Methods for correcting measurement signals

Abstract

The invention relates to a method for correcting measurement signals (MS1, MS2, MS3), wherein at least two measurement signals (MS1, MS2, MS3) are currently provided by a sensor unit (3), wherein at least two processed measurement signals (a, b) are generated based on the at least two currently provided measurement signals (MS1, MS2, MS3), from which, using angle-independent calculations and at least one correction coefficient (K), two corrected measurement signals (ac, bc) are generated, from which a corrected angle (WK) is calculated, wherein, for determining the at least one correction coefficient (K), a plurality of at least two measurement signals are provided in advance, wherein, based on the plurality of at least two previously provided measurement signals, two processed measurement signals are generated each, and a corresponding angular error is calculated based on the two processed measurement signals and a reference angle.wherein at least one correction parameter is determined based on at least one step of an iteratively applicable calculation method, wherein, based on the at least one correction parameter, the at least one correction coefficient (K) is determined such that a remaining angular error in the corrected angle (WK) is smaller than an angular error in an angle based on the two processed current measurement signals (a, b), and a sensor arrangement (1).

Description

[0001] The invention relates to a method for correcting measurement signals. The measurement signals can, for example, represent a rotational movement of a body detected by a sensor arrangement or the current angular position of the moving body. The present invention also relates to a sensor arrangement configured to perform such a method.

[0002] Sensor arrangements are known from the prior art that are used as rotary motion sensors to detect the rotational movement of a moving body or as linear displacement sensors to detect the linear movement of the moving body. In these arrangements, the current angular position of the moving body during rotation or the current position of the moving body during linear movement is not measured directly, but rather encoded into two orthogonal signals, generally referred to as the sine channel and the cosine channel, which form a vector in the complex plane. The actual angular position of the moving body or the current position of the moving body is then calculated using the arctangent function, whereby Cartesian coordinates can essentially be converted into a polar angle.The sine and / or cosine signals provided by the sensor arrays can contain errors, such as offset, amplitude mismatch, orthogonality error, nonlinearities, etc. These errors can be corrected, for example, analogously by an evaluation and control unit or digitally by appropriate evaluation software. To minimize angular error, corresponding correction coefficients should be calculated or determined as accurately as possible. For example, it is known to calculate the correction coefficients using a Fourier transform of the sine and / or cosine signals provided by the sensors. Since the current angular position is calculated and not directly measured, a distinction is made between a signal range and an angular range.Harmonic disturbances of a certain order in the signal domain can also lead to harmonics in the angular domain, albeit of different orders. The cause of this type of error depends on the measurement principle and is most often due to manufacturing tolerances and imperfections in the sensor design, for example, non-ideal magnetization and flux distribution in magnetic sensors.

[0003] From DE 102 60 862 A1, a method and a circuit arrangement for correcting an angle- and / or distance-measuring sensor arrangement are known, in which sinusoidal and cosine-shaped measurement signals are evaluated. The measurement signals are obtained by scanning a moving object. The angular errors or phase errors of the measurement signals are corrected by deriving constants from a plurality of measurement signals for estimating and correcting the angular error or the phase error and / or the amplitude of the measurement signals.

[0004] From DE 10 2004 029 815 A1, a method and an arrangement for correcting an angle- and / or distance-measuring sensor arrangement are known, in which sinusoidal and cosine-shaped measurement signals are evaluated, which are obtained by scanning a moving object. To correct the angular and / or phase errors of the measurement signals, the method consists of a calibration procedure and a subsequent correction procedure. In the calibration procedure, correction parameters are provided, and in the correction procedure, a corrected pair of measured values ​​is determined from each pair of measured values. Disclosure of the invention

[0005] The method for correcting measurement signals according to independent claim 1 has the advantage that correction coefficients can be calculated in such a way that the angular error after correction is reduced, preferably minimized. Embodiments of the method can also be used for "difficult" measurement signals where angular errors arise from harmonics of sine and / or cosine signals. Correction coefficients calculated using conventional methods are distorted by such harmonics, so that an achievable minimum of the angular error cannot be reached.

[0006] Embodiments of the invention perform an iterative calculation or determination of correction coefficients that enable compensation of first- and / or second-order electrical harmonic oscillations in the angular error, even if these are not caused, or not exclusively caused, by offset, amplitude mismatch, or orthogonality errors, but, for example, by second- or third-order electrical harmonic oscillations or harmonics of the encoder signals or sine and / or cosine signals. The measurement signals or encoder signals can also be provided by multiphase systems with more than two measurement signals or encoder signals, which can be transformed into the complex plane after appropriate transformation (e.g., Clarke transformation).For a periodicity greater than the value "1", a distinction is made between a mechanical and an electrical angle, which differs from the mechanical angle by the factor of the periodicity.

[0007] Embodiments of the present invention provide a method for correcting measurement signals. In this method, at least two measurement signals are provided by at least one sensor unit. Based on the at least two currently provided measurement signals, at least two processed measurement signals are generated. From these, two corrected measurement signals are generated using angle-independent arithmetic operations and at least one correction coefficient. A corrected angle is then calculated from these corrected signals.

