Method for approximating a measurement signal from a sensor element using a Kalman filter arrangement and a measurement arrangement

Abstract

According to the invention, a method for approximating a measurement signal from a sensor element using a Kalman filter arrangement (10) is claimed, wherein the measurement signal is supplied as an input measurement value (y) to a main filter (12) of the Kalman filter arrangement, and the main filter outputs an estimated value (x^) of a system state, which is determined relative to the input measurement value (y) of the measurement signal as a function of an estimated measurement noise parameter (R) and a system noise parameter (Q), wherein the main filter (12) is extended by parallel secondary filter arrangements (20, 30), wherein a first secondary filter arrangement (20) is configured for adaptively determining the measurement noise parameter (R) and a second filter arrangement (30) is configured for determining a main filter power (M) in order to adaptively determine the system noise parameter (Q) together with the measurement noise parameter (R). The invention further relates to a method with a filter group and a measurement arrangement.

Description

[0001] The invention relates to a method for approximating a measurement signal of a sensor element by means of a Kalman filter arrangement and to a measuring arrangement.

[0002] Generic Kalman filter arrangements are used to approximate a measured signal as closely as possible to a true system state.

[0003] Measurement signals from a sensor element can be corrupted by noise during transmission, whereby any deviation from the originally transmitted measurement signal can only be estimated at the receiver end. Furthermore, a true process value of a system state can be corrupted by the measurement method itself. For example, the sensor element may be designed as a vibration sensor, whereby the true vibration of a machine component, as a system state, can often only be estimated.

[0004] One approach to estimating original measurement signals or a system state is the application of a filter model described by Kalman. It models a system for calculating an estimated output value or an estimate, using past output values ​​and current measured values ​​for the measurement signal to be estimated. The so-called Kalman filter has the advantage of exploiting statistical properties of the measurement signal and the associated measured values ​​to adequately track rapid changes in the measurement signal to be estimated. The Kalman filtering method is particularly suitable for cases in which measured values ​​are determined stepwise or iteratively.

[0005] DE 10 2020 004 836 A1 shows methods for object tracking and fusion of at least two sensor signals, wherein two filters are executed to determine a measurement noise covariance of the sensor signals, wherein the two sensor signals, a first measurement noise covariance and a first system noise covariance are passed to a third filter and a fusion of the two sensor signals is carried out.

[0006] In detail, the Kalman filter is a filter that performs an exponential approximation of an input measurement value from the sensor element. The Kalman filter can be implemented in three preferred standard variants: alpha, beta, and / or gamma. These standard variants differ primarily in the number of mathematical derivatives used to model system behavior over time. The alpha filter preferably models the measured value in a time-independent manner as follows: x=y*K+(1−K)*x

[0007] Equation GL1, where x is the filtered estimate, y is the input measurement value, and K is a Kalman gain parameter. The Kalman gain parameter is preferably calculated using a measurement noise parameter R and a system noise parameter Q according to the following equation GL2: K=−1 / 2*Q / R+√((1 / 4*(Q / R)∧2+Q / R))

[0008] For the determination of the Kalman gain parameter K, further equations are preferably applicable to smooth the Kalman gain parameter if the measurement noise parameter R and / or the system noise parameter Q is / are changed. It is particularly relevant that the Kalman gain parameter K converges exponentially according to the formula GL2.

[0009] The measurement noise parameter R represents a variance, also known as the squared standard deviation, of the measured value y. The system noise parameter Q represents the variance, also known as the squared standard deviation, of the true system state z, specifically a true process value. In a standard Kalman filter or static Kalman filter, the parameters R and Q are manually set and are not automatically calculated or estimated. There are a multitude of ways in which the Kalman filters can be manually selected or adjusted, which complicates the use of the Kalman filter for new applications.

[0010] Manual adjustment of the parameters for the standard Kalman filter is preferably selected based on previously known measurement values. For example, the estimated measurement noise parameter R is preferably adjusted to a value for local noise in the measured value to achieve particularly good performance of the Kalman filter. However, such an estimation has the disadvantage that the filter does not function well if the measurement noise parameter changes during a measurement, for example, due to sudden measurement value jumps or peaks within the recorded measurement signal.

