Methods and systems for improvement of measurement efficiency in surveying

• US 20030058164A1
• Filed: 08/24/2001
• Published: 03/27/2003
• Est. Priority Date: 08/24/2001
• Status: Active Grant

• Current Assignee: Topcon GPS, LLC
• Original Assignee: Topcon GPS, LLC
• Inventors: Ashjaee, Javad, Zhdanov, Alexey Vladislavovich
• Granted Patent: US 6,633,256 B2
• Time in Patent Office: Days
• US Class Current: 342/357.17
• CPC Class Codes: G01C 15/00 Surveying instruments or accessories not provided for in groups G01C1/00 - G01C13/00
• CPC Class Codes: G01S 19/22 Multipath-related issues
• CPC Class Codes: G01S 19/44 Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method

Abstract

Methods and systems for measuring coordinates of a target, particularly under strong multipath conditions, are described. A satellite navigation system antenna and a tilt sensor are mounted on a range pole, with the sensor at the pole'"'"'s bottom tip. Signals from the antenna and tilt sensor are provided to a receiver, which computes the antenna'"'"'s coordinates from the antenna signals, and the pole tips position from the computed coordinates and the tilt data. The operator places the pole tip on the target and swings the pole by hand over an angle sector of 15 degrees while keeping the tip on the target. Height of the target can be computed with a single measurement set, and X-Y coordinates with just three measurement sets. The use of additional measurements reduces errors in the target'"'"'s coordinates since multipath errors are uncorrelated during movement of the antenna. Vertical alignment of the pole is unnecessary.

Claims

1. 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, 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 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 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 data representative thereof, 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, said method comprising;

(a) moving the moveable end of the structural member while keeping the pivot point of the structural member at the target point;

(b) determining a distance between the phase center of the antenna and the pivot point;

(c) obtaining, during the performance of step (a), one or more measured inclination values from the tilt sensor and one or more corresponding sets of measured antenna coordinates from the navigation system; and

(d) generating an estimate for at least one of the coordinates of the pivot point from the measured antenna coordinates, the measured inclination data, and the distance between the phase center of the antenna and the pivot point, 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.

2. The method of claim 1 wherein the structural member comprises a range pole having a first end as the pivot point, a second end as the moveable end, and a pole axis as the orientation axis, and wherein step (a) comprises the step of swinging the range pole.

3. The method of claim 1 wherein the orientation angle has 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, wherein step (d) generates the estimate without reliance on measured values of the azimuth angle φ

.

4. A method according to claim 1 wherein the first and second bases of the coordinate system span a plane which is perpendicular to the plumb-position axis;

wherein step (c) obtains two or more measured inclination values from the tilt sensor and two or more corresponding sets of measured antenna coordinates;

wherein the third basis comprising a Z-axis which is parallel to the plumb-position axis; and

wherein step (d) comprises;

generating an estimate of the Z-axis coordinate of the pivot point from one or more measured inclination values and the one or more corresponding sets of measured antenna coordinates; and

generating estimates of the coordinates of the pivot point in the first and second bases from two or more measured inclination values and the two or more corresponding sets of measured antenna coordinates.

5. A method according to claim 1 further comprising measuring the temperature of the tilt sensor, and wherein the measure inclination data is corrected to account for temperature effects on the sensor.

6. A method according to claim 1 wherein the tilt sensor is mounted on the structural member at a location which is closer to the pivot point than the moveable end.

7. A method according to claim 6 wherein the tilt sensor is mounted at the bottom end of the range pole.

8. A method according to claim 1 wherein the moveable end of the structural member is moved such that the orientation axis of the structural member moves within a sector angle relative to the plumb position axis of at least 5 degrees.

9. A method according to claim 1 wherein the structural member is rotated about the orientation axis during the performance of step (a).

10. A method according to claim 1 wherein said measured antenna coordinates and measured inclination data are obtained at a frequency of at least 1 Hz.

11. A method according to claim 1 wherein said step (d) is performed with two or more iterative processing steps while new measured antenna coordinates and new measure inclination data are obtained in a real-time environment, and wherein one or more of the iterative processing steps operate on the new measured antenna coordinates new measured inclination values as they are obtained.