[0008] To determine at least one correction coefficient, a plurality of at least two measurement signals is provided beforehand. Based on this plurality of at least two pre-provided measurement signals, two processed measurement signals are generated. Based on these two processed measurement signals and a reference angle, a corresponding angular error is calculated. Based on at least one step of an iteratively applicable calculation method, at least one correction parameter is determined. Based on this at least one correction parameter, the at least one correction coefficient is determined such that any remaining angular error in the corrected angle is smaller than any angular error in an angle based on the two processed measurement signals.

[0009] Furthermore, a sensor arrangement is proposed which includes at least one sensor unit and at least one evaluation and control unit and is designed to carry out such a procedure.

[0010] Embodiments of the invention introduce first- and second-order electrical harmonic oscillations into the angular error, which counteract and cancel out the corresponding harmonic oscillations present in the angular error. The amplitude and phase of the generated harmonic oscillations can be controlled by appropriately selecting the correction coefficients for offset, amplitude mismatch, and orthogonality. A particular advantage is that the calculated correction coefficients can be applied independently of the angle, which, unlike known harmonic compensation methods, avoids computationally intensive evaluation of trigonometric functions at the time of correction. The angle-independent application here means that the calculations are independent of, for example, the corrected angle or the angle based on the two processed measurement signals when applying the correction coefficients.The use of trigonometric functions for correction is, of course, possible. Furthermore, an angle-dependent correction, such as a harmonic correction, can be performed additionally, for example, before, after, or in parallel with the described angle-independent method.

[0011] The iterative calculation method can be understood as a calculation method that comprises only a single iteration step but can also be applied iteratively. Thus, the invention is based on an iterative determination of at least one correction coefficient for compensating an offset of the processed measurement signals. A single step of the iteratively applicable calculation method may be sufficient in this case.

[0012] Further correction coefficients to compensate for an amplitude mismatch and / or an orthogonality error and / or an angular offset can subsequently be determined in further steps of the iteratively applicable calculation procedure after applying the previously calculated correction coefficient for offset correction.

[0013] The determination of at least one correction coefficient can be achieved by solving a nonlinear optimization problem to minimize the sum of the squared angular errors. In contrast to standard methods for solving optimization problems, which are very complex to implement and require significant resources or computing power on a control unit, embodiments of the invention can advantageously perform an analytical approximation of an inverse Hessian matrix of the optimization problem. This significantly simplifies the implementation without compromising the convergence and accuracy of the computational method.

[0014] In this context, an evaluation and control unit can be understood as an electrical assembly, circuit, or device, such as a control unit, that processes, analyzes, or evaluates provided sensor signals. For example, the evaluation and control unit can comprise an ASIC (Application-Specific Integrated Circuit) or a microcontroller. The evaluation and control unit can have at least one interface, which may be implemented in hardware and / or software. In the case of a hardware implementation, the interfaces may, for example, be part of the ASIC. However, it is also possible for the interfaces to be separate integrated circuits or to consist at least partially of discrete components.In software-based training, the interfaces can be software modules, such as those found on a microcontroller alongside other software modules. A computer program product with program code stored on a machine-readable medium like semiconductor memory, hard disk storage, or optical memory is also advantageous. This code is used to perform the evaluation and determine at least one correction coefficient when the program is executed by the evaluation and control unit.

[0015] In this context, a sensor unit is understood to be a component comprising at least one sensor element that directly or indirectly provides a physical quantity or a change in a physical quantity and preferably converts it into an electrical sensor signal. For example, magnetic and / or inductive sensor elements can be used.

[0016] Embodiments of the invention can preferably be used in a vehicle, for example in the detection of a steering angle or in the detection of a pedal actuation and in the detection of a corresponding actuation path.

[0017] The measures and further developments listed in the dependent claims enable advantageous improvements to the method for correcting measurement signals specified in independent claim 1.

[0018] A particular advantage is that, when processing the majority of at least two pre-provided measurement signals and / or the at least two currently provided measurement signals, a transformation and / or a filtering of the at least two pre-provided measurement signals and / or the at least two currently provided measurement signals can be performed. For example, a first processed measurement signal from at least two pre-provided measurement signals and a first processed measurement signal from at least two currently provided measurement signals can each be based on a periodic sine function with a predefined period and assigned to a sine channel.A second processed measurement signal derived from at least two pre-provided measurement signals, and a second processed measurement signal derived from at least two currently provided measurement signals, can each be based on a periodic cosine function with a specified period and assigned to a cosine channel. Such a transformation can, for example, also include a "rudimentary" compensation for a known offset of the measurement signals, particularly if this offset is inherent to the device's design. The design-related offset can, for example, be caused by the offset of an analog-to-digital conversion, especially in the case of non-differential signal transmission.

[0019] In an advantageous embodiment of the method, the angular error can be minimized by the at least one correction coefficient determined through iterative application of the calculation method. This means that the iterative calculation method can be applied, for example, until the change in the at least one correction coefficient reaches a minimum value.

[0020] In a further advantageous embodiment of the method, an iterative Newton method can be applied as an iterative calculation method, which is based on a first partial derivative of a sum of squares of the angular error with respect to the at least one correction parameter or a quantity based thereon, or an approximation of a quantity based thereon.

