A boring tool that is moved by a drill string to form an underground bore. A transmitter transmits a time varying dipole field as a homing field from the boring tool. A pitch sensor detects a pitch orientation of the boring tool. A homing receiver is positionable at a target location for detecting the homing field to produce a set of flux measurements. A processing arrangement uses the pitch orientation and flux measurements with a determined length of the drill string to determine a vertical homing command for use in controlling depth in directing the boring tool to the target location such that the vertical homing command is generated with a particular accuracy at a given range between the transmitter and the homing receiver and which would otherwise be generated with the particular accuracy for a standard range, different from the particular range. An associated system and method are described.
Legal claims defining the scope of protection, as filed with the USPTO.
. In a system including a boring tool that is moved by a drill string using a drill rig that selectively extends the drill string to the boring tool to form an underground bore such that the drill string is characterized by a drill string length which is determinable, the transmitter configured for transmitting a including a pitch sensor for detecting a pitch orientation of the boring tool and for transmitting a dipole electromagnetic field, a homing apparatus comprising:
. The homing apparatus ofwherein the vertical homing command has a particular accuracy that is greater than another accuracy associated with the horizontal homing command for use in controlling depth in directing the boring tool to said target location.
. The homing apparatus ofwherein the homing receiver is configured in a way which produces an inaccuracy in said set of flux measurements as said measurement error which inaccuracy increases as a range between the homing receiver and the transmitter increases.
. The homing apparatus ofwherein said processing arrangement is configured to establish an uncorrected position of the boring tool along a nominal drill path in a vertical plane that contains an initial position of the transmitter and the homing receiver and to introduce a correction to that uncorrected position to establish a corrected position as part of generating the vertical homing command.
. The homing apparatus ofwherein said homing receiver includes an antenna arrangement having a set of three orthogonally opposed antennas for determining the set of flux measurements to provide three flux measurements taken along three orthogonally opposed directions.
Complete technical specification and implementation details from the patent document.
This application is a continuation of copending U.S. patent application Ser. No. 18/117,419, filed on Mar. 4, 2023, which is a continuation application of U.S. patent application Ser. No. 17/151,612 filed on Jan. 18, 2021 and issued as U.S. Pat. No. 11,598,198 on Mar. 7, 2023, which is a continuation application of U.S. patent application Ser. No. 16/161,043 filed on Oct. 15, 2018 and issued as U.S. Pat. No. 10,895,145, which is a continuation application of U.S. patent application Ser. No. 15/231,764, filed on Aug. 8, 2016 and issued as U.S. Pat. No. 10,107,090 on Oct. 23, 2018, which is a continuation application of U.S. patent application Ser. No. 13/761,632 filed on Feb. 7, 2013 and issued as U.S. Pat. No. 9,422,804 on Aug. 23, 2016, which is a continuation application of U.S. patent application Ser. No. 12/689,954 filed on Jan. 19, 2010 and issued as U.S. Pat. No. 8,381,836 on Feb. 26, 2013, the disclosures of which are incorporated herein by reference.
The present application is related generally to the field of underground directional drilling and, more particularly, to an advanced underground homing system, apparatus and method for directing a drill head to a homing target.
A boring tool is well-known as a steerable drill head that can carry sensors, transmitters and associated electronics. The boring tool is usually controlled through a drill string that is extendable from a drill rig. The drill string is most often formed of drill pipe sections, which may be referred to hereinafter as drill rods, that are selectively attachable with one another for purposes of advancing and retracting the drill string. Steering is often accomplished using a beveled face on the drill head. Advancing the drill string while rotating should result in the boring tool traveling straight forward, whereas advancing the drill string with the bevel oriented at some fixed angle will result in deflecting the boring tool in some direction. A number of approaches have been seen in the prior art for purposes of attempting to guide the boring tool to a desired location, a few of which will be discussed immediately hereinafter.