12. A method according to claim 1 wherein steps (a) and (c) are performed during a first duration of time with the obtained measured antenna coordinates and measured inclination data being stored in a computer readable medium, and wherein step (d) is performed during a subsequent time duration using the measured antenna coordinates and measured pole-inclination data stored in said computer readable medium.

13. A method according to claim 1 wherein step (c) obtains the measured antenna coordinates from a coordinates processor which determines the measured antenna coordinates relative to a base station with a baseline vector formed between the base station and the antenna'"'"'s phase center, and wherein the coordinates processor resolves the phase ambiguities of the satellites signals relative to the baseline vector.

14. A method according to claim 1 wherein the antenna receives a multipath satellite signal which causes a first error in the measured antenna coordinates and a second error in the estimate;

wherein step (c) obtains two or more measured inclination values from the tilt sensor and two or more corresponding sets of measured antenna coordinates from the navigation system; and

wherein step (d) generates the estimate from the measured antenna coordinates and measured inclination values such that the second error is less that the first error when the first error is obtained with the antenna positioned directly over the target point.

15. A method according to claim 1 wherein the antenna receives a multipath satellite signal which causes a first error in the measured antenna coordinates and a second error in the estimate;

wherein step (c) obtains three or more measured inclination values from the tilt sensor and three or more corresponding sets of measured antenna coordinates from the navigation system; and

wherein step (d) generates the estimate from the measured antenna coordinates and measured inclination data of the plurality of three or more different antenna positions such that the second error is less that the first error when the first error is obtained with the antenna positioned directly over the target point.

16. 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.

17. A method according to claim 16 wherein the first and second bases of the coordinate system span a plane which is perpendicular to the plumb-position axis;

wherein the third basis comprising a Z-axis which is parallel to the plumb-position axis; and

wherein step (c) comprises;

generating an estimate of the Z-axis coordinate of the pivot point from one or more sets of measured parameters and the one or more corresponding sets of measured antenna coordinates; and

generating estimates of the coordinates of the pivot point in the first and second bases from two or more sets of measured parameters and the two or more corresponding sets of measured antenna coordinates.

18. A method according to claim 16 wherein the antenna receives a multipath satellite signal which causes a first error in the measured antenna coordinates and a second error in the estimate;

wherein step (b) measures two or more sets of parameters of the orientation vector and obtains two or more corresponding sets of measured antenna coordinates; and

wherein step (d) generates the estimate from the sets of measured parameters and antenna coordinates such that the second error is less that the first error when the first error is obtained with the antenna positioned directly over the target point.

19. A method according to claim 16 wherein the antenna receives a multipath satellite signal which causes a first error in the measured antenna coordinates and a second error in the estimate;

wherein step (b) measures three or more sets of parameters of the orientation vector and obtains three or more corresponding sets of measured antenna coordinates; and

wherein step (d) generates the estimate from the sets of measured parameters and antenna coordinates such that the second error is less that the first error when the first error is obtained with the antenna positioned directly over the target point.

20. 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.

21. A survey apparatus according to claim 20 wherein the structural member comprises a range pole having a first end as the pivot point, a second end as the moveable end, and a pole axis as the orientation axis, and wherein step (a) comprises the step of swinging the range pole.

22. A survey apparatus according to claim 20 wherein the data processor is part of a satellite navigation system receiver.

23. The method of claim 20 wherein the orientation angle has 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, wherein the first program of instructions directs the data processor to generate the estimate without reliance on measured values of the azimuth angle φ

.

24. A survey apparatus according to claim 20 wherein the first and second bases of the coordinate system span a plane which is perpendicular to the plumb-position axis, wherein the third basis comprising a Z-axis which is parallel to the plumb-position axis, and wherein said program of instructions directs the data processor to generate an estimate of the Z-axis coordinate of the pivot point from the distance between the pivot point and the antenna, the measured antenna coordinates, and measured inclination data obtained at one or more of the time moments, and directs the data processor to generate estimates of the coordinates of the pivot point in the first and second bases from the measured antenna coordinates and inclination data obtained at three or more of the time moments.

