Position sensor system using an array of equally spaced magnetic sensors

Abstract

A system and method for determining the position and / or velocity of a rotating shaft includes: a target wheel for securing to the rotatable shaft, the target wheel including a plurality of north / south pole pairs, each pole of each north / south pole pair being substantially the same size; and a sensor assembly. The sensor assembly includes a first magnetic sensor array for sensing the pole pairs to provide cosine and sine signals, and a second magnetic sensor array for sensing the pole pairs to provide cosine and sine signals, wherein the second magnetic sensor array is disposed transversely to the first magnetic sensor array. An electronic processor is configured to receive inputs from the first magnetic sensor array and the second magnetic sensor array and determine the position and / or velocity of the shaft.

Description

[0001] Related applications

[0002] This patent application claims the benefit of previously filed, co-pending U.S. Provisional Patent Application No. 62 / 970,441, filed February 5, 2020, which is hereby incorporated by reference in its entirety. Technical Field

[0003] The present invention relates to position and / or speed sensing systems and methods. Background Art

[0004] Various absolute position sensors and associated signal processing techniques are known for determining the absolute position of a rotating or linearly moving target. For example, U.S. Patent No. 8,058,868 discloses an example of such an off-axis magnetic sensor that uses a dual-track multipole magnetic target with uniformly spaced and sized high-resolution magnetic poles. The '868 patent describes how to use a high-resolution Hall effect sensor (such as the Timken MPS160 or MPS512 sensor chip) to detect the local absolute position on a magnetic pole pair. The '868 patent also shows how to use a second magnetic track with one or more pole pairs to generate a coarse or low-resolution absolute position signal, which can then be used with a high-resolution Hall effect sensor (such as the Timken MPS160 or MPS512 sensor chip) to determine a fine or high-resolution absolute position over a longer arc or longer linear range. Summary of the Invention

[0005] The present invention contemplates improvements to the above described sensor arrangements and signal processing.

[0006] The present disclosure introduces techniques to effectively improve the accuracy of the output signal. The errors reduced include: (a) a one-per-revolution error due to an off-center condition of the target wheel, (b) an inter-cycle error due to small variations in the circumferential length of each magnet pole, (c) an inter-cycle error due to small variations in the sinusoidal shape of each magnet pole, and (d) an inter-cycle error due to small variations in distortion and noise differences in the sine and cosine signal paths within the sensor array integrated circuit for the magnetic sensor array.

[0007] In one embodiment, a system for determining the position and / or velocity of a rotatable shaft of a device includes: a target wheel for securing to the rotatable shaft, the target wheel comprising a plurality of north / south pole pairs, each pole of each north / south pole pair being substantially the same size; and a sensor assembly comprising: a first magnetic sensor array for sensing the pole pairs to provide cosine and sine signals; a second magnetic sensor array for sensing the pole pairs to provide cosine and sine signals, wherein the second magnetic sensor array is disposed transversely to the first magnetic sensor array; and an electronic processor configured to receive inputs from the first and second magnetic sensor arrays and determine the position and / or velocity of the shaft.

[0008] Another embodiment is directed to a method for determining the position and / or velocity of a rotatable shaft of a device. The method includes sensing a target wheel fixed to the rotatable shaft including a plurality of north / south pole pairs using a first magnetic sensor array to provide a cosine signal and a sine signal, and sensing the target wheel using a second magnetic sensor array for sensing pole pairs to provide a cosine signal and a sine signal, wherein the second magnetic sensor array is arranged transverse to the first magnetic sensor array. The method also includes summing the cosine signal and the sine signal from the first magnetic sensor array with the cosine signal and the sine signal from the second magnetic sensor array, and determining the position and / or velocity of the shaft from the summed cosine signal and the summed sine signal using an electronic processor.

[0009] In another embodiment, the second magnetic sensor array is oriented at a 180 mechanical angle relative to the first magnetic sensor array.

[0010] Other aspects of the invention will become apparent by consideration of the detailed description and accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 A top view of one embodiment of a target wheel is illustrated.