[0021] In a further advantageous embodiment of the method, the calculation of the at least one correction parameter can be based on at least one division of at least two cumulative sums. These at least two cumulative sums can be based on the majority of at least two pre-provided measurement signals and / or the previous and / or the current correction parameters and / or an associated angular error. When applying the method in a rotary motion sensor for detecting the rotational movement of a moving body, the majority of the at least two pre-provided measurement signals can preferably relate to a complete mechanical rotation of the moving body through 360 degrees.When applying the method in a linear displacement sensor to detect a linear movement of the moving body, the majority of the at least two pre-provided measurement signals can preferably relate to a complete range of motion of the linear movement of the moving body.

[0022] In a further advantageous embodiment of the method, the number of steps of the iterative Newton method can be fixed. This allows for a particularly simple implementation of the method. Alternatively, the number of steps of the iterative Newton method can depend on an evaluation of the majority of calculated angular errors. This evaluation can include an assessment of the harmonic components of the angular error.

[0023] Alternatively, the number of steps in the iterative Newton method can depend on an evaluation of the correction parameters determined in successive steps. For example, the iterative Newton method can preferably be terminated if the angular error is no longer reduced by the correction parameter determined in the subsequent step.

[0024] In a further advantageous embodiment of the method, an initial correction parameter can be specified, preferably estimated, before a first step of the iterative Newton method.

[0025] In a further advantageous embodiment of the method, the majority of calculated angular errors or the correction parameters determined in successive steps of the iterative Newton method can be subjected to at least one mathematical operation during evaluation, and the result of this mathematical operation can be compared with a corresponding threshold value. The iterative Newton method can be terminated if the result of the mathematical operation falls below the corresponding threshold value.

[0026] In a further advantageous embodiment of the method, the iterative Newton method can apply a diagonal approximation of an inverse Hessian matrix or an approximation of the diagonal approximation of the inverse Hessian matrix. In this way, at least two correction coefficients can be determined that are suitable for compensating a component of the angular error based on a harmonic oscillation of order "p". For example, a first correction coefficient can be determined that is suitable for compensating an offset error in a first processed measurement signal. Furthermore, a second correction coefficient can be determined that is suitable for compensating an offset error in a second processed measurement signal. Finally, at least one further correction coefficient can be determined that is suitable for compensating a first component of the angular error based on a harmonic oscillation of order "2p".For example, a third correction coefficient can be determined that is suitable for compensating for an amplitude mismatch in the at least two processed measurement signals. Furthermore, at least one additional correction coefficient can be determined that is suitable for compensating for a second component of the angular error based on a harmonic oscillation of order "2p". For example, a fourth correction coefficient can be determined that is suitable for compensating for an orthogonality error in the at least two processed measurement signals. Here, the value "p" corresponds to the period of the first and second processed measurement signals.

[0027] The angular error can also be subjected to a discrete Fourier transform. Based on coefficients of the discrete Fourier transform, at least one further correction coefficient can be determined. This at least one further correction coefficient can be suitable for compensating at least one component of the angular error based on a harmonic oscillation of order "2p". Alternatively, instead of determining the third and fourth correction coefficients using the iterative calculation method, the third and fourth correction coefficients, which are suitable for compensating a first component of the angular error based on a harmonic oscillation of order "2p", can be determined based on a third coefficient of the discrete Fourier transform. The first component can, for example, correspond to an imaginary part of order "2p" of the Fourier-transformed angular error.Here, the third correction coefficient can correspond to an equivalent relative amplitude of the sine channel. The fourth correction coefficient can correspond to an equivalent relative amplitude of the cosine channel. The third and fourth correction coefficients can also be simplified and combined into a single correction coefficient, which represents the ratio of the two correction coefficients.

[0028] In a further advantageous embodiment of the method, at least one additional correction coefficient can be determined which is suitable for compensating a component of the angular error based on an angular offset error. For example, a fifth correction coefficient can be calculated as the mean of the angular errors of the majority of at least two previously provided measurement signals.

[0029] Exemplary embodiments of the invention are shown in the drawings and are explained in more detail in the following description. In the drawings, identical reference numerals denote components or elements that perform the same or analogous functions. Brief description of the drawings Fig. Figure 1 shows a schematic flowchart of an embodiment of a method according to the invention for correcting measurement signals. Fig. Figure 2 shows a schematic representation of an embodiment of a sensor arrangement according to the invention during the determination of correction coefficients during the execution of the method according to the invention. Fig. 1. Fig. Figure 3 shows a schematic representation of the sensor arrangement according to the invention during a correction of measurement signals during the execution of the method according to the invention. Fig. 1. Embodiments of the invention

[0030] As from Fig. 1, Fig. 2 to Fig. As can be seen in Figure 3, the illustrated embodiment of a method 100 according to the invention for correcting measurement signals MS1, MS2, MS3 comprises a step S200 in which at least two measurement signals MS1, MS2, MS3 are currently provided by at least one sensor unit 3. In a step S210, at least two processed measurement signals a, b are generated based on the at least two currently provided measurement signals MS1, MS2, MS3. From these, in a step S220, two corrected measurement signals ac, bc are generated using angle-independent calculations and at least one correction coefficient K. From these, a corrected angle WK is calculated in a step S230. The method then returns to step S200. Additionally, in a vehicle application, the calculated angle WK can be output to higher-level vehicle functions in step S230.

