Method for determining at least one system state by means of a Kalman filter

Abstract

The present invention relates to a method for determining at least one system state with the aid of a Kalman filter, wherein at least one measurement value measured by at least one sensor of the system is fed to the Kalman filter, the method comprising at least the following steps: a) performing an estimation of the system state with the aid of a Kalman filter, wherein an estimation result and at least one information regarding the reliability of the estimation result are output, b) determining a difference between at least one model value belonging to the estimation and at least one measurement value belonging to the estimation, and c) using the determined difference to correct at least one information regarding the reliability of the estimation.

Description

Technical Field

[0001] The invention relates to a method for determining at least one system state by means of a Kalman filter, a computer program for carrying out the method, a machine-readable storage medium storing the computer program, and a system for determining the position of a mobile object, in particular a vehicle, which is designed to carry out the method. The invention can be used in particular in conjunction with at least partially automated or autonomous driving. Background Art

[0002] Kalman filters are used for iterative estimation of system states based on observations that are usually prone to error. Kalman filters have proven to be particularly advantageous for application cases in which sensor information from different sensors must be combined (or fused), in particular with model information. Kalman filters are also often used in embedded systems, since their calculations are advantageously accurate and robust. Furthermore, microcontrollers can advantageously perform the calculations of Kalman filters efficiently.

[0003] The Kalman filter equation can be described in matrix notation as follows:

[0004]

[0005]

[0006]

[0007]

[0008]

[0009] If there is a corresponding model variable with the same scale for each measured variable and / or vice versa for each model variable, in particular explicit equations with the notation K, ∑1, ∑0, ∑1, μ′, μ0, μ1 can be used. If this is not the case, for example, equations with the notation H, K′, P, R, Equations GL3 to GL5 for z. For numerical calculations, the equations can be brought into explicit form, in particular by dividing both sides of the equation(s) by H or H'.

[0010] Equations GL1 and GL2 describe the iterative estimation process of the Kalman filter, and equations GL3 to GL5 describe the correction or fusion of the iteratively estimated model values ​​with the measured values ​​detected by the sensor. For a more detailed explanation, refer to the combined Figure 1 Description of the typical structure of a Kalman filter.

[0011] Of course, the Kalman filter is relatively complex, and there are a large number of setting options (especially the system matrix F k , the variance matrix R of the measurement noise k and the variance matrix Q of the system noise k ), the setting options must be selected and / or set for the system behavior to be described accordingly. This makes the use of the Kalman filter for new applications and / or maintenance of existing applications difficult.

[0012] In some cases, so-called extended Kalman filters are also used in order to be able to model nonlinear dynamic processes, and / or so-called adaptive Kalman filters (or ROSE filters) are used in order to be able to automatically adapt a large number of setting options, in particular the matrix R of the measurement and system noise, during operation by means of additional filters. k and Q k The value of .

[0013] However, in this case, a relatively high level of effort is involved in designing or configuring the additional filter, wherein the ROSE filter and its additional filter are more difficult to configure. Summary of the invention

[0014] According to the invention, a method for determining at least one system state by means of a Kalman filter is proposed, wherein at least one measured value measured by at least one sensor of the system is fed to the Kalman filter, the method comprising at least the following steps:

[0015] a) performing an estimation of the system state by means of a Kalman filter, wherein an estimation result and at least one information item relating to the reliability of the estimation result are output,

[0016] b) determining a difference between at least one model value belonging to the estimate and at least one measured value belonging to the estimate,

[0017] c) Correcting at least one information about the reliability of the estimate using the determined difference.

[0018] The described sequence of steps a), b) and c) is exemplary and can be performed in the described sequence, for example, in a conventional operating sequence, at least in sequence, to perform the method. Alternatively or additionally, steps a), b) and c) can be performed at least partially in parallel or simultaneously. The method can be performed, for example, by a control device, i.e., for example, a (micro)controller, which can, for example, be a component of the system also described here.

