A method for adjusting a plurality of measurements

Abstract

The invention relates to a method (100) for adjusting a plurality of measurements of a hybrid positioning system, comprising the following steps, which are carried out by a data processing device: - Obtain (101) the majority of measurements with respect to at least two target objects, wherein the majority of measurements includes at least one distance measurement and / or at least one position measurement, - Linking (102) the plurality of measurements with a state estimation using a functional model for the hybrid positioning system, wherein the state estimation is related to the plurality of measurements with respect to a position and / or a distance measurement in relation to the at least two target objects, - Linearizing (103) the functional model using a Jacobi matrix J, where the Jacobi matrix J specifies the linear approximation of the functional model around a current state estimate, - Collecting (104) stochastic information regarding a distribution of measurement errors in a sparse matrix Q, - iterative compensation (105) of measurement uncertainty and / or measurement errors based on a weighted least-squares procedure using the linearized functional model and the collected stochastic information, - Adjusting (106) the majority of measurements based on compensation (105). Furthermore, the invention relates to a computer program and a device for this purpose.

Description

[0001] The invention relates to a method for adjusting a plurality of measurements. Furthermore, the invention relates to a computer program, a device, and a storage medium for this purpose. State of the art

[0002] Hybrid global satellite navigation systems (GNSS) and short-range (SL) distance-determining positioning systems have long been considered complementary technologies for providing accurate location information. GNSS systems, such as GPS, provide coarse location information with an accuracy of several meters, while SL distance-determining systems based on, for example, Sidelink Positioning Protocol (SLPP), Wi-Fi, or Bluetooth offer highly precise location information with an accuracy of centimeters to millimeters.

[0003] Traditional approaches to combining GNSS and SL distance measurements have focused on compensating for errors and uncertainties inherent in each system. These approaches typically involve complex signal processing algorithms that require significant computing resources and data storage. The limitations of these traditional approaches include their susceptibility to multipath effects, non-line-of-sight (NLOS) conditions, and high-performance requirements.

[0004] The development of hybrid distance-based positioning systems could revolutionize various applications that rely on accurate location information, including navigation, tracking, and surveillance. However, further research is needed to address the technical challenges associated with these systems, such as high-precision synchronization, coordinated transmission timing, and bandwidth management. Disclosure of the invention

[0005] It is therefore an object of the invention to improve absolute positioning information in a more efficient manner using distance measurements from different devices or functions.

[0006] According to aspects of the invention, a method with the features of claim 1, a computer program with the features of claim 9, a data processing device with the features of claim 10, and a computer-readable storage medium with the features of claim 11 are provided. Further features and details of the invention are disclosed in the respective dependent claims, in the description, and in the drawings. Features and details described in the context of the method also correspond to the computer program, the data processing device, and the computer-readable storage medium according to the invention, and vice versa in each case.

[0007] According to one aspect of the invention, a method for adjusting a plurality of measurements of a hybrid positioning system is provided. The method comprises the following steps, which are performed by a data processing device that may be part of the hybrid positioning system: - Obtaining the majority of measurements with respect to at least two target objects, wherein the majority of measurements include at least one distance measurement and / or at least one position measurement, - Linking the majority of measurements with a state estimation using a functional model for the hybrid positioning system, wherein the state estimation is related to the majority of measurements regarding a position and / or a distance measurement in relation to the at least two target objects, - Linearizing the functional model using a Jacobian matrix J, where the Jacobian matrix J specifies the linear approximation of the functional model around a current state estimate, - Collecting stochastic information regarding a distribution of measurement errors in a sparse matrix Q, - iterative compensation of measurement uncertainty and / or measurement errors based on a weighted least-squares method using the linearized functional model and the collected stochastic information, - Adjusting the majority of measurements based on compensation.