In one approach, the boring tool transmits an electromagnetic locating signal. Above ground, a portable detection device, known as a walkover detector, is movable so as to characterize the positional relationship between the walkover detector and the boring tool at a given time. The boring tool can be located, for example, by moving the walkover detector to a position that is directly overhead of the boring tool or at least to some unique point in the field of the electromagnetic locating signal. In some cases, however, a walkover locator is not particularly practical when drilling beneath some sort of obstacle such as, for example, a river, freeway or building. In such cases, other approaches may be more practical.
Another approach that has been taken by the prior art, which may be better adapted for coping with obstacles which prevent access to the surface of the ground above the boring tool, resides in what is commonly referred to as a “steering tool.” This term has come to describe an overall system which essentially predicts the position of the boring tool, as it is advanced through the ground using a drill string, such that the boring tool can be steered from a starting location while the location of the boring tool is tracked in an appropriate coordinate system relative to the starting position. Arrival at a target location is generally determined by comparing the determined position of the boring tool with the position of the desired target in the coordinate system.
Steering tool systems are considered as being distinct from other types of locating systems used in horizontal directional drilling at least for the reason that the position of the boring tool is determined in a step-wise fashion as it progresses through the ground. Generally, in a traditional steering tool system, pitch and yaw angles of the drill-head are measured in coordination with extension of the drill string. From this, the drill-head position coordinates are obtained by numerical integration step-by-step from one location to the next. Nominal or measured drill rod lengths can serve as a step size during integration. One concern with respect to conventional steering tools is a tendency for positional error to accumulate with increasing progress through the ground up to unacceptable levels. This accumulation of positional error is attributable to measurement error in determining the pitch and yaw angles at each measurement location. One technique in the prior art in attempting to cope with the accumulation of positional error resides in attempting to measure the pitch and yaw parameters with the highest possible precision, for example, using an optical gyroscope in an inertial guidance system. Unfortunately, such gyroscopes are generally expensive.
Another approach that has been taken by the prior art, which is also able to cope with drilling beneath obstacles, is a homing type system. In traditional homing systems, the boring tool includes a homing transmitter that transmits an electromagnetic signal. A homing receiver is positioned at a target location or at least proximate to a target location such as, for example, directly above the target location. The homing receiver is used to receive the electromagnetic signal and to generate homing commands based on characteristics of the electromagnetic signal which indicate whether the boring tool is on a course that would ultimately cause it to be directed to the target location. Generally, identifying the particular location of the boring tool is not of interest since the boring tool will ultimately arrive at the target location if the operator follows the homing commands as they are issued by the system. Applicants recognize, however, that such traditional homing systems are problematic with respect to use at relatively long ranges between the homing receiver and the boring tool, as will be discussed in detail below.
The foregoing examples of the related art and limitations related therewith are intended to be illustrative and not exclusive. Other limitations of the related art will become apparent to those of skill in the art upon a reading of the specification and a study of the drawings.
The following embodiments and aspects thereof are described and illustrated in conjunction with systems, tools and methods which are meant to be exemplary and illustrative, not limiting in scope. In various embodiments, one or more of the above-described problems have been reduced or eliminated, while other embodiments are directed to other improvements.
In general, a system includes a boring tool that is moved by a drill string using a drill rig that selectively extends the drill string to the boring tool to form an underground bore such that the drill string is characterized by a drill string length which is determinable. In one aspect, a homing apparatus includes a transmitter, forming part of the boring tool, for transmitting a time varying dipole field as a homing field. A pitch sensor is located in the boring tool for detecting a pitch orientation of the boring tool. A homing receiver is positionable at least proximate to a target location for detecting the homing field to produce a set of flux measurements. A processing arrangement is configured for using the detected pitch orientation and the set of flux measurements in conjunction with a determined length of the drill string to determine a vertical homing command for use in controlling depth in directing the boring tool to the target location such that the vertical homing command is generated with a particular accuracy at a given range between the transmitter and the homing receiver and which would otherwise be generated with the particular accuracy for a standard range, that is different from the particular range, without using the determined length of the drill string. A display indicates the vertical homing command to a user. In one feature, the boring tool is sequentially advanced through a series of positions along the underground bore and, at each one of the positions (i) the pitch orientation is detected by the pitch sensor, (ii) the homing receiver produces the flux measurements and (iii) the drill string is of the determined length such that at least the set of flux measurements is subject to a measurement error and the processing arrangement is configured for determining the vertical homing command, at least in part, by compensating for the measurement error, which measurement error would otherwise accumulate from each one of the series of positions to a next one of the series of positions, to cause the particular range to be greater than the standard range.
