SENSOR SYSTEM AND METHOD FOR MEASURING A PROCESS VALUE OF A PHYSICAL SYSTEM

Abstract

The present disclosure describes a sensor system for measuring a process value of a physical system, including: a plurality of sensors, wherein each sensor is configured to generate a sense signal as a function of the process value at a given time; a system state corrector configured to determine an actual system state of the physical system at a given state update cycle; a system state predictor configured to determine a predicted system state of the physical system at a given prediction cycle from a previous system state at a previous state update cycle; a sense signal predictor configured to determine predicted sense signals at the given prediction cycle from the predicted system state by applying a first operation to the predicted system state using a sense signal model of the physical system for predicting the sense signals.

Claims

1. A sensor system for measuring a process value of a physical system, comprising: a plurality of sensors wherein each sensor is configured to generate a sense signal as a function of the process value at a given time; a system state corrector configured to determine an actual system state of the physical system at a given state update cycle, wherein the system state comprises the process value at the given state update cycle and at least a first order derivative of the process value at the given state update cycle; a system state predictor configured to determine a predicted system state of the physical system at a given prediction cycle from a previous system state at a previous state update cycle; a sense signal predictor configured to determine predicted sense signals at the given prediction cycle from the predicted system state by applying a first operation to the predicted system state using a sense signal model of the physical system for predicting the sense signals; wherein the system state corrector is configured to determine the actual system state at the given state update cycle by applying a second operation to the predicted system state according to an error signal representative of the difference between a set of acquired sense signals acquired from the sense signals each at the given prediction cycle and the corresponding predicted sense signals for each of the acquired sense signals .

2. The sensor system as claimed in claim 1, wherein the set of the acquired sense signals comprises one sense signal from one of the sensors, or a plurality of sense signals from more than one but less than all of the sensors such that the set of the acquired sense signals contains only a partial information of the system state, wherein the partial information is not sufficient to deterministically identify the system state at the state update cycle.

3. The sensor system as claimed in claim 1, wherein the set of the acquired sense signals comprises sense signals from more than one or all of the sensors, wherein each of the acquired sense signals corresponds to the same given time.

4. The sensor system as claimed in claim 1, wherein the set of the acquired sense signals comprises sense signals from more than one or all of the sensors, wherein at least two of the acquired sense signals correspond to different given times.

5. The sensor system as claimed in claim 1, wherein the set of the acquired sense signals comprises selected sense signals from more than one but less than all of the sensors, wherein, among all of the sense signals, at the prediction cycle the selected sense signals contain a more accurate information of the system state or have at least first order derivatives with a larger absolute value than the non-selected sense signals.

6. The sensor system as claimed in claim 1, wherein the sense signal predictor is configured to determine only the predicted sense signals corresponding to the set of acquired sense signals at the given prediction cycle.

7. The sensor system as claimed in claim 1, wherein the first and second operations constitute an extended Kalman filter or a non-linear Kalman filter.

8. The sensor system as claimed in claim 1, wherein the first operation comprises a multi-order harmonic expansion as a function of the process value.

9. The sensor system as claimed in claim 1, wherein the process value is a position of a position indicator being movable relative to the sensors.

10. The sensor system as claimed in claim 1, further comprising at least one analog-to-digital converter for quantizing at least one of the sense signals generated by the sensors and for providing the quantized sense signals as the acquired sense signals.

11. A method for measuring a process value of a physical system, comprising the steps of: (i) providing a plurality of sensors each generating a sense signal as a function of the process value at a given time; (ii) determining an actual system state of the physical system at a given state update cycle, wherein the system state comprises the process value at the given state update cycle and at least a first order derivative of the process value at the given state update cycle; (iii) determining a predicted system state of the physical system at a given prediction cycle from a previous system state at a previous state update cycle; (iv) determining predicted sense signals at the given prediction cycle from the predicted system state by applying a first operation to the predicted system state using a sense signal model of the physical system for predicting the sense signals; wherein step is carried out by applying a second operation to the predicted system state according to an error signal representative of the difference between a set of acquired sense signals acquired from the sense signals each at the given prediction cycle and the corresponding predicted sense signals for each of the acquired sense signals.