[0008] This enables the compensation of uncertainties and the adjustment of measurements to improve state estimation in a hybrid positioning system that combines GNSS and SR, preferably SLPP, distance measurements. Furthermore, the advantage is that the use of SR, preferably 5G Sidelink distance determination, and GNSS measurements provides more accurate absolute positioning and distance measurements. This also allows the knowledge of the a priori uncertainty distribution to be effectively used to appropriately compensate for these uncertainties and adjust the measurements, leading to more accurate state estimations. Moreover, the invention can utilize multiple measurements over time to increase the system's overdetermination, resulting in even more accurate state estimation.The invention's ability to accurately estimate the covariance matrix of the state estimation provides a more reliable confidence measure in the estimator, thus enabling informed decision-making. By incorporating SLPP distance measurements into the hybrid positioning system, this feature enables improved accuracy in position estimation, particularly in environments with limited GNSS signal availability.

[0009] The hybrid positioning system can be understood as a positioning system or positioning device that includes at least one GNSS unit and at least one short-range distance determination unit. Preferably, the hybrid positioning system includes a GNSS unit and a communication unit configured for sidelink distance determination, particularly according to 3GPP standards.

[0010] The functional model is designed to link the plurality of measurements, which include at least one distance measurement and / or at least one position measurement, with the state estimation, which includes position and / or distance information for at least two targets. The functional model can be a function designed to map the state estimation as input to the plurality of measurements as output. The functional model is preferably a non-linear model.

[0011] The least-squares method can be understood as a technique used to find the best-fitting curve or line to a given set of data points by minimizing the sum of the squares of the differences between the observed values ​​and the values ​​predicted by the model. It is widely used in regression analysis to determine the parameters of a model that best explains the relationship between independent and dependent variables. Applying this technique has the effect of allowing the parameters of complex models (polynomial, exponential, etc.) to be estimated by extending the least-squares method to non-linear regression.

[0012] The Jacobian matrix (J) describes the linear approximation of the functional model f(x) around the current state estimate x. It represents the derivative of each output with respect to each input and yields the rate of change of measurements y with respect to the states x. In other words, it quantifies how the measurements change when the states are slightly altered.

[0013] The state estimation is related to the position and distance measurements of at least two targets, e.g., at least two user devices (UEs), such as vehicles. The state estimation can include the absolute and / or relative position and / or velocity and / or acceleration and / or the absolute and / or relative heading of the at least two targets. Preferably, the state estimation includes the coordinates (x, y) and possibly other states, such as velocity and acceleration, of at least two UEs, such as vehicles, estimated based on combined measurements of distance determination (e.g., SLPP distance determination, UWB, etc.) and absolute positioning (e.g., GNSS).

[0014] It is possible that the weighted least squares method includes the following steps: - Computing a normal matrix N from the Jacobian matrix J and from the sparse matrix Q based on a matrix P of weights, where the matrix P is a function of the sparse matrix Q, and where J is the Jacobian matrix evaluated with the current state estimation, - Refining the state estimation depending on the calculation, - Updating the function that yields P from the sparse matrix Q, and - preferably updating the covariance matrix and / or cofactor matrix of the state estimation.

[0015] This means that the weighted least squares method includes the steps of refining the state estimate by iteratively updating the estimate based on the normal matrix N, taking into account the uncertainty information provided by the sparse matrix Q.

[0016] This enables a more accurate and robust state estimation. Benefits of this feature include improved accuracy in state estimation, increased resilience to noise and disturbance in the measurement data, and improved overall performance of the hybrid positioning system. Furthermore, it allows for the incorporation of prior knowledge or historical information into the weighting process, facilitating better handling of uncertain or ambiguous measurements. Additionally, the update process, particularly the iterative update process, allows the algorithm to adapt to changing environmental conditions and dynamic scenarios, resulting in a more responsive and reliable estimation.

[0017] It is also possible that the update includes at least one of the following additional steps: - Adjusting the uncertainty compensation using a machine learning technique based on training a neural network on previous measurements - Estimating the covariance and / or cofactor matrix of the state estimation, - Grouping the majority of measurements to apply a Helmert variance component estimation.

