Position sensing system using magnetic targets

Abstract

A system for sensing relative spatial positions of two physical components uses one or more sensors on one component and a single sensing target on the other component. The sensing target generates a spatially-varying magnetic field along a measurement path corresponding to a selected range of motion between the two physical components, and the sensors measure magnetic field strength in first, second, and third sensing directions. The spatially-varying magnetic field produces first, second, and third signals from the first, second, and third directions. The first and second signals are out of phase, and repeat as the first component moves relative to the second component. The absolute spatial position of the first component relative to second component is known when the third signal satisfies a selected index criterion when the position of the first component coincides with a selected index position of the sensors along the measurement path.

Description

[0001] POSITION SENSING SYSTEM USING MAGNETIC TARGETS FIELD The present disclosure relates in general to systems for sensing a spatial position of a first physical component relative to a second physical component (alternatively referred to as “position sensing systems”). In particular, the present disclosure relates to non-contact position sensing systems using magnetometer sensors carried by the first physical component and permanent- magnet sensing targets carried by the second physical component. BACKGROUND Position sensing systems are commonly used to measure the spatial position (or movement) of a first physical component relative to a second physical component along a measurement path and have one or more sensing elements provided by one or more sensors carried by the first physical component. Each sensing element is associated with a measurement channel and produces a signal that depends on the position of a sensing target carried by the second physical component. The relative movement between the two physical components may be linear, rotational, or curvilinear. In cases where position measurement must have high resolution and also must cover a large range of motion, many position sensing systems have two measurement channels (channel “^^” and channel “^^”) that produce repeating waveform signals with a 90-degree phase difference (also referred to as “two signals in quadrature”) within the measurement range of motion. For example, many commercially available incremental optical encoders produce two repeating square waveform signals in quadrature. Other known position sensing systems produce two repeating sinusoidal waveform signals in quadrature and may be referred to as “sine encoders” or “sine-cosine encoders”. U.S. Patent No. 7,741,839 (Jarrad) discloses a non-contacting position sensor comprising a magnet and a magnetic flux sensor. The magnet generates a flux field with a flux direction that rotates along the length of the magnet. The flux sensor “creates three intermediary electrical signals Sx, Sy, and Sz that are proportional to the strength of the magnetic field in each direction… [and] calculates the output signal by using a proportion of the arctangent of the ratio of these flux densities. This signal has a saw-tooth shape and represents the flux direction that is independent of flux density amplitude variations.” US 7,741,839 further states that “FIG. 10 shows the output signals Sx and Sz from sensor 50 corresponding to the Bx and Bz flux vectors for magnet 60. The Sy signal is not shown in FIG. 10 as it is not needed to determine the position of the magnet 60.” Persons of ordinary skill in the art will observe a discrepancy between the above-quoted text and FIG. 10 in US 7,741,839 since FIG. 10 in fact shows two sinusoidal curves labelled “Sx” and “Sy” and a saw-tooth-shaped curve labelled “Arctan (Sx / Sy)”. Despite the discrepancy in the labelling of the curves, persons of ordinary skill will understand that: • two of the three intermediary electrical signals of the flux sensor are used to calculate the output arctangent signal representing the flux direction; • these two of the three intermediary electrical signals vary sinusoidally as the flux sensor moves along the length of the magnet; and • the third intermediary electrical signal of the flux sensor is not needed to determine the position of the magnet relative to the flux sensor. US 7,741,839 does not disclose use of the third intermediary electrical signal of the flux sensor in determining the position of the magnet relative to the flux sensor. U.S. Patent No. 8,072,209 (Jerance et al.) discloses a non-contacting position sensor comprising at least one permanent magnet and at least one magnetosensitive element. The magnet “generates a magnetic field whose tangential component (X), normal component (Y), and transverse component (Z) relative to the magnet are substantially sinusoidal, over a large portion of the stroke. The components Y and Z have the same phase, while the component X is phase shifted by one quarter of one period.” When a position sensing system produces two signals in quadrature with multiple waves within the measurement range of motion, no combination of two signal values is unique; i.e., the position sensing system will generate the same combination of the two signal values at multiple measurement positions. Consequently, any particular output could occur at multiple positions of the first physical component relative to the second physical component. To overcome this limitation, prior art position sensing systems commonly have a third sensing element associated with a third measurement channel (channel “^^”) to produce a third signal (alternatively referred to as an “indexing signal”). The indexing signal depends on the position of an additional sensing target (alternatively referred to as an “indexing target”) rather than the sensing target(s) for channel ^^and channel ^^. The indexing signal has a unique value associated with a unique spatial position of the first physical component relative to the second physical component along the measurement path. Therefore, when the unique value of the index signal is detected, the unique spatial position of the first physical component relative to the second physical component is known and can be associated with a specific wave of the multiple waves from channels ^^and ^^within the measurement range of motion. BRIEF SUMMARY The present disclosure teaches non-limiting embodiments of a system for sensing a spatial position of a first physical component relative to a second physical component using a single magnetic sensing target (alternatively referred to herein as “a position sensing system”). Position sensing systems in accordance with the present disclosure improve upon prior art magnetic position sensing systems by using only a single sensing target to produce two sinusoidal signals in quadrature and a third “indexing” signal. In contrast, prior art systems use one or more sensing targets to produce two sinusoidal signals in quadrature and an additional sensing target to produce a third indexing signal. One exemplary and non-limiting embodiment of a position sensing system in accordance with the present disclosure comprises: (a) one or more sensors carried by the first physical component for measuring magnetic field strength in a first sensing direction, a second sensing direction, and a third sensing direction, with the third sensing direction not being parallel to the first sensing direction and not being parallel to the second sensing direction; and (b) a single sensing target carried by the second physical component, with the sensing target comprising one or more permanent magnets configured to generate a spatially-varying magnetic field with a selected wavelength that repeats at least once along a measurement path corresponding to a selected range of motion between the first and second physical components; wherein the one or more sensors and the sensing target are configured such that the spatially- varying magnetic field will produce: (A) a first signal from the first sensing direction, wherein the first signal will repeat when the first physical component is moved relative to the second physical component through the selected range of motion; (B) a second signal from the second sensing direction, wherein the second signal will repeat and will be out of phase with the first signal when the first physical component is moved relative to the second physical component through the selected range of motion; and (C) a third signal from the third sensing direction, wherein the third signal will satisfy at least one of one or more selected index criteria when the position of the first physical component is coincident with a selected index position of the one or more sensors along the measurement path, such that the absolute spatial position of the first physical component relative to second physical component will then be known. In one embodiment, the sensing target may comprise a plurality of magnets positioned at a uniform spacing along the measurement path. All of the plurality of magnets may be physically identical, with identical magnetization vector angles (shown in the illustrated examples of this disclosure, by way of non-limiting example only, as 45 degrees), differing only in their positions along the measurement path and the spatial orientations of their magnetization vectors. In the illustrated embodiments of this disclosure, the plurality of magnets are uniformly spaced along the measurement path, and the first and second signals have sinusoidal waveforms having a wavelength equal to twice the magnet spacing. The first and second signals are orthogonal to each other, but this is by way of non-limiting example only. The second