[0031] To determine at least one correction coefficient K, a plurality N of at least two measurement signals MS1 is determined in a preliminary step S100. j, MS2 j , MS3 j is provided. Based on the plurality N of at least two pre-provided measurement signals MS1 j, MS2 j , MS3 j In step S110, two processed measurement signals are each used. j , b j generated. Based on the two processed measurement signals a j , b j and a reference angle WR, a corresponding angular error dW is calculated in one step S120. j calculated. Based on at least one step of an iteratively applicable calculation method, at least one correction parameter P is calculated in step S130. i determined. In step S140, based on at least one correction parameter P, a correction parameter is determined. iwhich determines at least one correction coefficient K such that a remaining angular error dW in the corrected angle WK is smaller than an angular error dW in an angle W which is based on the two processed current measurement signals a, b.

[0032] As from Fig. 2 and Fig. As can be seen further in Figure 3, the illustrated embodiment of the sensor arrangement 1 according to the invention comprises at least one sensor unit 3 and at least one evaluation and control unit 10 and is designed to carry out the method 100 according to the invention. In the illustrated embodiment, the sensor arrangement 1 comprises only one sensor unit 3 and only one evaluation and control unit 10 with several functional blocks for carrying out the method 100.

[0033] As from Fig. As can be seen further in Figure 2, the sensor unit 3 provides three measurement signals MS1 for determining the at least one correction coefficient K for a plurality N of samples or measurements in the illustrated embodiment. j, MS2 j , MS3; ready. When processing the plurality N of three pre-provided measurement signals MS1. j, MS2 j , MS3 j In a first transformation block 12, a Clarke transformation is performed on each of the three previously provided measurement signals MS1. j, MS2 j , MS3 j into a first processed measurement signal a based on a periodic sine function with a predetermined period "p". j and into a second processed measurement signal b based on a periodic cosine function with the specified period "p". j This is carried out. The first processed measurement signal a jassigned to a sine channel 12.1, and the second processed measurement signal b j is assigned to a cosine channel 12.2.

[0034] As an iterative calculation method for determining the at least one correction coefficient K, a first calculation block 14 of the evaluation and control unit 10 in the illustrated embodiment applies an iterative Newton method, which is based on a first partial derivative of a sum of squares of the angular error dW j with regard to at least one correction parameter P i or a quantity based thereon, or an approximation of a quantity based thereon. Here, the sum of the squared angular errors dW is used. j The correction coefficient K, determined by iterative application of the calculation method, is preferably minimized. In the illustrated embodiment, the at least one correction parameter P corresponds to this. ia correction vector. One step of the iteratively applicable calculation method results in the illustrated embodiment of the method 100 according to equation (1). Pk+1=Pk−[D1D2D3D4]

[0035] Here, P k+1 the new estimate for at least one correction parameter P i , and P k is the previous estimate of at least one correction parameter P i or an initial starting value P0 of the at least one correction parameter P i .

[0036] The calculation of at least one correction parameter Pi is based on at least one division of at least two cumulative sums. These at least two cumulative sums are based on the plurality N of at least two pre-provided measurement signals MS1. j, MS2 j , MS3 j and / or the previous and / or the current correction parameters P iand / or an associated angular error dW j The iterative calculation method, or iterative Newton's method, terminates, for example, through convergence or after a certain number of iterations. The number of iterations can be predefined. Alternatively, the number of steps in the iterative Newton's method can be determined by evaluating the plurality N of calculated angular errors dW. j dependent. The evaluation includes, for example, an analysis of the harmonic components of the angular error dW. j In another alternative, the number of steps of the iteratively applicable calculation method or the iterative Newton method depends on an evaluation of the correction parameters P determined in successive steps of the iterative Newton method. i dependent. The evaluation considers the majority N of calculated angular errors dW. jor the correction parameters P determined in successive steps of the iterative Newton method i The system is subjected to at least one mathematical operation, and the result of this operation is compared to a corresponding threshold. The iterative calculation method, or the iterative Newton method, terminates if the result of the operation falls below the threshold.

[0037] In the illustrated embodiment, four divisions D1, D2, D2, D4 of each of two cumulative sums according to equations (2), (3), (4), (5) are used to determine the at least one correction parameter P i to calculate. K1=D1=S1S2=∑j=1NdWj(acjnj2)∑j=1N(acj2nj4) K2=D2=S3S4=∑j=1NdWj(−bcjnj2)∑j=1N(bcj2nj4) K3=D3=S5S6=∑j=1NdWj(acjbcjnj2)∑j=1N(acj2bcj2nj4) K4=D4=S7S8=∑j=1NdWj(acj2−bcj22nj2)∑j=1N((acj2−bcj2)24nj4)

[0038] Here, ac j a corrected processed first measurement value, bc j a corrected processed second measurement value and n j is a vector length of a vector which, according to equation (6), is derived from the corrected processed first measurement ac j and the corrected processed second measurement bc j results and is calculated by calculation block 14 of the evaluation and control unit 10. nj=acj2−bcj2

[0039] Preferably, common factors, such as the squared vector length n, are used. j , the fourth power of the vector length n j and / or the factors (ac j * bc j ) or ((ac j ) 2 * (bc j ) 2 ) only once per angular position or "pair of values" a j , b jcalculated by calculation block 14 of evaluation and control unit 10 and then reused.

