Method for magnetic field-based recognition of a reference point

Abstract

The invention relates to a method for magnetic field-based detection of a reference point when performing multiple series of measurements to create a magnetic field map for a rail network. The method comprises the following steps: A first series of measurements is performed to determine a magnetic field at multiple reference points within a specified section of the rail network. A second series of measurements is performed to determine the magnetic field at multiple reference points within the specified section of the rail network. At each of the reference points, the magnetic field is detected using a magnetic field sensor and the position of the reference point is detected using a position sensor. A local magnetic field signature is recorded at each reference point and stored in a database. Each local magnetic field signature represents the local magnetic field in the area around the reference point.At least one magnetic field signature recorded during the second measurement series is compared with the magnetic field signatures recorded during the first measurement series. Identity between a reference point recorded within the second measurement series and a reference point already recorded in the first measurement series is detected if the magnetic field signature to the reference point from the second measurement series exhibits a minimum similarity to the magnetic field signature to the reference point from the second measurement series.

Description

[0001] The present invention relates to a method for magnetic field-based detection of a reference point when performing multiple measurement series to create a magnetic field map for a rail network. Furthermore, the invention relates to a method for creating a magnetic field map in which the inventive, magnetic field-based detection of a reference point is used. Furthermore, the present invention relates to a method for magnetic field-based position determination for a rail vehicle in which a magnetic field map created by the inventive method is used.

[0002] Positioning methods play a particularly important role in various application areas. For example, the precise determination of the position of a rail vehicle is essential if it is to be controlled autonomously or if the position data is to be used to optimize traffic management.

[0003] Various positioning methods are widely known. These methods are often based on global navigation satellite systems (GNSS). However, this approach is not feasible or only partially feasible in certain scenarios. For example, GNSS methods cannot be used in tunnels. Therefore, in certain scenarios, it may be preferable to use magnetic field-based methods.

[0004] Magnetic field-based methods for position determination are known in various forms. Some of these methods utilize a magnetic field map in which information about a magnetic field at various reference points is stored. The magnetic field can be based on the Earth's magnetic field or, alternatively, be induced by magnets that are actively deployed in a specific environment to generate a (locally) significantly varying magnetic field. If a precise magnetic field map exists for a specific environment within which the magnetic field differs at different locations, the current position of an object can be deduced from knowledge of the magnetic field.

[0005] However, the precise creation of magnetic field maps presents a particular challenge in practice. This is primarily due to the fact that, in order to create a magnetic field map, both the magnetic field at individual reference points and the exact position of these reference points must be known. However, this requires that the position of the reference point can be determined with sufficient accuracy without relying on GNSS data.

[0006] Various methods for creating the aforementioned magnetic field maps are known from the state of the art. Graph-based methods for simultaneous positioning and map creation (also known as graph simultaneous localization and mapping or graph SLAM) have proven particularly suitable for this purpose (see [1], [2]). In these methods, a route is traveled several times. Each time the route is covered, a series of measurements is taken in which the magnetic field is measured at predetermined reference points (also known as nodes) (position and magnetic field of the respective reference point). The probable position of the individual reference points is then determined from the information obtained within the individual series of measurements using statistical methods.

[0007] The above method requires comparing the reference points acquired in a series of measurements with those from previous series of measurements in order to identify previously recorded reference points. If a reference point acquired during a series of measurements is recognized in a subsequent series of measurements, this information can be used to more precisely determine the position of the reference points within the map data. However, in practice, identifying the reference points presents a non-trivial challenge.

[0008] Therefore, it is an object of the present invention to provide a method which allows a reliable detection of a reference point when carrying out several series of measurements to create a magnetic field map for a rail network.