signal is out of phase with the first signal, leading the first signal by 90 degrees (i.e., one-quarter of the wavelength of the sinusoidal signals). The third signal may vary monotonically when and as the first physical component moves relative to the second physical component. In one embodiment, the plurality of magnets may comprise two or more sets of magnets. The magnets of at least one of the two or more sets of magnets are oriented with their magnetization vectors having a non-zero component parallel with the third sensing direction. In one particular variant embodiment, the plurality of magnets may comprise: • a first set of magnets each oriented with its magnetization vector having a non-zero component toward the third sensing direction; and • a second set of magnets each oriented with its magnetization vector having a non-zero component opposite the third sensing direction. In other embodiments, the single sensing target comprises one or more magnets that extend the length of the measurement path. The magnets are magnetized with a spatially-varying magnetic field having a component that is parallel to the third sensing direction that varies spatially along the measurement path. The one or more magnets may be magnetized (by way of non- limiting example) using a method in accordance with U.S. Patent No. 7,741,839. In embodiments in which the sensing target comprises a plurality of magnets, the magnets may be physically identical (including their magnetizations), differing only with respect to their orientations and positions along the measurement path. However, this is not essential, and variant embodiments may comprise magnets that are not physically identical. By way of non-limiting examples, at least one of the selected index criteria may be (1) that the third signal equals a selected threshold value, (2) that the third signal is greater than a selected threshold value, or (3) that the third signal is less than a selected threshold value. As further non-limiting examples, the selected index criteria may be based on a combination of the first, second, and third signals, or may be based on a gap distance between the one or more sensors and the sensing target. The gap distance may be determined, for example, from a magnitude of a two-dimensional vector defined by the first signal and the second signal, or from a magnitude of a three-dimensional vector defined by the first signal, the second signal, and the third signal. Other non-limiting examples of selected index criteria include: • that the third signal equals a selected threshold value and has a positive slope at the selected threshold value; • that the third signal equals a selected threshold value and has a negative slope at the selected threshold value; • that the third signal is greater than a selected threshold value along a selected interval of the measurement path that is less than the selected wavelength; • that the third signal is less than a selected threshold value along a selected interval of the measurement path that is less than the selected wavelength; • that the third signal is greater than a first threshold value, and less than a second threshold value; and • that the third signal is greater than a first threshold value, and less than a second threshold value, wherein the first threshold value corresponds to a first position of the first physical component relative to the second physical component and the second threshold value corresponds to a second position of the first physical component relative to the second physical component, wherein the interval between the first and second position is less than one wavelength long. • The system as in the previous claim, if said selected index criterion is met then the position of the first physical component relative to the second physical component will be known to be within said interval. In one variant embodiment, there are at least two selected index criteria, with the first selected index criterion corresponding to a first position of the first physical component relative to the second physical component, and the second selected index criterion corresponding to a second position of the first physical component relative to the second physical component, wherein the interval between the first and second positions is less than one wavelength long, and wherein the first and second selected index criteria form a selected index interval criterion. If the third signal is between the first selected index criterion threshold and the second index criterion threshold, then the selected index interval criteria will have been satisfied. If the selected index interval criteria have been satisfied, then the position of the first physical component relative to the second physical component will be known to be within the interval between the first position and the second position. As will be apparent to persons of ordinary skill in the art, embodiments of position sensing systems in accordance with the present disclosure may use or incorporate one or more processors or processing circuits configured to monitor the one or more sensors and to collect data from the first, second, and third signals. The one or more processors may be configured to track relative movement of the first and second physical component using any suitable known method. As well, the one or more processors can be configured to detect when the third signal satisfies any one of the one or more selected index criteria, in which event the absolute position of the first physical component relative to the second physical component will be known and recorded. By way of non- limiting example, one or more such processors or processing circuits could be provided in the form of microprocessor, microcomputers, digital logic circuits, FPGAs (field-programmable gate arrays), or ASICs (application-specific integrated circuits). Alternatively, the functionalities of such processors or processing circuits could be realized, in whole or in part, using analog electronics that effectively have the same functionalities. BRIEF DESCRIPTION OF DRAWINGS Embodiments in accordance with the present disclosure will now be described with reference to the accompanying figures, in which numerical references denote like parts, and in which: FIGURE 1 is a diametric schematic view of a magnetometer sensor for measuring magnetic field strength in three orthogonal sensing directions. FIGURE 2 is a diametric schematic view of a permanent magnet having a component- level cartesian coordinate system defined by axes ^′, ^′, and ^′. FIGURE 3 depicts the angle of magnetization of the permanent magnet in FIG 2 in the ^′-^′ plane (i.e., a plane defined by the ^′ and ^′ axes). FIGURE 4 is a diametric schematic view of a first exemplary embodiment of a position sensing system in accordance with the present disclosure comprising a sensor as in FIG.1 and a sensing target, with the sensing target comprising a plurality of permanent magnets as in FIG. 2. FIGURE 5 is a graph showing example measurement data from the first and second sensing directions of the sensor as it moves along the measurement path of the position sensing system of FIG. 4. FIGURE 6 is a graph showing a measurement vector angle calculated from the measurement signal data in FIG. 5. FIGURE 7 is a graph showing example measurement data from the third sensing direction of the sensor as it moves along the measurement path of the position sensing system of FIG. 4. FIGURE 8 is a graph showing measurement vector angle ^^^as related to gap distance for system 100 at three different sensor positions. FIGURE 9 is a graph showing signal ^^as related to gap distance for system 100 at three different sensor positions. FIGURE 10 is a graph showing the magnitude of a two-dimensional measurement vector ^^^as related to gap distance at three different sensor positions. FIGURE 11A is a diametric schematic view of a second exemplary embodiment of a position sensing system in accordance with the present disclosure comprising a sensor as in FIG. 1 and a sensing target, with the sensing target comprising a plurality of permanent magnets as in FIG. 2. FIGURE 11B is a diametric schematic view of a variant embodiment of the position sensing system in FIG. 11A wherein the sensing target is configured such that index position 212B is offset compared to index position 212A. FIGURE 12 is a graph showing example measurement data from the first and second sensing directions of the sensor as it moves along the measurement path of the position sensing systems in FIGS. 11A and 11B. FIGURE 13 is a graph showing a measurement vector angle calculated from the measurement signal data in FIG. 12. FIGURE 14 is a graph showing example measurement data from the third sensing direction of the sensor as it moves along the measurement path of the position sensing systems of FIG. 11A and FIG. 11B. FIGURE 15 is a diametric schematic view of a third exemplary embodiment of a position sensing system in accordance with the present disclosure comprising a sensor as in FIG. 1 and a sensing target, with the sensing target comprising a plurality of permanent magnets as in FIG. 2. FIGURE 16 is a graph showing example measurement data from the first and second sensing directions of the sensor as it moves along the measurement path of the position sensing system of FIG. 15. FIGURE 17 is a graph showing a measurement vector angle calculated from the measurement signal data in FIG. 15. FIGURE 18 is a graph showing example measurement data from the third sensing direction of the sensor as it moves along the measurement path of the position sensing system of FIG. 15. FIGURE 19A is a diametric schematic view of a fourth exemplary embodiment of a position sensing system in accordance with the present disclosure comprising a sensor as in FIG.1 and a sensing