?measurements?►Clustering and parameter estimationClustering and parameter estimation►Specification of an algorithmSpecification of an algorithm

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Ultrasonic Sonar Sensor

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Ultrasound Ultrasound Physics of sonars Physics of sonars►The large difference in the acoustic impedance The large difference in the acoustic impedance

between most solid surfaces appear as acoustic between most solid surfaces appear as acoustic reflectors.reflectors.

►Further, the generally large wavelengths of Further, the generally large wavelengths of ultrasonic energy emitted in air ensure that most ultrasonic energy emitted in air ensure that most reflections are specular.reflections are specular.

►We assume at the lowest level that each sonar We assume at the lowest level that each sonar measurement is generated by an element of the measurement is generated by an element of the set of basic features set of basic features P={planar reflective patches, P={planar reflective patches, outer diffractive corners, inner reflective corners}outer diffractive corners, inner reflective corners}

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Ultrasound Ultrasound What can be inferred from a single sonar? What can be inferred from a single sonar?

►All the one can infer from a single measurment is All the one can infer from a single measurment is the existence of an element of the existence of an element of P P at the distance at the distance rr somewhere along the boundary of the transmitted somewhere along the boundary of the transmitted cone truncated at range cone truncated at range rr..

P={planar reflective patches, outer diffractive P={planar reflective patches, outer diffractive corners, inner reflective corners}corners, inner reflective corners}

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►In the case of planar reflective patches, the patch In the case of planar reflective patches, the patch has orientation tangential to the acoustic wave has orientation tangential to the acoustic wave fronts.fronts.

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►In 3D the region of the location of the reflective In 3D the region of the location of the reflective patch forms a section of the surface of a sphere, patch forms a section of the surface of a sphere, centered at the transducer and of solid angle centered at the transducer and of solid angle 22пп(1-cos (1-cos αα)) steradians, where steradians, where αα is the half-width is the half-width of ultrasonic emission cone.of ultrasonic emission cone.

αα ≈ 15º => ≈ 15º =>

surface of area = surface of area = 22ппr²r²(1-cos (1-cos αα) ) ≈ 0.214r²≈ 0.214r²

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Ultrasound Ultrasound What can be expected from multiple measurements? What can be expected from multiple measurements?

► For multiple measurements generated by For multiple measurements generated by the same planar the same planar surface, all arcs, in the noise free to the case, share a surface, all arcs, in the noise free to the case, share a common tangentcommon tangent; corners (both inner reflective and outer ; corners (both inner reflective and outer diffractive) induce measurements whose arcs intersect at diffractive) induce measurements whose arcs intersect at the corner. In general a smooth curve defined the corner. In general a smooth curve defined parametrically by piecewise differentiable, will parametrically by piecewise differentiable, will induce measurements such that the arc corresponding to induce measurements such that the arc corresponding to each measurements intersects the curve at a pointeach measurements intersects the curve at a point

where both curve and arc share the tangent where both curve and arc share the tangent of orientation at that point.of orientation at that point.

))(),(( tsts yx

))(),(( tsts yx

))(),(( tsts yx

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Ultrasound Ultrasound Clustering and parameter estimation Clustering and parameter estimation

►Finding subsets among the set of all Finding subsets among the set of all measurements such that in each subset, all measurements such that in each subset, all measurements in a cluster share a common measurements in a cluster share a common tangent (in 2D)tangent (in 2D)

► In general, the problem is exponential in natureIn general, the problem is exponential in nature►To reduce the problem to polynomial, other To reduce the problem to polynomial, other

information must be utilizedinformation must be utilized

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Clustering and parameter estimationClustering and parameter estimationParameter estimationParameter estimation

►Data reduction: for each subset, a small number Data reduction: for each subset, a small number of parameters must be extractedof parameters must be extracted

►The representative parameters need to be The representative parameters need to be updated as:updated as: Subsets merge or divided Subsets merge or divided The new data addedThe new data added

►There is a trade-off involved in the There is a trade-off involved in the computational effort invested in the computational effort invested in the data data associationassociation and and parameter estimationparameter estimation problems problems

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Clustering and parameter estimationClustering and parameter estimationParameter estimation Parameter estimation (continue)(continue)

More strict parameters

data association:data association: lower the rate of occurrencelower the rate of occurrenceof outliers in any particular clusterof outliers in any particular clusterparameter estimation: parameter estimation: Easier parameterEasier parameterestimationestimation

Less strict parameters

data association:data association: the higher likelihood of the higher likelihood of outliers in a clusteroutliers in a clusterparameter estimation: parameter estimation: hard parameterhard parameterestimationestimation

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UltrasoundUltrasound Specification of an algorithm Specification of an algorithm ►We would like an algorithm which:We would like an algorithm which:

Aggregates sonic dataAggregates sonic data accumulated from arbitrary accumulated from arbitrary transducer locationstransducer locations

Performs the Performs the clustering techniqueclustering technique A A tractabletractable and and efficientefficient clustering algorithmclustering algorithm to to

overcome it’s exponential natureovercome it’s exponential nature Is Is robust in the face of noiserobust in the face of noise in the environment in the environment High High SoundnessSoundness and and completenesscompleteness factors factors