12. The method as claimed in claim 11, wherein the set of the acquired sense signals comprises sense signals from more than one or all of the sensors, wherein each of the comprised sense signals is acquired from the respective sensors at the same given time.

13. The method as claimed in claim 11, wherein the set of the acquired sense signals comprises sense signals from more than one or all of the sensors, wherein at least two of the acquired sense signals is acquired at different given times.

14. The method as claimed in claim 11, wherein selected sense signals from more than one but less than all of the sensors are selected to constitute the set of the acquired sense signals such that, among all of the sense signals, at the prediction cycle the selected sense signals contain a more accurate information of the system state or have at least first order derivatives with a larger absolute value than the non-selected sense signals.

15. The method as claimed in claim 11, wherein an extended Kalman filter or a non-linear Kalman filter is constituted by the first and second operations.

16. The method as claimed in claim 11, wherein, in the first operation, a multi-order harmonic expansion is used as a function of the process value.

17. The method as claimed in claim 11, wherein a position of a position indicator being movable relative to the sensors is measured as the process value.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0056] These and other features and advantages of the disclosed embodiments will be apparent from the following description of non-limiting embodiments of the disclosed embodiments which will be elucidated below with reference to the drawing.

[0057] In the drawing, schematically:

[0058] FIG. 1 shows a functional diagram of an exemplary embodiment of a sensor system for measuring a process value of a physical system according to an embodiment.

[0059] FIG. 2 illustrates a functional part of the sensor system of FIG. 1 in more detail.

[0060] FIG. 3 shows the timely course of sense signals, acquired sense signals, and determined system states of the sensor system of FIG. 1.

[0061] FIG. 4 shows a functional diagram of another exemplary embodiment of a sensor system for measuring a process value of a physical system according to an embodiment.

[0062] FIG. 5 illustrates a functional part of the sensor system of FIG. 4 in more detail.

[0063] FIG. 6 shows the timely course of sense signals, acquired sense signals, and determined system states of the sensor system of FIG. 4 according to an exemplary first operational mode.

[0064] FIG. 7 shows the timely course of sense signals, acquired sense signals, and determined system states of the sensor system of FIG. 4 according to an exemplary second operational mode.

[0065] FIG. 8 shows the timely course of sense signals, acquired sense signals, and determined system states of the sensor system of FIG. 4 according to an exemplary third operational mode.

[0066] FIG. 9 shows a flowchart of an exemplary embodiment of method for measuring a process value of a physical system according to an embodiment.

[0067] In the various figures, equivalent elements with respect to their function are usually provided with the same reference numerals/signs so that these elements are usually described only once.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

[0068] Various embodiments will now be described by means of the Figures.

[0069] FIG. 1 shows a functional diagram of an exemplary embodiment of a sensor system 1 for measuring a process value φ(t) of a physical system 2 according to an embodiment. As illustrated in FIG. 1, the exemplary sensor system 1 comprises a plurality of sensors HE.sub.i, namely r sensors, i.e. i=1 . . . r. In the present example, the sensors HE.sub.i are magnetic sensors, such as Hall sensors for example, to sense a magnetic field. The magnetic field is generated by a position indicator 7 rotatable relative to the sensors HE.sub.i as indicated by a respective arrow in FIG. 1. Furthermore, the position indicator 7 is formed by a permanent magnet in the exemplary case having poles N(orth) and S(outh). The magnet may be connected to a drive shaft of a motor (not shown), e.g. an electric motor, however, without being limited thereto. It is to be understood that the magnetic field may be generated by other means than a permanent magnet, for example by an electric current flowing through an electromagnetic coil, a solenoid, an electric conductor and the like.

[0070] Consequently, the process value φ(t) being measured by the sensor system 1 of FIG. 1 is an angular position of the position indicator 7 when rotating relative to the sensors HE.sub.i arranged circumferentially arranged around the position indicator 7.

[0071] Each sensor HE.sub.i is configured to generate a sense signal q.sub.i(t) as a function of the process value φ(t) at a given time t.sub.k, t.sub.i,k.