[0012] Figure 2 Shown for around Figure 1 One embodiment of a target wheel extending the magnet pattern.

[0013] Figure 3 A top view of the sensor assembly is shown.

[0014] Figure 4 A block diagram is shown for one embodiment of a position sensing system including a sensor assembly.

[0015] Figure 5 One embodiment of a schematic diagram of a summing circuit is illustrated.

[0016] Figure 6Three combined graphs for signals from a magnetic sensor array are illustrated.

[0017] Figure 7 Diagrams showing target wheel run-out and shaft deflection are illustrated.

[0018] Figure 8 Three combined graphs are illustrated for comparison and to illustrate the errors.

[0019] Figure 9 Three combined graphs for signals from a magnetic sensor array are illustrated.

[0020] Figure 10 A top view of another sensor assembly having four magnetic sensor arrays is shown. DETAILED DESCRIPTION

[0021] Before any embodiment of the present invention is explained in detail, it will be understood that the present invention is not limited in its application to the details of the construction and the arrangement of parts set forth in the following description or illustrated in the following drawings. The present invention is capable of realizing other embodiments and can be practiced or implemented in various ways. Moreover, it will be understood that the words and terms used herein are for descriptive purposes and should not be considered restrictive. The use of "including," "comprising," or "having" and variations thereof herein is intended to encompass the items listed thereafter and their equivalents as well as additional items. Unless otherwise specified or limited, the terms "mounted," "connected," "supported," and "coupled" and variations thereof are used broadly and encompass direct and indirect mounting, connection, support, and coupling. Furthermore, "connected" and "coupled" are not limited to physical or mechanical connections or couplings.

[0022] As should also be apparent to one of ordinary skill in the art, the systems shown in the figures are models of what an actual system might be. As mentioned, many of the modules and logical structures described can be implemented in software executed by a microprocessor or similar device, or can be implemented in hardware using various components including, for example, an application specific integrated circuit ("ASIC"). Terms such as "processing unit" and "electronic processor" can include or represent both hardware and / or software. Therefore, the claims should not be limited to specific examples or terms or to any specific hardware or software implementation or combination of software or hardware.

[0023] Figure 1 One embodiment of a circular shaped multi-pole magnet target wheel 20 is shown and includes a hub 24 having an opening 28 for receiving a rotatable shaft. The hub 24 includes spaced apertures 32 for mounting to the shaft for rotation therewith. The target wheel 20 includes an outer multi-pole magnetic ring 36 extending entirely therearound. Figure 2The multi-pole magnetic ring 36 represents a single track of north / south pole pairs, and is preferably a single high-resolution track of magnets comprising twenty-five pole pairs or north / south pole pairs. Each pole of each north / south pole pair is of the same size (e.g., arc length). In other embodiments, the high-resolution track of the target wheel 20 may have more or fewer pole pairs. Other embodiments with multiple tracks are also contemplated, including a second reference track for determining the absolute position of the target wheel 20 and the shaft.

[0024] Figure 3 Illustrated is a top view of a magnetic position sensor assembly 50 including an inner rim 54 for securing alignment with the rotatable shaft and target wheel 20. The magnetic position sensor assembly 50 includes an outer rim 56 and has a generally horseshoe or "C" shaped annular body.

[0025] Figure 3 The magnetic position sensor assembly 50 shown in FIG includes a first magnetic sensor array 60 and a second magnetic sensor array 66. Both the magnetic sensor arrays 60 and 66 sense the pole pairs of the target wheel 20 to provide cosine and sine signals. The second magnetic sensor array 66 is arranged transversely to the first magnetic sensor array 60 or at an angle of 180 mechanical degrees relative to the first magnetic sensor array 60 and is aligned across the central axis of the rotatable shaft (not shown), which is arranged within the open side of the sensor assembly 50 near its inner edge 54. Therefore, the magnetic sensor arrays 60 and 66 are intended to be arranged equidistantly around the central axis of the rotatable shaft and relative to it, and the line drawn between the magnetic sensor arrays 60 and 66 is intended to intersect the central axis of the rotatable shaft. Each of the magnetic sensor arrays 60 and 66 can include a series of sensing elements, such as Hall effect sensors. In one embodiment, the first magnetic sensor array 60 is a first Hall effect sensor array and the second magnetic sensor array 66 is a second Hall effect sensor array, each of which includes 16 sensing elements.