[0019] The method advantageously implements the provision of a Kalman filter with a plausibility test of the predictions (or estimates) and / or measurements. In this context, the method can be particularly useful for extending a (typical) Kalman filter so that differences or inconsistencies due to (measurement) errors and / or large inaccuracies arising in the modeling and / or configuration and / or due to disturbed measured values ​​deviating from the considered reference situation can be identified. The difference between the modeled value and the measured value is already determined in the usual Kalman filter in the bracketed expression in the equation GL4 above. There, however, the difference is only used in determining the fused (new) state vector , or only attributed to model values ​​or model states. This can also be performed in this way in the method described here. In addition, it is now proposed again here that the difference is in particular attributed to information about the reliability of the estimate, in particular to the estimate uncertainty (symbol: P or Σ0) and / or the measurement uncertainty (symbol: R or Σ1). This helps in a particularly advantageous manner: the level of the difference (directly) affects the level of at least one measure of the estimate reliability. Thus, for example, the measure of the estimate uncertainty (symbol: P) and / or the measurement uncertainty (symbol: R) can change according to or based on the determined difference, in particular with an increase in the difference. Therefore, the method allows for the first time in a particularly advantageous manner that the distance between (mutually belonging) model values ​​and measured values ​​can also directly affect the information about the reliability of the estimate result.

[0020] Taking the differences into account in the manner described and (correspondingly) reducing at least one information item about the reliability of the estimate, in particular in the case of large distances between model value and measured value, is particularly advantageous for safety-critical applications. Safety-critical application cases of particular interest are in particular at least partially automated or autonomous driving, in which the reliability of the estimate result is usually within a defined bandwidth and / or should be as precisely as possible. Furthermore, the method can help: when differences (of the physical variable) have been identified or determined, for example the measured value can be weighted more heavily than the disturbed model value and vice versa.

[0021] The method is particularly helpful for (continuously) determining the system state with the help of a Kalman filter and based on sensor data. The measured values ​​of multiple different or different types of sensors of the system can be fed to the Kalman filter so that the estimation is performed taking into account the measured values. At least one system state can, for example, include a mobile object or a mobile part that moves along the surface, such as a (current) (self) position of a (motor) vehicle (car), a ship, an aircraft, a smart phone or a smart watch. In addition, at least one system state can include the (current) speed, (current) direction of movement and / or (current) acceleration of the object. The use of the described method is in principle advantageous for any sensor data fusion task, i.e., for example, for determining the position of a vehicle, object recognition and / or driving dynamics regulation. In addition, the described method can also be used to model the transmission characteristics of the sensor, so as to, for example, reduce measurement noise and other interfering effects on the sensor signal.

[0022] In step a), an estimation of the system state is performed by means of a Kalman filter, wherein an estimation result and at least one information related to the reliability of the estimation result are output. For example, a particularly corrected or fused (or new) model value vector (symbol: μ') and / or a particularly corrected or fused (or new) state vector (symbol: ) as the estimation result. As the associated information about the reliability of the estimation result, for example, the estimation uncertainty, ie, for example, the covariance matrix (symbol: P′) in particular corrected or fused, can be output. k or Σ').

[0023] In step b), the difference between at least one model value belonging to the estimate and at least one measured value belonging to the estimate is determined. For example, the difference between the model value belonging to the estimate or the model value vector belonging to the estimate (symbol: μ0) and the measured value belonging to the estimate or the measured value vector belonging to the estimate (symbol: μ1) can be determined. In particular, the model value and / or the measured value can be included in the calculation of the difference as a square. Preferably, when calculating the difference, the mean square error between the model value vector (symbol: μ0) and the fused model value vector (symbol: μ') and / or the mean square error between the measured value vector (symbol: μ1) and the fused model value vector (symbol: μ') is taken into account, in particular added. Both of these can be weighted with the corresponding d covariance matrix of the model value vector or the measured value vector.

[0024] In step c), at least one information about the reliability of the estimate is corrected using the determined differences. The information about the reliability of the estimate that is corrected here can be, for example, the information about the reliability of the estimate result mentioned in step a). In this case, in step c), for example, the uncertainty of the fused estimate, i.e., for example, the covariance matrix of the fused estimate (symbol: P′) can be corrected, for example, by adding the determined differences. k or Σ'). Alternatively or cumulatively, in step c), for example, the (unfused) estimation uncertainty (symbol: P) and / or the measurement uncertainty (symbol: R) can be corrected. In this case, for example, the covariance matrix (symbol: Σ0) of the model value vector (symbol: μ0) and / or the covariance matrix (symbol: Σ1) of the measured value vector (symbol: μ1) can be corrected, in particular by adding the determined differences.