[0072] Further regarding FIG. 1, the sensor system 1 comprises a system state corrector 3 configured to determine an actual system state {right arrow over (x)}.sub.k|k of the physical system 2 at a given state update cycle k. The state update cycle k corresponds to the aforementioned time instant t.sub.k. As illustrated in FIG. 1, the system state {right arrow over (x)}.sub.k|k comprises the process value φ.sub.k|k (here a digital representation of the process value φ(t) at the given state update cycle k and a first order derivative ω.sub.k|k (also a digital representation) of the process value φ(t) at the given state update cycle k. As the process value φ(t) to be measured by the sensor system 1 is an angle, the first order derivative ω.sub.k|k is an angular velocity of the position indicator 7. It is to be understood that still higher order derivatives may be included in the system state {right arrow over (x)}.sub.k|k as well, such as a second order derivative of the process value φ(t) which would represent an angular acceleration of the position indicator 7.

[0073] Further, the sensor system 1 illustrated in FIG. 1 also comprises a system state predictor 4 configured to determine a predicted system state {right arrow over (x)}.sub.k|k−1 of the physical system 2 at a given prediction cycle k from a previous system state {right arrow over (x)}.sub.k−1|k−1 at a previous state update cycle k−1. As shown in the functional diagram in FIG. 1, the previous system state from a previous state update cycle k−1 is provided by a delay unit 6. In a simple implementation, this delay unit may be a memory unit (e.g. RAM, Register of μP or μC and the like) storing at least one system state {right arrow over (x)}.sub.k|k after being output by the state corrector 3 so that it can be used in a subsequent state update cycle as the previous system state {right arrow over (x)}.sub.k−1|k−1.

[0074] Still further, the sensor system 1 comprises a sense signal predictor 5 configured to determine predicted sense signals {circumflex over ({right arrow over (q)})}.sub.k|k−1 at the given prediction cycle k from the predicted system state {right arrow over (x)}.sub.k|k−1 by applying a first operation to the predicted system state {right arrow over (x)}.sub.k|k−1 using a sense signal model N (cf. FIG. 2) of the physical system 2 for predicting the sense signals {circumflex over ({right arrow over (q)})}.sub.k|k−1. In the present case, the sense signal model N is a model matrix having as many rows as available sensors and sense signals, respectively, to predict the sense signals {circumflex over ({right arrow over (q)})}.sub.k|k−1 at the given prediction cycle k. In other words, the model matrix N describes the measuring process of the physical system 2. The information thereof may be obtained in an additional calibration process of the sensor system 1 which may be performed once before the first operation of the sensor system 1.

[0075] Yet further, the system state corrector 3 of the sensor system 1 in FIG. 1 is configured to determine the actual system state {right arrow over (x)}.sub.k|k at the given state update cycle k by applying a second operation K, in the present case a Kalman filter operation, to the predicted system state {right arrow over (x)}.sub.k|k−1 according to an error signal {right arrow over (y)}.sub.k|k−1 (cf. FIG. 2) representative of the difference between a set of acquired sense signals {right arrow over (q)}.sub.k acquired from the sense signals q.sub.i(t) at the given prediction cycle k and the corresponding predicted sense signals {circumflex over ({right arrow over (q)})}.sub.k|k−1 for each of the acquired sense signals {right arrow over (q)}.sub.k.

[0076] In the presented example of the sensor system 1 in FIG. 1, the set of the acquired sense signals {right arrow over (q)}.sub.k always comprises sense signals q.sub.i(t) from all of the sensors HE.sub.i, i.e. each of the acquired sense signals {right arrow over (q)}.sub.k relates to the same given time instant t.sub.k at the given prediction cycle k (uniform sampling). To this end, a multichannel analog-to-digital converter ADC.sub.m is provided in the sensor system 1. Each channel of the multichannel ADC.sub.m is connected to a respective one of the sensors HE.sub.i to facilitate simultaneous acquisition of all sense signals q.sub.i(t) at the time instant t.sub.k. After the A/D conversion, the multichannel ADC.sub.m outputs the digital representations of the sense signals q.sub.i(t) as the acquired sense signals {right arrow over (q)}.sub.k.

[0077] FIG. 2 illustrates a functional part of the sensor system 1 of FIG. 1 in more detail. The functional part shown in detail in FIG. 2 corresponds to the dashed box in FIG. 1.