[0011] A static Kalman filter may be sufficient or even desirable in some scenarios. However, if it is used to predict a process value with many unpredictable changes, the Kalman filter is preferably designed to be adaptive in order to cope with the changing conditions. In particular, for nonlinear dynamic systems or measurement signals with unpredictably abrupt measured value changes, the Kalman filter can have additional subfilters to automatically adapt to the numerous setting options for measurement noise and system noise during the runtime of the measurement signal. For example, a so-called ROSE filter can be used for this purpose, which is published in Marchthaler, R. and Dingler, S., Kalman Filter: Introduction to State Estimation and its Application for Embedded Systems, Springer-Vieweg (2017). The ROSE filter has a main filter and two subfilter arrangements.

[0012] To adaptively determine the measurement noise parameter R, the ROSE filter comprises a first sub-filter arrangement with a static alpha-Kalman filter. A temporally subsequent input measurement value is input into this alpha-Kalman filter to determine a predicted output value. The deviation value is then calculated as the difference between the newly predicted output value and the measured value. A squared deviation value is then multiplied by a correction parameter to compensate for the deviation caused by the approximation of the alpha-Kalman filter. After the variance has been calculated, it is passed through another alpha-Kalman filter, using the following equation GL3: R=dyR2*α*γ+(1−α)*R

[0013] The equation GL3 gives dyR as the deviation value, γ as the correction parameter and α as an attenuation parameter for the alpha Kalman filter.

[0014] For adaptive determination of the system noise parameter, in addition to estimating the measurement noise parameter, a main filter performance is determined using a second sub-filter arrangement. A deviation value of the main filter is determined and fed to a static alpha-Kalman filter. In other words, the only difference from the prediction of the measurement noise parameter is that the prediction, from which the difference to the measured value is derived, is provided by the main filter and not by an alpha-Kalman sub-filter. The main filter performance is calculated using the following equation GL4, where dy is the deviation value of the main filter: M=dy2*α*γ+(1−α)*M

[0015] The estimation of the system noise parameter is simplified by calculating the variance of the predicted, in particular filtered, main filter power M as follows using equation GL5: Q=M−R−P

[0016] P is used as an intermediate value to calculate the Kalman gain parameter. The intermediate value P is intended to add stability to the ROSE filter and compensate for an already specified high Kalman gain parameter.

[0017] A disadvantage of the well-known ROSE filter has been found to be the considerable effort required to design and configure additional secondary filter arrangements. Furthermore, it has been shown that an implementation of the ROSE filter for measurement signals with abrupt changes in the measured value is very susceptible to overshooting of a sudden rising measurement signal edge, especially of a target measured value or target signal.

[0018] The object of the invention is to propose a method for approximating a measurement signal by means of a Kalman filter arrangement, which is easier to configure while avoiding the problems known from the prior art and provides improved approximation even for discontinuous measurement signals.

[0019] Furthermore, the task is to specify a measuring arrangement for processing measured values ​​of a sensor element by means of a Kalman filter arrangement.

[0020] The problem is solved with regard to the method by the features of claim 1 and with regard to the measuring arrangement by the features of claim 6.

[0021] Advantageous embodiments of the invention are specified in the subclaims.

[0022] According to the invention, a method for approximating a measurement signal of a sensor element using a Kalman filter arrangement is claimed. The measurement signal is fed to a main filter of a Kalman filter arrangement as an input measurement value, and the main filter outputs an estimated value of a system state that is determined from the input measurement value of the measurement signal as a function of an estimated measurement noise parameter and a system noise parameter. In particular, the estimated value is exponentially approximated to the input measurement value of the measurement signal, the approximation being dependent on a Kalman gain parameter that is determined by estimating the measurement noise parameter and the system noise parameter.The main filter is extended by parallel secondary filter arrangements, wherein a first secondary filter arrangement is designed for the adaptive determination of the measurement noise parameter and a second secondary filter arrangement is designed for the determination of a main filter power in order to adaptively determine the system noise parameter together with the measurement noise parameter.

[0023] The method comprises the following steps according to the invention to react to unpredictable and sudden changes in the measured value within the measurement signal, which are listed in a preferred order. Any modification, in particular a parallel evaluation of the steps, is possible.