[0025] Using the difference advantageously helps by considering the measured values ​​(symbol: ) and the modeled state (symbol: ) Improve or correct the variance (symbol: P′) calculated from the above equation (GL5) k ). In this case, in particular the measured value (symbol: ) and modeling states (symbols: ) can improve the calculated variance (symbol: P′) when there is an unbelievably large difference or large difference (symbol: D or d) between k ) However, it is advantageous to take the differences into account continuously, in particular not only in the case of incredibly large differences.

[0026] The correction can be carried out in particular by adapting the probability density distribution (symbol: P′) of at least one information item about the reliability of the estimate, in particular the fused model uncertainty. k Or Σ'). The adaptation can be performed, for example, in such a way that the probability density distribution can be broadened and / or a greater overlap with the probability density distribution of the model uncertainty (symbol: P or Σ0) and the measurement uncertainty (symbol: R or Σ1) can be achieved. This can advantageously help to better take into account the following situation, in which, although the measured value and the model value are each calculated with a (hypothetical) high certainty, they are actually far apart from each other. Therefore, the correction can help unknown measurement errors and / or model design errors to advantageously influence the estimate less strongly.

[0027] According to an advantageous design scheme, it is proposed that the system is a system for determining the position of a (motorized) vehicle. The system can be at least partially arranged in or at the vehicle. For example, the vehicle can be advantageously designed for at least partially automatic and / or autonomous driving operation by means of a correspondingly configured control device. The control device can be connected to the system in order to obtain position data from the system. The system can include multiple, especially different or different types of sensors. The sensor can, for example, include at least one GNSS sensor and an (optical or acoustic) environmental sensor, i.e., for example, a camera sensor, a LIDAR sensor, a RADAR sensor, an ultrasonic sensor, etc. The measured values ​​of the sensor can be fused by means of the method described herein or by means of a Kalman filter.

[0028] According to another advantageous design, it is proposed that the correction according to step c) is performed continuously. In other words, this can also be described in particular such that a difference is determined at as many time steps as possible of the Kalman filter and used for correction, in particular added to at least one information about the reliability of the estimate. For example, continuous correction differs from a threshold comparison for a plausibility check, in which a correction is only performed when the determined difference is above a defined threshold. In contrast, the continuous determination of the difference according to step c) and the use of the difference for correction advantageously contribute to the detection of the degree of plausibility and can be taken into account continuously. In this case, intervention can be performed, in particular depending on this degree. This enables advantageous monitoring, which in particular differs from a threshold comparison and is continuous.

[0029] According to another advantageous design, it is proposed that the difference is used to correct at least one confidence value of at least one model value of the Kalman filter and / or at least one confidence value of at least one measurement value of the Kalman filter. Here, for example, the difference can be used to correct the dispersion value of at least one model value or model value vector (symbol: μ0) and / or the dispersion value of at least one measurement value or measurement value vector (symbol: μ1), for example, by adding the difference (or the degree of the difference) to the relevant value. The difference can preferably be used to calculate the variance or covariance matrix (symbol: Σ0) of at least one model value or model value vector (symbol: μ0) and / or the variance or covariance matrix (symbol: Σ1) of at least one measurement value or measurement value vector (symbol: μ1), for example, by adding the difference to the relevant variance or covariance matrix.

[0030] According to another advantageous embodiment, it is provided that the difference is determined or calculated using the following elements:

[0031] at least one (estimated) model value,

[0032] at least one (estimated) measurement,

[0033] at least one fused model value (that is, an estimate of the fusion of the model value and the measured value), and

[0034] At least one Kalman gain, or at least one covariance of at least one measurement value and at least one covariance of at least one model value are used instead of the Kalman gain.

[0035] In particular, the (corresponding) mean square errors of the model values ​​and / or the measured values ​​can be determined. The determined mean square errors can be added to form the difference. Preferably, the mean square errors between the model values ​​and the fused model values ​​and / or the mean square errors between the measured values ​​and the fused model values ​​are taken into account, in particular added, when calculating the difference. Both can be weighted with the corresponding covariance of the model values ​​or the measured values.