25. A survey apparatus according to claim 20 further comprising a temperature sensor which measures the temperature of the tilt sensor, and wherein the measure inclination data is corrected to account for temperature effects on the sensor.

26. A survey apparatus according to claim 20 wherein the tilt sensor is mounted on the structural member at a location which is closer to the pivot point than the moveable end.

27. A survey apparatus according to claim 21 wherein the tilt sensor is mounted at the bottom end of the range pole.

28. A survey apparatus according to claim 20 wherein said program of instructions directs the data processor to generate the estimate by a series of iterations while new measured antenna coordinates and new measure inclination data are obtained in a real-time environment, and directs the data processor to use the new measured antenna coordinates new measured inclination data in one or more of the iterations as they are obtained.

29. 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.

30. A survey apparatus according to claim 29 wherein a set of measured antenna coordinates is generated from the measured satellite pseudorange data and carrier phase data stored in said second computer readable medium and from measured satellite pseudorange data and satellite carrier phase data from a base station;

wherein there is a distance between the pivot point and a point on the antenna as measured along the orientation axis, and wherein said survey apparatus further comprises;

a second data processor which receives the generated set of antenna coordinates and the measured inclination data stored in said second computer readable medium; and

a second program of instructions stored on a computer readable medium which directs the second data processor to generate an estimate for at least one of the coordinates of the pivot point from the distance between the pivot point and the antenna, the measured antenna coordinates and the measured inclination data of a plurality of time moments.

31. 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.

32. The survey apparatus of claim 31 wherein the first and second bases of the coordinate system span a plane which is perpendicular to the plumb-position axis;

wherein the third basis comprising a Z-axis which is parallel to the plumb-position axis; and

wherein the first program of instructions directs the first data processor to generate an estimate of the Z-axis coordinate of the pivot point from one or more sets of measured parameters and the one or more corresponding sets of measured antenna coordinates, and directs the first data processor to generate estimates of the coordinates of the pivot point in the first and second bases from two or more sets of measured parameters and the two or more corresponding sets of measured antenna coordinates.

33. 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.

34. A survey apparatus according to claim 33 wherein a set of measured antenna coordinates is generated from the measured satellite pseudorange data and carrier phase data stored in said second computer readable medium and from measured satellite pseudorange data and satellite carrier phase data from a base station;

and wherein said survey apparatus further comprises;

a second data processor which receives the generated set of antenna coordinates and the measured inclination data stored in said second computer readable medium; and

a second program of instructions stored on a computer readable medium which directs the second data processor to generate an estimate for at least one of the coordinates of the pivot point from parameters of the orientation vector and the measured antenna coordinates of a plurality of time moments.

35. 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 Z_ai 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 z_t which is representative of the estimated position of the pivot point along the Z-axis, said estimated Z-axis coordinate z_t being generated according to a form which is equivalent to;

z_t=E{z_ai−

r cos θ

_i}, i=1 . . . N,

 

where E {} is the mean value operator, i is an index over the measurement sets, and θ

_i is the inclination angle indicated by the measured inclination value of the i-th measurement set; and

(d) providing the estimated Z-axis coordinate z_t as an estimate for the Z-axis coordinates of the target point.

36. The method of claim 35 further comprising the steps of:

receiving M additional measurement sets with M being equal to one or more;

generating a revised estimated value z_t,rev of the estimated Z-axis coordinate z, according to a form which is equivalent to;

z_t,rev=E{N·

z_t, z_aj−

r cos θ

_j}, j=1 . . . M,

 

where E {} is the mean value operator, j is an index over the additional measurement sets, z_aj is the measured Z-axis antenna coordinate of the j-th additional measurement set, and where θ

_j is the inclination angle indicated by the measured inclination value of the j-th additional measurement set; and

providing the estimated revised estimated value z_t,rev as an estimate for the Z-axis coordinates of the target point.

37. The method of claim 35 wherein the structural member comprises a range pole having a first end as the pivot point, a second end as the moveable end, and a pole axis as the orientation axis, and wherein step (a) comprises the step of swinging the range pole.