[0040] The sums S1, S2, S3, S4, S5, S6, S7, S8 in equations (2) to (5) are cumulatively summed in each iteration step during a movement across the measurement range and evaluated at the end of the measurement range to obtain the new estimate for the at least one correction parameter P i to obtain the corresponding iteration step. Preferably, the sampling takes place at regular intervals during the movement with respect to the reference angle WR. j instead, or the measurement signals MS1 j, MS2 j , MS3 j or the processed measurement signals a j , b jare interpolated to uniform intervals. After each step of the iterative calculation method or the iterative Newton method, a correction parameter P is applied in a determination block 16 of the evaluation and control unit 10. i The at least one correction coefficient K is determined and evaluated. If the determined at least one correction coefficient K fulfills the conditions mentioned above, then the iterative calculation method or the iterative Newton method is terminated. The iterative calculation method or the iterative Newton method can be terminated after the first step if the at least one correction parameter P is based on the initial starting value P0. iThe correction coefficient K is based on the conditions. If the determined at least one correction coefficient K does not meet the above-mentioned conditions, then the iterative calculation method or the iterative Newton method is continued with the next iteration step. After completion of the iterative calculation method or the iterative Newton method, the at least one correction coefficient K is output and preferably stored in a memory 18. Iteration steps following the first iteration step can be performed with newly acquired measurement signals MS1 during a mechanical movement. j , MS2 j , MS3; can be performed. Alternatively, the measurement signals MS1 can also be used in a subsequent iteration step. j, MS2 j , MS3 j and / or the processed measurement signals a j , b jData from a previous iteration step can be reused and stored, for example, in a buffer. This saves on repeated mechanical movement and offers the advantage that the process can be carried out in a shorter time.

[0041] In the illustrated embodiment, a first correction coefficient K1 is determined by a first division D1 of a first sum S1 and a second sum S2 according to equation (2). A second correction coefficient K2 is determined by a second division D2 of a third sum S3 and a fourth sum S4 according to equation (3). Here, the first and second correction coefficients K1 and K2 are suitable for correcting a component of the angular error dW based on a harmonic oscillation of order "p". j to compensate. Here, the value "p" corresponds to a number of periods of the first and second processed measurement signals a. j , bj The first correction coefficient K1 is used to compensate for an offset error in the processed first measurement signal aj. The second correction coefficient K2 is used to compensate for an offset error in the processed second measurement signal b. j to compensate.

[0042] A third correction coefficient K3 is determined by a third division D3 of a fifth sum S5 and a sixth sum S6 according to equation (4). The third correction coefficient K3 is suitable for correcting a first component of the angular error dW based on a harmonic oscillation of order “2p”. j to compensate. The third correction coefficient K3 is used to compensate for an amplitude mismatch in the at least two processed measurement signals a j , b j to compensate. Here, the value "p" corresponds to a number of periods of the first and second processed measurement signals a. j , b j .

[0043] A fourth correction coefficient K4 is determined by a fourth division D4 of a seventh sum S7 and an eighth sum S8 according to equation (5). The fourth correction coefficient K4 is suitable for correcting a second component of the angular error dW based on a harmonic oscillation of order “2p”. j to compensate. The fourth correction coefficient K4 is used to correct an orthogonality error in the at least two processed measurement signals a j , b j to compensate. Here, the value "p" corresponds to a number of periods of the first and second processed measurement signals a. j , b j .

[0044] In the illustrated embodiment of method 100, the four correction coefficients K1, K2, K3, K4 are used to correct the processed first measurement signal ac. j according to equation (7) and the corrected processed second measurement signal bc jto be calculated according to equation (8). In this embodiment, the processed second measurement signal b serves as the basis. j as a reference for amplitude and orthogonality, and is therefore offset-compensated only using the second correction coefficient K2. This choice is arbitrary. Naturally, a choice of the processed first measurement signal a is also possible. j This can be used as an amplitude and orthogonality reference. Alternatively, an amplitude mismatch and an orthogonality error can be applied proportionally to the processed first measurement signal a. j and on the processed second measurement signal b j This can be done, for example, indirectly by correcting the absolute amplitudes of the processed first measurement signal a. j and the processed second measurement signal b j possible. acj=K3(aj−K1)−K4bcj bcj=(bj−K2)

[0045] When the iterative calculation method or the iterative Newton method is carried out by the calculation block 14 of the evaluation and control unit 10, an initial correction parameter P0 is specified, preferably estimated, before the first step of the iterative calculation method or the iterative Newton method. The initial correction parameter P0 is used to adjust the corresponding first and second measurement signals a, which are sampled during a first movement across the measuring range. i , b i to correct the first N corrected processed first measurement signals ac i to be calculated according to equation (7) and the first N corrected processed second measurement signals bc iThe electrical angular errors dWj for a corresponding sample j are calculated according to equation (8). The calculation is performed in the calculation block 14 of the evaluation and control unit 10 based on the corrected, processed first measurement signal ac. j of the sine channel 12.1 and the corrected processed second measurement signal bc j of the cosine channel 12.2 taking into account a provided corresponding reference angle WR j The reference angle WR j This can be provided, for example, by a drive system of a moving body whose angular position or position is to be determined. dWj=(arctan(acj(W)bcj(W)))−(p∗WRj)

[0046] Equation (9) is only valid for a limited range of the electric angle W, since the quadrants are ambiguous and division by zero may occur. In practice, this problem is solved by a modified arctangent function with two arguments, denoted as atan2(a j ,b j ) is known. Here, the arctan result is unwrapped to remove the influence of discontinuities.