[0036] For example, the difference may be determined according to the following formula (Equation GL6), which is particularly useful for the purpose of derivation and / or understanding of the following display equation:

[0037]

[0038] Where d describes the differences, μ0 describes the model values, μ1 describes the measured values, μ' describes the fused model values, Σ0 describes the covariance of the model values, Σ1 describes the covariance of the measured values ​​and Σ' describes the covariance of the fused model values. In principle, the named variables can be one-dimensional or multidimensional. In the multidimensional case, accordingly, D is the difference matrix, μ0 is the model value vector, μ1 is the measured value vector, μ' is the fused model value vector, Σ0 is the covariance matrix of the model value vector, Σ1 is the covariance matrix of the measured value vector and Σ' is the covariance matrix of the fused model value vector. In this case, the covariance matrix of the fused model value vector can be determined using the following formula (Equation GL6a):

[0039]

[0040] Therefore, the difference between the model and the measured values ​​can advantageously be determined based on the sum of the squared deviations between the modeled value μ0 and the fused mean value μ' relative to the variance Σ0 of the modeled value and the squared deviations between the measured value μ1 and the fused mean value μ' relative to the variance Σ1 of the measured value, wherein the sum is weighted by the variance Σ' calculated so far.

[0041] Subsequently or in step c), when calculating the variance (symbol: Σ' or P' k) or when recalculating the (fused) variance (the (fused) variance previously calculated in said time step) (performed in the same time step), the difference or the measure of the difference determined in this way is added. In this case, the determined difference or the measure of the difference, for example the variance or the covariance matrix (symbol: Σ0) of at least one model value or model value vector (symbol: μ0) and / or the variance or the covariance matrix (symbol: Σ1) of at least one measured value or measured value vector (symbol: μ1) can be added thereto.

[0042] Typically, the Kalman filter works in an iterative manner, where the estimate for a particular time step is based on or built on the estimate for the previous (previous) time step. In particular, the model values ​​of the previous time step are used when modeling according to, for example, equations GL1 and GL2. However, in the case of fusion according to, for example, equations GL3 to GL5, the model and measurement values ​​of the current time step are used. In the formula given above for determining the difference d, in particular the variance Σ0, Σ1 (and Σ' if necessary) of the current time step and the model and measurement values ​​μ0, μ1 and μ' of the current time step are used to calculate the difference d. For this purpose, equation GL6a can be advantageously brought into equation GL6.

[0043] The difference d calculated therefrom in the current time step can be used for correction in the current or possibly subsequent (next) time step. Accordingly, the difference d in the current time step or, if necessary, the previous (previous) time step can be used in the current time step for correction. Alternatively, it can also be provided that the current time step is calculated multiple times or in multiple calculation steps.

[0044] In particular, in order to be able to advantageously use the difference d calculated in the current time step directly for correction in the current time step or otherwise to be able to advantageously avoid additional calculation steps in the current time step if necessary, it is preferred to introduce the Kalman gain (symbol: K') into equation GL6.

[0045] The difference can be determined by introducing the Kalman gain according to the following formula (Equation GL6b):

[0046] d=(μ0-μ′) 2 +K((μ1-μ′) 2 -(μ0-μ′) 2 ) (Equation GL6b)

[0047] Where d describes the difference matrix, μ0 describes the model value vector, μ1 describes the measurement value vector, μ' describes the fused model value vector, and K describes the Kalman gain. By using the Kalman gain according to equation GL6b, matrix inversion can also be avoided in an advantageous manner, thereby saving calculation time.

[0048] In a particularly advantageous manner, the formula can also be simplified from equation GL6 by means of Kalman gain and coefficient formation or equation GL6b can be simplified by means of coefficient formation, so that no additional division or (unnecessary) multiple calculations are required. The corresponding simplified formula is given in the following equation GL7:

[0049] d = w0 + K (w1 - w0) (Equation GL8)

[0050] Here, the coefficients w_0 and w_1 and / or the coefficient matrices W0 and W1 may be determined according to the following equations (GL8 and GL9):

[0051] w0=(μ0-μ′) 2 (Equation GL9)

[0052] w1=(μ1-μ′) 2 (Equation GL10)

[0053] In this case, it can be provided ideally that the coefficients w0 and w1 and / or the coefficient matrices W0 and W1 are calculated only once per time step. This can advantageously contribute to the microcontroller being able to perform the calculation steps of the filter significantly faster.