[0078] As clearly shown, the sense signal predictor 5 uses the sense signal model N which describes the measurement process of the physical system 2 to predict the predicted signals {circumflex over ({right arrow over (q)})}.sub.k|k−1. From information gathered at the calibration phase of the sensor system 1, the model matrix N and the characteristics n of (possibly present) higher harmonics is identified. To this end, the model matrix N may comprise row and column entries, wherein, for example, each row may relate to the sense signal of one sensor (i.e. the number of rows may equal the total number of different sensors) and the column entries of the model matrix N (i.e. the entries of each row) may refer to the components of a total number m of considered harmonics which may be assessed during the calibration process as already mentioned further above.

[0079] In general, a pair of cos (n*x), sin (n*x) is a single harmonic of order n, i.e. a full complex harmonic order as the natural space is the complex numbers. Therefore, all harmonics of order equal to 1 or greater than 1 consist of two components (i.e. sine and cosine), and a 0.sup.th order has only one component which is the constant “1”.

[0080] As shown in FIG. 2, in the illustrated exemplary embodiment of the predictor 5, two full complex harmonics of order 1 and n, respectively, are used in the prediction operation, wherein—without being mandatory—the optional 0.sup.th harmonic (entry “1”) is used in this example as well to compensate for a constant offset (e.g. a sensor offset). It is to be noted that the constant term (0.sup.th order), if present, is not mandatory to be considered at this specific place/operation as it may be possible to subtract a constant offset by other means as well. The total number m of the harmonics used, i.e. the specific characteristic(s)/components of each harmonic as well as the optional compensation for a constant offset, may be chosen according to specific application requirements.

[0081] This allows for an accurate and fast prediction of the predicted signals {circumflex over ({right arrow over (q)})}.sub.k|k−1 form the predicted system state {right arrow over (x)}.sub.k|k−1 provided by the system state predictor 4. The system state corrector 3 may then adapt the Kalman filter operation to evaluate the corrected system state {right arrow over (x)}.sub.k|k from the error signal, i.e. the difference between the acquired (measured) sense signals {right arrow over (q)}.sub.k at the given prediction cycle k and the corresponding predicted signals {circumflex over ({right arrow over (q)})}.sub.k|k−1 at the same given prediction cycle k: {right arrow over (y)}.sub.k|k−1={right arrow over (q)}.sub.k−{circumflex over ({right arrow over (q)})}.sub.k|k−1.

[0082] It is to be noted that, in the present example of the sensor system 1, each state update cycle corresponds to one single prediction cycle, therefore each of these cycles may be indexed by the same index letter k.

[0083] Furthermore, an integral part of the Kalman filtering process is the prediction and the correction of the so-called state covariance, a calculation, which includes estimates of the noise affecting the dynamic physical system and the measurement/acquisition process.

[0084] FIG. 3 shows the timely course of the sense signals q.sub.i(t), corresponding acquired sense signals {right arrow over (q)}.sub.k and determined system states {right arrow over (x)}.sub.k|k of the sensor system 1 of FIG. 1 in the case of six (r=6) individual sensors HE.sub.i generating the sense signals q.sub.i(t).

[0085] In FIG. 3, the acquired sense signals {right arrow over (q)}.sub.k, their digital representations being indicated by solid line boxes below the timely course of the respective sense signals q.sub.i(t), and the updated system states {right arrow over (x)}.sub.k|k are shown for three state update cycles k=1 . . . 3. In the graphs depicting the updated system states {right arrow over (x)}.sub.k|k the state update cycles k are represented by their corresponding times t.sub.1, t.sub.2, and t.sub.3. In the graphs depicting the sense signals q.sub.i(t) the state update cycles k (being equivalent to the prediction cycles k in this case) for each signal channel i are represented by their corresponding times t.sub.i,1 . . . t.sub.i,3.