[0009] To achieve the above-mentioned object, the present invention provides a method for magnetic field-based detection of a reference point in

[0010] Carrying out several series of measurements to create a magnetic field map for a rail network is proposed, whereby the method comprises the following steps: Carrying out a first series of measurements to determine a magnetic field at a plurality of reference points within a predetermined section of the rail network, wherein at each of the reference points the magnetic field is detected using a magnetic field sensor and the position of the reference point is detected using an odometer, wherein at each reference point a local magnetic field signature is recorded and stored in a database, and each local magnetic field signature represents the local magnetic field in the area around the reference point, wherein the magnetic field signatures recorded during the first series of measurements have a length l sig1 ;Carrying out a second series of measurements to determine the magnetic field at a plurality of reference points within the specified section of the rail network, wherein the magnetic field is recorded at each of the reference points using the magnetic field sensor and the position of the reference point is recorded using an odometer, wherein a local magnetic field signature is recorded for each reference point, and each local magnetic field signature represents the local magnetic field in the area around the reference point, wherein the magnetic field signatures recorded during the second series of measurements have a length l sig2 ; comparing at least one magnetic field signature recorded during the second series of measurements or a section of this magnetic field signature with the magnetic field signatures recorded during the first series of measurements;and detecting the identity between a reference point recorded within the second series of measurements and a reference point already recorded in the first series of measurements, provided that the magnetic field signature or the section of the magnetic field signature for the reference point from the second series of measurements has a minimum similarity to the magnetic field signature for the reference point from the first series of measurements. ;

[0011] The method according to the invention allows for reliable and precise detection of previously recorded reference points within the specified route section. This increases the precision when creating a magnetic field map. The method according to the invention advantageously does not require the introduction of additional magnets into the route section. However, additional magnets can optionally be provided to specifically adapt the magnetic field based on the Earth's magnetic field.

[0012] The magnetic field signatures recorded during the first and second series of measurements comprise N measured values, which may, for example, border on the reference point. N can, for example, be 100, 200, or 300, whereby a magnetic field sensor can, for example, be recorded with a measuring frequency of 100 Hz. The measured data can preferably be interpolated, whereby the number of values ​​within a magnetic field signature can be increased. Each measured value can, for example, contain a vector that describes the magnetic field at the respective measuring point. It can also be provided that the measured values ​​are designed such that the reference point lies within the defined measuring range. For example, the reference point can also be centrally located within the measuring range.

[0013] An odometer in the sense of the present invention generally measures the distance traveled by a vehicle and is therefore also referred to as a distance measuring device. The distance traveled relative to a reference point is measured, which is why the measurement results exhibit increasing measurement error as the measuring distance increases.

[0014] The local magnetic field signatures are recorded using the odometer and the magnetic field sensor, respectively, whereby a local magnetic field signature describes the magnetic field in the immediate vicinity of a reference point.

[0015] The length of the magnetic field signatures recorded during the first series of measurements are preferably identical (l sig1 = l sig2 )

[0016] Even though the method according to the invention has been described above with two series of measurements, it is obvious to the person skilled in the art that in practice the performance of more than two series of measurements is desirable and contributes to an increased precision of the method.

[0017] In some embodiments of the method according to the invention, it can be provided that the method comprises the following steps: Comparing a section of a magnetic field signature recorded during the second series of measurements with the magnetic field signatures recorded during the first series of measurements, wherein the section of the magnetic field signature recorded during the second series of measurements has a length l section and wherein l section < l sig2 applies; wherein during the comparison of the section of the signature recorded during the second series of measurements with the magnetic field signatures recorded during the first series of measurements, a successive comparison of said section with mutually shifted sections of a magnetic field signature recorded during the first series of measurements takes place.

[0018] By using the section of the magnetic field signature (instead of the entire magnetic field signature) and the sliding comparison with one magnetic field signature at a time from the first measurement series, several technical advantages are achieved. In particular, this ensures that a reference point is detected even if it is detected at positions that are offset from one another in the first and second measurement series. This significantly increases the reliability of the reference point detection and thus makes the inventive method more robust against measurement inaccuracies of the odometer. The smaller l section is selected compared to l sig2, the greater the detection tolerance when comparing the section of the magnetic field signature from the second measurement series with the magnetic field signatures from the first measurement series.In addition, the sliding comparison makes it possible to not only detect one reference point, but also to simultaneously detect the distance of the detected reference point between the first and second series of measurements.

[0019] In some preferred embodiments of the invention, it can be provided that l section is a maximum of 75% of l sig2, that l section is preferably a maximum of 50% of l sig2 and that l section is particularly preferably a maximum of 25% of l sig2. The choice of the length of the section of the magnetic field signature l section depends on several factors. If the section is chosen too small, the precision of the detection during adjustment decreases. If the section is chosen too large, the detection tolerance decreases, so that reference points that are slightly shifted between the first and second series of measurements cannot be detected.