[0054] use and Equations GL8 and GL9 can be adapted to the case where the measurement and model value vectors are or may be of different dimensions if necessary (with the aid of the so-called observation or transposition matrix H k ) is reformulated as the following equations GL10 and GL11:

[0055]

[0056]

[0057] Accordingly, according to a particularly preferred embodiment, it can be provided that the difference is determined according to the following formula (Equation GL7a):

[0058] D=W0+H k K′(W1-W0) (Equation GL13a)

[0059] where D describes the difference matrix, W0 and W1 describe the coefficient matrices, K′ describes the Kalman gain matrix, and H k Describes the transposed matrix, where the coefficient matrix is ​​determined according to the previous formula (Equations GL10 and GL11).

[0060] For example, in order to advantageously correct the variance of the fusion (symbol: P′ k Or ∑′) expands the above formula (GL5) in the following way:

[0061]

[0062] Observation matrix H k With its transposed matrix The product of H and , gives the identity matrix I and can be added in explicit form for the following transformation of the equation. The explicit representation (see equation GL12a) can be obtained by shortening H k and A corresponding display is particularly advantageous, in particular for calculations using a microcontroller.

[0063]

[0064] The observation matrix H k The product of the Kalman gain matrix K' can also be obtained by expanding H k and Shortened to derive as follows:

[0065]

[0066] Alternatively, according to a preferred embodiment, the following formula can be used to correct the fused covariance P′ k :

[0067]

[0068] Where I describes the identity matrix, K' describes the Kalman gain matrix, and H k Describe the observation matrix, P k describes the covariance matrix and D describes the dissimilarity matrix.

[0069] According to another advantageous embodiment, it is proposed that the influence of the determined difference on at least one information about the reliability of the estimate is weighted by means of at least one weighting factor or a weighting matrix. The at least one weighting factor or the at least one weighting matrix can advantageously cause the determined difference (or the measure of the difference) to act as specifically as possible on the following scatter values ​​(e.g. the following items of the covariance matrix): the model values ​​or measured values ​​to which the scatter values ​​(items) belong are (presumed) more prone to error or at least (presumed) to error than other values. For example, this can help to weight the measured values ​​more heavily relative to the disturbed model values ​​and vice versa. The weighting factors or the at least one weighting matrix can be specified, for example, in the design of the Kalman filter, or can be dynamically changed or adapted during operation, preferably by a higher-level function or a (system) control device above the Kalman filter level, in particular in order to achieve at least one of the aforementioned effects.

[0070] The weight factor or weight matrix (symbol: E1) can be integrated into the above equation GL12c according to the following equation GL13, for example:

[0071]

[0072] For example, the weighting matrix E1 may be multiplied element-by-element by the differences.

[0073] In the case when the sensor signal is subject to unusually strong interference, but the model value can be particularly trusted or the sensor signal is (at least presumably) more interfered than the model value, it is preferred that the deviation (at least also) acts on the covariance matrix (symbol: Σ1) or the measurement uncertainty (symbol: R) of the measurement vector. In this case, the difference D, which is weighted by the matrix E2, is advantageously added in a targeted manner to the equation GL3a of the variance matrix of the measurement noise (symbol: R):

[0074]

[0075] Alternatively or additionally, in order to expand equation GL12c, equation GL12c can also be expanded with matrix E3 and difference D, i.e. the increased difference D leads to more consideration of the model values ​​(in particular the model uncertainty P k Without the need to directly improve):

[0076]

[0077] In order to avoid possible algebraic loops according to the above equations (in particular GL14 and GL15) in this exemplary embodiment, it is possible, for example, to use D from the preceding (previous) time step and / or to calculate the current time step multiple times.

[0078] In order to take into account the differences, an alternative and relatively simple possibility may be, for example, that the differences can be added to equation GL2. Here, the differences can advantageously be weighted with a weighting matrix E4. This is illustrated in the following equation GL16:

[0079]

[0080] For example, the decision at which point in the set of equations a difference acts or should act on the set of equations can be fixedly predetermined, for example in the design of the Kalman filter, or can be predetermined, in particular dynamically, by a (higher-level) control device of the system.