[0086] The system state vector {right arrow over (x)}.sub.k|k consisting of the components angle φ.sub.k|k and angular velocity ω.sub.k|k is updated in each of the three denoted update cycles k at time instants t.sub.k. In the illustrated operation mode “uniform sampling” of the sensor system 1 of FIG. 1, the system state {right arrow over (x)}.sub.k|k is updated after each complete signal acquisition and prediction cycle using the difference (error signal) {right arrow over (y)}.sub.k|k−1={right arrow over (q)}.sub.k−{circumflex over ({right arrow over (q)})}.sub.k|k−1 (r-vector) between the corresponding predicted sense signals {right arrow over (q)}.sub.k and the acquired sense signals {circumflex over ({right arrow over (q)})}.sub.k|k−1 acquired at the same time instants t.sub.1,k=t.sub.2,k=. . . =t.sub.6,k. As examples, the system state graph indicates the state update cycles k=2 and k=3 by dash-dotted vertical lines at the time instants t.sub.2, t.sub.3 after completion of a full sense signal acquisition cycle.

[0087] FIG. 4 shows a functional diagram of another exemplary embodiment of a sensor system 10 for measuring a process value φ(t)) of a physical system, e.g. the physical system 2 of FIG. 1, according to an embodiment.

[0088] Essentially, the sensor system 10 of FIG. 4 differs from the sensor system 1 shown in FIG. 1 in the following features: [0089] Non-uniform sampling: The r channels for the sense signals q.sub.i(t) are now multiplexed and discretized in a single-channel ADC to sequentially obtain the signals q.sub.i,k, i=1, . . . , r [0090] Each of these r different sense signals q.sub.i(t) is used in turn in a related prediction and correction step sequence as before in the case of the uniform sampling approach.

[0091] In the case of the sensor system 10, the sampling period may be chosen by a factor 1/r smaller, i.e. T.fwdarw.T/r. In this way the same overall signal rate r/T is maintained as before in the case of the uniform sampling approach used with the sensor system 1 of FIG. 1.

[0092] FIG. 5 illustrates a functional part of the sensor system 10 of FIG. 4 in more detail. The functional part shown in detail in FIG. 5 corresponds to the dashed box in FIG. 4.

[0093] During the i-th part-cycle {i,k} of the illustrated non-uniform sampling case, only the appropriate i-th row of the model matrix N.sub.ij, wherein j=1, . . . , 2m or j=1, . . . , 2m+1 depending on the presence of the constant component (e.g. sensor offset), is used to predict the corresponding i-th signal value {circumflex over (q)}.sub.i,k|k−1. Nonetheless, the prediction depends on all previous state information as before, i.e. considering the components/characteristics of the total number m of the harmonics used which have been assessed during the calibration process for example.

[0094] As already mentioned herein, a pair of cos (n*x), sin (n*x) is a single harmonic of order n, i.e. a full complex harmonic order as the natural space is the complex numbers. Therefore, all harmonics of order equal to 1 or greater than 1 consist of two components (i.e. sine and cosine), and a 0.sup.th order has only one component which is the constant “1”.

[0095] In the example depicted in FIG. 5, two full complex harmonics of order 1 and n, respectively, are used in the prediction operation, wherein—without any limitation thereto—the optional 0.sup.th harmonic (entry “1”) is used in this example as well to compensate for a constant offset (e.g. sensor offset). As mentioned above, the constant term is not mandatory to be considered at this specific place/operation as it may be possible to subtract a constant offset by other means as well. The total number m of the harmonics used, i.e. the specific characteristic(s)/components of each harmonic as well as the optional compensation for a constant offset, may be chosen according to specific application requirements.

[0096] The Kalman filter operations provide update formulas for the corrected state {right arrow over (x)}.sub.k|k depending on the scalar difference y.sub.i,k|k−1=q.sub.i,k−{circumflex over (q)}.sub.i,k|k−1 of the predicted and acquired sense signals for the i-th channel.

[0097] As in the case of the sensor system 1 of FIG. 1, the system state evaluations are adjoined by the corresponding state-covariance predictions and corrections (not shown in the figure).

[0098] FIG. 6 shows the timely course of the sense signals q.sub.i(t), acquired sense signals q.sub.i,k and determined system states of the sensor system 10 of FIG. 4 according to an exemplary first operational mode, i.e. operational mode “non-uniform sampling with single sense signal update”.

[0099] As shown in FIG. 6, the two upper graphs illustrating the system state {right arrow over (x)}.sub.k|k show the state vector consisting of the components angle φ.sub.k|k and angular velocity ω.sub.k|k which are updated in state update cycles k at time instants t.sub.k.