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Definition of two concepts Definition of two concepts

►Soundness factor:Soundness factor: indicates what indicates what fraction of fraction of detected featuresdetected features really exist really exist

►Completeness factor:Completeness factor: indicates the indicates the proportion proportion of extant featuresof extant features which are detected by use of which are detected by use of the algorithmthe algorithm

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The issue of representationThe issue of representation

►Transform all the data to a vector spaceTransform all the data to a vector space►Consider, a representation which records each arc Consider, a representation which records each arc

as the 4-tupleas the 4-tuple (x, y, (x, y, θθ, r), r)

►Thus in an unknown environment, the problem of Thus in an unknown environment, the problem of finding a vertical surface can be stated as:finding a vertical surface can be stated as:We have a set , find a subset We have a set , find a subset such that all points in are coplanar insuch that all points in are coplanar insubspace. and can be contained in an interval of subspace. and can be contained in an interval of size size αα in the in the ΘΘ subspace subspace

RYXA Pose of the transducer

Range measurement AA

A RYX

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Global positioning system Global positioning system (GPS)(GPS)

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Global positioning system (GPS)Global positioning system (GPS)

►Introduction to GPSIntroduction to GPS What is GPSWhat is GPS How GPS worksHow GPS works

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GPS Block IIR SatelliteGPS Block IIR Satellite

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Introduction to GPSIntroduction to GPS

►What is GPSWhat is GPS The Global Positioning System (GPS) is a The Global Positioning System (GPS) is a

worldwide radio-navigation system formed worldwide radio-navigation system formed from a from a constellation of 24 satellitesconstellation of 24 satellites and their and their ground stationsground stations

GPS receivers use these satellites as GPS receivers use these satellites as reference reference pointspoints to calculate positions and time to calculate positions and time

Originally known as Navigation System with Originally known as Navigation System with Timing And Ranging (NAVSTAR)Timing And Ranging (NAVSTAR)

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How GPS Works (Six Steps)How GPS Works (Six Steps)

1. Triangulation1. Triangulation

2. Distance2. Distance

3. Clocks3. Clocks

4. Satellite Position4. Satellite Position

5. Coordinate system5. Coordinate system

6. Errors6. Errors

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TriangulationTriangulation►Number of SatellitesNumber of Satellites

One distance = sphereOne distance = sphere Two distances = circleTwo distances = circle Three distances = two pointsThree distances = two points Four distances = one pointFour distances = one point Three distances + earths surface = one pointThree distances + earths surface = one point

►LockingLocking 1,2 satellites - No lock, course time1,2 satellites - No lock, course time 3 Satellites - 2D positioning (Earth’s surface assumed)3 Satellites - 2D positioning (Earth’s surface assumed) 4 Satellites - 3D positioning (Lat/Lon/Alt)4 Satellites - 3D positioning (Lat/Lon/Alt)

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TriangulationTriangulation - critical points- critical points

►Position is calculated from distance Position is calculated from distance measurements (ranges) to satellites.measurements (ranges) to satellites.

►Mathematically we need four satellite ranges to Mathematically we need four satellite ranges to determine exact position.determine exact position.

►Three ranges are enough if we reject ridiculous Three ranges are enough if we reject ridiculous answers or use other tricks.answers or use other tricks.

►Another range is required for calculation of Another range is required for calculation of time.time.

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DistanceDistance

►DistanceDistance = Speed × Time ? = Speed × Time ? 180 miles = 60 miles per hour × 3 hours180 miles = 60 miles per hour × 3 hours

►Speed of radio wavesSpeed of radio waves ? ? 186 kmps186 kmps

►TimeTime 0.06 second0.06 second

►DistanceDistance = 186000 mps × 0.06 s = 186000 mps × 0.06 s D = 11,160 milesD = 11,160 miles

►AccuracyAccuracy (+/- 0.000,000,001 sec) = +/- 1 ns (+/- 0.000,000,001 sec) = +/- 1 ns

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DistanceDistance►How does a receiver time the signal travel?How does a receiver time the signal travel?

Satellites send a pseudo-random codeSatellites send a pseudo-random code►(each sends its own song of 1’s and 0’s)(each sends its own song of 1’s and 0’s)

Receiver matches its calculated sequence with the Receiver matches its calculated sequence with the received signal by delaying more or less it’s signalreceived signal by delaying more or less it’s signal

The amount of delay = the transit time!The amount of delay = the transit time!

►How does the receiver separate the signals of How does the receiver separate the signals of each of the satellites?each of the satellites? Each satellite has it’s own sequence (song) Each satellite has it’s own sequence (song)

calculated through a formulacalculated through a formula Formula is conveyed in data from the satellitesFormula is conveyed in data from the satellites

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Distance Distance - critical points- critical points

►Distance to satellites is determined by measuring Distance to satellites is determined by measuring signal travel time.signal travel time.