In another aspect, a system includes a boring tool that is moved by a drill string using a drill rig that selectively extends the drill string to the boring tool to form an underground bore such that the drill string is characterized by a drill string length. One embodiment of a method includes transmitting a time varying dipole field from the boring tool as a homing field. A pitch orientation of the boring tool is detected using a pitch sensor located in the boring tool. A homing receiver is positioned at least proximate to a target location for detecting the homing field to produce a set of flux measurements. A length of the drill string is determined. A processor is configured for using the detected pitch orientation and the set of flux measurements in conjunction with the established length of the drill string to determine a vertical homing command for use in controlling depth in directing the boring tool to the target location such that the vertical homing command is generated with a particular accuracy at a given range between the transmitter and the homing receiver and which would be generated with the particular accuracy for a standard range, that is different from the particular range, without using the determined length of the drill string, and indicating the vertical homing command to a user. In one feature, the boring tool is sequentially advanced through a series of positions along the underground bore and, at each one of the positions (i) the pitch orientation is detected using the pitch sensor, (ii) the flux measurements are produced by the homing receiver and (iii) establishing the determined length of the drill string is established such that at least the set of flux measurements is subject to a measurement error. The vertical homing command is determined, at least in part, by compensating for the measurement error, which measurement error would otherwise accumulate from each one of the series of positions to a next one of the series of positions, to cause the particular range to be greater than the standard range.
In still another aspect, a system includes a boring tool that is moved by a drill string using a drill rig that selectively extends the drill string to the boring tool to form an underground bore such that the drill string is characterized by a drill string length which is determinable. A homing apparatus includes a transmitter, forming part of the boring tool, for transmitting a time varying electromagnetic homing field. A pitch sensor is located in the boring tool for detecting a pitch orientation of the boring tool. A homing receiver is provided that is positionable at least proximate to a target location for detecting the homing field to produce a set of flux measurements. A processing arrangement is configured for using the detected pitch orientation and the set of flux measurements in conjunction with a determined length of the drill string to determine a vertical homing command and a horizontal homing command such that the vertical homing command has a particular accuracy that is different from another accuracy associated with the horizontal homing command for use in controlling depth in directing the boring tool to the target location. In one feature, the particular accuracy of the vertical homing command is greater than the other accuracy of the horizontal homing command.
In yet another aspect, a system includes a boring tool that is moved by a drill string using a drill rig that selectively extends the drill string to the boring tool to form an underground bore such that the drill string is characterized by a drill string length which is determinable. A method includes transmitting a time varying electromagnetic homing field from the boring tool. A pitch orientation of the boring tool is detected. A homing receiver is positioned at least proximate to a target location for detecting the homing field to produce a set of flux measurements. The detected pitch orientation and the set of flux measurements are used in conjunction with a determined length of the drill string to determine a vertical homing command and a horizontal homing command such that the vertical homing command has a particular accuracy that is different from another accuracy associated with the horizontal homing command for use in controlling depth in directing the boring tool to the target location. In one feature, the particular accuracy of the vertical homing command is generated as being more accurate than the other accuracy of the horizontal homing command.