target, with the sensing target comprising a plurality of permanent magnets. FIGURE 19B is a diametric schematic view of a variant embodiment of the position sensing system in FIG. 19A wherein the sensing target is configured such that index position 412B is offset compared to index position 412A. FIGURE 20 is a graph showing example measurement data from the first and second sensing directions of the sensor as it moves along the measurement path of the position sensing system of FIG. 19A and FIG. 19B. FIGURE 21 is a graph showing a measurement vector angle calculated from the measurement signal data in FIG. 20. FIGURE 22 is a graph showing example measurement data from the third sensing direction of the sensor as it moves along the measurement path of the position sensing systems in FIGS. 19A and 19B. FIGURE 23 is a diametric schematic view of a sensor assembly comprising two magnetometer sensors for measuring magnetic field strength in three sensing directions. FIGURE 24 is a diametric schematic view of a first exemplary embodiment of a position sensing system in accordance with the present disclosure comprising a sensor assembly as in FIG. 23 and a sensing target comprising a plurality of permanent magnets as in FIG. 2. FIGURE 25 is a graph showing example measurement data from the first and second sensing directions of the sensor assembly as it moves along the measurement path of the position sensing system of FIG. 24. FIGURE 26 is a graph showing a measurement vector angle calculated from the measurement signal data in FIG. 25. FIGURE 27 is a graph showing example measurement data from the third sensing direction and a derived signal as the sensor assembly moves along the measurement path of the position sensing system of FIG. 24. DETAILED DESCRIPTION FIG.1 is a diametric schematic view of a magnetometer sensor 101. Sensor 101 measures magnetic field strength in a first sensing direction ^^, a second sensing direction ^^orthogonal to sensing direction ^^, and a third sensing direction ^^orthogonal to both sensing direction ^^and sensing direction ^^. FIG. 2 is a diametric schematic view of a permanent magnet ^, shown by way of non- limiting example as being shaped as a rectangular prism and having a component-level cartesian coordinate system comprising three orthogonal axes ^′, ^′, and ^′. Permanent magnet ^ has a magnetization represented by a pseudovector ^, as shown in FIGS. 2 and 3. Pseudovector ^ (alternatively referred to as “magnetization vector ^”) is oriented in the ^^-^′ plane orthogonal to the ^′ axis and at a selected magnetization angle ^ relative the ^′ axis. In this non-limiting embodiment, the selected magnetization angle ^ is 45 degrees. First Exemplary Embodiment FIG. 4 is a diametric schematic view of a first non-limiting embodiment 100 of a position sensing system in accordance with the present disclosure. System 100 has three orthogonal global axes ^, ^, and ^ and a linear measurement path 103 parallel to the ^ axis. System 100 comprises a sensor 101 as in FIG. 1 carried by a first physical component and a sensing target 102 carried by a second physical component. Measurement path 103 is associated with a range of relative motion between the first and second physical components. Sensing target 102 comprises a plurality of permanent magnets ^ arranged along measurement path 103 to generate a spatially- varying magnetic field. When the first physical component moves relative to the second physical component, sensor 101 will move along measurement path 103 at a gap distance ^ above sensing target 102. Permanent magnets ^ of sensing target 102 are positioned along measurement path 103 at a uniform spacing ^. Permanent magnets ^ may be identical in terms of their physical shape and size and their selected magnetization angle ^ (shown by way of non-limiting example as 45 degrees), and differing only in their individual physical orientations and positions along measurement path 103. FIG. 4 shows eight permanent magnets (labeled ^^through ^^) of sensing target 102.Odd-numbered permanent magnets (e.g., ^^,^^,^^, ^^) are oriented with the direction of theirmagnetization vectors ^ having a component oriented toward the negative ^ axis. Even-numbered permanent magnets (e.g., ^^,^^, ^^,^^) are oriented with the direction of theirmagnetization vectors ^ having a component oriented toward the positive ^ axis. Permanent magnets located along the negative portion of the ^ axis (e.g., ^^through ^^) are oriented with their magnetization vectors ^ having a component oriented toward the negative ^ axis. Permanent magnets located along the positive portion of the ^ axis (e.g., ^^through ^^) are oriented with their magnetization vectors ^ having a component oriented toward the positive ^ axis. Additional permanent magnets ^ may be provided along the measurement path to the left and right of the eight magnets shown in FIG. 4, as indicated by ellipsis symbols, to extend the measurement range. Additional permanent magnets ^ to the left would be arranged to repeat the pattern (i.e., spacing and alternating orientations) of permanent magnets ^^through ^^. Additional permanent magnets ^ to the right would be arranged to repeat the pattern of permanent magnets ^^through ^^. FIGS. 5 and 7 are graphs showing measurement signals from sensor 101 as it moves along measurement path 103 of position sensing system 100 (as the first physical component moves relative to the second physical component). FIG. 5 shows a signal ^^from sensing direction ^^and a signal ^^from sensing direction ^^. Signals ^^and ^^are sinusoidal with a wavelength ^ that is twice the magnet spacing ^. Signal ^^is out of phase with signal ^^, leading by 90 degrees of phase (i.e., one quarter of the wavelength ^) of the sinusoidal signals. FIG. 7 shows a signal ^^from sensing direction ^^, which varies monotonically with sensor position along the measurement path. A two-dimensional measurement vector ^^^in the ^-^ plane may be defined by signals ^^^ = !"^ "^#An associated measurement vector magnitude‖^^^‖may be calculated as follows: An associated measurement vector angle ^^^may be calculated using a two-argument variant ofthe arctangent function to produce an output in the range −( < ^^^ ≤ ( radians (i.e., -180 degrees< ^^^ ≤ 180 degrees): In terms of the more common one-argument arctangent function atan 4567, the two-argumentvariant of the arctangent function atan228, 93 may be expressed as: FIG. 6 is a graph showing measurement vector angle ^^^calculated from signals ^^and ^^shown in FIG. 5. Measurement vector angle ^^^may be used to determine the position and direction of motion of sensor 101 as it moves along measurement path 103. Measurement vector angle ^^^decreases when sensor 101 moves in the positive ^ axis direction, and measurement vector angle ^^^increases when sensor 101 moves in the negative ^ axis direction. (This is equivalent to determining whether signal ^^leads or lags signal ^^, which may be done using prior art signal processing techniques.) However, measurement vector angle ^^^does not provide sufficient information by itself to determine a unique position of sensor 101 because signals ^^and ^^(and, therefore, measurement vector angle ^^^) repeat every wavelength ^ along measurement path 103. As illustrated in FIG. 7, selected index criteria based on signal ^^may be used to identify selected index positions of sensor 101 along measurement path 103 (i.e., positions of the first physical component relative to the second physical component). In this first exemplary and non- limiting embodiment, a first selected index criterion may be used to identify a first index position 111 located at sensor position 4.5, where signal ^^equals a first selected threshold value of 0 mT (milliTesla). In general, signals ^^, ^^, and ^^will vary with the gap distance ^. However, the measurement vector angle ^^^, which is calculated from the ratio of signals ^^to ^^, is insensitive to gap distance ^. For illustration, FIG.8 shows that the measurement vector angle ^^^does not change with gap distance ^ at three different sensor positions (which is also generally true at all sensor positions) along measurement path 103. FIG.9 is a graph showing the relationships between signal ^^and gap distance ^ of system 100 at sensor positions 4.5, 5.5, and 7.5. Signal ^^is 0 mT at sensor position 4.5, where it is also insensitive to variations in gap distance ^. Thus, the selected index criterion used to identify index position 111 (i.e., sensor position 4.5 in this example) is independent of gap distance ^. Non-zero threshold values of signal ^^may also be used for selected index criteria. A second selected index criterion may be used to identify a second index position 112 located at sensor position 3.5, where signal ^^equals a second selected threshold value of -12.1 mT. A third selected index criterion may be used to identify a third index position 113 located at sensor position 5.5, where signal ^^equals a third selected threshold value of 12.1 mT. In applications where gap distance ^ varies, a single value of signal ^^may not provide sufficient information to identify a unique sensor position. For example, consider sensor positions 5.5 and 7.5 which both correspond to a measurement vector angle ^^^of 180 degrees due to the repeating character of signals ^^to ^^. Referring to FIG.9, a signal ^^reading of 12.1 mT might indicate either a sensor position of 5.5 at a gap distance ^ of 4.0, or a sensor position of 7.5 at a gap distance ^ of 7.5. This uncertainty may be resolved by determining gap distance ^ and then adjusting the threshold value of the selected index criterion according to gap distance ^. As a non-limiting example, gap distance ^ may be determined based on measurement vector magnitude‖^^^‖. Sensor position may be determined from measurement vector angle ^^^, which is insensitive to gap distance. FIG.10 shows that at sensor positions 4.5, 5.5, and 7.5, the relationships between measurement vector magnitude‖^^^‖and gap distance ^ are the same and are monotonic. Thus, gap distance ^ may be determined from signals ^^and ^^, and then an appropriate threshold value may be chosen for the selected index criterion for index position 113. When any one selected index criterion is satisfied, the absolute position of sensor 101 along measurement path 103 is then known. In this first exemplary and non-limiting embodiment, the selected index positions along the measurement path occur at measurement vector angles ^^^of 0 degrees and 180 degrees. It will be apparent to persons of ordinary skill in the art that index positions may be selected at other locations corresponding to other values of measurement vector angle ^^^. In alternative embodiments, gap distance ^ may be determined using a three-dimensional measurement vector ^^^^instead of two-dimensional measurement vector ^^^. Three- dimensional measurement vector ^^^^may be defined by signals ^^, ^^and ^^. ^^^^ = !"