[0024] According to a preferred first step, the main filter performance is determined from the input measured value and a previous estimated value of the main filter. After a preferred second step, the measurement noise parameter is transferred to the second secondary filter arrangement, and a difference value between the main filter performance and the measurement noise parameter is evaluated. The difference value is then preferably transferred, together with the measurement noise parameter, to a system noise estimate. After a preferred third step, a recalculation of a system noise estimate is triggered if a comparison value between the difference value and the measurement noise parameter exceeds a predefined limit. In particular, a sudden change in the measured value can be detected based on the comparison value.

[0025] In this context, a larger main filter power preferably indicates a larger variance of the main filter estimate compared to the input measurement value.

[0026] The invention recognizes the advantage that, by evaluating a comparison value and recalculating it, the multitude of parameters for estimating the measurement noise parameter and the main filter performance do not have to be manually adjusted and adapted, but rather only the required precision with the predefined limit value needs to be manually specified. This significantly simplifies the adjustment of the filter arrangement. Furthermore, the invention has the advantage that adaptation to sudden changes in the measured value occurs automatically and the accuracy of the approximation to a strongly varying input measured value is improved. In particular, the proposed measurement filter arrangement can reduce overshoot of the estimated value and approximate the input measured value with a shorter control time. Overall, the method enables simpler operation and an improved approximation of measurement signals.

[0027] Preferably, for recalculating the system noise parameter of a previous time step, it is increased by a proportion of the measurement noise parameter depending on the level of the comparison value.

[0028] If no sudden change in the measured value is detected, the system noise parameter of the main filter is preferably reduced exponentially, whereby preferably no recalculation is carried out, but the system noise parameter is passed directly to the main filter.

[0029] According to a preferred embodiment, the recalculation of the system noise parameter is carried out over a reaction time with a number of measurements parameterized in order to confirm the detection of the sudden change in the measured value over n measurements, wherein after the reaction time has elapsed, the estimated value is adjusted to the change in the measured value with a time delay.

[0030] Such a recalculation over multiple measurements has the advantage that the filter can be implemented more stably and at the same time more agilely. This stability results in particular from the fact that the filter always has at least n measurements that can be used to converge to a system state. Improved agility preferably results from the fact that the determination of the main filter performance and the measurement noise parameter is performed over n measurements to recalculate the system noise parameter. Changes due to a sudden change in the measured value, especially for the main filter performance, can be more easily detected.

[0031] Particularly preferably, maximum value filtering is performed using the first secondary filter arrangement to stabilize the measurement noise parameter, with the second secondary filter arrangement evaluating a discrepancy integral of the difference value between the main filter power and the measurement noise parameter over the reaction time. The comparison value is calculated from a ratio between the discrepancy integral and a product of the maximum noise parameter and the number of measurements. The limit value is preferably reached if the discrepancy integral is greater than the product of the maximum noise parameter and the number of measurements.

[0032] Preferably, the use of maximum value filtering of the measurement noise parameters over the response time ensures that measurement noise itself is not detected as a sudden change in the measured value. It is preferably assumed that the measurement noise parameter exhibits a smaller change compared to the measured value jumps in the measurement signal. In particular, it is assumed that the level of measurement noise is highly unlikely to change over time and that maximum filtering also represents the measurement noise over a longer period of time.

[0033] The discrepancy integral over the response time is preferably evaluated as follows from the difference evaluation between the main filter performance and the measurement noise parameter: Mc=∫i=−n0(M(i+t)−R(i+t))di

[0034] GL6 specifies Mc as the discrepancy integral, t as the current measurement number, and n as the number of response time measurements. Instead of a direct comparison between the maximum noise parameter and the main filter performance, the result of the difference evaluation M - R is summed and stored over the most recent measurements. Depending on the desired limit value, the discrepancy integral, also called the comparison integral, is then compared with the product of the maximum noise parameter and the number of measurements to determine whether the system noise parameter needs to be recalculated. In other words, the limit value is selected or replaced by setting the response time. This has the advantage that, with the selected response time, only one parameter needs to be selected to adaptively determine the system noise parameter.