[0020] According to one embodiment of the method according to the invention, it can also be provided that l section is at least 20% of l sig2, that preferably l section is at least 40% of l sig2 and that particularly preferably l section is at least 70% of l sig2.

[0021] According to some embodiments of the method according to the invention, it can be provided that at least one local magnetic field signature within the first measurement series and / or within the second measurement series reproduces the magnetic field in a range of 100 m to 500 m, preferably in a range of 200 to 400 m, wherein the range includes the associated reference point. The selection of such measurement ranges for recording the magnetic field signatures has proven suitable in practice, so that reliable detection of the reference points can be achieved. If the magnetic field signature reproduces a smaller range, the detection of the reference points becomes more difficult, while the precision of the position determination decreases if the magnetic field signature reproduces a significantly larger range. The stated value ranges therefore represent a compromise that has proven successful in practice.

[0022] Furthermore, the method according to the invention can provide for the recording of at least one local magnetic field signature by detecting the magnetic field in the vicinity of a reference point at a measurement frequency of ≥ 10 Hz or ≥ 30 Hz or ≥ 50 Hz, preferably at a measurement frequency of ≥ 100 Hz and particularly preferably at a measurement frequency of ≥ 200 Hz. This enables high-resolution detection of a characteristic magnetic field around a reference point, thereby increasing the detection accuracy of the reference points. Furthermore, the high-resolution detection of the magnetic field in the vicinity of a reference point means that fewer reference points need to be considered overall.

[0023] Preferably, it can be provided that the comparison of at least one magnetic field signature recorded during the second series of measurements or a section of this magnetic field signature with the magnetic field signatures recorded during the first series of measurements is carried out based on a correlation calculation. This allows the degree of similarity to be determined in a simple manner, so that a reliable decision regarding the identity of two reference points can be made based on the result of the correlation calculation. If the correlation calculation is carried out between a section of a magnetic field signature recorded during the second series of measurements and the magnetic field signatures of the first series of measurements, the distance between two reference points identified as identical in the first and second series of measurements can be determined.In this case, the magnetic field signatures of the first measurement series are longer than the section of the magnetic field signature recorded during the second measurement series. Therefore, the correlation coefficients for all positions of the section within the local measurement signature of the first measurement series can be advantageously evaluated by "sliding" the section over the local measurement signature of the first measurement series. The largest determined correlation coefficient can be determined and stored together with the position at which this maximum was determined. After the comparison for a section of a magnetic field signature of the second measurement series has been compared with all possible local magnetic field signatures from the first measurement series, a final check can be performed to determine whether the largest of the determined correlation coefficients exceeds a specified threshold.If this is the case, the identity between the reference points can be detected and, at the same time, the shift between the first and second series of measurements. In this way, the sliding adjustment in combination with the correlation calculation allows reliable detection of a reference point and its distance between two series of measurements. If the local maps of the different reference points overlap, the identity of several reference points and the respective shift can also be determined. This is the case, for example, if a reference point is provided every 50 m and the local maps have a length of 200 m. Several correct loop closures can then be detected (at least partially) and inserted into the graph.Accordingly, according to some embodiments of the present invention, it may be provided that a magnetic field signature describes the magnetic field along a path that is longer than the distance between two reference points. It may also be provided that the path described by a magnetic field signature is at least twice as long, at least three times as long, or at least four times as long as the distance between two reference points.

[0024] In some preferred embodiments of the invention, it can be provided that a correlation coefficient is calculated to determine the similarity of a magnetic field signature recorded during the second series of measurements with several magnetic field signatures recorded during the first series of measurements, wherein the correlation coefficient with the largest value is compared with a predetermined correlation threshold, and an identity between a reference point recorded during the second series of measurements and a reference point recorded during the first series of measurements is detected if the correlation coefficient with the largest value exceeds the predetermined correlation threshold. This allows the sensitivity of the detection of a reference point to be adjusted, whereby the threshold can be adjusted depending on the application area and requirements.