38. The method of claim 35 wherein step (a) comprises receiving length r from an external source, and wherein step (b) comprises receiving the one or more measurement sets from an external source.

39. 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.

40. The method of claim 39 wherein the coordinate system comprises Cartesian coordinate system with the first basis comprising an X-axis and the second basis comprising a Y-axis;

wherein said method generates an estimated X-axis coordinate x_t which represents the estimated position of the pole'"'"'s first end along the X-axis of the coordinate system, and an estimated Y-axis coordinate y_t which represents the estimated position of the pole'"'"'s first end along the Y-axis of the coordinate system;

wherein the first measured antenna coordinate of each i-th measurement set comprises an X-axis coordinate x_ai which represents the measured position of the antenna'"'"'s phase center along the X-axis of the coordinate system, and wherein the second measured antenna coordinate of each i-th measurement set comprises a Y-axis coordinate y_ai which represents the measured position of the antenna'"'"'s phase center along the Y-axis of the coordinate system, where the index “

i”

represents the identity of the measurement set and the corresponding relationship;

wherein each relationship of step (c) comprises a first equation which is equivalent to the form;

(x_ai−

x_t)²+(y_ai−

y_t)²=(r sin θ

_i)², where θ

_i is the pole'"'"'s inclination angle indicated by the measurement set'"'"'s measured pole inclination value.

41. The method of claim 39 further comprising receiving a temperature value representative of the temperature during which the measurement sets were made, and correcting the measured inclination values of the measurement sets based on the measured temperature value.

42. 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.

43. The method of claim 42 wherein the coordinate system comprises Cartesian coordinate system with the first basis comprising an X-axis and the second basis comprising a Y-axis;

wherein said method generates an estimated X-axis coordinate x_t which represents the estimated position of the pivot point along the X-axis of the coordinate system, and an estimated Y-axis coordinate y_t which represents the estimated position of the pivot point along the Y-axis of the coordinate system;

wherein the first measured antenna coordinate of each i-th measurement set comprises an X-axis coordinate x_ai which represents the measured position of the antenna'"'"'s phase center along the X-axis of the coordinate system, and wherein the second measured antenna coordinate of each i-th measurement set comprises a Y-axis coordinate Y_ai which represents the measured position of the antenna'"'"'s phase center along the Y-axis of the coordinate system, where the index “

i”

represents the identity of the measurement set and the corresponding relationship;

wherein each relationship of step (c) comprises a first equation which is equivalent to the form;

{(x_ai−

x_t)²+(y_ai−

y_t)²}^½

=r sin θ

_i, where θ

_i is the inclination angle indicated by the measurement set'"'"'s measured inclination value.

44. The method of claim 43 wherein step (d) comprises the step of generating the estimated coordinates x_t and y_t of the pivot point from a non-linear least-squares fitting of the estimated coordinates x_t and y_t to the first equations of the relationships.

45. The method of claim 44 wherein the non-linear least-squares fitting comprises one or more iterations of generating values for the estimated coordinates x_t and y_t, each iteration being represented by an index k, and further comprises steps of:

(e) selecting a set of initial iteration values x_t,k and y_t,k for the estimated coordinates x_t and y_t for the first iteration (k=1);

wherein each iteration comprises the steps of;

(f) forming a plurality of difference quantities m_k[i] (i=1, 2, . . . , N) corresponding to the number N of relationships, each difference quantity being proportional to the difference between the left and right sides of the first equation of the corresponding relationship with the iteration values x_t,k and y_t,k being used in the first equations in place of the estimated coordinates x_t and y_t, a vector M_k represents the plurality of difference quantities m_k[i] (i=1, 2, . . . , N);

(g) forming a first derivative matrix H_k which comprises the first derivatives of the difference quantities m_k[i] (i=1, 2, . . . , N) with respect to the estimated coordinate values x_t and y_t, matrix H_k having a transpose matrix matrix H′

_k;