^ "^ "^# An associated measurement vector magnitude ‖^^^^‖ may be calculated which also has a monotonic relationship with gap distance ^. Second Exemplary Embodiment FIG. 11A is a diametric schematic view of a second non-limiting embodiment 200A of a position sensing system in accordance with the present disclosure. System 200A has three orthogonal global axes ^, ^, and ^ and a linear measurement path 203 parallel to the ^ axis. System 200A comprises a sensor 101 as in FIG. 1 carried by a first physical component and a sensing target 202A carried by a second physical component. Measurement path 203 is associated with a range of relative motion between the first and second physical components. Sensing target 202A comprises a plurality of permanent magnets ^ arranged along measurement path 203 to generate a spatially varying magnetic field. When the first physical component moves relative to the second physical component, sensor 101 will move along measurement path 203 at a gap distance ^ above sensing target 202A. Permanent magnets ^ of sensing target 202A are positioned along measurement path 203 at a uniform spacing ^. Permanent magnets ^ may be identical in terms of their physical shape and size and their selected magnetization angle ^ (shown by way of non-limiting example as 45 degrees), and differing only in their individual physical orientations and positions along measurement path 203. FIG.11A shows 18 permanent magnets (labeled ^^through ^^^) of sensing target 202A.Odd-numbered permanent magnets (e.g., ^^,^^,^^, … ,^^^) are oriented with the direction oftheir magnetization vectors ^ having a component oriented toward the negative ^ axis. Even-numbered permanent magnets (e.g., ^^,^^, ^^, … ,^^^) are oriented with the direction of theirmagnetization vectors ^ having a component oriented toward the positive ^ axis. Permanent magnets ^^through ^^and ^^^through ^^^are oriented with the direction of their magnetization vectors ^ having a component oriented toward the negative ^ axis. Permanent magnets ^^through ^^^are oriented with the direction of their magnetization vectors ^ having a component oriented toward the positive ^ axis. Additional permanent magnets ^ may be provided along the measurement path to the left and right of the eighteen magnets shown in FIG. 11A, as indicated by ellipsis symbols, to extend the measurement range. Additional permanent magnets ^ to the left would be arranged to repeat the pattern (i.e., spacing and alternating orientations) of permanent magnets ^^through ^^. Additional permanent magnets ^ to the right would be arranged to repeat the pattern of permanent magnets ^^^through ^^^. FIG.11B is a diametric schematic view of a variant embodiment 200B of position sensing system 200A. System 200B comprises sensor 101 carried by a first physical component and a sensing target 202B carried by a second physical component. Sensing target 202B differs from sensing target 202A by the orientation of one magnet. Nine magnets in system 200A are oriented with the direction of their magnetization vectors ^ having a component oriented toward the negative ^ axis, compared to eight magnets in system 200A. The orientation of permanent magnet ^^^of sensing target 202B is the same as the orientation of permanent magnet ^^^. In contrast, the orientation of permanent magnet ^^^of sensing target 202A in FIG. 11A is the same as the orientation of permanent magnet ^^^. FIGS. 12 and 14 are graphs showing measurement signals from sensor 101 as it moves along measurement path 203 of position sensing systems 200A and 200B (as the first physical component moves relative to the second physical component). FIG. 12 shows a signal ^^from sensing direction ^^and a signal ^^from sensing direction ^^. Signals ^^and ^^are sinusoidal with a wavelength ^ that is twice the magnet spacing ^. Signal ^^is out of phase with signal ^^, leading by 90 degrees of phase (i.e., one quarter of the wavelength ^) of the sinusoidal signals. FIG. 14 shows a signal ^^^for system 200A and a signal ^^Gfor system 200B from sensing direction ^^. FIG. 13 is a graph showing a measurement vector angle ^^^calculated from signals ^^and ^^as sensor 101 moves along measurement path 203. Measurement vector angle ^^^may be used to determine the position and direction of motion of sensor 101 as it moves along measurement path 203. Measurement vector angle ^^^decreases when sensor 101 moves in the positive ^ axis direction, and measurement vector angle ^^^increases when sensor 101 moves in the negative ^ axis direction. However, measurement vector angle ^^^alone does not provide sufficient information to determine a unique position of sensor 101 because signals ^^and ^^ (and, therefore, measurement vector angle ^^^) repeat in value every wavelength ^ along measurement path 203. As illustrated in FIG. 14, selected index criteria based on signal ^^^may be used to identify selected index positions of sensor 101 along measurement path 203 (i.e., positions of the first physical component relative to the second physical component). In this second exemplary and non-limiting embodiment, a first selected index criterion may be used to identify a first selected index position 211 located at sensor position 4.5, where signal ^^^has a positive slope at a selected first threshold value of 0 mT. A second selected index criterion may be used to identify a second selected index position 212A located at sensor position 14.5 where signal ^^^has a negative slope at a second selected threshold value of 0 mT. Index point 211 can be distinguished from index point 212A by the slope of signal ^^^. When one selected index criterion is satisfied, the absolute position of sensor 101 along measurement path 203 is then known. For system 200B, the first selected criterion and first selected index position 211 are the same as in system 200A. The second selected index criterion for system 200B may be defined similarly as in system 200A, wherein a second selected index position 212B is located at sensor position 13.5 where signal ^^Ghas a negative slope at a second selected threshold value of 0 mT. Additionally or alternatively, index position 211 can be distinguished from index position 212B based on the measurement vector angle ^^^, which has a value of zero degrees at index position 211 and a value of 180 degrees at index position 212B. When one selected index criterion is satisfied, the absolute position of sensor 101 along measurement path 203 is then known. Since the measurement vector angle ^^^is calculated from signals ^^and ^^, selection criteria equivalent to those disclosed above may be expressed in terms of signals ^^, ^^and ^^^for system 200A and in terms of signals ^^, ^^, and ^^Gfor system 200B. Third Exemplary Embodiment FIG.15 is a diametric schematic view of a third non-limiting embodiment 300 of a position sensing system in accordance with the present disclosure. System 300 has three orthogonal global axes ^, ^, and ^ and a linear measurement path 303 parallel to the ^ axis. System 300 comprises a sensor 101 as in FIG. 1 carried by a first physical component and a sensing target 302 carried by a second physical component. Measurement path 303 is associated with a range of relative motion between the first and second physical components. Sensing target 302 comprises a plurality of permanent magnets ^ arranged along measurement path 303 to generate a spatially varying magnetic field. When the first physical component moves relative to the second physical component, sensor 101 will move along measurement path 303 at a gap distance ^ above sensing target 302. The permanent magnets ^ of sensing target 302 are placed along measurement path 303 with a uniform spacing ^. The permanent magnets ^ are physically identical, have the same selected magnetization angle ^ of 45 degrees, and differ only in their physical orientation and placement location along measurement path 303. FIG.15 shows ten permanent magnets (labeled ^^through ^^H) of sensing target 302. Odd-numbered permanent magnets (e.g., are oriented with the direction of their magnetization vectors ^ having acomponent oriented toward the negative ^ axis. Even-numbered permanent magnets(^^,^^,^^, are oriented with the direction of their magnetization vectors ^ having acomponent oriented toward the positive ^ axis. Permanent magnets ^^and ^^are oriented with the direction of their magnetization vectors ^ having a component oriented toward the positive ^ axis. The remaining permanent magnets of sensing target 302 are oriented with the direction of their magnetization vectors ^ having a component oriented toward the negative Z axis. Additional permanent magnets ^ may