Precise location and orientation of a concealed dipole transmitter
View Patent ↗A method for determining the location of an underground sonde transmitter is disclosed. In some embodiments, the method includes measuring a set of complex electromagnetic field magnitude and phase strengths at one or more of positions while traversing a target sonde path at any angle using one or more electromagnetic coil sensors, modeling a set of expected complex electromagnetic strengths of a hypothetical sonde at the one or more of positions for one or more of the electromagnetic coil sensors, the set of expected electromagnetic field values corresponding to a model for the target sonde, and estimating parameters related to the target sonde based on the residual error between the measured set of complex electromagnetic field values and the modeled set of expected complex electromagnetic field strengths, wherein a final estimated parameter set is determined after the residual error has converged to a minimum tolerance.
1. A method for determining the location and orientation of a sonde, the method comprising:
measuring a set of complex electromagnetic field magnitude and phase strengths at one or more positions while traversing a target sonde path at any angle using one or more electromagnetic coil sensors;
modeling a set of expected complex electromagnetic strengths of a hypothetical sonde at each of the one or more positions for one or more of the electromagnetic coil sensors, the set of expected electromagnetic field values corresponding to a model for the target sonde; and
estimating parameters related to the target sonde based on a residual error between the measured set of complex electromagnetic field values and the modeled set of expected complex electromagnetic field strengths, wherein a final estimated parameter set is determined after the residual error has converged to a minimum tolerance.
2. The method of claim 1 , wherein the parameters related to the target sonde include at least:
a 3-dimensional position of the target sonde relative to one or more of the electromagnetic coil sensors.
3. The method of claim 1 , wherein the parameters related to the target sonde include at least:
a 3-dimensional position of the target sonde relative to one or more of the electromagnetic coil sensors; and
an off-axis yaw angle of the target sonde from a reference direction relative to one or more of the electromagnetic coil sensors.
4. The method of claim 1 , wherein the parameters related to the target sonde include at least:
a 3-dimensional position of the target sonde relative to one or more of the electromagnetic coil sensors;
an off-axis yaw angle of the target sonde from a reference direction relative to one or more of the electromagnetic coil sensors; and
a pitch angle of the target sonde relative to one or more of the electromagnetic coil sensors.
5. The method of claim 1 , wherein the target sonde comprises a multi-axis dipole transmitter transmitting at a unique operating frequency per axis.
6. The method of claim 5 , wherein the parameters related to the target sonde include at least:
a 3-dimensional position of the target sonde relative to one or more of the electromagnetic coil sensors;
an off-axis yaw angle of the target sonde from a reference direction relative to one or more of the electromagnetic coil sensors;
a pitch angle of the target sonde relative to one or more of the electromagnetic coil sensors; and
a roll angle of the target sonde about its longitudinal axis.
7. The method of claim 1 , wherein modeling the set of expected complex field strengths includes optimizing each of the sets of individual models related to each of the one or more electromagnetic coil sensors at the receiver and each of one or more target sonde target transmitter directions.
8. The method of claim 7 , wherein optimizing includes applying a Levenburg-Marquardt algorithm.
9. The method of claim 1 , further comprising determining a confidence bound for each of the parameters after the residual error has converged to a minimum tolerance.
10. A method for tracking the location and orientation of a dipole transmitter target sonde between two arbitrary points comprising a known beginning point and a known ending point, comprising:
computing a first optimal path for the target sonde between the beginning point and the ending point;
measuring a set of complex electromagnetic field magnitude and phase values at one of a plurality of incremental positions of target sonde following the optimal path using a plurality of electromagnetic coil sensors;
generating a set of expected complex electromagnetic field values of a hypothetical sonde at the one incremental position based on an extended Kalman filter for each of the electromagnetic coil sensors, the set of expected complex electromagnetic field values corresponding to a model for the target sonde; and
estimating a revised optimal path of the target sonde from the one incremental position to the ending point based on the residual error between the measured field values and the expected field values.
11. The method of claim 10 , wherein a receiver utilized to measure the set of complex electromagnetic field values is fixed aboveground and the target sonde is in motion underground.
12. The method of claim 10 , wherein a receiver utilized to measure the set of complex electromagnetic field values is in motion aboveground and the target sonde is fixed underground.
13. The method of claim 10 , wherein a receiver utilized to measure the set of complex electromagnetic field values is in motion above ground, the target sonde is in motion underground, and the motion of the receiver is tracked across the ground by a position system.
14. The method of claim 13 , wherein the motion of receiver is decoupled from the motion of the target sonde.