[0081] A particularly preferred embodiment is described below with the aid of the following, exemplary pseudocode, which can be implemented as a computer program in particular within a continuous loop, in which differences are inserted at a plurality of positions in the set of equations in order to be able to act in particular on the model uncertainty (symbol: P), the measurement uncertainty (symbol: R) and the fused model uncertainty (symbol: P'), and in which the differences are weighted at the corresponding positions with their own weighting matrix (E1 to E4):

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090] D=W0+H k K′(W1-W0)

[0091]

[0092] In this case, the values ​​of the matrices E1 to E4 can determine the influence of the differences on the corresponding calculation steps.

[0093] According to another advantageous embodiment, it is proposed that the determined differences are filtered by means of a low-pass filter. Since in principle a large difference in difference is formed with each calculation step, it is advantageous to filter the differences by means of a low-pass filter. The filtered differences can be used, for example, for correction in one or more of equations GL13 to GL16.

[0094] According to another aspect, a computer program for executing the method proposed here is provided. In other words, this relates in particular to a computer program (product) comprising instructions which, when the program is executed by a computer, cause the computer to execute the method described here.

[0095] According to another aspect, a machine-readable storage medium is provided, on which the computer program provided herein is stored or stored. The machine-readable storage medium is typically a computer-readable data carrier.

[0096] According to another aspect, a system for determining the position of a mobile object such as a vehicle is also proposed, which is designed to perform the method described herein. The system for determining the position of a mobile object can be set and designed, for example, to determine the own position of the mobile object and / or to measure the relative position relative to other, especially moving mobile objects, i.e., for example, traffic participants. The system can, for example, include motion and position sensors, which are designed to perform the method described herein. In addition, the motion and position sensors can, for example, also receive GNSS data and / or environmental sensor data (from environmental sensors of the mobile object or vehicle). In order to perform the method, the system can, for example, include a computing device, i.e., for example, a (micro)controller, which can access the computer program also described herein. Here, the storage medium can, for example, also be a component of the system or connected to it.

[0097] The details, features and advantageous embodiments discussed in conjunction with the method may also be present in the computer program and / or storage medium and / or system described herein, and vice versa. In this regard, for a more detailed characterization of the features, reference is made fully to the statements made there. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] The solution proposed here and its technical scope are explained in more detail below with reference to the accompanying drawings. It should be noted that the present invention is not intended to be limited to the embodiments shown. In particular, unless otherwise explicitly stated, some aspects of the facts explained in the figures can also be extracted and combined with other components and / or cognitions from other figures and / or this specification. The accompanying drawings schematically show:

[0099] Figure 1 shows a typical signal flow diagram of a Kalman filter according to the prior art,

[0100] Figure 2 An exemplary process of the method described here is shown.

[0101] Figure 3 An exemplary system for determining a vehicle position is shown.

[0102] Figure 4 shows an exemplary signal flow diagram of a Kalman filter,

[0103] Figure 5 Another exemplary signal flow diagram of a Kalman filter is shown,

[0104] Figure 6 and Figure 7 A diagram showing a probability density distribution according to the prior art,

[0105] Figure 8Show that you can use Figure 4 A graphical representation of the probability density distribution of an embodiment implementation in , and

[0106] Fig. 9 Show that you can use Figure 5 Graph of the probability density distribution achieved by the embodiment in . DETAILED DESCRIPTION

[0107] Figure 1 The typical structure of a Kalman filter according to the prior art is schematically shown. The Kalman filter equation on which the structure is based can be described as follows using matrix notation:

[0108]

[0109]

[0110]

[0111]

[0112]

[0113] Here, equation (GL1) describes the state vector based on the previous time step (iterative estimate) System Matrix F k , control matrix B k and control vector The estimated state vector Here, the state vector usually describes the mean of a Gaussian distribution. In other words, according to equation (GL1), the new best estimate is the sum of the previous best estimates The forecast created in adds corrections for known external influences.

[0114] Here, equation (GL2) describes the estimated state vector The covariance matrix P of the Gaussian distribution k The covariance matrix is ​​based on the covariance matrix P of the previous time step (iterative estimation). k-1 、System matrix F k and system noise Q k In other words, according to equation (GL2), the new (estimated) uncertainty P k From the old uncertainty P k-1 The prediction has additional uncertainty from the environment.

[0115] Equation (GL3) describes the so-called Kalman gain K or Kalman gain matrix K'. The Kalman gain is based on the covariance matrix P k , observation matrix H kand measurement noise R k The covariance matrix of is formed. k It can be compared with the observation matrix H k Form the covariance matrix Σ0 of the model value vector μ0.