be provided along the measurement path to the left and right of the ten magnets shown in FIG. 15, as indicated by ellipsis symbols, to extend the measurement range. Additional permanent magnets ^ to the left would be arranged to repeat the pattern (i.e., spacing and alternating orientations) of permanent magnets ^^through ^^. Additional permanent magnets ^ to the right would be arranged to repeat the pattern of permanent magnets ^^through ^^H. FIGS. 16 and 18 are graphs showing measurement signals from sensor 101 as it moves along measurement path 303 of position sensing system 300 (as the first physical component moves relative to the second physical component). FIG. 16 shows a signal ^^from sensing direction ^^and a signal ^^from sensing direction ^^. Signals ^^and ^^are sinusoidal with a wavelength ^ that is twice the magnet spacing ^. Signal ^^is out of phase with signal ^^, leading by 90 degrees of phase (i.e., one quarter of the wavelength ^) of the sinusoidal signals. FIG. 17 is a graph showing a measurement vector angle ^^^calculated from signals ^^and ^^as sensor 101 moves along measurement path 303. FIG.18 shows a signal ^^from sensing direction ^^. Measurement vector angle ^^^may be used to determine the position and direction of motion of sensor 101 as it moves along measurement path 303. However, measurement vector angle ^^^does not provide sufficient information by itself to determine a unique position of sensor 101 because signals ^^and ^^(and, therefore, measurement vector angle ^^^) repeat in value every wavelength ^ along measurement path 303. As illustrated in FIG. 18, selected index criteria based on signal ^^^may be used to identify selected index positions of sensor 101 along measurement path 303 (i.e., positions of the first physical component relative to the second physical component). In this third exemplary and non-limiting embodiment, a first selected index criterion may be used to identify a first selected index location 311 located at sensor position 5.5, where signal ^^exceeds a selected threshold value of -3.48 mT and measurement vector angle ^^^is zero. A second selected index criterion may be used to identify a second selected index position 312 located at sensor position 4.5, where signal ^^has a positive slope at a second selected threshold value of -3.48 mT. A third selected index criterion may be used to identify a third selected index position 313 located at sensor position 6.5, where signal ^^has a negative slope at a third selected threshold value of -3.48 mT. When one selected index criterion is satisfied, the absolute position of sensor 101 along measurement path 303 is then known. Alternatively, a selected index criterion may be used to identify a selected index interval that is less than one wavelength ^ long, and then any selected index position within the selected index interval may be identified using measurement vector angle ^^^. As an example, a selected index interval between sensor positions 4.5 and 6.5 may be identified where signal ^^is greater than a selected threshold value of -3.48 mT, and then index position 311 is located where measurement vector angle ^^^is 0 degrees. Fourth Exemplary Embodiment FIG. 19A is a diametric schematic view of a fourth non-limiting embodiment 400A of a position sensing system in accordance with the present disclosure. System 400A has three orthogonal global axes, ^, ^, and ^ and a linear measurement path 403 parallel to the ^ axis. System 400A comprises a sensor 101 as in FIG. 1 carried by a first physical component and a sensing target 402A carried by a second physical component. Measurement path 403 is associated with a range of relative motion between the first and second physical components. Sensing target 402A comprises a plurality of permanent magnets arranged along measurement path 403 to generate a spatially varying magnetic field. When the first physical component moves relative to the second physical component, sensor 101 will move along measurement path 403 at a gap distance ^ above sensing target 402A. Permanent magnets of sensing target 402A are positioned along measurement path 403 with uniform spacing ^. FIG.19A shows eighteen permanent magnets (labeled through ^^^)of sensing target 402A. Odd-numbered permanent magnets (e.g., ^^,^^, … ,^^^) are orientedwith the direction of their magnetization vectors ^ having a component oriented toward thenegative ^ axis. Even-numbered permanent magnets (e.g., ^^,^^, … ,^^^) are oriented with thedirection of their magnetization vectors ^ having a component oriented toward the positive ^ axis. Permanent magnets ^^,^^,^^^, and ^^^have a selected magnetization vector angle ^^of 45 degrees. Permanent magnets ^^and ^^are oriented with the direction of their magnetization vectors ^ having a component oriented toward the positive ^ axis. Permanent magnets ^^^and ^^^are oriented with the direction of their magnetization vectors ^ having a component oriented toward the negative ^ axis. The remaining permanent magnets of sensing target 402A have a selected magnetization angle ^Hof zero degrees, such that their magnetization vectors ^ are orthogonal to the ^ axis. Additional permanent magnets ^ may be provided along the measurement path to the left and right of the eighteen magnets shown in FIG. 19A, as indicated by ellipsis symbols, to extend the measurement range. Additional permanent magnets ^ to the left would be arranged to repeat the pattern (i.e., spacing and alternating orientations) of permanent magnets ^^and ^^. Additional permanent magnets ^ to the right would be arranged to repeat the pattern of permanent magnets ^^^and ^^^. FIG.19B is a diametric schematic view of a variant embodiment 400B of position sensing system 400A. System 400B comprises sensor 101 carried by a first physical component and a sensing target 402B carried by a second physical component. Sensing target 402B differs from sensing target 402A by the orientation of two specific magnets; i.e., the orientations of permanent magnets ^^^and ^^^of sensing target 402B are reversed in comparison to the orientations of permanent magnets ^^^and ^^^of sensing target 402A. FIG.20 and 22 show measurement signals from sensor 101 as it moves along measurement path 403 of position sensing systems 400A and 400B (as the first physical component moves relative to the second physical component). FIG. 20 shows a signal ^^from sensing direction ^^and a signal ^^from sensing direction ^^. Signals ^^and ^^are sinusoidal with a wavelength ^ that is twice the magnet spacing ^. Signal ^^is out of phase with signal ^^, leading by 90 degrees of phase (i.e., one quarter of the wavelength ^) of the sinusoidal signals. FIG.21 a graph showing a measurement vector angle ^^^calculated from signals ^^and ^^as sensor 101 moves along measurement path 403. FIG.22 shows a signal ^^^for system 400A and a signal ^^Gfor system 400B from sensing direction ^^. Measurement vector angle ^^^may be used to determine the position and direction of motion of sensor 101 as it moves along measurement path 403. However, measurement vector angle ^^^alone does not provide sufficient information to determine a unique position of sensor 101 because signals ^^and ^^, and thus measurement vector angle ^^^repeat in value every wavelength ^ along measurement path 403. As illustrated in FIG. 22, selected index criteria based on signal ^^^may be used to identify selected index positions of sensor 101 along measurement path 403 (i.e., positions of the first physical component relative to the second physical component). In this fourth exemplary and non-limiting embodiment, a first selected index criterion may be used to identify a first index position 411 located at sensor position 5.5, where signal ^^^is greater than a selected threshold value of 17.5 mT and measurement vector angle ^^^is zero. A second selected index criterion may be used to identify a second index position 412A located at sensor position 13.5 where signal ^^^is less than a selected threshold value of -17.5 mT and measurement vector angle ^^^is zero. A third selected index criterion may be used to identify a third index position 413 located at sensor position 4.5, where signal ^^^has a positive slope at a third selected threshold value of 17.5 mT. A fourth selected index criterion may be used to identify a fourth index position 414 located at sensor position 6.5, where signal ^^^has a negative slope at a fourth selected threshold value of 17.5 mT. A fifth selected index criterion may be used to identify a fifth index position 415 located at sensor position 12.5, where signal ^^^has a negative slope at a fifth selected threshold value of -17.5 mT. A sixth selected index criterion may be used to identify a sixth index position 416 located at sensor position 14.5, where signal ^^^has a positive slope at a sixth selected threshold value of -17.5 mT. Determining the slope of signal ^^^requires measuring the direction of movement of the first physical component relative to the second physical component, which may be done using measurement vector angle ^^^(and thus, using signals ^^and ^^). When one selected index criterion is satisfied, the absolute position of sensor 101 along measurement path 403 is then known. Alternatively, a selected index criterion may be used to identify a selected index interval that is less than one wavelength ^ long, and then any selected index position within the selected index interval may be identified using measurement vector angle ^^^. As examples with systems 400A and 400B, a selected index interval between sensor positions 4.5 and 6.5 may be identified where signal ^^^is greater than a selected threshold value of 17.5 mT, and then index position 411 is located where measurement vector angle ^^^is 0 degrees. With system 400A, a selected index interval between