[0025] The method according to the invention can also provide for the comparison of the reference point acquired during the second series of measurements with the reference points acquired during the first series of measurements to be carried out selectively, so that the comparison is carried out only with selected reference points for which there is a higher probability of the reference points being identical. In other words, the comparison is thus limited to a predetermined range, whereby the limitation can preferably be based on the odometer measurement data.If 100 reference points were determined during the first series of measurements and, during the second measurement, it can be assumed that a newly acquired reference point can only be identical to one of the reference points 83 to 87 of the first series of measurements due to the existing, erroneous odometer measurement data, the comparison of the newly acquired reference point (during the second series of measurements) can be limited to the reference points 83 to 87 of the first series of measurements. This can increase the efficiency of the method, so that the correlation calculation is limited to only a selection of the reference points.

[0026] In addition, the precision of the recognition process is increased because the risk of incorrect assignment of the reference points is reduced.

[0027] In addition, the method according to the invention can provide for the values ​​of the recorded local magnetic field signatures to be interpolated.

[0028] Preferably, the odometer can be provided with a speed sensor designed to detect the speed of a wheel of a rail vehicle and / or a Doppler radar sensor designed to measure the speed of the rail vehicle. However, other methods known from the prior art for direct or indirect distance measurement can also be implemented. For indirect distance measurement, for example, speed sensors can be used, whose measurement results are integrated.

[0029] In addition, the present invention proposes a method for creating a magnetic field map for a section of track within a rail network, the method comprising the following steps: Creating a magnetic field map for a route section using a graph-based method for simultaneous positioning and mapping, SLAM, detection of reference points that have already been recorded in previous measurement series using one of the above reference point detection methods.

[0030] Furthermore, it can be provided that an edge is added within the SLAM graph between a reference point from the second measurement series and a reference point from the first measurement series, provided that an identity between the reference points has been detected. The added edge describes the displacement between two reference points. The distance is also determined by the magnetic field.

[0031] Furthermore, the present invention proposes a method for determining the position of a rail vehicle within a rail network, wherein the rail vehicle has a magnetic field sensor and the method comprises the following steps: Creating a magnetic field map for a section of track within a rail network according to one of the previous methods for creating a magnetic field map; detecting a magnetic field using the magnetic field sensor; comparing the magnetic field with the magnetic field map; and determining the position of the rail vehicle within the rail network depending on the previously detected magnetic field and the created magnetic field map.

[0032] Further advantageous embodiments of the present invention will be discussed in more detail below.

[0033] As stated above, the present invention relates, among other things, to a method for creating magnetic field maps along railway tracks, even in scenarios where GNSS positioning is not possible. The proposed method can be used to improve existing SLAM methods (in particular pose graph SLAM). The advantage of pose graph SLAM is that the problem can be formulated as a sparse graph, which can be solved efficiently in terms of computational complexity and memory requirements. According to one aspect of the present invention, each node in the pose graph can be assigned a local magnetic field map (also referred to as a local magnetic field signature), which is generated from the measurements of an odometer and a magnetometer.These local maps are then used to detect loop closures (also called loop-closure detection) between nodes and calculate their relative positions. Since loop closures can only be detected for nodes or reference points that are close to each other, the resulting graph is sparse and optimization can be performed efficiently, allowing the algorithm to be applied to long distances. To evaluate the proposed method, a dataset recorded with Deutsche Bahn's advanced TrainLab, which traveled at speeds of up to 100 km / h, is used. In addition,

[0034] Simulations were performed to evaluate a scenario not covered by the measurements. motivation

[0035] Magnetic field-based train localization has the potential to enable localization even in areas where GNSS is not available, such as tunnels, without the need to install special trackside localization devices such as balises or radio beacons. Magnetic localization is a fingerprinting method and requires a map that links a specific magnetic fingerprint or pattern to the position where the pattern is located. Unfortunately, creating the map requires a position reference system (e.g., GNSS), which leads to a chicken-and-egg problem. The magnetic localization system requires a map, and creating the map requires a reference position. This type of problem arises in many applications, such as robotics, which has led to the development of a variety of simultaneous localization and mapping (SLAM) algorithms.Initially, SLAM was based on extended Kalman filters, whose complexity increased quadratically with the number of observed landmarks and which had only low accuracy for highly nonlinear problems. Therefore, particle filters and Rao-Blackwellized particle filters in the form of the well-known FastSLAM algorithm were introduced as alternatives. While the above-mentioned solutions are based on filters, alternatives have also been proposed that attempt to find a solution to the SLAM problem through optimization. In particular, graph-based methods were introduced, which are now considered state of the art for SLAM due to their computational efficiency and stability. In SLAM, a distinction is also made between landmark-based and landmark-free approaches. In the present invention, a landmark-free approach can preferably be used, which can be found, for example, in [1].In addition, the present invention proposes improvements over the method described in [2], introducing a new loop closure detection and preferably introducing a-priori information edges and absolute measurement edges, which are required due to the limited freedom in the trajectory of the train when taking measurements. Graph-based SLAM