[0018] This has the advantage of significantly improving uncertainty compensation and accuracy. Furthermore, using machine learning or variance component estimation (VCE) to estimate the weight matrix P advantageously enables adaptive and robust weight adjustments based on previous measurements. Estimating a covariance or cofactor matrix provides further information about the distribution of uncertainties, allowing for more accurate state estimations. Additionally, grouping the majority of measurements using Helmert variance component estimation can reduce the impact of noisy or outlier measurements on the overall position calculation, leading to improved reliability and accuracy.

[0019] Helmert variance component estimation (Helmert-VCE) can be understood as a method advantageously used to estimate variance components in linear models such as those for this invention. This technique is particularly useful in geodesy, surveying, and other fields where precise measurements and adjustments are necessary. The method relies on the Helmert transformation, which converts correlated observations or measurements into uncorrelated ones, thus facilitating the estimation of variance components for various sources of measurement error. Helmert-VCE is widely used in the adjustment of geodetic and surveying networks to accurately estimate the coordinates of points while taking into account various sources of error.

[0020] It is possible that the procedure includes the following further step: - Providing a loss function based on a priori knowledge to measure the quality of the weight determination of the matrix P of weights.

[0021] This improves the method's ability to determine the optimal weights in the compensation process. This feature enables more accurate and reliable estimations of the state variables, as it provides a mechanism for evaluating the quality of the weight determination.

[0022] The loss function can be designed to reflect specific aspects of the problem, such as the expected distribution of uncertainties or the desired level of accuracy. By incorporating this information into the optimization process, the method can adaptively adjust the weights to better fit the available data and prior knowledge. Furthermore, this feature allows the method to learn from previous measurements and improve its performance over time. The loss function can be used to refine the weight determination based on the results obtained during the compensation process, thereby iteratively refining the state estimation.

[0023] Furthermore, providing a loss function allows for the integration of additional constraints or regularization terms, which can further improve the robustness and accuracy of the method.

[0024] It is also possible that the stochastic information includes at least one of the following: - an a priori covariance matrix or a variance for indirect measurements, - a cofactor matrix for direct measurements.

[0025] This feature enables a more comprehensive representation of uncertainty in the hybrid positioning system. By including an a priori covariance matrix, or variance for indirect measurements, the algorithm can better account for any underlying uncertainties that may exist. Furthermore, including a cofactor matrix for direct measurements allows the system to explicitly model the relationships between the different measurements, resulting in improved estimation accuracy and robustness. This feature can also be particularly useful in scenarios with a high degree of uncertainty or variability in the measurements, such as in dense foliage environments or adverse weather conditions. By incorporating this additional information, the algorithm can better adapt to these challenging situations and provide more accurate location estimates.

[0026] It is possible that the functional model is selected from the group that includes first values ​​for absolute positioning measurement in two dimensions and / or second values ​​for distance measurement and / or third values ​​for angle measurement.

[0027] This allows for the advantageous use of flexibility in the selection of functional models that accommodate different environmental conditions and acquisition modalities. Furthermore, this feature enables a more robust and accurate hybrid positioning system, as it allows the selection of the most suitable model based on the specific application or scenario.

[0028] For example, in areas with dense vegetation or tall buildings, absolute positioning measurements can be affected by multipath effects or signal blocking. In such cases, selecting distance measurement models that utilize SLPP technology can provide more accurate and reliable location information. Alternatively, in areas with strong electromagnetic interference (EMI) or multipath effects, angle measurement models can provide a more stable reference frame for hybrid positioning. This flexibility in selecting functional models can be particularly useful in urban canyon environments, where signals are frequently affected by EMI and physical obstacles.

[0029] It is also possible that the process includes at least one of the following steps during the receiving phase: - Collecting absolute position estimates and / or distance determination information between the at least two target objects and / or angular information between the at least two target objects, - Collecting distance and / or angle information from a fixed anchor, in particular a Road Side Unit (RSU).

[0030] This feature enables improved accuracy in determining the position of at least two target objects, such as vehicles. The collection of absolute position estimates, distance information between the vehicles, and angular information between the vehicles provides additional data points that can be used to refine the positioning estimates.