[0035] Through the aforementioned parameterization and recalculation over the response time, the control time and transient response of the filter arrangement can be advantageously shortened in the event of signal changes, while still ensuring long-term stability. In other words, the filter arrangement can achieve relatively high long-term stability even with short response times. A particularly characteristic of the parameterized recalculation is a certain dead time of the filtered estimate during the response time, during which the filter arrangement preferably waits for further input measured values ​​to confirm the detection of a sudden change in the measured value. Subsequently, the filtered estimate preferably jumps abruptly to the new curve and settles again in the shortest possible time.

[0036] According to a further development, it is preferred that the recalculation over the reaction time be parameterized by means of a storage unit for the input measured value and the determination of a discrepancy integral, whereby the oldest stored values ​​up to the most recent value are evaluated sequentially. In particular, this is a so-called FIFO buffer.

[0037] In addition, the invention also relates to a method for approximating a measurement signal by means of a filter group, wherein the filter group forms at least one previously described first Kalman filter arrangement and at least one second Kalman filter arrangement, wherein the at least one first filter arrangement is designed to estimate a measurement signal with sudden changes in the measured value, wherein the at least one second Kalman filter arrangement is designed under the assumption of a measurement signal without sudden changes in the measured value, wherein the at least one first and the at least one second Kalman filter arrangement are implemented in parallel and the estimated values, the main filter powers, the measurement noise parameters and the system noise parameters of the filter arrangements are compared together in a fusion unit in order to determine the most probable estimated value for the measurement signal.

[0038] Preferably, setting parameters of the at least one second Kalman filter arrangement can be selected with respect to a preferably constant measurement signal to enable an even better approximation of the measurement signal outside of areas with abrupt changes in the measured value. In other words, the second Kalman filter arrangement is more accurate for constant measurement signals, while the first Kalman filter arrangement enables a more accurate approximation of the measured value for changing signals.

[0039] Particularly preferably, a plurality of first and / or a plurality of second Kalman filter arrangements can be used, each of which achieves an improved approximation with predetermined setting parameters for different measurement signals. For example, the first Kalman filter arrangements can have different limit values ​​and / or preferably different response times.

[0040] To select the preferred filter arrangement, the different system noise parameters are preferably weighted if the at least one first and at least one second filter arrangement have already closely approximated the system state. If a larger deviation from the system state exists, the main filter performances of the filter arrangements are preferably compared to evaluate the most probable estimate.

[0041] Furthermore, the invention relates to a measuring arrangement for processing measured values ​​of a sensor element with a Kalman filter arrangement or a filter group and a control unit for carrying out the above-mentioned method, wherein the measuring arrangement has an input interface for receiving the measured values ​​and an output interface for outputting filtered output values.

[0042] Preferably, the measuring arrangement is designed by means of a storage unit to store and evaluate input measured values ​​in a parameterized manner over a reaction time, wherein filtered estimated values ​​of the measuring arrangement for a sudden change in the measured value of the measuring signal are tracked over the reaction time.

[0043] In particular, the filtered estimated value shows a characteristic dead time depending on the reaction time, during which the filter arrangement preferably waits for further input measured values ​​in order to confirm the detection of a sudden change in the measured value and wherein the estimated value is subsequently adapted to the sudden change in the measured value.

[0044] The invention is explained in more detail below using exemplary embodiments with reference to the drawings.

[0045] They show schematically: Fig. 1a Block diagram of a ROSE filter arrangement, Fig. 1b Measured value approximation with a simulated ROSE filter arrangement according to the Fig. 1a, Fig. 2a Block diagram of an adapted Kalman filter arrangement, Fig. 2b Measured value approximation using an embodiment of the Kalman filter arrangement according to the Fig. 2a, Fig. 3 Measured value approximation using a Kalman filter arrangement according to the Fig. 2a

[0046] In the following description of the preferred embodiments, like reference numerals designate like or comparable components.

[0047] The Fig. 1a shows a simulated ROSE filter arrangement 11 from the prior art, wherein the Rose filter arrangement comprises a main filter 12 and two parallel secondary filter arrangements 20, 30 for adaptively determining a measurement noise parameter R, a main filter power M, and a system noise parameter Q by a separate system noise estimator 40. A noisy input measured value y of a measurement signal is fed to the two secondary filter arrangements 20, 30 and the main filter 12.