[0047] In the illustrated embodiment, the iterative Newton-Raphson method applies a diagonal approximation of an inverse Hessian matrix or an approximation of the diagonal approximation of the inverse Hessian matrix. This avoids the numerically expensive inversion of the Hessian matrix or the solution of a system of linear equations. Instead, the easily computed cumulative sums D1, D2, D3, D4 are used. The diagonal approximation simplifies the matrix inversion to a simple division. As an example, a vector (10) corresponding to an identity correction is specified as the initial correction parameter P0. To further simplify the cumulative sums D1, D2, D3, D4, the partial derivatives for the Newton-Raphson method can be calculated assuming that the correction parameter P0 corresponds to the vector (10). This does not significantly affect the convergence of the method. P0=

[0010]

[0048] Based on vector (10), the first correction coefficient K1, the second correction coefficient K2, and the fourth correction coefficient K4 each have the value "0". The third correction coefficient K3 has the value "1". Therefore, the corrected, processed first measurement signal corresponds to ac. j before the first iteration step, the processed first measurement signal a j and the corrected processed second measurement signal bc j Before the first iteration step, this corresponds to the processed second measurement signal b j .

[0049] In the illustrated embodiment, the determination block 16 additionally determines a fifth correction coefficient K5, which is suitable for calculating a component of the angular error dW that is based on an angular offset error. jto compensate. To avoid numerical problems, the angular error in the cumulative sums D1, D2, D3, D4 can advantageously be corrected with the fifth correction coefficient K5, in particular by subtracting K5. Particularly advantageously, alternatively or in addition to unwrapping the angular error, the value "pi" can be added to the calculated angular error, the result normalized modulo "2 * pi", and then the value "pi" subtracted again, as can be seen from equation (9A). With a suitable choice of the fifth correction coefficient K5, explicit unwrapping can thus be avoided in many cases. The fifth correction coefficient K5 is advantageously chosen such that the offset of the angular error is as small as possible. For example, K5 can be determined from the first observed, uncorrected angular error. Subsequently calculated angular errors can then be corrected directly with K5. dWj=(((arctan(acj(W)bcj(w)))−(p∗WRj)−K5+π)mod 2π)−π

[0050] In an alternative embodiment of method 100 (not shown), only the first correction coefficient K1 and the second correction coefficient K2 are determined using the iteratively applicable calculation method or the iterative Newton method, respectively. To determine the third correction coefficient K3 and the fourth correction coefficient K4, the angular error dW is used. j The data is subjected to a discrete Fourier transform (DFT). For this purpose, the evaluation and control unit 10, in a transformation block not shown in detail, subjects the angular error dW to the data. j The discrete Fourier transform (DFT) calculates the coefficients X[0], X[p], X[2p], which are used to determine the third correction coefficient K3 and the fourth correction coefficient K4. From the amplitude-normalized discrete Fourier transform (DFT) of the angular error dW jThe coefficients X[0], X[p], X[2p] of the discrete Fourier transform DFT are calculated according to equations (11) and (12) over N samples across the entire mechanical measuring range. X=DFT{dWj} X[k]={1N∑j=0N−1dWjk=02N∑j=0N−1dWje−2πijkNk>0

[0051] Here, a real part of "X[0]" is equal to the mean value of the angular error dW. j The magnitude of “X[k]” is equal to the amplitude of a sine curve of the k-th harmonic oscillation, provided that the angular error dW j is real, where "i" is the imaginary unit. To calculate the third correction coefficient K3 and the fourth correction coefficient K4, a third coefficient X[2p] of the discrete Fourier transform (DFT) is used, which is based on a harmonic oscillation of order "2p". Here, the value "p" corresponds to the period p of the first and second processed measurement signals a. j , b j .

[0052] Preferably, the discrete Fourier transform (DFT) is calculated in several cumulative sums of the individual signals from the two corrected, processed measurement signals ac. j , bc j calculated angular error dW j carried out, which is based on the majority N of the three processed measurement signals a j , b j based on the three previously provided measurement signals MS1 j, MS2 j , MS3 j based on. Alternatively, the discrete Fourier transform (DFT) can be applied to the entirety of the respective processed measurement signals derived from the two corrected signals ac. j , bc j calculated angular errors dW j be applied.