[0116] Equation (GL4) describes the correction of the estimated state vector with the measured value or model value vector μ0, and the measured value vector z k Or μ1. Therefore, the corrected or fused model value vector μ' or the new state vector is obtained from equation (GL4) The model value vector or state vector can be used as input for a temporally subsequent estimation step.

[0117] The equation (GL5) describes the state vector Or the covariance matrix P of the model value vector μ0 k Or Σ0 determines the corrected or fused covariance matrix P′k or Σ′. Here, the measurement value vector z k Or the covariance matrix R of μ1 k or Σ1 is used together via the Kalman gain K.

[0118] Therefore, equations (GL1) and (GL2) describe the iterative estimation process of the Kalman filter. The estimation process is Figure 1 In the figure, it is indicated by reference numeral 10. Equations (GL3) to (GL5) describe the subsequent correction or fusion of the iteratively estimated model values ​​with the measured values ​​detected by the sensor. The correction or fusion is Figure 1 The corrected or fused (new) model values ​​can be used in subsequent iterations of the estimation process 10. Figure 1 Return arrow in the description.

[0119] Figure 2 An exemplary sequence of the method proposed here is shown schematically. The method is used to determine at least one system state by means of a Kalman filter, to which at least one measured value measured by at least one sensor of the system is fed. The system can be, for example, a system for determining the position of a vehicle.

[0120] The order of steps a), b) and c) shown by blocks 110, 120 and 130 is exemplary and can be traversed at least once in the order shown to perform the method. In addition, steps a), b) and c) can also be performed at least partially in parallel or simultaneously.

[0121] In block 110, according to step a), an estimation of the system state is performed by means of a Kalman filter, wherein the estimation result and at least one information pertaining to the reliability of the estimation result are output. In block 120, according to step b), a difference between at least one model value belonging to the estimation and at least one measured value belonging to the estimation is determined.

[0122] For example, the following elements can be used to determine differences:

[0123] at least one model value,

[0124] At least one measurement value,

[0125] at least one ensemble model value, and

[0126] At least one Kalman gain, or at least one covariance of at least one measurement value and at least one covariance of at least one model value are used instead of the Kalman gain.

[0127] Here, for example, the difference can be determined using the following formula:

[0128]

[0129] Where d describes the difference, μ0 describes the model value, μ1 describes the measured value, μ' describes the fused model value, Σ0 describes the variance of the model value, Σ1 describes the variance of the measured value and Σ' describes the variance of the fused model value, and the variance Σ' of the fused model value can be determined according to the following formula:

[0130]

[0131] In block 130, according to step c), the determined difference is used to correct at least one information about the reliability of the estimate. Advantageously, the correction is performed continuously. The difference can also advantageously be used to correct at least one confidence value of at least one model value of the Kalman filter and / or at least one confidence value of at least one measurement value of the Kalman filter.

[0132] It can also be provided that the influence of the determined differences on the at least one information item about the reliability of the estimate is weighted by means of a weighting matrix. Furthermore, the determined differences can also be filtered, for example, by means of a low-pass filter.

[0133] Figure 3 An exemplary system 1 for determining the position of a vehicle 2 is schematically shown. The system 1 is configured and designed to carry out the method described here.

[0134] Figure 4 Show Figure 1 An exemplary expansion of the signal flow diagram in . Figure 4A Kalman filter signal flow diagram can be used to implement an embodiment of the method described herein. Here, the difference D between the measured value z and the model value x increases the estimation uncertainty P'. For this purpose, equation GL5 is replaced by GL12 as an example. In the case of model errors that lead to large deviations of the model value x from the measured value z, the model value x can advantageously be adapted to the measured value z more quickly. This advantageously helps the Kalman filter model to become more robust with respect to design errors.

[0135] Figure 5 Show Figure 1 Another alternative exemplary expansion of the signal flow graph in . Figure 5 A Kalman filter signal flow diagram of , can exemplarily implement another embodiment of the method described herein. Here, the difference D between the measured value z and the model value x reduces the influence of the measured value z on the model value. For this purpose, the equation for calculating the Kalman gain K' (the above equation GL3) is replaced by equation GL14. This makes the Kalman filter model more robust to measurement errors. In order to Figure 5 In an embodiment of , possible algebraic loops are avoided, for example, D from the previous (previous) time step can be used and / or the calculation steps of the current time step can be calculated multiple times.