[0031] This has the advantage that the method can integrate data from fixed anchors, such as RSUs, providing additional information about the location and orientation of vehicles. This can be particularly useful in areas where GNSS signals are weak or unreliable, enabling more accurate positioning even in challenging environments. Furthermore, this feature allows for a hybrid approach that combines the strengths of different positioning technologies, such as SLPP distance determination and absolute GNSS positioning. By fusing data from multiple sources, the method can produce more robust and reliable positioning estimates that can be used to enable various applications, such as vehicle-to-everything (V2X) communication and autonomous driving.

[0032] It is also possible that obtaining the majority of measurements is based on a time coherence interval depending on the mobility of at least two targets.

[0033] By considering the target's mobility, the system can advantageously adapt its measurement acquisition process to better capture the target's movement and improve the overall accuracy of the positioning calculation. Furthermore, incorporating a time coherence interval allows the system to adapt to changes in the target's movement pattern, making it more robust against sudden changes or unexpected movements. This feature also enables effective operation in various scenarios, such as high-speed traffic, pedestrian zones, and even stationary environments. This feature can be implemented using a variety of techniques, such as machine learning algorithms that learn from previous measurements to adapt the measurement acquisition process based on the target's mobility pattern.Advanced signal processing techniques that take into account the movement of the target and adjust the measurement acquisition process accordingly.

[0034] The invention offers several advantages for various applications, such as real-time tracking, where the system can provide real-time location information for destinations with varying mobility, enabling more accurate and effective tracking. Another application is intelligent transportation systems, where this feature can advantageously be used to optimize traffic flow, reduce congestion, and improve road safety. Finally, the invention offers advantages in location-based services: by accurately tracking destinations with varying mobility, this feature can enable the provision of personalized location-based services such as navigation and recommendation systems.

[0035] In another aspect of the invention, a computer program, in particular a computer program product, may be provided, comprising instructions which, when executed by a computer, cause the computer to perform the method according to the invention. Thus, the computer program according to the invention may have the same advantages as those described in detail with reference to a method according to the invention.

[0036] In another aspect of the invention, a data processing device may be provided that is designed to execute the method according to the invention. For example, the device may be a computer that executes the computer program according to the invention. The computer may include at least one processor that can be used to execute the computer program. Furthermore, a non-volatile data storage device may be provided in which the computer program can be stored and from which the computer program can be read by the processor for execution.

[0037] According to another aspect of the invention, a computer-readable storage medium can be provided, comprising the computer program according to the invention and / or instructions which, when executed by a computer, cause the computer to perform the steps of the method according to the invention. The storage medium can be configured as a data storage device such as a hard disk and / or non-volatile memory and / or a memory card and / or a solid-state drive. The storage medium can, for example, be integrated into the computer.

[0038] Furthermore, the method according to the invention can be implemented as a computer-implemented method. Alternatively, at least one of the disclosed method steps can be computer-implemented and / or automated.

[0039] Further advantages, features, and details of the invention will become apparent from the following description, in which embodiments of the invention are described in detail with reference to the drawings. In this context, the features mentioned in the claims and in the description can be essential to the invention individually or in any combination. The drawings show: Fig. 1: A method, a computer program, a storage medium and a device according to embodiments of the invention, Fig. 2: A schematic diagram of an embodiment according to the invention.

[0040] The core of the invention is a hybrid positioning system or device that combines distance measurements, such as SLPP distance determination, with absolute positioning, such as GNSS, to improve the accuracy and reliability of estimating the states (positions) of at least two units (vehicles). The system can effectively utilize knowledge of an a priori distribution of measurement uncertainty and / or measurement errors to compensate for uncertainties and adjust the measurements. The system can employ compensation methods to improve state estimations with respect to a position and / or distance measurement relative to at least two targets.

[0041] In one possible embodiment, the system can comprise two devices, for example, two user devices (UEs).

