Methods and systems for improvement of measurement efficiency in surveying

A method of estimating the position of a target point within a coordinate system using a structural member having pivot point placed at the target point and a moveable end having at least one degree of freedom, and using a satellite navigation system having an antenna mounted to the moveable end, the coordinate system having three bases for defining the coordinates of the system and a plumb-position axis oriented within the coordinate system which is collinear with the direction of gravitational pull at the target point, the structural member having an orientation vector with an origin at the pivot point, an end-point located at a point on the antenna, a length r, an inclination angle θ relative to the plumb-position axis, and an azimuth angle φ about the plumb-position axis and in a plane which is perpendicular to the plumb-position axis and which intersects the pivot point, the radius r and angles θ and φ being parameters of the orientation vector and at least one of the parameters being adjusted by the structural member, the antenna having a phase center, the satellite navigation system measuring the position of the antenna's phase center and providing measured coordinates therefor within the coordinate system as its output data, said method comprising the steps of:

• (a) moving the moveable end of the structural member while keeping the pivot point of the structural member at the target point;
• (b) measuring, during the performance of step (a), two or more sets of parameters of the orientation vector and obtaining two or more corresponding sets of measured antenna coordinates from the navigation system, each measured set of parameters of the orientation vector having at least two of the parameters r, θ, and φ;
• and
• (c) generating an estimate for at least one of the coordinates of the pivot point from the measured parameters of the orientation vector and the measured antenna coordinates, the estimate for said at least one of the coordinates of the pivot point being an estimate for at least one of the coordinates of the target point.

A survey apparatus for use with a global positioning satellite system to measure the coordinates of a target point within a coordinate system, the coordinate system having three bases for defining the coordinates of the system and a plumb-position axis oriented within the coordinate system which is collinear with the direction of gravitational pull at the target point, the survey apparatus comprising:

• a satellite navigation system receiver having an antenna and an output providing measured antenna coordinates representative of the position of a phase center of the antenna;
• a structural member having a pivot point for placement at the target point, a moveable end for holding the antenna and having at least one degree of freedom, an orientation axis passing through the pivot point and a point on the antenna, and a distance between the pivot point and said point on the antenna as measured along the orientation axis;
• a tilt sensor mounted to structural member and having an output that provides measured inclination data which is representative of the angle between the orientation axis and the plumb-position axis;
• a data processor which receives the measured inclination data output by said tilt sensor and the measured antenna coordinates output by said satellite navigation system;
• and
• a first program of instructions stored on a computer-readable medium which directs the data processor to generate an estimate for at least one of the coordinates of the pivot point from the distance, the measured antenna coordinates, and the measured inclination data.

A survey apparatus for use with a global positioning satellite system to measure the coordinates of a target point within a coordinate system, the coordinate system having three bases for defining the coordinates of the system and a plumb-position axis oriented within the coordinate system which is collinear with the direction of gravitational pull at the target point, the survey apparatus comprising:

• a satellite navigation system receiver having an antenna and providing a plurality of measured satellite pseudorange data and satellite carrier phase data;
• a structural member having a pivot point for placement at the target point, a moveable end for holding the antenna and having at least one degree of freedom, and an orientation axis between the pivot point and a point on the antenna;
• a tilt sensor mounted to structural member and having an output that provides measured inclination data which is representative of the angle between the orientation axis and the plumb-position axis;
• a first data processor which receives the measured inclination data output by said tilt sensor and the measured pseudorange and carrier phase data from the satellite navigation system at a plurality of time moments;
• and
• a first program of instructions stored on a first computer-readable medium which directs the first data processor to store the measured inclination data and the measured pseudorange and carrier phase data for a plurality of time moments in a second computer readable medium.

A survey apparatus for use with a global positioning satellite system to measure the coordinates of a target point within a coordinate system, the coordinate system having three bases for defining the coordinates of the system and a plumb-position axis oriented within the coordinate system which is collinear with the direction of gravitational pull at the target point, the survey apparatus comprising:

• a satellite navigation system receiver having an antenna, the antenna having a phase center, the satellite navigation system measuring the position of the antenna's phase center and providing measured coordinates therefor within the coordinate system as its output data;
• a structural member having a pivot point for placement at the target point, a moveable end configured to hold the antenna and having at least one degree of freedom, and an orientation vector with an origin at the pivot point, an end-point located at a point on the antenna, a length r, an inclination angle θ relative to the plumb-position axis, and an azimuth angle φ about the plumb-position axis and in a plane which is perpendicular to the plumb-position axis and which intersects the pivot point, the radius r and angles θ and φ being parameters of the orientation vector and at least one of the parameters being adjusted by the structural member;
• a first sensor configured to measure one of the parameters of the orientation vector and provide measured values thereof, and an second sensor configured to measure another one of the parameters of the orientation vector and provide measured values thereof;
• a first data processor which receives the measured parameters and the measured antenna coordinates;
• and
• a first program of instructions stored on a computer-readable medium which directs the first data processor to generate an estimate for at least one of the coordinates of the pivot point from the measured parameters of the orientation vector and the measured antenna coordinates.