[0048] For adaptive determination of the measurement noise parameter R, the ROSE filter arrangement 11 has a first secondary filter arrangement 20 with a first static Kalman filter 21. A subsequently input measured value y is input into the Kalman filter 21 to determine a predicted output value. Subsequently, a deviation value dyR is calculated as the difference between the predicted output value and the input measured value y. A squared deviation value dyR 2 is then multiplied by a correction parameter to compensate for the deviation caused by the approximation of the first Kalman filter. Subsequently, the squared deviation value dyR 2to another static Kalman filter 21 to determine the measurement noise parameter R. In parallel, a main filter power M is determined by means of a second secondary filter arrangement 30. In this case, a deviation value dy of the main filter 12 is determined, which is dependent on the noisy input measured value y. A squared deviation value dy 2 is fed to a static Kalman filter 21 and corrected with a correction parameter.

[0049] Preferably, the Kalman filters 21 are designed as alpha filters, wherein the correction parameters and filter parameters for the alpha filter for determining the measurement noise parameter R and the main filter power M can have different values.

[0050] The measurement noise parameter R and the main filter power M are fed together with an intermediate value P as an estimation error of the system state directly to a recalculation of the system noise parameter Q. Furthermore, a noise-free input value u is fed to the main filter 12 and an estimated value x^ for a system state is output using the system noise parameter Q

[0051] The Fig. Figure 1b shows an example of an estimated value x^ of the ROSE filter 11, which is approximated to an input measured value y of a measurement signal in order to estimate a true system state value z, which is evaluated here by simulation. The measurement signal exhibits a sudden change in the measured value 50, with the estimated value x^ strongly overshooting in the range of the change in the measured value 50 and requiring a control time Tr to approximate the system state value z.

[0052] The Fig. Fig. 2a shows a preferred embodiment of a Kalman filter arrangement 10 according to the invention with a main filter 12 and two secondary filter arrangements 20, 30 for the adaptive determination of the measurement noise parameter R and the system noise parameter Q. In contrast to the known ROSE filter arrangement 11 according to the Fig. 1a, in a preferred first method step according to the invention, the main filter power M is determined from the input measured value y and a previous estimated value x^ of the main filter 12. In a preferred second step, in particular a difference evaluation 32, the measurement noise parameter R is evaluated by the second secondary filter arrangement 30, and a difference value MR between the main filter power M and the measurement noise parameter R is evaluated and transferred to a system noise estimator 40. According to a preferred third method step, a system noise estimator 40 is recalculated 16 if a comparison value between the difference value MR and the measurement noise parameter R exceeds a predefined limit and a sudden change in the measured value 50 is detected. The Kalman filter arrangement 10 preferably has a buffer 14 in order to feed a previous input measured value y back to the filtering for the recalculation 16.In this case, the system noise parameter Q of a previous time step is preferably increased by a proportion of the measurement noise parameter R depending on the magnitude of the comparison value. If no sudden change in the measured value 50 is detected, the system noise parameter Q is preferably reduced exponentially and preferably passed directly to the main filter 12 for approximating the input measured value y.

[0053] To evaluate the measurement noise parameter R and the main filter power M, both secondary filter arrangements 20, 30 preferably have static Kalman filters 21, in particular alpha-beta filters. Through the difference evaluation 32 and the recalculation 16, an estimated value x^ for the main filter power M can be directly obtained. Alternatively, other filtering methods can also be used to estimate the main filter power M and the measurement noise parameter R.

[0054] The Fig. 2b shows an example of an output of an estimated value x^ for a sudden change in the measured value 50, where, in comparison to the evaluation using the ROSE filter according to the Fig. 1b a significantly shorter control time Tr can be achieved.

[0055] Particularly preferably, the recalculation is carried out over a reaction time nr with a number of measurements n in order to confirm the detection of the sudden change in the measured value 50 over n measurements. If a significant deviation of the estimated value x^ from the input measured values ​​y parameterized over the reaction time nr is detected in the last n measurements, a recalculation 16 of these n measurements can preferably be carried out with an adjusted system noise parameter Q in order to adapt the estimated value x^ more quickly to the new or jumpy system state. Preferably, after the reaction time nr has elapsed, the estimated value x^ is adjusted with a time delay to track the change in the measured value 50. Such adjustment is described in the Fig. 3, where the estimated value x^ is adjusted in steps to the input measured value y.