[0042] The problem according to the invention is formulated as follows: y=f(x)+v where y is the vector of the plurality of measurements, also called observations, f is the function that links the state estimation to the measured or observed values, and v can be noise. In this embodiment, f is non-linear as f(x→)=[xAyAxByB(xB−xA)2+(yB−yA)2] Where x→=[xAyAxByB] The state vector corresponds to the two pairs of coordinates that are being estimated.

[0043] In f, the first four observations are observations from the Global Navigation Satellite System (GNSS), and the last observation is the Sidelink (SL) distance determination. The problem can be linearized using J, the Jacobian matrix of f: y−v=Jx. Furthermore, some information about the distribution of measurement or observation errors may be available. This information could be provided, for example, as a covariance matrix of the GNSS measurements and a standard deviation (SL) of the distance measurement. This would be an ideal information scenario, in other words, the best-case scenario. More often, however, only information about the GNSS measurements, such as cofactor matrices, may be available.

[0044] In this embodiment, it is advantageous to effectively utilize the fact that the problem is overestimated, meaning that more measurements than state estimates or states are provided (here: 5 measurements for 4 states). Furthermore, information about the uncertainty distribution is available. This allows for the determination of a weight in the compensation process, along with the determination of the functional model (mentioned above) in the hybrid positioning system, which incorporates GNSS- and SLPP-based information. This also enables the use of compensation models, also called fitting procedures, to improve the state estimation.

[0045] In this embodiment, the two devices or UEs were each used with a coordinate estimation and a distance measurement between the two. In alternative embodiments, the system can be extended to include more devices or moving points, as well as more distance measurements between these points. Optionally, it is also possible to add fixed objects, devices, or points, such as a Road Site Unit (RSU), to such a system. This would not add more states to be estimated, but would increase the number of measurements by adding more sidelink distance measurements. Furthermore, it is possible to add or introduce angle measurements (AoA or AoD measurements).

[0046] Fig. Figure 1 shows a method 100, a data processing device 10, a computer program 20 and a computer-readable storage medium 15 according to embodiments of the invention.

[0047] Fig. Figure 1 shows in particular an embodiment of a method 100 for adjusting a plurality of measurements, comprising the following steps which are carried out by a positioning system: In a first step 101, the majority of measurements with respect to at least two target objects are obtained, wherein the majority of measurements include at least one distance measurement and / or at least one position measurement. In a next step 102, the majority of measurements are linked to a state estimate using a functional model for a hybrid positioning system. The state estimate is related to the majority of measurements with respect to a position and / or a distance measurement with respect to the at least two target objects. In a next step 103, the functional model is linearized using a Jacobian matrix J. The Jacobian matrix J specifies the linear approximation of the functional model around the current state estimate. In a next step 104, stochastic information regarding a distribution of measurement errors in a sparse matrix Q is collected.In step 105, any uncertainty in the measurements and / or the measurement errors or the distribution of the measurement errors is iteratively compensated based on a weighted least-squares procedure using the functional model and the collected stochastic information. In a subsequent step 106, the majority of measurements are adjusted based on the compensation in step 105.

[0048] Fig. Figure 2 shows a schematic diagram of an embodiment according to the invention. In particular, it shows Fig. 2 an exemplary procedure for adjusting the measurements for a positioning system according to embodiments of the invention.

[0049] In a first step, the system receives a plurality of measurements, also called observations, regarding target objects, in particular at least two target objects. These observations can be represented in a vector y. The plurality of measurements can include absolute position estimates of the target objects or objectives from the GNSS, distance measurements between the target objects, or angular information between the objectives. The distance measurements can be provided by SLPP rangefinding, ultra-wideband (UWB) rangefinding, or similar methods. The angular information can be provided by sidelink angle of arrival (AoA) or angle of departure (AoD).

[0050] Optionally, distance and / or angle information can be provided by a fixed anchor such as a Road Site Unit (RSU), which would add measurements but not an unknown condition to be estimated.