sensor positions 12.5 and 14.5 may be identified where signal ^^^is less than a selected threshold value of -17.5 mT, and then index position 412A is located where measurement vector angle ^^^is 0 degrees. With the teachings of the present disclosure, it will be readily apparent to persons of ordinary skill in the art that a sensing target may comprise more than two sets of magnets having different magnetization vector angles and suitably arranged to define additional selected index criteria. For system 400B, the first, third, and fourth selected index criteria and selected index positions 411, 413 and 414 are the same as in system 400A. The second, fifth, and sixth index criteria for system 400B may be defined similarly as in system 200A, wherein: • a second index position 412B is located at sensor position 14.5 where signal ^^Gis less than a second selected threshold value of -17.5 mT and the value of measurement vector angle ^^^is 180 degrees; • a fifth index position 415B is located at sensor position 13.5, where signal ^^Ghas a negative slope at a fifth selected threshold value of -17.5 mT; and • a sixth index position 416B is located at sensor position 15.5 where signal ^^Ghas a positive slope at a sixth selected threshold value of -17.5 mT. When one selected index criterion is satisfied, the absolute position of sensor 101 along measurement path 403 is then known. Fifth Exemplary Embodiment FIG. 23 is a diametric schematic view of a sensor assembly 501 comprising a bi-axial magnetometer sensor 501A and a single-axis magnetometer sensor 501B for measuring magnetic field strength in three sensing directions. FIG.24 is a diametric schematic view of a fifth non-limiting embodiment 500 of a position sensing system in accordance with the present disclosure. System 500 has three orthogonal global axes J, K, and ^ and a linear measurement path 103 parallel to the J axis. System 500 comprises sensor assembly 501 as in FIG.23 and sensing target 102 (identical to sensing target 102 of system 100 shown in FIG. 4). Sensor 501A measures magnetic field strength in a first sensing direction ^^parallel to the ^ axis, and in a third sensing direction ^^oriented in the ^-^ plane at a selected angle ϒ of 45 degrees from sensing direction ^^. Sensor 501B measures magnetic field strength in a second sensing direction ^^also aligned with the J axis and is located a distance of one quarter wavelength ^ from sensor 501A. Sensing target 102 comprises a plurality of permanent magnets ^ arranged along measurement path 103 to generate a spatially varying magnetic field. When the first physical component moves relative to the second physical component, sensor assembly 501 will move along measurement path 103 at a gap distance ^ above sensing target 102. FIG. 25 is a graph showing a signal ^^from sensing direction ^^and a signal ^^from sensing direction ^^as sensor assembly 501 moves along measurement path 103 of system 500 (as the first physical component moves relative to the second physical component). These signals and the calculated measurement vector angle ^^^(shown in FIG. 26) are the same as signals ^^and ^^and the measurement vector angle ^^^of system 100 shown in FIGS. 5 and 6. Measurement vector angle ^^^may be used to determine the position and direction of motion of sensor assembly 501 as it moves along measurement path 103. However, measurement vector angle ^^^alone does not provide sufficient information to determine a unique position of sensor 101 because signals ^^and ^^, and thus measurement vector angle ^^^repeat in value every wavelength ^ along measurement path 103. FIG.27 is a graph showing a signal ^^from sensing direction ^^of system 500 as sensor assembly 501 moves along measurement path 103 of system 500 (as the first physical component moves relative to the second physical component). A derived signal ^′^may be calculated from signals ^^and ^^, where derived signal ^′^is a component of signal ^^that is orthogonal to signal ^^and in the direction of the ^ axis: ""′ ^ "^ =s n N − ^i tanNAs illustrated in FIG.27, derived signal ^′^of system 500 is the same as signal ^^of system 100 (shown in FIG. 7). Selected index criteria based on derived signal ^′^(and thus based on signal ^^from third sensing direction ^^) may be used to identify selected index positions (or selected index intervals of signals ^^and ^^) along measurement path 103. The selected index criteria applied to signal ^^of system 100 to identify selected index positions 111, 112, and 113 may be applied to derived signal ^′^of system 500 to identify selected index positions 511, 512, and 513. When one selected index criterion is satisfied, the absolute position of sensor assembly 501 along measurement path 103 is then known. Additional Discussion In the above-disclosed non-limiting embodiments, repeating signals ^^and ^^are orthogonal (i.e., having a phase difference of 90 degrees). However, it is not essential for these repeating signals to be orthogonal to one another. Methods to correct for non-orthogonality can be found in the prior art (such as, for example, on page 16 in Texas Instruments document “TIDUC07” from March 2022, and on page 10 in Allegro document “AN296280” from March 2018). It will be readily appreciated by persons of ordinary skill in the art that measurement vector OJK(calculated from repeating signals P^and P^) is sufficient to identify the position and movement of the first physical component relative to the second physical component within any single wave of the spatially-varying magnetic field along the measurement path. Thus, identifying an index position along the measurement path also identifies an index interval corresponding to a specific wave of the spatially-varying magnetic field along the measurement path. Furthermore, identifying a selected index interval of the spatially-varying magnetic field that is less than one wavelength long also identifies any selected index points within the selected index interval. In the position sensing system embodiments described and illustrated herein, sensing targets may comprise a plurality of magnets, each individual magnet having uniform magnetization. but this is by way of non-limiting example only. Sensing targets may comprise one or more permanent magnet that extend the length of the measurement path and are magnetized with a spatially-varying magnet field using a method in accordance with US 7,741,839. FIG. 11 of US 7,741,839 shows a “magnetizing fixture 200” for a “magnet 60”. Magnetizing fixture 200 includes a “wire 202” having U-shaped portions that lie on a plane parallel to the ^-^ plane. Magnetizing fixture 200 creates a magnetization pattern in magnet 60 with a flux direction that changes or rotates in the ^-^ plane along the length of the magnet 60. Sensing targets may comprise a magnet made of a flexible magnetic material that is twisted along the measurement path such that the third signal ^^varies as a function of the position of the first physical component relative to the second physical component. Instead of twisting the magnet after magnetization, magnetizing fixture 200 may be modified by twisting the U-shaped portions of wire 202 around the ^ axis of magnetizing fixture 200 which creates a corresponding twist in the magnetization pattern of the magnet. In the position sensing system embodiments described and illustrated herein, the relative movement between the two physical components may follow a straight (linear) measurement path, but this is by way of non-limiting example only. In alternative embodiments, the configuration of the measurement path may be nonlinear, such as (for example) rotational or curvilinear, and the measurement path may pitch, yaw, or roll along its length. ### It will be readily appreciated by persons of ordinary skill in the art that various modifications to embodiments of systems in accordance with the present disclosure may be devised without departing from the scope of the present teachings, including modifications which may use equivalent structures or materials hereafter conceived or developed, or equivalent mathematical functions. It is to be especially understood that the scope of the present disclosure is not intended to be limited to described or illustrated embodiments and example data, and that the substitution of a variant of a described, recited, or illustrated element or feature, without any substantial resultant change in functionality, will not constitute a departure from the scope of the disclosure. In this patent document, any form of the word “comprise” is to be understood in its non limiting sense to mean that any element or feature mentioned following such word is included, but elements and features not specifically mentioned are not excluded. A reference to an element or feature by the indefinite article "a" does not exclude the possibility that more than one such element or feature is present, unless the context clearly requires that there be one and only one such element or feature. Any term describing an interaction between elements is not meant to limit the interaction to direct interaction between the subject elements, and may also include indirect interaction between the elements such as through secondary or intermediary structure. Relational and conformational terms such as (but not limited to) “orthogonal”, “sinusoidal”, “identical”, “coincident”, “equal”, and “uniform spacing” are not intended to denote or require absolute mathematical or geometrical precision. Accordingly, such terms are to be understood as denoting or requiring substantial precision only (e.g., “substantially orthogonal”, “substantially sinusoidal”, “substantially identical”, “substantially coincident”, “substantially equal”, or “substantially uniform spacing”) unless the context clearly requires otherwise.