[0026] Figure 3 The sensor assembly 50 shown in FIG. 5 includes a printed circuit board 70 having various circuits and an electronic processor 80 that receives position signals from the magnetic sensor arrays 60, 66. In one embodiment, the electronic processor 80 takes the form of an application specific integrated circuit (ASIC).

[0027] Figure 4A block diagram of one embodiment of a position and velocity determination system 100 including a first magnetic sensor array 60 and a second magnetic sensor array 66 is shown. The position / velocity determination system 100 includes a summing circuit 110 disposed on a printed circuit board to receive sine and cosine signals from the magnetic sensor arrays 60 and 66. The summing circuit 110 provides a summed input or summed signal to an electronic processor 80 disposed on a printed circuit board 70. The electronic processor 80 communicates with a memory 130 disposed on the printed circuit board 70. In one embodiment, the electronic processor 80 provides a position or velocity output 135 to another device.

[0028] Figure 5 One embodiment of a schematic diagram of a summing circuit 110 including a pair of amplifiers 140, 144 is illustrated. The summing circuit 110 is configured to sum the sine and cosine signals for each of the magnetic sensor arrays 60, 66. In one embodiment, the summing circuit 110 includes an analog-to-digital converter (ADC) and provides the summed cosine and sine signals as a digital signal to the electronic processor 80.

[0029] In one embodiment, separate analog to digital converters are provided for converting the analog cosine and sine signals into digital signals. In another embodiment, separate ADCs (not shown) are provided with the electronic processor 80 to convert the analog cosine and sine signals into digital signals.

[0030] In one embodiment, memory 130 includes a program storage area and a data storage area. The program storage area and the data storage area may include a combination of different types of memory, such as read-only memory ("ROM"), random access memory ("RAM") (e.g., dynamic RAM ["DRAM"], synchronous DRAM ["SDRAM"], etc.), electrically erasable programmable read-only memory ("EEPROM"), flash memory, a hard drive, an SD card, or other suitable magnetic, optical, physical, or electronic memory devices. Electronic processor 80 is connected to memory 130 and executes software instructions that can be stored in the RAM of memory 130 (e.g., during execution), the ROM of memory 130 (e.g., on a substantially permanent basis), or another non-transitory computer-readable medium. The included software for the processes and methods for the position sensing system may be stored in memory 130. The software may include firmware, one or more application programs, program data, filters, rules, one or more program modules, and other executable instructions. In some embodiments, electronic processor 80 includes internal memory.

[0031] The position and velocity determination system 100 includes a position and / or velocity output 135 provided from the electronic processor 80 , which provides the position or velocity of the rotatable shaft to another device, such as a control device, for control and / or display purposes.

[0032] operate

[0033] In operation, target wheel 20 is fixed to a rotatable shaft. Sensor assembly 50 is positioned adjacent target wheel 20 such that first and second magnetic sensor arrays 60, 66 are aligned with multi-pole magnetic ring 36 to sense the magnet and its movement.

[0034] The first magnetic sensor array 60 and the second magnetic sensor array 66 sense the Figure 5 The summing circuit 110 shown in FIG. 1 sums the cosine signal and the sine signal. Figure 6 A graph 160 of the Sine 1 signal and the Cosine 1 signal is shown at the top of the graph in volts versus phase angle. The Sine 2 signal and the Cosine 2 signal are shown in the middle of the graph 160. The sum of the Sine 1 signal plus the Sine 2 signal and the sum of the Cosine 1 signal and the Cosine 2 signal are shown in FIG. Figure 6 is shown at the lowest point in the graph.