A survey apparatus for use with a global positioning satellite system to measure the coordinates of a target point within a coordinate system, the coordinate system having three bases for defining the coordinates of the system and a plumb-position axis oriented within the coordinate system which is collinear with the direction of gravitational pull at the target point, the survey apparatus comprising:

• a satellite navigation system receiver having an antenna, the antenna having a phase center, the receiver providing a plurality of measured satellite pseudorange data and satellite carrier phase data;
• a structural member having a pivot point for placement at the target point, a moveable end configured to hold the antenna and having at least one degree of freedom, and an orientation vector with an origin at the pivot point, an end-point located at a point on the antenna, a length r, an inclination angle θ relative to the plumb-position axis, and an azimuth angle φ about the plumb-position axis and in a plane which is perpendicular to the plumb-position axis and which intersects the pivot point, the radius r and angles θ and φ being parameters of the orientation vector and at least one of the parameters being adjusted by the structural member;
• a first sensor configured to measure one of the parameters of the orientation vector and provide measured values thereof, and an second sensor configured to measure another one of the parameters of the orientation vector and provide measured values thereof;
• a first data processor which receives the measured parameters and the measured pseudorange and carrier phase data from the satellite navigation system at a plurality of time moments;
• and
• a first program of instructions stored on a computer-readable medium which directs the first data processor to store the measured parameters and the measured pseudorange and carrier phase data for a plurality of time moments in a second computer readable medium.

A method of estimating the position of a target point within a coordinate system using a structural member having pivot point for contacting the target point and a moveable end having at least one degree of freedom, a satellite navigation system having an antenna mounted to the moveable end, and a tilt sensor, a plumb-position axis being present within the coordinate system which is collinear with the direction of gravitational pull at the target point, the coordinate system having three bases for defining the coordinates of the system with one of the bases comprising a Z-axis parallel to the plumb-position axis, the pivot point having a respective set of coordinates which describe its location within the coordinate system, the structural member having an orientation axis passing through the pivot point and a point on the antenna, the tilt sensor measuring an inclination angle (θ) between the orientation axis and the plumb-position axis and providing measured inclination value representative thereof, the antenna having a phase center and the satellite navigation system measuring the position of the antenna's phase center and providing measured coordinates therefor within the coordinate system, said method comprising the steps of:

• (a) obtaining a length r representative of a distance from the pivot point to the phase center of the antenna;
• (b) obtaining a number N of one or more measurement sets, each measurement set comprising a measured Z-axis coordinate zai which represents the measured position of the antenna's phase center along the Z-axis of the coordinate system and a corresponding measured inclination value which is substantially representative of the inclination angle between the orientation axis and the plumb-position, wherein the index “i” represents the identity of the measurement set;
• (c) generating an estimated Z-axis coordinate zt which is representative of the estimated position of the pivot point along the Z-axis, said estimated Z-axis coordinate zt being generated according to a form which is equivalent to:
• zt=E{zai−r cos θi}, i=1 . . . N,
• where E {} is the mean value operator, i is an index over the measurement sets, and θi is the inclination angle indicated by the measured inclination value of the i-th measurement set;
• and
• (d) providing the estimated Z-axis coordinate zt as an estimate for the Z-axis coordinates of the target point.

A method of estimating the position of a target point within a coordinate system using a range pole having a first end for contacting the target point, a second end for holding a satellite navigation system antenna which has a phase center, and an axis between the pole's first and second ends, a plumb-position axis oriented within the coordinate system which is collinear with the direction of gravitational pull at the target point, the coordinate system having three bases for defining the coordinates of the system with the first and second bases spanning a plane which is perpendicular to the plumb-position axis and the third basis comprising a Z-axis which is parallel to the plumb-position axis, the first pole end having a respective set of first, second, and third coordinates which describe its location along the first, second, and third bases, respectively, of the coordinate system, the pole having an inclination angle (θ) between its axis and the plumb-position axis, said method comprising the steps of:

• (a) obtaining a length r representative of the distance from the first end of the pole to the phase center of the antenna as measure along the pole's axis;
• (b) obtaining a number N of two or more measurement sets, each measurement set comprising a first coordinate representative of the measured position of the antenna's phase center along the first basis of the coordinate system, a second coordinate representative of the measured position of the antenna's phase center along the second basis of the coordinate system, and a corresponding pole inclination value representative of the pole's inclination angle;
• (c) selecting two measurement sets and forming two corresponding relationships therefor, each relationship using the measured antenna coordinates and measured pole inclination value of its corresponding measurement set, each relationship describing a locus of estimated first and second coordinates for the pole's first end, the locus being such that a line which starts from a first point located at the first two measured antenna coordinates of the measurement set and any third antenna coordinate and which is drawn to any second point on said locus which is a distance r from the first point has an inclination angle which is equal to the angle indicated by the measured pole inclination value of the measurement set;
• (d) generating two possible sets of estimates for the first and second coordinates of the pole's first end from the relationships;
• (e) receiving an additional position of antenna's phase center measured at an inclination angle of the pole's axis which is less than the inclination angles of the selected measurement sets;
• and
• (f) detecting the one of the two possible sets of estimates whose first and second coordinates are closest to the first and second coordinates of the additional position of the antenna's phase center and providing said set as an estimate of the first and second coordinates of the target point.

A method of estimating the position of a target point within a coordinate system using a structural member having pivot point for contacting the target point and a moveable end having at least one degree of freedom, a satellite navigation system having an antenna mounted to the moveable end, and a tilt sensor, a plumb-position axis being present within the coordinate system which is collinear with the direction of gravitational pull at the target point, the coordinate system having three bases for defining the coordinates of the system with the first and second bases spanning a plane which is perpendicular to the plumb-position axis and the third basis comprising a Z-axis which is parallel to the plumb-position axis, the pivot point having a respective set of coordinates which describe its location within the coordinate system, the structural member having an orientation axis passing through the pivot point and a point on the antenna, the tilt sensor measuring an inclination angle (θ) between the orientation axis and the plumb-position axis and providing measured inclination value representative thereof, the antenna having a phase center and the satellite navigation system measuring the position of the antenna's phase center and providing measured coordinates therefor within the coordinate system, said method comprising the steps of:

• (a) obtaining a length r representative of a distance from the pivot point to the phase center of the antenna;
• (b) obtaining a number N of three or more measurement sets, each measurement set comprising a first coordinate representative of the measured position of the antenna's phase center along the first basis of the coordinate system, a second coordinate representative of the measured position of the antenna's phase center along the second basis of the coordinate system, and a corresponding measured inclination value which is substantially representative of the measured inclination angle between the orientation axis and the plumb-position;
• (c) forming a number N of relationships with each relationship corresponding to a respective measurement set and using the measured antenna coordinates and measured inclination value of its corresponding measurement set, each relationship describing a locus of estimated first and second coordinates for the pivot point, said locus being such that a line which starts from a first point located at the first two measured antenna coordinates of the measurement set and any third antenna coordinate and which is drawn to any second point on said locus which is a distance r from the first point has an inclination angle which is equal to the angle indicated by the measured pole inclination value of the measurement set;
• and
• (d) generating a set of estimates for the first and second coordinates of the pivot point from the relationships and providing said estimates as estimates for the first and second coordinates of the target point.

A computer program product for directing a computer processor to estimate the position of a target point within a coordinate system using data derived from a structural member having pivot point for contacting the target point and a moveable end having at least one degree of freedom, a satellite navigation system having an antenna mounted to the moveable end, and a tilt sensor, the coordinate system having three bases for defining the coordinates of the system, a plumb-position axis oriented within the coordinate system which is collinear with the direction of gravitational pull at the target point, the pivot point having a respective set of coordinates which describe its location within the coordinate system, the structural member having an orientation axis passing through the pivot point and a point on the antenna, the tilt sensor measuring an inclination angle (θ) between the orientation axis and the plumb-position axis and providing measured inclination value representative thereof, the antenna having a phase center and the satellite navigation system measuring the position of the antenna's phase center and providing measured coordinates therefor within the coordinate system, the computer program product comprising:

• a computer-readable medium;
• a first set of instructions embodied on the computer-readable medium which directs the data processor to obtain a length r which is representative of a distance from the pivot point to a point on the antenna;
• a second set of instructions embodied on the computer-readable medium which directs the data processor to obtain a number N of one or more measurement sets, each measurement set comprising a set of one or more measured antenna coordinates which are representative of the measured position of the antenna's phase center within the coordinate system, and further comprising a corresponding measured inclination value representative of the inclination angle provided by the tilt sensor;
• a third set of instructions embodied on the computer-readable medium which directs the data processor to generate an estimate for at least one of the coordinates of the pivot point from the plurality of measurement sets;
• and
• a fourth set of instructions embodied on the computer-readable medium which directs the data processing system to provide the estimate for the at least one of the coordinates of the pivot point as an estimate for at least one of the coordinates of the target point.