[0002] LIST OF COMPONENTS AND FEATURES Feature Number Description 100 position sensing system 101 triaxial magnetometer 102 sensing target 103 measurement path 111 first index position 112 second index position 113 third index position 200A position sensing system 200B position sensing system 202A sensing target 202B sensing target 203 measurement path 211 first index position 212A second index position 212B second index position 300 position sensing system 302 sensing target 303 measurement path 311 first index position 312 second index position 313 third index position 400A position sensing system 400B position sensing system Feature Number Description 402A sensing target 402B sensing target 403 measurement path 411 first index position 412A second index position 412B second index position 413 third index position 414 fourth index position 415A fifth index position 415B fifth index position 416A sixth index position 416B sixth index position 500 position sensing system 501A one bi-axial or two single-axis magnetometers 501B one single-axis magnetometer 511 first index position 512 second index position 513 third index position first sensing direction^^second sensing direction^^third sensing direction ^^^ third sensing direction signal from sensing direction ^^^^signal from sensing direction ^^ Feature Number Description ^^signal from sensing direction ^^^^^signal from sensing direction ^^^^Gsignal from sensing direction ^^^^^ signal from sensing direction ^^^ ^ wavelength of repeating signals ^^and ^^^^,^^,^^, … permanent magnets of sensing target^ magnetization vector of permanent magnet ^ magnetization vector angle of permanent magnet ϒ angle of third sensing direction ^^^ relative to first sensing direction ^^^ spacing of permanent magnets along measurement path ^′ component cartesian x axis of individual permanent magnet ^′ component cartesian y axis of individual permanent magnet ^′ component cartesian z axis of individual permanent magnet ^^^two-dimensional measurement vector ^^^^three-dimensional measurement vector ^^^measurement vector angle (i.e., angle of measurement vector ^^^in global ^-^ plane)^global cartesian x axis of position sensing system ^ global cartesian y axis of position sensing system ^ global cartesian z axis of position sensing system