[0035] There are various numerical methods for combining cosine and sine signals, such as one or more of the group consisting of: for example, simple summation before individually calculating the phase angle, phase angle averaging after individually calculating the phase angle, and vector summation for an exact result. Figure 3 The pair of magnetic sensor arrays 60 , 66 shown in FIG. 5 are displaced 180 mechanical degrees apart and may also be considered dual magnetic sensor arrays.

[0036] The electronic processor 80 receives the summed cosine and sine values and executes program or method steps to determine the position and / or rotational speed of the rotatable shaft. The position or speed is provided to a display and / or control device via a position / speed output 135 from the electronic processor 80.

[0037] Target wheel deflection and shaft deflection

[0038] Figure 7 A clock face diagram for explaining target wheel deflection and axis deflection errors is shown. The box containing the number "12" represents the first magnetic sensor array 60, and the box containing the clock number "6" represents the second magnetic sensor array 66. The central axis 175 represents the axis transverse to Figure 7 The central axis of the rotatable shaft is shown as a dashed line 180 between the magnetic sensor arrays 60, 66. Thus, the central axis 175 of the rotatable shaft is completely located between the magnetic sensor arrays 60, 66 in terms of distance and direction.

[0039] Target wheel deflection or shaft deflection is caused by various factors, including misalignment, vibration or use / wear. In such an instance, the center axis 175 is displaced to Figure 7 175X. Therefore, as shown by dashed line 180X, the central axis and the rotational axis supporting target wheel 20 are misaligned. Of course, multi-pole magnetic ring 36 is not properly aligned with magnetic sensor arrays 60, 66. However, the relative positions of target wheel deflection or shaft deflection will be balanced by the positions of magnetic sensor arrays 60, 66 at an angle of 180 degrees. The distance offset by one magnetic sensor array 60 matches the opposite distance offset by the other magnetic sensor array 66.

[0040] Figure 8 A graph 190 comparing the accuracy of a single magnetic sensor array and a pair of magnetic sensor arrays 60 , 66 when the target wheel is off-center and not perfectly aligned with the magnetic sensor arrays 60 , 66 is shown.

[0041] Figure 8 The top of the graph 190 shows the sum of the sine 1 + sine 2 signals and the sum of the cosine 1 and cosine 2 signals. The middle graph shows the arc minute error for sine 1 and cosine 1 for a single magnetic sensor array. The arc minute range for the error for a single magnetic sensor array is -10 to 10 arc minutes. The bottom graph shows the arc minute error for (sine 1 + sine 2) and (cosine 1 + cosine 2). The error range is from 0.05 arc minutes to -0.05 arc minutes. Therefore, for Figure 3 With the arrangement shown in FIG. 6 , having magnetic sensor arrays 60 , 66 arranged at 180 mechanical degrees, the theoretical improvement is significant.

[0042] Second embodiment

[0043] The second embodiment provides a unique and non-intuitive configuration to the first embodiment discussed above by maintaining the magnetic sensor arrays 60, 66 in a manner such that Figure 3 , but then one magnetic sensor array 66 is positioned at the same position without lateral or vertical displacement rotated 180 degrees around itself (from Figure 3The second magnetic sensor array 66 is positioned 180 degrees rotated, or reversed, in the same position (replacing the upper side with the perspective of the second magnetic sensor array). As a result of the reversed orientation, the sine signal path of the second magnetic sensor array provides a cosine signal, and the cosine signal path of the second magnetic sensor array provides a sine signal. The sine signal from one of the magnetic sensor arrays 60, 66 can then be added or summed with the cosine signal of the other magnetic sensor array, and the cosine signal from one magnetic sensor array can be added or summed with the sine signal of the other magnetic sensor array. By using opposite signal paths in the second magnetic sensor array, the benefits of reducing systematic errors in the magnetic sensor arrays 60, 66 are achieved, as well as a better balance of delay, nonlinearity, and impedance characteristics of the final signal resulting from the summation of the sine and cosine signals. This arrangement is provided for an even number of magnetic pole pairs or north / south pole pairs.