[0053] The fifth correction coefficient K5 corresponds, according to equation (13), to a real part RE of the first coefficient X[0] of the discrete Fourier transform DFT and is given as the mean of the angular errors dW. jcalculated. The individual angular errors dW j are based on an angle W, which is derived from the plurality N of the corrected processed measurement signals ac. j , bc j is determined, and the corresponding reference angle WR j The fifth correction value, K5, can be determined as a mean angular deviation between the measured angle W and the reference angle WR. j can be interpreted, which may be caused, for example, by the installation of sensor unit 3. K5=Re{X[0]}

[0054] Based on the third coefficient X[2p] of the discrete Fourier transform DFT and the fifth correction coefficient K5, the third correction coefficient K3 is calculated according to equation (14). In the illustrated embodiment, the first correction coefficient K1 and the second correction coefficient K2 are also taken into account when calculating the improved third correction coefficient K3' according to equation (14A). K3=1−Im{X[2p]e−i2(K5)}1+Im{X[2p]e−i2(K5)}cos(K4) K3'=1−Im{X[2p]e−i2(K5)}+12((K2)2−(K1)2)1+Im{X[2p]e−i2(K5)}+12((K2)2−(K1)2)cos(K4')

[0055] Based on the third coefficient X[2p] of the discrete Fourier transform DFT and the fifth correction coefficient K5, the fourth correction coefficient K4 is calculated according to equation (15). In the illustrated embodiment, the first correction coefficient K1 and the second correction coefficient K2 are also taken into account when calculating the improved fourth correction coefficient K4' according to equation (15A). K4=2Re{X[2p]e−i2(K5)} K4'=2Re{X[2p]e−i2(K5)}+(K1)(K2)) vK4=K4'−(112(K4')3)

[0056] Additionally, when calculating a further improved fourth correction coefficient vK4 according to equation (15B), a third power of the improved fourth correction coefficient K4 can be used. This allows for a smaller residual error in cases of large orthogonality errors. Furthermore, a tangent function can be applied to K4 or K4' for further improvement.

[0057] In the calculations of the third and fourth correction coefficients K3, K4, as well as the improved third and fourth correction coefficients K3', K4', and the further improved fourth correction coefficient vK4, the fifth correction coefficient K5 is used in each case to compensate for the influence of the mean angular deviation. Alternatively, this can also be done by already calculating the angular error dW. j is compensated with a correction coefficient similar to the fifth correction coefficient K5, which is achieved, for example, by an additional prior calculation of the angular error dW. j is determined.

[0058] As from Fig. As can be seen further in Figure 3, the sensor unit 3 provides three current measurement signals MS1, MS2, and MS3 based on a current sampling or measurement in the illustrated embodiment. During the processing of the three current measurement signals MS1, MS2, and MS3, the first transformation block 12 performs the Clarke transformation of the three currently provided measurement signals MS1, MS2, and MS3, transforming them into a first processed measurement signal a based on a periodic sine function with a predefined period p and into a second processed measurement signal b based on a periodic cosine function with the predefined period p. The first processed measurement signal a is assigned to the sine channel 12.1, and the second processed measurement signal b is assigned to the cosine channel 12.2.

[0059] As from Fig.As can be seen further in Figure 3, in the illustrated embodiment, a correction block 20 generates the first corrected measurement signal ac according to equation (16) based on the processed current first measurement signal a, the processed current second measurement signal b, the first correction coefficient K1, the second correction coefficient K2, the third correction coefficient K3 and the fourth correction coefficient K4. The correction coefficients K1, K2, K3, K4 are provided by the storage unit 18. ac=(K3(a−K1))−(K4(b−K2))

[0060] Based on the processed current second measurement signal b and the second correction coefficient K2, the correction block 20 generates the second corrected measurement signal bc according to equation (17). The second correction coefficient K2 is provided by the storage unit 18. bc=(b−K2)

[0061] Advantageously, the calculation of the corrected, processed second measurement signal bc from equation (17) can be reused in equation (16). In output block 22, the corrected angle WK is calculated and output from the corrected measurement signals ac and bc. Here, any remaining angular error dW in the corrected angle WK is smaller than an angular error dW in an angle based on the two processed but uncorrected measurement signals a and b. Additionally, an angular offset in the corrected angle WK can be compensated for using the fifth correction coefficient K5.