[0100] In the illustrated first operational mode, the system state {right arrow over (x)}.sub.k|k is updated at t.sub.k after each new sense signal acquisition process using the scalar difference y.sub.i,k|k−1=q.sub.i,k−{circumflex over (q)}.sub.i,k|k−1 between predicted and acquired (measured) sense signals at time t.sub.i,k for the i-th sensor channel. As examples, the graphs indicate the system state update cycles k=9 and k=10 by dash-dotted vertical lines at time instants t.sub.9, t.sub.10 after measuring the sensor channels i=3 and i=4, respectively.

[0101] FIG. 7 shows the timely course of the sense signals q.sub.i(t), acquired sense signals q.sub.i,k and determined system states {right arrow over (x)}.sub.k|k of the sensor system 10 of FIG. 4 according to an exemplary second operational mode, i.e. operational mode “non-uniform sampling multi-signal update”.

[0102] In FIG. 7, the two upper graphs illustrating the system state {right arrow over (x)}.sub.k|k show the state vector consisting of the components angle φ.sub.k|k and angular velocity ω.sub.k|k which are updated in state update cycles k at time instants t.sub.k.

[0103] In the illustrated second operational mode, the system state {right arrow over (x)}.sub.k|k is updated each time after a group/set of sense signals q.sub.i,k is acquired. In the example, the groups consist of two sensors each, measured at time instants t.sub.i,k, t.sub.i+1,k. Then, the difference

[00001]$\left(\begin{array}{c}{y}_{i,k.Math.k-1}\\ y_{i+1,k|k-1}\end{array}\right)=\left(\begin{array}{c}{q}_{i,k}\\ q_{i+1,k}\end{array}\right)-\left(\begin{array}{c}{\hat{q}}_{i,k.Math.k-1}\\ {\hat{q}}_{i+1,k|k-1}\end{array}\right)$

is used for the state update calculation, i.e. (only) the difference between predicted and measured sensor signal channels i and i+1. As examples, the graphs indicate the state update cycles k=4 and k=5 at instants t.sub.4, t.sub.5 by dash-dotted vertical lines after measuring the sensor channels i=1,2 and i=3,4, respectively.

[0104] FIG. 8 shows the timely course of the sense signals q.sub.i(t), acquired sense signals q.sub.i,k and determined system states {right arrow over (x)}.sub.k|k of the sensor system 10 of FIG. 4 according to an exemplary third operational mode, i.e. operational mode “non-uniform sampling with full signal update”.

[0105] Again in FIG. 8, the upper two graphs illustrating the system state {right arrow over (x)}.sub.k|k show the state vector consisting of the components phase φ.sub.k|k and angular velocity ω.sub.k|k in state update cycle k at time instant t.sub.k.

[0106] In the illustrated third operational mode, the system state {right arrow over (x)}.sub.k|k is updated after each complete sense signal acquisition cycle using the difference {right arrow over (y)}.sub.k|k−1={right arrow over (q)}.sub.k−{circumflex over ({right arrow over (q)})}.sub.k|k−1 (r-vector) between the corresponding predicted and measured/acquired sense signals at time instants t.sub.1,k, . . . , t.sub.6,k. As examples, the graphs indicate the state update cycles k=1 and k=2 at time instants t.sub.1, t.sub.2 by dash-dotted vertical lines after measuring the last sensor channel i=6 at t.sub.6,1 and t.sub.6,2, respectively.

[0107] FIG. 9 shows a flowchart of an exemplary embodiment of method 100 for measuring a process value φ(t) of a physical system, such as the physical system 2 in FIG. 1, according to embodiment employed in the sensor system 1 of FIG. 1.