In a further aspect, a system includes a boring tool that is moved by a drill string using a drill rig that selectively extends the drill string to the boring tool to form an underground bore such that the drill string is characterized by a drill string length which is determinable and in which the boring tool is configured for transmitting an electromagnetic homing field. An improvement includes configuring an arrangement for using at least the electromagnetic homing field to determine a vertical homing command and a horizontal homing command such that the vertical homing command has a particular accuracy that is different from another accuracy associated with the horizontal homing command for use in controlling depth in directing the boring tool to the target location. In one feature, the arrangement is further configured for generating the particular accuracy of the vertical homing command as being more accurate than the other accuracy of the horizontal homing command.
In addition to the exemplary aspects and embodiments described above, further aspects and embodiments will become apparent by reference to the drawings and by study of the following descriptions.
The following description is presented to enable one of ordinary skill in the art to make and use the invention and is provided in the context of a patent application and its requirements. Various modifications to the described embodiments will be readily apparent to those skilled in the art and the generic principles taught herein may be applied to other embodiments. Thus, the present invention is not intended to be limited to the embodiment shown, but is to be accorded the widest scope consistent with the principles and features described herein including modifications and equivalents, as defined within the scope of the appended claims. It is noted that the drawings are not to scale and are diagrammatic in nature in a way that is thought to best illustrate features of interest. Descriptive terminology such as, for example, upper/lower, front/rear, vertically/horizontally, inward/outward, left/right and the like may be adopted for purposes of enhancing the reader's understanding, with respect to the various views provided in the figures, and is in no way intended as being limiting.
Turning now to the figures, wherein like components are designated by like reference numbers whenever practical, attention is immediately directed to, which illustrate an advanced homing tool system that is generally indicated by the reference numberand produced according to the present disclosure.is a diagrammatic elevational view of the system, whereasis a diagrammatic plan view of the system, each figure showing a regionin which a homing operation is underway. Systemincludes a drill righaving a carriagereceived for movement along the length of an opposing pair of railswhich are, in turn, mounted on a frame. A conventional arrangement (not shown) is provided for moving carriagealong rails. A boring toolincludes an asymmetric face() and is attached to a drill stringwhich is composed of a plurality of drill pipe sections, several of which are indicated. It is noted that the drill string is partially shown due to illustrative constraints. Generally, the drill rig hydraulically pushes the drill string into the ground with selective rotation. Pushing with rotation is intended to cause the boring tool to travel straight ahead while pushing without rotation is intended to cause the boring tool to turn, based on the orientation of asymmetric face. A pathof the boring tool includes a series of positions that are designated as k=1,2,3,4 etc. as the boring tool is advanced through the ground. The current position of the boring tool is position k with the next position to be position k+1. The portion of pathalong which the boring tool has already traveled is shown as a solid line while a dashed line′, in, illustrates the potential appearance of the path ahead of the boring tool resulting from the homing procedure. The increment between the positions k and k+1 can correspond to the length of one pipe section, although this is not a requirement. Boring toolenters the ground at, however, the subject homing process can begin at position k=1 at a depth Dbelow a surfaceof the ground, where a pointon the surface of the ground serves as the origin of a coordinate system. As will be seen, the homing operation can be initiated at pointwhere the boring tool initially enters the ground. While a Cartesian coordinate system is used as the basis for the coordinate system employed by the various embodiments disclosed herein, it is to be understood that this terminology is used in the specification and claims for descriptive purposes and that any suitable coordinate system may be used.
As the drilling operation proceeds, respective drill pipe sections, which may be referred to interchangeably as drill rods, are added to the drill string at the drill rig. A most recently added drill rodis shown on the drill rig. An upper endof drill rodis held by a locking arrangement (not shown) which forms part of carriagesuch that movement of the carriage in the direction indicated by an arrow() causes sectionto move therewith, which pushes the drill string into the ground thereby advancing the boring operation. A clamping arrangementis used to facilitate the addition of drill pipe sections to the drill string. The drilling operation can be controlled by an operator (not shown) at a control consolewhich itself can include a telemetry sectionconnected with a telemetry antenna, a display screen, an input device such as a keyboard, a processor, and a plurality of control leverswhich, for example, control movement of carriage.