[0044] For arrangements including an odd number of magnetic pole pairs or north / south pole pairs, the orientation of the second sensor array 66 does not need to be rotated to have the same switched sine and cosine signals as set forth above.

[0045] Third embodiment

[0046] Another unique and non-intuitive modification to the above configuration is to shift the magnetic sensor arrays 60 and 66 by both 180 mechanical degrees and 90 electrical degrees. The result is that the sine signal path in the second magnetic sensor array 66 produces a cosine signal, and the cosine signal path produces an inverted sine signal. This technique is particularly suitable for differential signals such as those produced by the Timken MPS160 and MPS512 sensor arrays. The two differential sine signals from the two magnetic sensor arrays 60 and 66 are summed to produce an improved sine signal. By replacing cosine+ with cosine- from one of the magnetic sensor arrays and cosine+ with cosine-, the cosine signal from one magnetic sensor array 60 is summed with the inverted cosine from the other magnetic sensor array 66. This combination of signals can reduce the sum of systematic errors in the magnetic sensor arrays 60 and 66, and provide a better balance of delay, nonlinearity, and impedance characteristics of the final summed signal from the sine and cosine sources. The two techniques described in the second and third embodiments above can also be combined. In the case of an even number of pole-pair magnets, the second sensor array 66 may be shifted a further 90 electrical degrees.

[0047] Figure 9 is an example of the summation of signals from magnetic sensor arrays 60 , 66 that are 180 mechanical degrees + or −90 electrical degrees apart. Figure 9 shows how the first magnetic sensor array 60 and the second magnetic sensor array 66 sense the Figure 5The summing circuit 110 shown in FIG. 1 sums the cosine signal and the sine signal. Figure 9 A graph of the sine 1 signal and the cosine 1 signal is shown at the top of the graph in volts versus phase angle. The sine 2 signal and the cosine 2 signal are shown in the middle of the graph 200. The sum of the sine 1 signal plus the cosine 2 signal and the sum of the cosine 1 signal minus the sine 2 signal are shown in FIG. Figure 9 is shown at the lowest point in the graph.

[0048] The arrangement disclosed above is also applicable to more than two magnetic sensor arrays 60, 66. For example, a three-sensor design can also reduce errors caused by the triangular shape of the magnet.

[0049] Two pairs of magnetic sensor arrays embodiment

[0050] A further improvement to the position and velocity determination system 100 is achieved by using Figure 10 The unique spatial configuration shown is achieved with an array of four magnetic sensors. Figure 10 Illustrated is a top view of magnetic position sensor assembly 250. Magnetic position sensor assembly 250 includes an inner edge 254 for securing alignment with the rotatable shaft and target wheel 20. Magnetic position sensor assembly 250 includes an outer edge 256 and defines a generally horseshoe or "C" shaped annular body.

[0051] The magnetic position sensor assembly 250 includes a first magnetic sensor array 260 and a second magnetic sensor array 266 defining a first magnetic sensor array pair. Both magnetic sensor arrays 260 and 266 sense pole pairs of the target wheel 20 to provide cosine and sine signals. The second magnetic sensor array 266 is arranged transversely to the first magnetic sensor array 260 or at an angle of 180 mechanical degrees. Thus, the magnetic sensor arrays 260 and 266 are arranged equidistantly about the central axis of the rotatable shaft, and a line drawn between the magnetic sensor arrays 260 and 266 is intended to intersect the central axis of the rotatable shaft. Each magnetic sensor array 260 and 266 may include a series of sensing elements, such as Hall effect sensors.