(h) forming a plurality N of second derivative matrices G_k,i (i=1, 2, . . . , N) of the difference quantities M_k[i] (i=1, 2, . . . , N), the elements of each i-th matrix G_k,i (i=1, 2, . . . , N) comprising the second derivatives of m_k[i] with respect to the estimated coordinate values x_t and y_t; and

(i) with a vector X_k representing the iteration values x_t,k and y_t,k, generating a set of updated iteration values x_t,k+1 and y_t,k+1 according to a form which is equivalent to;

$X_{k+1}=X_k-{\left(H_k^{\mathrm{\prime <br><br>}}<br><br>H_k+\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>m_k<br><br>\left[i\right]<br><br>G_{k_i}\right)}^{-1}<br><br>H_k^{\mathrm{\prime <br><br>}}<br><br>M_k$

 

where vector X_k+1 represents the updated iteration values x_t,k+1 and y_t,k+1 and where the operator ( )<sup>−

1</sup> denotes matrix inversion.

46. The method of claim 45 further comprising the steps of:

repeating steps (f)-(i) one or more times to provide one or more corresponding iterations, at least one component of vector X_k being set equal to its corresponding component of X_k+1 prior to the start of each such iteration; and

thereafter providing the components of X_k+1 as estimates for the first and second coordinates of the target point.

47. The method of claim 45 further comprising:

receiving M additional measurement sets with M being equal to one or more;

forming M additional relationships corresponding to the M additional measurement sets;

repeating steps (f)-(i) one or more times to provide one or more corresponding iterations, at least one component of vector X_k being set equal to its corresponding component of X_k+1 prior to the start of each such iteration, wherein M_k, H_k, and the series of second derivative matrices G_k,i (i=1, . . . [N+M]) are expand to be representative of the additional relationships for at least one repeated iteration; and

thereafter providing the components of X_k+1 as estimates for the first and second coordinates of the target point.

48. The method of claim 45 wherein the first derivatives of matrix H_k are computed with x_t=x_t,k and y_t=y_t,k, and wherein the second derivative elements of matrices G_k,i (i=1, 2, . . . , N) are computed with x_t=x_t,k and y_t=y_t,k.

49. The method of claim 42 wherein said method further computes an estimated Z-axis coordinate z_t which is representative of the estimated position of the pivot point along the Z-axis of the coordinate system;

wherein at least one measurement set has a Z-axis coordinate which is representative of the measured position of the antenna'"'"'s phase center along the Z-axis of the coordinate system; and

wherein said method further comprises the step of generating, from a selected measurement set which has a Z-axis coordinate z_aS, the estimated Z-axis coordinate z_t according to a form which is equivalent to z_t=z_aS−

r cos θ

_S, where θ

_S is the inclination angle indicated by the measured inclination value of the selected measurement set, and the step of providing the estimated Z-axis coordinate z_t as estimates for the first and second coordinates of the target point.

50. The method of claim 42 wherein said method further computes an estimated Z-axis coordinate z_t which is representative of the estimated position of the pivot point along the Z-axis of the coordinate system;

wherein each i-th measurement set has a Z-axis coordinate z_ai which is representative of the measured position of the antenna'"'"'s phase center along the Z-axis of the coordinate system;

wherein said method further comprises the step of generating the estimated Z-axis coordinate z_t according to a form which is equivalent to;

z_t=E{z_ai−

r cos θ

_i}, i=1 . . . N,

where E{} is the mean value operator, and the step of providing the estimated Z-axis coordinate z_t as estimates for the first and second coordinates of the target point.

51. The method of claim 44 wherein the non-linear least-squares fitting comprises one or more iterations of generating values for the estimated coordinates x_t and y_t, each iteration being represented by an index k, and further comprises the steps of:

(e) selecting a set of initial iteration values x_t,k, and y_t,k, for the estimated coordinates x_t and y_t for the first iteration (k=1);

wherein each iteration comprises the steps of;

(f) forming a plurality of difference quantities m_k[i] (i=1, 2, . . . , N) corresponding to the number N of relationships, each difference quantity being proportional to the difference between the left and right sides of the first equation of the corresponding relationship with the iteration values x_t,k and y_t,k being used in the first equations in place of the estimated coordinates x_t and y_t, a vector M_k represents the plurality of difference quantities m_k[i] (i=1, 2, . . . , N);