Still referring to, in one embodiment, systemcan include a drill string measuring arrangement having a stationary ultrasonic transmitterpositioned on drill frameand an ultrasonic receiverwith an air temperature sensor() positioned on carriage. It should be noted that the positions of the ultrasonic transmitter and receiver may be interchanged with no effect on measurement capabilities. Transmitterand receiverare each coupled to processoror a separate dedicated processor (not shown). In a manner well known in the art, transmitteremits an ultrasonic wavethat is picked up at receiversuch that the distance between the receiver and the transmitter may be determined to within a fraction of an inch by processorusing time delay and temperature measurements. By monitoring movements of carriage, in which drill stringis either pushed into or pulled out of the ground, and clamping arrangement, processorcan accurately track the length of drill stringthroughout a drilling operation to within a particular measurement accuracy. While it is convenient to perform measurements in the context of the length of the drill rods, with measurement positions corresponding to the ends of the drill rods, it should be appreciated that this is not a requirement and the ultrasonic arrangement can provide the total length of the drill string at any given moment in time. Further, in another embodiment, the length of the drill string can be determined according to the number of drill rods multiplied by nominal rod length. In this case, the rod length may be of a nominal value subject to some manufacturing tolerance at least with respect to its length. In one version of this embodiment, the drill string measurement arrangement can count the drill rods. In another version of this embodiment, the operator can count the drill rods. Of course, in either case, the number of drill rods that is counted can be correlated to the length that is determined by ultrasonic measurement, although there is no requirement for precision overall drill string length measurement.
Referring to, boring toolincludes a mono-axial antenna (not shown) such as a dipole antenna oriented along an elongation axis of the boring tool and which is driven to emit a dipole magnetic homing signal(only one flux line of which is partially shown). As an example of a boring tool incorporating such a mono-axial antenna in its transmitter arrangement, see FIG. 9 of U.S. Pat. No. 5,155,442 (hereinafter, the '442 patent) entitled POSITION AND ORIENTATION LOCATOR/MONITOR and its associated description. This latter patent is commonly owned with the present application and hereby incorporated by reference. As will be described in detail hereinafter, homing signalis monitored by a homing receiverwhich will be described in detail at an appropriate point hereinafter. The boring tool is equipped with a pitch sensor (not shown) for measurement of its pitch orientation as is described, for example, in the '442 patent. As is also well known, the pitch orientation and other parameters of interest can be modulated onto the homing signal for remote reception and decoding. In other embodiments, measured parameters can be transferred to the drill rig using a wire-in-pipe configuration such as is described, for example, in U.S. Pat. No. 7,150,329 entitled AUTO-EXTENDING/RETRACTING ELECTRICALLY ISOLATED CONDUCTORS IN A SEGMENTED DRILL STRING, which is commonly owned with the present application and incorporated herein by reference. The parameters may be used at the drill rig and/or transferred to a remote location, for example, by telemetry section. It is noted, however, that the measurement of yaw is not necessary and, therefore, there is no need for a yaw sensor in the boring tool. It is well known that yaw angle is a parameter that is generally significantly more difficult to measure, as compared to pitch orientation. Accordingly, there is some benefit associated with techniques such as described herein which do not rely on measured yaw orientation.