[0052] Figure 10 The magnetic position sensor assembly 250 shown in FIG includes a third magnetic sensor array 281 and a fourth magnetic sensor array 287 defining a second magnetic sensor array pair. Both magnetic sensor arrays 281, 287 sense pole pairs of the target wheel 20 to provide cosine and sine signals. Figure 10 The fourth magnetic sensor array 287 is shown disposed transversely to the third magnetic sensor array 281 or at an angle of 180 mechanical degrees relative to the third magnetic sensor array.

[0053] The third magnetic sensor array 281 and the fourth magnetic sensor array 287 are respectively disposed adjacent to the first magnetic sensor array 260 and the second magnetic sensor array 266. The close proximity results in advantages for installation and maintenance. Figure 10 The sine and cosine signals of at least the third and fourth sensor arrays are provided to an additional summing circuit or to summing circuit 110 for summing with the cosine and sine signals from the first magnetic sensor array pair defined by first magnetic sensor array 260 and second magnetic sensor array 266.

[0054] The additional third and fourth magnetic sensor arrays 281 and 287 are used to improve the overall performance of the position / velocity determination system 100 by increasing the signal-to-noise ratio of the sine and cosine signals, because each magnetic sensor array 260, 266, 281, 287 increases the total signal without increasing the total signal noise. The magnetic sensor arrays 260, 266, 281, 287 are also used to average the signals from the multi-pole magnet target wheel 20. Because errors in the positions of the magnetic poles on the target wheel are averaged to produce an overall sine and cosine signal (which has reduced error and more accurate angular position), this special averaging produces a more accurate and constant signal. At least one more additional magnetic sensor array pair is contemplated to reduce errors. Furthermore, in some embodiments, additional pairs of magnetic sensors are provided to sense a second magnetic track and obtain an absolute position for the shaft.

[0055] Those skilled in the art will appreciate that for any of the disclosed embodiments having a single circular track, additional tracks can be selected to have relative positions as desired, such that any of the tracks can be configured as an outer track, an inner track, or a middle track. Corresponding additional magnetic sensor arrays are contemplated for sensing the additional tracks. In some embodiments, the absolute position of the shaft is detected and a Gray code segment is provided as the magnet. In other embodiments, the position is calibrated.

[0056] Various features and advantages of the invention are set forth in the following claims.

Claims

1. A system for determining the position and / or velocity of a rotatable shaft of a device, the system comprising: a target wheel for securing to a rotatable shaft, the target wheel comprising a plurality of north / south pole pairs, each pole of the north / south pole pairs being substantially the same size; and A sensor assembly comprising: a first magnetic sensor array for sensing the pole pairs to provide cosine and sine signals; a second magnetic sensor array for sensing the pole pairs to provide cosine and sine signals, wherein the second magnetic sensor array is disposed transversely to the first magnetic sensor array and aligned with the first magnetic sensor array across a central axis of the rotatable shaft, and the second magnetic sensor array is disposed transversely to the first magnetic sensor array at an angle of 180 mechanical degrees; an electronic processor configured to receive input from the first magnetic sensor array and the second magnetic sensor array and determine a position and / or velocity of the shaft; and a summing circuit configured to sum the sine signal from the first magnetic sensor array and the sine signal from the second magnetic sensor array, and to sum the cosine signal from the first magnetic sensor array and the cosine signal from the second magnetic sensor array, and wherein the summing circuit provides the summed sine signal and the summed cosine signal to the electronic processor.

2. The system according to claim 1, wherein: The summed cosine signal and the summed sine signal increase accuracy when the target wheel is offset relative to the central axis of the rotatable shaft.

3. The system according to claim 1, wherein: The first magnetic sensor array is a first Hall effect sensor array and the second magnetic sensor array is a second Hall effect sensor array.

4. The system according to claim 3, wherein: The first Hall effect sensor array and the second Hall effect sensor array each include 16 sensing elements.

5. The system according to claim 1, wherein The second magnetic sensor array is positioned rotated 180 degrees or reversed at the same location, wherein the sine signal path of the second magnetic sensor array provides a cosine signal and the cosine signal path of the second magnetic sensor array provides a sine signal.