[0136] Figure 6 By way of example, a diagram of a probability density distribution according to the prior art is shown, as can be seen in Figure 1 The use of the Kalman filter shown in Figure 1 is derived here. Figure 6 A plausible probability density distribution is shown. In the case of a plausible probability density distribution, the surfaces of the Gaussian bells of the measurement z and the model x strongly overlap. The Gaussian bell x' merged therefrom is located between the other two Gaussian bells. In addition, the Gaussian bell is narrower and taller.

[0137] Figure 7 Another illustration of a probability density distribution according to the prior art is shown by way of example, as can be seen in Figure 1 The use of the Kalman filter shown in Figure 1 is derived here. Figure 7 shows an implausible probability density distribution. In the case of an implausible probability density distribution, both the measurement z and the model x are very certain to be correct, but they output values ​​that strongly deviate from each other. The faces of the Gaussian bells of the measurement z and the model x barely overlap, but the Kalman filter still computes the fused Gaussian bell x' in the usual way.

[0138] The Gaussian clock x' fused from it is located between the other two Gaussian clocks. However, this Gaussian clock is too narrow and / or too high. The fused Gaussian clock x' must actually be wider and / or have a greater overlap with the other clocks. The process described here can help solve the problem.

[0139] Figure 8 Show that you can use Figure 4 . It can be seen that by considering the probability density distribution according to Figure 4 The difference D can achieve that the fused Gaussian clock x' is wider and has a greater overlap with the other clocks. This advantageously allows for the presence of implausible probability density distributions (Gaussian clocks z and x; see Figure 7 ) is now also reflected in the fused Gaussian clock x'.

[0140] Fig. 9 Show that you can use Figure 5 . It can be seen that by considering the probability density distribution according to Figure 5 The difference D can achieve that the fused Gaussian clock x' has a greater overlap with at least one of the other Gaussian clocks. This advantageously allows for the presence of implausible probability density distributions (Gaussian clocks z and x; see Figure 7 ) is now also reflected in the fused Gaussian clock x'.

[0141] The method described herein and the system described herein allow, inter alia, one or more of the following advantages:

[0142] • The Kalman filter is advantageously more robust against interfering signals, measurement errors, model inaccuracies, and / or other design errors.

[0143] Advantageously, cost savings can be achieved when parameterizing the Kalman filter.

[0144] • The difference calculation can also be advantageously introduced into the extension of the Kalman filter.

Claims

1. A method for determining at least one vehicle state by means of a Kalman filter, wherein at least one measured value measured by at least one sensor of the vehicle is fed to the Kalman filter, the method comprising at least the following steps: a) performing an estimation of the vehicle state by means of the Kalman filter, wherein an estimation result and at least one information item relating to the reliability of the estimation result are output, b) determining a difference between at least one model value belonging to the estimation result and at least one measured value belonging to the estimation result, c) correcting at least one information about the reliability of the estimation result using the determined difference, d) Based on the estimation result, performing at least a partially automated driving operation or an autonomous driving operation using a control device of the vehicle. The method of claim 1 , wherein the vehicle status is the location of the vehicle.

3. The method according to claim 1 or 2, wherein the correction according to step c) is performed continuously.

4. The method according to claim 1 or 2, wherein the difference is used to correct at least one confidence value of at least one model value of the Kalman filter and / or at least one confidence value of at least one measurement value of the Kalman filter.

5. The method according to claim 1 or 2, wherein the difference is determined using the following elements: at least one model value, At least one measurement value, at least one fused model value, and At least one Kalman gain, or at least one covariance of the at least one measurement value and at least one covariance of the at least one model value are used instead of the Kalman gain. 6 . The method according to claim 1 , wherein the influence of the determined differences on the at least one information about the reliability of the estimation result is weighted by means of at least one weighting matrix.

7. The method according to claim 1 or 2, wherein the determined differences are filtered by means of a low-pass filter.

8. A computer program product for performing the method according to any one of claims 1 to 7. 9 . A machine-readable storage medium on which a computer program is stored, the computer program being designed to execute the method according to claim 1 .

10. A system (1) for determining the position of a vehicle, the system being designed to carry out the method according to any one of claims 1 to 7.

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