is a diagrammatic view, in perspective, which illustrates details of one embodiment of portable homing receiver. The homing receiver includes a three-axis antenna clusterfor measuring three orthogonally arranged components of magnetic flux in a coordinate system that can be fixed to the homing receiver itself having axes designated as b, band band, of course, transformed to another coordinate system such as what may be referred to as a global coordinate system in the context of which the homing operation can be performed. In one embodiment, the global coordinate system can be the X,Y,Z. One useful antenna cluster contemplated for use herein is disclosed by U.S. Pat. No. 6,005,532 entitled ORTHOGONAL ANTENNA ARRANGEMENT AND METHOD which is commonly owned with the present application and is incorporated herein by reference. Antennais electrically connected to a receiver sectionwhich can include amplification and filtering circuitry, as needed. Homing receiverfurther may include a graphics display, a telemetry arrangementhaving an antennaand a processing sectioninterconnected appropriately with the various components. The processing section can include one or more microprocessors, DSP units, memory and other components, as needed. It is noted that, for the most part, inter-component cabling has not been illustrated in order to maintain illustrative clarity, but is understood to be present and may readily be implemented by one having ordinary skill in the art in view of this overall disclosure. It should be appreciated that graphics displaycan be a touch screen in order to facilitate operator selection of various buttons that are defined on the screen and/or scrolling can be facilitated between various buttons that are defined on the screen to provide for operator selections. Such a touch screen can be used alone or in combination with an input devicesuch as, for example, a keypad. The latter can be used without the need for a touch screen. Moreover, many variations of the input device may be employed and can use scroll wheels and other suitable well-known forms of selection device. The telemetry arrangement and associated antenna are optional. The processing section can include components such as, for example, one or more processors, memory of any appropriate type and analog to digital converters. Generally, the homing receiver can be configured for direct placement on surfaceof the ground, however, an ultrasonic transducer (not shown) can be provided for measuring the height of the homing receiver above the surface of the ground. One highly advantageous ultrasonic transducer arrangement is described, for example, in the above incorporated '442 patent.
As will be further described, Applicant recognizes that the accuracy of homing commands depends directly on the accuracy of fluxes measured at the homing receiver. Since dipole field signal strength (see item, in) decreases in inverse proportion to distance to the third power, homing accuracy can diminish rapidly with relatively larger distances between the homing transmitter of boring tooland homing receiver. In this regard, it should be appreciated that the weakest signal and, hence, the lowest accuracy in a typical homing procedure will be encountered at the start of the operation when separation between the homing transmitter and the homing receiver is usually at a maximum. In a conventional homing system, this initial separation can be beyond the range at which the homing receiver is capable of receiving the homing signal.
The homing technique and apparatus disclosed herein increases the range over which vertical homing is accurate. Accurate and useful homing commands can be generated over distances much larger than the typical range of 40 feet or so, using a typical battery powered homing transmitter. At a given range between the boring tool and the homing receiver, vertical homing accuracy is remarkably enhanced by using flux measurements in conjunction with integrating pitch for a determined drill string length, as will be further discussed at an appropriate point below.
The following nomenclature is used in embodiments of the homing procedure described herein and is provided here as a convenience for the reader.
Referring to, prior to homing, the user may place homing receiveron the ground ahead of the homing transmitter and above a specified target location T, pointing in the drilling direction in one embodiment. Note that the receiver x axis faces to the right in the view of. That is, the x axis of the receiver, along which flux bis measured, faces away from the drill rig at least approximately in the drilling direction. In another embodiment, the center of tri-axial antennaof the homing receiver may be chosen as a target T′. This set-up procedure determines an X, Z coordinate system used during homing () where X is horizontal and Z is vertical. A Y axis extends horizontally and orthogonal to the X,Z plane completing a right handed Cartesian coordinate system. The use of this particular coordinate system which may be referred to herein as a master or global coordinate system, should be considered as exemplary and not limiting. Any suitable coordinate system may be used including Cartesian coordinate systems having different orientations and polar coordinate systems. It should be appreciated that the drill path is not physically confined to the X,Z plane such that homing along a curved path can be performed. The technique described herein, however, does not account for divergence of the boring tool out of the X, Z plane or for yaw angles out of the X, Z plane as represented by boring tool′ (shown in phantom in) for purposes of producing enhanced vertical homing commands while still producing remarkable results. At the time of setup, the X,Z axes define a vertical plane that contains the center of the transmitter antenna at the start of homing and the center of antennaof homing receiver. These axes can remain so defined for the remainder of the homing procedure. In the present example, the origin of this system is located at pointon the surface of the ground above the center of the homing transmitter antenna in boring toolat position k=1 with the boring tool at a depth D. The depth at Dcan be measured, for example, by a walk-over locator or using a tape-measure if the initial position of the boring tool has been exposed. Hence, the initial homing transmitter position becomes
In an embodiment where the origin of the coordinate system is defined at point, where the boring tool enters the ground, the origin of the coordinate system is at the center of the transmitter antenna with D=0.