6. The system according to claim 5, wherein: Using opposite signal paths in the second magnetic sensor array results in summing of the cosine signals and summing of the sine signals and provides a reduction in systematic errors in the first and second magnetic sensor arrays and a balance of delays, nonlinearities, and impedances of the summed cosine and summed sine signals.

7. The system according to claim 1, wherein: The second magnetic sensor array is disposed transversely to the first magnetic sensor array at an angle of 180 mechanical degrees and shifted by 90 electrical degrees, wherein a sine signal path of the second magnetic sensor array provides a cosine signal and a cosine signal path of the second magnetic sensor array provides an inverted sine signal.

8. The system according to claim 1, wherein: The target wheel includes a single track of north / south pole pairs.

9. The system according to claim 1, wherein: The target wheel includes a high-resolution magnetic track of north / south pole pairs and a reference magnetic track, wherein the system determines the absolute position of the shaft.

10. The system according to claim 9, wherein: The first magnetic sensor array and the second magnetic sensor array define a first magnetic sensor array pair for sensing the high resolution magnetic track, and the sensor assembly includes at least one additional magnetic sensor array pair configured to sense the high resolution magnetic track.

11. The system according to claim 1, wherein: The first magnetic sensor array and the second magnetic sensor array define a first magnetic sensor array pair, and the sensor assembly includes a third magnetic sensor array for sensing the pole pairs to provide cosine signals and sine signals and a fourth magnetic sensor array for sensing the pole pairs to provide cosine signals and sine signals, wherein the fourth magnetic sensor array is arranged transversely to the third magnetic sensor array, and wherein the third magnetic sensor array and the fourth magnetic sensor array define at least a second magnetic sensor array pair to improve the accuracy of the position and / or the velocity determined for the axis.

12. The system according to claim 11, wherein The electronic processor is configured to receive input from at least the first magnetic sensor array pair and the second magnetic sensor array pair to determine the position and / or the speed of the shaft.

13. The system of claim 1, wherein: Combining the cosine signal and the sine signal includes one of the group consisting of: performing a simple summation before individually calculating the phase angle, performing phase angle averaging after individually calculating the phase angle, and performing a vector summation.

14. A method for determining the position and / or velocity of a rotatable shaft of a device, comprising: sensing a target wheel fixed to a rotatable shaft including a plurality of north / south pole pairs using a first magnetic sensor array to provide a cosine signal and a sine signal; sensing the target wheel using a second magnetic sensor array for sensing the pole pairs to provide a cosine signal and a sine signal, wherein the second magnetic sensor array is disposed transversely to the first magnetic sensor array and aligned with the first magnetic sensor array across a central axis of the rotatable shaft, and the second magnetic sensor array is disposed transversely to the first magnetic sensor array at an angle of 180 mechanical degrees; summing the cosine signal and the sine signal from the first magnetic sensor array with the cosine signal and the sine signal from the second magnetic sensor array; as well as The position and / or velocity of the shaft is determined from the summed cosine signal and the summed sine signal using an electronic processor.

15. The method according to claim 14, wherein The second magnetic sensor array is arranged transversely to the first magnetic sensor array at an angle of 180 mechanical degrees.

16. The method according to claim 14, wherein The first and second magnetic sensor arrays are disposed on a sensor assembly including the electronic processor, the electronic processor being configured to receive input from the first and second magnetic sensor arrays for determining the position and / or the speed of the shaft.

17. The method according to claim 14, wherein The summing of the cosine signal and the sine signal from the first magnetic sensor array and the cosine signal and the sine signal from the second magnetic sensor array is provided by a summing circuit.

18. The method according to claim 15, wherein The first and second magnetic sensor arrays are disposed on a sensor assembly including the electronic processor, the electronic processor being configured to receive input from the first and second magnetic sensor arrays for determining the position and / or the speed of the shaft, and Wherein, the summing of the cosine signal and the sine signal from the first magnetic sensor array and the cosine signal and the sine signal from the second magnetic sensor array is provided by a summing circuit.

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