(g) forming a first derivative matrix H_k which comprises the first derivatives of the difference quantities m_k[i] (i=1, 2, . . . , N) with respect to the estimated coordinate values x_t and y_t, matrix H_k having a transpose matrix matrix H′

_k;

(h) with a vector X_k representing the iteration values x_t,k and y_t,k, computing a set of updated iteration values x_t,k+1 and y_t,k+1 according to a form which is equivalent to;

X_k+1=X_k−

T_k(H_k′

H_k)<sup>−

1</sup> H_k′

M_k

 

where vector X_k+1 represents the updated iteration values x_t,k+1 and y_t,k+1, where T_k is a scalar value greater than zero, and where the operator ( )<sup>−

1</sup> denoted matrix inversion.

52. The method of claim 51 further comprising the steps of:

repeating steps (f)-(i) one or more times to provide one or more corresponding iterations, at least one component of vector X_k being set equal to its corresponding component of X_k+1 prior to the start of each such iteration; and

thereafter providing the components of X_k+1 as estimates for the first and second coordinates of the target point.

53. The method of claim 51 further comprising:

receiving M additional measurement sets with M being equal to one or more;

forming M additional relationships corresponding to the M additional measurement sets;

repeating steps (f)-(i) one or more times to provide one or more corresponding iterations, at least one component of vector X_k being set equal to its corresponding component of X_k+1 prior to the start of each such iteration, wherein M_k and H_k are expand to be representative of the additional relationships for at least one repeated iteration; and

thereafter providing the components of X_k+1 as estimates for the first and second coordinates of the target point.

54. The method of claim 51 wherein the first derivatives of matrix H_k are computed with x_t=x_t,k and y_t=y_t,k.

55. The method of claim 42 wherein said method further computes an estimated Z-axis coordinate z_t which is representative of the estimated position of the pivot point along the Z-axis of the coordinate system;

wherein at least one measurement set has a Z-axis coordinate which is representative of the measured position of the antenna'"'"'s phase center along the Z-axis of the coordinate system; and

wherein said method further comprises the step of generating, from a selected measurement set which has a Z-axis coordinate z_aS, the estimated Z-axis coordinate z_t according to a form which is equivalent to z_t=z_aS−

r cos θ

_S, where θ

_s is the inclination angle indicated by the measured inclination value of the selected measurement set, and the step of providing the estimated Z-axis coordinate z_t as estimates for the first and second coordinates of the target point.

56. The method of claim 52 wherein said method further computes an estimated Z-axis coordinate Z_t, which is representative of the estimated position of the pivot point along the Z-axis of the coordinate system;

wherein each i-th measurement set has a Z-axis coordinate z_ai which is representative of the measured position of the antenna'"'"'s phase center along the Z-axis of the coordinate system;

wherein said method further comprises the step of generating the estimated Z-axis coordinate z_t according to a form which is equivalent to;

z_t=E{z_ai−

r cos θ

_i}, i=1 . . . N,

where E{} is the mean value operator, and the step of providing the estimated Z-axis coordinate z_t as estimates for the first and second coordinates of the target point.

57. The method of claim 42 wherein the structural member comprises a range pole having a first end as the pivot point, a second end as the moveable end, and a pole axis as the orientation axis, and wherein step (a) comprises the step of swinging the range pole.

58. The method of claim 42 wherein step (a) comprises receiving length r from an external source, and wherein step (b) comprises receiving the measurement sets from an external source.

59. 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.

60. The method of claim 59 wherein the data processor comprises a first input port coupled to an output of the tilt sensor to receive the sensor'"'"'s measured pole inclination value, and a second input port coupled to an output of the satellite navigation system to receive the sensor'"'"'s measured pole inclination value;

wherein the second set of instructions includes a first group of instructions which directs the data processor to determine when a set of measured antenna coordinates are provided on the second port and a second group of instructions which directs the data processor to read the antenna coordinates from the second port and the inclination value from the first port at substantially the same time.