►Assume satellite and GPS receiver generate Assume satellite and GPS receiver generate same pseudo-random codes at the same time. same pseudo-random codes at the same time.

►By synchronizing the pseudo-random codes, the By synchronizing the pseudo-random codes, the delay in receiving the code can be found.delay in receiving the code can be found.

►Multiply delay time by the speed of light to get Multiply delay time by the speed of light to get distancedistance

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SynchronizationSynchronization►Satellites timing is extremely accurate.Satellites timing is extremely accurate.

precise atomic clocks on board. precise atomic clocks on board.

►All satellite clocks are synchronized and they All satellite clocks are synchronized and they send their codes at a known timesend their codes at a known time

►Ground GPS unit synchronizes its clock with the Ground GPS unit synchronizes its clock with the satellitessatellites Four satellites with same time = only one correct Four satellites with same time = only one correct

solution for 1. time and 3. distancessolution for 1. time and 3. distances►(4 Equations, 4 unknowns)(4 Equations, 4 unknowns)

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Synchronization Synchronization - critical points- critical points►Accurate timing allows distance to satellites to Accurate timing allows distance to satellites to

be measuredbe measured►Satellites achieve accurate timing with on-board Satellites achieve accurate timing with on-board

atomic clocks. atomic clocks. ►Receiver clocks can be accurate because an extra Receiver clocks can be accurate because an extra

satellite range measurement can remove errors. satellite range measurement can remove errors.

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Where are the satellites? Where are the satellites? (ephemeris)(ephemeris)

►Satellites are launched into Satellites are launched into precise orbitsprecise orbits►GPS receivers GPS receivers use an almanac to calculate accurate use an almanac to calculate accurate

positionspositions for the satellites (ephemeris) for the satellites (ephemeris)►Almanac is sent from satellitesAlmanac is sent from satellites►US Airforce measures error in ephemeris (satellite US Airforce measures error in ephemeris (satellite

position and speed) when they fly over C. Springsposition and speed) when they fly over C. Springs►Corrected ephemeris info is sent up to the satelliteCorrected ephemeris info is sent up to the satellite

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ephemeris ephemeris - critical points- critical points

►Satellite position (ephemeris) must be known as Satellite position (ephemeris) must be known as a reference for range measurements. a reference for range measurements.

►GPS satellite orbits are very predictable. GPS satellite orbits are very predictable. ►Minor variations in their orbits are measured by Minor variations in their orbits are measured by

the Department of Defense. the Department of Defense. ►The ephemeris error information is sent to the The ephemeris error information is sent to the

satellites, to be transmitted along with the timing satellites, to be transmitted along with the timing signals. signals.

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Coordinate SystemsCoordinate Systems

►ECEF CoordinatesECEF Coordinates Latitude/Longitude/AltitudeLatitude/Longitude/Altitude

►Degrees Minutes Seconds (Ag Hall, OSU USA)Degrees Minutes Seconds (Ag Hall, OSU USA) Latitude 36Latitude 3600 07’ 29” N 07’ 29” N Longitude 97Longitude 9700 04’ 21” W 04’ 21” W

Latitude = degrees from equator N or SLatitude = degrees from equator N or S Longitude = degrees from Greenwitch E or WLongitude = degrees from Greenwitch E or W Altitude = Meters above reference geoidAltitude = Meters above reference geoid

►GPS uses WGS84 Ellipsoid GPS uses WGS84 Ellipsoid (ECEF – global datum)(ECEF – global datum) Can be transformed to: NAD27, NAD83 Can be transformed to: NAD27, NAD83 (Local datum)(Local datum)

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Coordinate Systems Coordinate Systems (continue)(continue)

►UTMUTM Cartesian positioning in metersCartesian positioning in meters Abbreviation for “Abbreviation for “Universal Transverse Mercator”Universal Transverse Mercator”

Divided into cartesian zonesDivided into cartesian zones 6600 wide, 84 wide, 8400 North to 80 North to 8000 south south

►DatumsDatums Specify a starting point for measurement and Specify a starting point for measurement and

coordinate systemcoordinate system►eg.: (NAD 1927 or NAD 1983)eg.: (NAD 1927 or NAD 1983)

Important to account for error between datums.Important to account for error between datums.►Set the appropriate datum on the GPS unitSet the appropriate datum on the GPS unit

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Computation of distance along Computation of distance along LongitudeLongitude

SLon=R

R

SLonR=6,433,000m

~31.2 m/s

South

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Computation of distance along Computation of distance along LatitudeLatitude

SLat=R40R40

R40=R cos

~25.6 m/s

South

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Error BudgetError Budget

Typical Error in Meters (per satellite) Standard GPS Differential GPS

Satellite Clocks 1.5 0Orbit Errors 2.5 0Ionosphere 5 0.4Troposphere 0.5 0.2Receiver Noise 0.3 0.3Multipath 0.6 0.6SA 30 0

Typical Position Accuracy Horizontal 50 1.3Vertical 78 23-D 93 2.8

Trimble Navigation Limited

7676

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Documents

Localization; review GPS and sonar sensors