Claims

[1] Method (100) for correcting measurement signals (MS1, MS2, MS3), wherein at least two measurement signals (MS1, MS2, MS3) are currently provided by at least one sensor unit (3) (S200), wherein at least two processed measurement signals (a, b) are generated based on the at least two currently provided measurement signals (MS1, MS2, MS3) (S210), from which two corrected measurement signals (ac, bc) are generated using angle-independent calculations and at least one correction coefficient (K) (S220), from which a corrected angle (WK) is calculated (S230), wherein a plurality (N) of at least two measurement signals (MS1) are pre-processed to determine the at least one correction coefficient (K). j , MS2 j , MS3 j ) is provided (S100), based on the plurality (N) of at least two pre-provided measurement signals (MS1) j , MS2 j , MS3 j ) each two processed measurement signals (aj , b j ) are generated (S110), based on the two processed measurement signals (a j , b j ) and a reference angle (WR j ) a corresponding angular error (dW) j ) is calculated (S120), wherein at least one correction parameter (P) is calculated based on at least one step of an iteratively applicable calculation method. i ) is determined (S130), where at least one correction parameter (P) is based on the i ) the at least one correction coefficient (K) is determined (S140) such that a remaining angular error (dW) in the corrected angle (WK) is smaller than an angular error (dW) in an angle (W) based on the two processed current measurement signals (a, b). [2] Method (100) according to claim 1, characterized by , that during the processing of the majority (N) of at least two pre-provided measurement signals (MS1) j , MS2 j , MS3 j) and / or of the at least two currently provided measurement signals (MS1, MS2, MS3) a transformation and / or a filtering of the at least two previously provided measurement signals (MS1) j , MS2 j , MS3 j ) and / or the measurement is carried out using at least two currently available measurement signals (MS1, MS2, MS3). [3] Method (100) according to claim 1 or 2, characterized by , that a first processed measurement signal (a j ) of at least two pre-provided measurement signals (MS1) j , MS2 j , MS3 j ) and a first processed measurement signal (a) from at least two currently provided measurement signals (MS1, MS2, MS3) each based on a periodic sine function with a predetermined period (p) and assigned to a sine channel (12.1), and a second processed measurement signal (b j ) of at least two pre-provided measurement signals (MS1) j , MS2 j , MS3j ) and a second processed measurement signal (b) from at least two currently provided measurement signals (MS1, MS2, MS3) each based on a periodic cosine function with the specified period (p) and assigned to a cosine channel (12.2). [4] Method (100) according to any one of claims 1 to 3, characterized by , that the angular error (dW) j ) is minimized by at least one correction coefficient (K) determined by iterative application of the calculation method. [5] Method (100) according to any one of claims 1 to 4, characterized by , that an iterative Newton method is applied as an iteratively applicable calculation method, which is based on a first partial derivative of a sum of squares of the angular error (dW). j ) with regard to at least one correction parameter (P i ) or a quantity based on it or an approximation of a quantity based on it. [6] Method (100) according to any one of claims 1 to 5, characterized by , that the calculation of at least one correction parameter (P i ) is based on at least one division of at least two cumulative sums. [7] Method (100) according to claim 6, characterized by , that the at least two cumulative sums are based on the majority (N) of at least two pre-provided measurement signals (MS1) j , MS2 j , MS3 j ) and / or the previous and / or the current correction parameters (P i ) and / or an associated angular error (dW) j are based on... [8] Method (100) according to any one of claims 5 to 7, characterized by , that a number of steps of the iterative Newton method is fixed. [9] Method (100) according to any one of claims 5 to 7, characterized by, that a number of the steps of the iterative Newton method depend on an evaluation of the majority (N) of calculated angular errors (dWj). [10] Method (100) according to claim 9, characterized by , that the assessment includes an evaluation of harmonic components of the angular error (dWj). [11] Method (100) according to any one of claims 5 to 7, characterized by , that a number of the steps of the iterative Newton method depend on an evaluation of the correction parameters (P) determined in successive steps of the iterative Newton method i is dependent on. [12] Method (100) according to any one of claims 5 to 11, characterized by , that an initial correction parameter (P0) is specified, preferably estimated, before a first step of the iterative Newton method. [13] Method (100) according to any one of claims 9 to 12, characterized by, that the majority (N) of calculated angular errors (dWj) or the correction parameters (P) determined in successive steps of the iterative Newton method i ) are subjected to at least one mathematical operation during the evaluation and the result of the at least one mathematical operation is compared with a corresponding threshold, whereby the iterative Newton method is terminated if the result of the at least one mathematical operation falls below the corresponding threshold. [14] Method (100) according to any one of claims 5 to 13, characterized by , that the iterative Newton method applies a diagonal approximation of an inverse Hessian matrix or an approximation of the diagonal approximation of the inverse Hessian matrix. [15] Method (100) according to claim 14, characterized by, that at least two correction coefficients (K1, K2) are determined which are suitable to compensate for a component of the angular error (dWj) based on a harmonic oscillation of order (p). [16] Method (100) according to claim 14 or 15, characterized by , that at least one further correction coefficient (K3) is determined which is suitable to compensate for a first component of the angular error (dWj) based on a harmonic oscillation of order (2p). [17] Method (100) according to any one of claims 14 to 16, characterized by , that at least one further correction coefficient (K4) is determined which is suitable to compensate for a second component of the angular error (dWj) based on a harmonic oscillation of order (2p). [18] Method (100) according to claim 14, characterized by, that the angular error (dWj) is subjected to a discrete Fourier transformation (DFT), whereby at least one further correction coefficient (K3, K4) is determined based on coefficients (X[0], X[p], X[2p]) of the discrete Fourier transformation (DFT). [19] Method (100) according to claim 18, characterized by , that the at least one further correction coefficient (K3, K4) is suitable to compensate for at least one component of the angular error (dWj) based on a harmonic oscillation of order (2p). [20] Method (100) according to any one of claims 14 to 19, characterized by , that additionally at least one correction coefficient (K5) is determined which is suitable to compensate for a component of the angular error (dWj) based on an angular offset error. [21] Sensor arrangement (1) comprising at least one sensor unit (3) and at least one evaluation and control unit (10) and configured to perform the method (100) according to any one of claims 1 to 20.

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