[0051] In a next step, 202, the majority of measurements can be linked to a state estimation using a functional model for the hybrid positioning system. The functional model can be a model as described above. In this embodiment of Fig. 2. The following exemplary model can be used: Xi = Xi in the case of absolute positioning measurement, and Yi = Yi in the case of absolute positioning measurement (xB−xA)2+(yB−yA)2 In the case of distance measurement.

[0052] For example, if a target or object is located at a fixed position and is furthermore located with uncertainty, it can only be one pair of coordinates in the expression. (10−xA)2+(2−yA)2 for a distance measurement between an object A and an RSU located at position coordinate (10, 2).

[0053] Furthermore, the function "arctan2(y B - y A , x B - x A )“ is used for angle information in the case of an angle measurement between two targets A and B in the functional model.

[0054] Arctan2(y,x) is the two-argument arctangent, and it is an angle measure (in radians) between the positive x-axis and the ray from the origin to the point (x, y) in the Cartesian plane.

[0055] In the next step 203, the functional model is linearized using the Jacobian matrix J of f: y−v=Jx.

[0056] This linearization simplifies the calculation and analysis of the measurements as inputs.

[0057] In step 204, stochastic information can be collected in a sparse matrix Q to interpret the results of the outputs of the functional model.

[0058] For example, if an a priori covariance matrix for indirect measurements such as GNSS or a variance for direct measurements such as SL distance determination is optionally known, they can be placed directly into the sparse matrix as a block diagonal matrix.

[0059] If only the cofactor matrix is ​​known, then these are placed in the sparse matrix in place of the covariance or variances, and a further estimation step is then carried out.

[0060] In a next step 205, the uncertainty can be iteratively compensated, for example by using a so-called weighted least squares method.

[0061] The weighted least squares method includes, as an example, the following steps: In step 205a, a normal matrix N is calculated from the Jacobi matrix J and the sparse matrix Q based on a matrix P of weights, where the matrix P is a function of the sparse matrix Q, and where J is the Jacobi matrix evaluated with the current state estimation. - Refining the state estimation depending on the calculation, - Updating the function that yields P from the sparse matrix Q, and - Updating the covariance matrix of the state estimation.

[0062] Based on the fact that a given matrix P of weights is a function of the sparse matrix Q, the normal matrix N = J can be T PJ is calculated, where J is the Jacobian matrix evaluated with the current state estimate. This will lead to linearization errors in the first estimate, which is the starting point of an iterative process to be performed.

[0063] In step 205b, the state estimation is refined, whereby the state can be modeled as x^=N−1JTPy.

[0064] Then, in step 205c, the function that yields P from the matrix Q is updated, and in step 205d, the covariance matrix of the state estimation is calculated using σ^o2 updated, which is called the unitary variance factor (explained below).

[0065] In a next step 206, the majority of measurements can be adjusted based on the results of the compensation step 205 if the least-squares method is used based on steps 205a to 205d.

[0066] In another embodiment, step 205c can be performed using machine learning. This can take prior measurements to yield the weight matrix, with an optional intermediate step to estimate the covariance and / or cofactor matrix.

[0067] In another embodiment, in step 205c the function can be a modified VCE (variance component estimation) that uses a neural network or any machine learning technique trained on previous measurements.

[0068] In another embodiment, a loss function can be based on a corrected residual vector: V=y−Jx

[0069] For example, a unitary variance factor can be calculated: σ^o2=VTPVn−m

[0070] where n is the number of observations and m is the number of observations.

[0071] In this case, it is advantageous to group the observations in order to apply, for example, a Helmert VCE. In this process, the weight matrix is ​​then estimated iteratively at the same time as the state.

[0072] In another embodiment, the loss function uses other a priori knowledge to measure the quality of the weight determination.

[0073] In another embodiment, the system receives multiple measurements over time within a time coherence interval that depends on the mobility of the nodes in order to increase the overdetermination of the system, as explained above.

[0074] In another embodiment, a machine learning-based approach can be provided for learning the optimal compensation weights. In this embodiment, a trainable function is used or implemented, such as a neural network with a set of trainable parameters, where the neural network's weights can be updated based on experience gained through the collection of input data.