Claims

1. WHAT IS CLAIMED IS:

1. A system for sensing a spatial position of a first physical component relative to a second physical component, said system comprising: (a) one or more sensors carried by the first physical component and being configured for measuring magnetic field strength in a first sensing direction, a second sensing direction, and a third sensing direction, said third sensing direction not being parallel to the first sensing direction and not being parallel to the second sensing direction; and (b) a single sensing target carried by the second physical component, said sensing target comprising one or more permanent magnets configured to generate a spatially-varying magnetic field with a selected wavelength that repeats at least once along a measurement path corresponding to a selected range of motion between the first and second physical components; wherein the one or more sensors and the sensing target are configured such that the spatially- varying magnetic field will produce: (A) a first signal from the first sensing direction, wherein said first signal will repeat when the first physical component is moved relative to the second physical component through the selected range of motion; (B) a second signal from the second sensing direction, wherein said second signal will repeat and will be out of phase with the first signal when the first physical component is moved relative to the second physical component through the selected range of motion; and (C) a third signal from the third sensing direction, wherein said third signal will satisfy at least one of one or more selected index criteria when the position of the first physical component is coincident with a selected index position of the one or more sensors along the measurement path, such that the absolute spatial position of the first physical component relative to the second physical component will be known.

2. The system as in Claim 1 wherein: (a) the sensing target comprises a plurality of magnets placed with a uniform spacing along the measurement path, each magnet having a magnetization vector; (b) the plurality of magnets comprises two or more sets of magnets; and (c) the magnets of at least one of the two or more sets of magnets are oriented with their magnetization vectors having a non-zero component parallel with the third sensing direction.

3. The system as in Claim 1, wherein: (a) the sensing target comprises one or more magnets placed along the measurement path; and (b) each magnet is magnetized with a spatially-varying magnetic field having a non-zero component parallel to the third sensing direction.

4. The system as in Claim 3, wherein the sensing target comprises a single magnet magnetized with a spatially-varying magnetic field having a component parallel to the third sensing direction that varies spatially along the measurement path.

5. The system as in Claim 2, wherein the magnets are physically identical and differ only with respect to their orientations and positions along the measurement path.

6. The system as in Claim 2, wherein the sensing target comprises: (a) a first set of magnets each oriented with its magnetization vector having a non- zero component toward the third sensing direction; and (b) a second set of magnets each oriented with its magnetization vector having a non- zero component opposite the third sensing direction.

7. The system as in any one of Claims 1-6, wherein at least one of the selected index criteria is that the third signal equals a selected threshold value.

8. The system as in Claim 7, wherein the at least one of the selected index criteria is that the third signal equals a selected threshold value and has a positive slope at the selected threshold value.

9. The system as in Claim 7, wherein the at least one of the selected index criteria is that the third signal equals a selected threshold value and has a negative slope at the selected threshold value.

10. The system as in any one of Claims 1-6, wherein at least one of the selected index criteria includes the condition that the third signal is greater than a selected threshold value along a selected interval of the measurement path that is less than the selected wavelength.

11. The system as in any one of Claims 1-6, wherein at least one of the selected index criteria includes the condition that the third signal is less than a selected threshold value along a selected interval of the measurement path that is less than the selected wavelength.

12. The system as in any one of Claims 1-11, wherein at least one of the selected index criteria is based on a combination of the first, second, and third signals.

13. The system as in any one of Claims 7-11, wherein the selected threshold value is based on a gap distance between the one or more sensors and the sensing target.

14. The system as in Claim 13, wherein the gap distance is determined from a magnitude of a two-dimensional vector defined by the first signal and the second signal.

15. The system as in Claim 13, wherein the gap distance is determined from a magnitude of a three-dimensional vector defined by the first signal, the second signal, and the third signal.

16. The system as in any one of Claims 1-7, wherein the third signal will vary monotonically when and as the first physical component moves relative to the second physical component.

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