Homing receiver position coordinates designated as X, Zcan be measured before homing begins. In addition, the average length of drill rods LR can determined for use in embodiments where the drill rig does not monitor the length of the drill string. For purposes of the present description, it will be assumed that drill rods are to be counted and that homing command determinations are made on a rod by rod basis such that the average drill rod length is relevant. The user can specify the depth of the target Dbelow the homing receiver so that target position coordinates, designated as X, Zr, can be obtained from
During homing, flux components are measured using antennaof the homing receiver for use in conjunction with the measured pitch, designated as ϕ, of the boring tool at each k position. The homing system utilizes an estimate of pitch measurement uncertainty σand of the measurement uncertainties of the 2 fluxes in the vertical X,Z plane which are denominated as σ,σ, respectively. In addition, measurement uncertainties σ,σ, σare utilized where σis the measurement uncertainty of depth Zat position k, the value σ, is the measurement uncertainty of the position of homing receiveron the X axis, and the value σis the measurement uncertainty of the position of homing receiveron the Z axis. Note that σ=0 since X=0 according to the definition above of the selected coordinate system. It should be appreciated that the various measurement uncertainties can be empirically obtained in a straightforward manner by evaluating and comparing repeat measurements of the quantity of interest. The uncertainty of locator position measurements is readily available from the manufacturer of distance measuring devices. Although the position of the homing receiver can be determined in any suitable manner, suitable handheld or tripod mounted laser devices are readily commercially available for measuring the homing receiver position coordinates. For example, the Leica Disto™ D5 can be used which has a range of over 300 feet and a built-in pitch sensor. In other embodiments, standard surveyor instrumentation can be used to determine the homing receiver position/coordinates prior to homing.
In one embodiment, the method is based on two types of equations, referred to as process equations and measurement equations. The following process equations are chosen where the dot symbol denotes derivatives with respect to arc length s along the axis of the drill rod or drill string:
For vertical homing, the flux components b,binduced at the homing receiver are measured. They can be expressed in terms of transmitter position X,Z, homing receiver position X,Zand pitch ϕ. This leads to the following measurement equation written in vector form as
where
Above, the prime symbol denotes the transpose of a vector.
Equations (5) and (6) are ordinary differential equations for the two unknown transmitter position coordinates X, Z. Vector Equation (7) can be written as two scalar equations for the flux components band balong the X and Z axes. It should be appreciated that these equations represent an initial value problem since Equations (5) and (6) can be integrated along arc length S starting from known initial values X,Zat k=1. Equations (5), (6) and (7) couple flux measurements at the homing receiver to the transmitter position such that enhanced accuracy homing commands can be generated as compared to homing commands that are generated based solely on flux measurements, as in a conventional homing system.
The foregoing initial value problem can be solved using either a nonlinear solution procedure, such as the method of nonlinear least squares, the SIMPLEX method, or can be based on Kalman filtering. The latter will be discussed in detail beginning at an appropriate point below. Initially, however, an application of the SIMPLEX method will be described where the description is limited to the derivation of the nonlinear algebraic equations that are to be solved at each drill-path position. Details of the solver itself are well-known and considered as within the skill of one having ordinary skill in the art in view of this overall disclosure.
The present technique and other solution methods can replace the derivatives {dot over (X)},Ż in Equations (5) and (6) with finite differences that are here written as:
Resulting algebraic equations read:
The flux measurement Equations (7-12) provide two additional algebraic equations written as:
Here, transmitter pitch and fluxes are measured at the (k+1)position. The distance between transmitter and homing receiver is obtained from the corresponding distance vector which reads
Furthermore, we use
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December 18, 2025
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