[0075] According to embodiments of the invention, a hybrid model is used, as opposed to using a neural network to solve the entire inference task. The neural network is used in parallel with the existing algorithm. Thus, the goal of the model is not to replace the above algorithmic steps, but instead to compensate for the inaccuracies introduced by the approximations.

[0076] In another embodiment, the neural network can receive the covariance matrices, the variances, as input. Based on these parameters, it outputs a correction term e, which can be added to the actual state estimate x̂.

[0077] The above explanation of the embodiments describes the present invention in the context of examples. Of course, individual features of the embodiments can be freely combined with one another, provided that this is technically feasible without departing from the scope of protection of the present invention.

Claims

[1] Method (100) for adjusting a plurality of measurements of a hybrid positioning system comprising the following steps, which are carried out by a data processing device (10): - Obtain (101) the majority of measurements with respect to at least two target objects, wherein the majority of measurements includes at least one distance measurement and / or at least one position measurement, - Linking (102) the plurality of measurements with a state estimation using a functional model for the hybrid positioning system, wherein the state estimation is related to the plurality of measurements with respect to a position and / or a distance measurement in relation to the at least two target objects, - Linearizing (103) the functional model using a Jacobi matrix J, where the Jacobi matrix J specifies the linear approximation of the functional model around a current state estimate, - Collecting (104) stochastic information regarding a distribution of measurement errors in a sparse matrix Q, - iterative compensation (105) of measurement uncertainty and / or measurement errors based on a weighted least-squares procedure using the linearized functional model and the collected stochastic information, - Adjusting (106) the majority of measurements based on compensation (105). [2] Method (100) according to claim 1, characterized by , that the weighted least squares method comprises the following steps: - Computation (205a) of a normal matrix N from the Jacobi matrix J and from the sparse matrix Q based on a matrix P of weights, where the matrix P is a function of the sparse matrix Q, and where J is the Jacobi matrix evaluated with the current state estimation, - Refining (205b) the state estimation depending on the calculation (205a), - Updating (205c) the function that yields P from the sparse matrix Q, and - preferably updating (205d) a covariance matrix and / or cofactor matrix of the state estimation. [3] Method (100) according to claim 2, characterized by , that updating (205c) the function includes at least one of the following additional steps: - Adjusting the uncertainty compensation using a machine learning technique based on training a neural network on previous measurements, - Estimating the covariance and / or cofactor matrix of the state estimation, - Grouping the majority of measurements to apply a Helmert variance component estimation. [4] Method (100) according to claim 2 or 3, characterized by , that the procedure (100) further includes the following step: - Providing a loss function based on a priori knowledge to measure the quality of the weight determination of the matrix P of weights. [5] Method (100) according to any one of the preceding claims, characterized by that the stochastic information includes at least one of the following: - an a priori covariance matrix or a variance for indirect measurements, - a cofactor matrix for direct measurements. [6] Method (100) according to any one of the preceding claims, characterized by , that the functional model is selected from the group that includes first values ​​for absolute positioning measurement in two dimensions and / or second values ​​for distance measurement and / or third values ​​for angle measurement. [7] Method (100) according to any one of the preceding claims, characterized by , that the procedure (100) during the receiving (101) includes at least one of the following further steps: - Collecting absolute position estimates and / or distance determination information between the at least two target objects and / or angular information between the at least two target objects, - Collecting distance and / or angle information from a fixed anchor. [8] Method (100) according to any one of the preceding claims, characterized by , that obtaining (101) the majority of measurements is based on a time coherence interval depending on a mobility of at least two targets. [9] Computer program (20) comprising instructions which, when the computer program (20) is executed by a computer (10), cause the computer (10) to execute the method (100) according to any of the preceding claims. [10] Data processing device (10) comprising means for carrying out the method (100) according to any one of claims 1 to 8. [11] Computer-readable storage medium (15) comprising instructions which, when executed by a computer (10), cause the computer (10) to perform the steps of the method (100) according to any one of claims 1 to 8.

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