[0056] Further preferably, the estimation methods for the main filter power M and the measurement noise parameter R are also parameterized as a function of the response time nr using the parameterized input measured values ​​y. In this case, the input measured value y is preferably parameterized and recalculated in a buffer 14 according to the number of measurements n, wherein the buffer 14 is preferably designed as a FIFO buffer. Advantageously, calibration of the static Kalman filters 21 can therefore be dispensed with, with filtering preferably only depending on a cyclic input of the input measured value y.

[0057] Again Fig. 2a, the parameterized input measured value y is particularly preferably fed into the first secondary filter arrangement 20 for estimating the measurement noise parameter R. To stabilize the measurement noise parameter R, a maximum value filtering 22 is carried out to determine a maximum noise parameter Rmax. Preferably, the maximum value filtering 22 is also carried out over the response time nr using a FIFO buffer. The maximum value filtering 22 always supplies the maximum value of R that is currently in the buffer storage, whereby the length of the buffer storage depends on the response time nr. The maximum noise parameter Rmax is then passed on to the main filter 12 and a product of the maximum noise parameter and the number of measurements Rmax * n is passed on to the system noise estimation 40. The measurement noise parameter R is then passed on to the second secondary filter arrangement 30 and the difference evaluation 32.

[0058] In parallel with the measurement noise parameter evaluation, the main filter power M is calculated using the second secondary filter arrangement 30 by using the estimated value x^ of the main filter 12. The estimated value x^ is preferably already updated to a timestamp of the current input measured value y. Subsequently, the main filter power M and the measurement noise parameter R of the first secondary filter arrangement 20 are fed to the difference evaluation 32. In an integration step 34, a discrepancy integral is calculated over the difference value MR and the response time nr, wherein a FIFO buffer is preferably used as an intermediate storage to sum the difference value MR over the length of the response time nr. The discrepancy integral is subsequently forwarded to the system noise estimation 40.

[0059] In the system noise estimation 40, the discrepancy integral evaluation from the integration step 34 is compared with the product of the maximum noise parameter Rmax over the number of measurements n as a reference value. A recalculation 16 is preferably triggered if the discrepancy integral, as a limit value, is greater than the specified product and a module for recalculating the input measured value y is currently inactive. Otherwise, the newly determined system noise parameter Q is preferably simply fed to the main filter 12.

[0060] If the recalculation 16 of the input measured value y has been triggered, a recalculation of the input measured value y in the buffer 14 is activated, wherein the aforementioned steps for evaluating the system noise parameter Q are repeated using the two secondary filter arrangements 20, 30, and the input measured value y is replaced by buffered input measured values ​​y . Preferably, the steps are repeated for each value in the buffer, from the oldest to the newest. Further preferably, the recalculation 16, in particular a recalculation module, is transferred to a passive state if the aforementioned calculation for the newest input measured value y is completed.

[0061] The Fig. 3 shows an example measurement signal with input measurement value y and an estimated value x^, where in comparison to the Fig. 2b, the control time Tr can be further shortened by the aforementioned parameterization via the reaction time nr. In particular, the filtered estimated value x^ shows a certain dead time during the reaction time nr, during which the filter arrangement 10 waits for further measured values ​​in order to also adjust a sudden change in the measured value 50 in a sudden manner. The approximation adjusts itself in a very short time, in particular with a much more stable and precise course compared to the ROSE filter according to the Fig. 1b.

[0062] According to a preferred embodiment, a filter group 100 with multiple system models is used, in particular at least one previously described first Kalman filter arrangement 100, 100a. In parallel, further second Kalman filter arrangements 100b can be used, each having a different system model. In particular, the system model of a main filter 12 of the Kalman filter arrangements 100a, 100b can be selected differently. Each Kalman filter arrangement 100a, 100b forwards the current estimated values ​​x^i, the main filter powers Mi, the measurement noise parameters Ri, and the system noise parameters Qi to a fusion unit 18, where i indicates the index value of the various filter arrangements. The fusion unit 18 then calculates a new, unified prediction, in particular the most probable current system state x^a, and preferably outputs a first index value within a system state vector x^a to a user as output.