[0108] As illustrated, the method 100 comprises the steps: [0109] Step 101: [0110] Providing a plurality of sensors HE.sub.i each generating a sense signal q.sub.i(t) as a function of the process value φ(t) at a given time t.sub.k. [0111] Step 101: [0112] Determining an actual system state {right arrow over (x)}.sub.k|k of the physical system 2 at a given state update cycle k, wherein the system state {right arrow over (x)}.sub.k|k comprises the process value φ.sub.k|k at the given state update cycle k and at least a first order derivative ω.sub.k|k of the process value φ(t) at the given state update cycle k. [0113] Step 103: Outputting the determined system state {right arrow over (x)}.sub.k|k. [0114] Step 104: [0115] Determining a predicted system state {right arrow over (x)}.sub.k|k−1 of the physical system 2 at a given prediction cycle k,{i,k} from a previous system state {right arrow over (x)}.sub.k−1|k−1 at a previous state update cycle k−1. [0116] Step 105: [0117] Determining predicted sense signals {circumflex over ({right arrow over (q)})}.sub.k|k−1, {circumflex over (q)}.sub.i,k|k−1 at the given prediction cycle k,{i,k} from the predicted system state {right arrow over (x)}.sub.k|k−1 by applying a first operation to the predicted system state {right arrow over (x)}.sub.k|k−1 using a sense signal model N of the physical system 2 for predicting the sense signals {circumflex over ({right arrow over (q)})}.sub.k|k−1, {circumflex over (q)}.sub.i,k|k−1.

[0118] Further in the method 100 illustrated in FIG. 9, step 101 is carried out by applying a second operation K to the predicted system state {right arrow over (x)}.sub.k|k−1 according to an error signal {right arrow over (y)}.sub.k|k−1, y.sub.i,k|k−1 representative of the difference between a set of acquired sense signals {right arrow over (q)}.sub.k, q.sub.i,k acquired from the sense signals q.sub.i(t) each at the given prediction cycle k,{i,k} and the corresponding predicted sense signals {circumflex over ({right arrow over (q)})}.sub.k|k−1, {circumflex over (q)}.sub.i,k|k−1 for each of the acquired sense signals {right arrow over (q)}.sub.k, q.sub.i,k.

[0119] If method 100 will be employed for operating the sensor system 1 of FIG. 1, the method 100 will only perform an outer loop 106 because for each state update cycle k there is only one prediction cycle k, i.e. acquisition and prediction of all sense signals in steps 101 and 105 is always performed simultaneously, i.e. at the same single time instant t.sub.k.

[0120] On the other hand, if method 100 will be employed for operating the sensor system 10 of FIG. 4, in the second and third operational modes of sensor system 10 shown in FIGS. 7 and 8, the method 100 will also perform an inner loop 107 in which a plurality of sense signals q.sub.i,k is acquired and a plurality of correspondingly sense signals {circumflex over (q)}.sub.i,k|k−1 is predicted each at different prediction cycles {i,k} corresponding to different time instants t.sub.i,k.

[0121] It is to be noted that, in order to further improve the accuracy of the prediction of the predicted system state, the system state predictor may additionally use a second order derivative of the process value of the last system state {right arrow over (x)}.sub.k−1|k−1, i.e. also an angular acceleration α in addition to the angular velocity ω and the angle φ shown in the system state predictors 4 and 12 in FIGS. 2 and 5, respectively.

[0122] Moreover, another route of possible further improvements addresses the sense signal model N. In the sensor systems 1 and 10 shown in FIGS. 2 and 5, respectively, the prediction of the sense signals {circumflex over ({right arrow over (q)})}.sub.k|k−1, {circumflex over (q)}.sub.i,k|k−1 only depends on the angle φ.sub.k|k−1 but not on the angular velocity ω.sub.k|k−1. However, real hardware cannot measure instantaneously and is therefore also affected by the predicted rotational speed ω.sub.k|k−1. Also modelling this dependency (e.g. using an integral of the state components over the measurement time interval), will have the beneficial effects that longer measurement times will reduce the signal noise in the acquired sense signals {right arrow over (q)}.sub.k, q.sub.i,k, and that the improved model for predicting the sense signals {circumflex over ({right arrow over (q)})}.sub.k|k−1, {circumflex over (q)}.sub.i,k|k−1=f(φ.sub.k|k−1, ω.sub.k|k−1, T/r) allows for an even more accurate system state correction.

[0123] While the various embodiments have been illustrated and described in detail in the drawings and the foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive.

[0124] From reading the present disclosure, other modifications will be apparent to persons skilled in the art. Such modifications may involve other features which are already known in the art and which may be used instead of or in addition to features already described herein.

[0125] Variations to the disclosed embodiments can be understood and effected by those skilled in the art, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality of elements or steps. The mere fact that certain measures are recited in different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

[0126] Any reference signs in the claims should not be construed as limiting the scope thereof.