Claims

[1] Method for approximating a measurement signal of a sensor element by means of a Kalman filter arrangement (10), wherein the measurement signal is supplied to a main filter (12) of the Kalman filter arrangement (10) as an input measurement value (y) and the main filter outputs an estimated value (x^) of a system state, which is determined from the input measurement value (y) of the measurement signal as a function of an estimated measurement noise parameter (R) and a system noise parameter (Q), wherein the main filter (12) is extended by parallel secondary filter arrangements (20, 30), wherein a first secondary filter arrangement (20) is designed for adaptively determining the measurement noise parameter (R) and a second secondary filter arrangement (30) is designed for determining a main filter power (M) in order to adaptively determine the system noise parameter (Q) together with the measurement noise parameter (R), with the following steps: - determining the main filter performance (M) from the input measured value (y) and a previous estimated value (x^) of the main filter (12), - feeding the measurement noise parameter (R) to the second sub-filter arrangement (30) and evaluating a difference value (MR) between the main filter power (M) and the measurement noise parameter (R), - triggering a recalculation (16) of a system noise estimate (40) if a comparison value between the difference value (MR) and the measurement noise parameter (R) exceeds a predefined limit value and a sudden change in the measured value (50) is detected. [2] Method according to claim 1, characterized by that during a recalculation (16) the system noise parameter (Q) of a previous time step is increased by a proportion of the measurement noise parameter (R) depending on a level of the comparison value. [3] Method according to claim 1 or 2, characterized bythat the recalculation (16) is carried out parameterized over a reaction time (nr) with a number of measurements (n) in order to confirm the detection of the sudden change in the measured value (50) over n measurements, wherein after the reaction time (nr) has elapsed the estimated value (x^) is adjusted with a time delay to the change in the measured value (50). [4] Method according to claim 3, characterized by that a maximum value filtering (22) for determining a maximum noise parameter (Rmax) is carried out by means of the first secondary filter arrangement (20) for stabilizing the measurement noise parameter (R), wherein the second secondary filter arrangement (30) evaluates a discrepancy integral (Mc) of the difference value (MC) over the reaction time (nr), wherein the comparison value is calculated from a ratio between the discrepancy integral (Mc) and a product of the maximum noise parameter with the number of measurements (Rmax*n). [5] Method according to claim 3 and 4, characterized bythat the recalculation (16) is carried out over a reaction time (nr) by means of a storage unit for the input measured value (y) and the determination of the discrepancy integral (Mc), wherein the oldest stored values ​​up to the most recent value are evaluated one after the other. [6] Method for approximating a measurement signal by means of a filter group (100), wherein the filter group (100) forms at least one first Kalman filter arrangement (100a) according to one of claims 1 to 5 and at least one second Kalman filter arrangement (100b), wherein the at least one first filter arrangement (100a) is designed to estimate a measurement signal with abrupt changes in the measured value (50), wherein the at least one second Kalman filter arrangement (100b) is designed under the assumption of a measurement signal without abrupt changes in the measured value (50), wherein the at least one first and the at least one second Kalman filter arrangements (100a, 100b) are executed in parallel and the estimated values ​​(x^i), the main filter powers (Mi), the measurement noise parameters (Ri) and the system noise parameters (Qi) of the filter arrangements (100a, 100b) are compared together in a fusion unit (18) in order to determine the most probable To determine the estimated value (x^a). [7] Measuring arrangement for processing measuring signals of a sensor element with a Kalman filter arrangement and a control unit for carrying out the method according to one of claims 1 to 6, wherein the measuring arrangement has an input interface for accepting the measured values ​​and an output interface for outputting filtered output values. [8] Measuring arrangement according to claim 7, characterized by that the measuring arrangement is designed by means of a storage unit to store and evaluate input measured values ​​(y) of the measuring signal over a reaction time (nr) in a parameterized manner, wherein filtered estimated values ​​(x^) of the measuring arrangement for a sudden change in the measured value (50) of the measuring signal are tracked over the reaction time (nr).

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