[0036] The following briefly summarizes the fundamentals of graph-based SLAM. More specifically, the SLAM method with pose-graph optimization will be explained, which does not directly estimate the map. Instead, it only optimizes the series of poses. The desired map can then be created based on the resulting trajectory.

[0037] The starting point for the derivation of graph-based SLAM is the definition of the cost function to be optimized. In this specific case, the cost function is the full posterior probability density function (pdf) over the trajectory of a train x p x Z , Y where and y are two sets of measurements and the trajectory is represented by a sequence x of train positions contained in a vector x = [ x 1 , ··· , x N ] are summarized, whereby 11 is the i-th train position along the route. The theorem contains measurements their ∈ that describe how two positions 11 and xj with i ≠ j are related to each other in the trajectory. Since the position of a train along the track is considered here, the position is one-dimensional, and z ijis basically just a measure of the distance between 11 and xj . This type of measurement can be obtained from an odometer or distance measuring device, which measures the distance traveled by the train between two positions, or, as will be explained in more detail in the next sections, this information can also be obtained from the magnetic field itself. In contrast to the quantity contains the amount y absolute information about a specific position. Therefore, an element yi of y only with one position 11 The following is a position 11 also referred to as nodes, and measurements are referred to as edges. This will be explained in more detail below in connection with the derivation of the cost function.

[0038] The goal of optimization is to find the maximum a-posteriori estimate (MAP) x ^ = arg max x p x Z , Y .

[0039] To perform the optimization, it is advantageous to decompose the posterior expression into a more suitable form. In a first step, the law of conditional probabilities is applied to the posterior expression to obtain the following: p x Z , Y ∝ p Z , Y x p x .

[0040] Note that the right-hand side of the above expression is only proportional to the posterior expression. However, this does not change the position of the maximum. In a second step, the right-hand side in (3) is further decomposed. p x Z , Y ∝ p Z , Y x p x = p Z x p Y x p x = p x ∏ i j ∈ C Z p z i , j x i x j ∏ i ∈ C Y p y i x i .

[0041] The elements of the set C z are pairs of node indices for which a relative measurement in is contained, and the amount Contains the indices of positions for which an absolute measurement exists. For simplicity, only one relative measurement per node pair and one absolute measurement per node are considered here, but extension to multiple measurements is easily possible.

[0042] The last two terms in (4) are the product of the probability densities of the individual measurements. For each of the measurements, the probability density is assumed to be Gaussian. For the relative measurements in the probability density is given by p z i , j x i x j = N z i , j ; z ˜ x i x j , Ω ij − 1 where the mean is determined by the predicted measurement z ( 11 , xj ) is given, which for the 1D case considered here is simply z ( xi< , xj< ) = xi< - xj< is.

[0043] For the absolute measurements in y, the probability depends only on one node p y i x i = N y i x i Ω i − 1 .

[0044] For the pdf p(x), it is assumed that only information about the first node is available. Therefore, it is set to p x 0 = N x 0 x ˜ 0 Ω 0 − 1 . Setting Ω 0 to a high value anchors the node to the mean x 0 of p(x). This mean value can be determined, for example, by GNSS before trains enter a tunnel. If absolute measurements are not available, the first node can be used to define the coordinate system.

[0045] For cost functions of the above form, it is useful to optimize the logarithm of the cost function. Using the Gaussian pdfs in (5)-(7), the following expression is obtained: c x = x 0 − x ˜ 0 2 Ω 0 + ∑ i ∈ C y y i − x i 2 Ω i + ∑ i j ∈ C z z i , j − z ˜ x i x j 2 Ω ij = e p x 2 Ω 0 + ∑ i j ∈ C z e ij x 2 Ω ij + ∑ i ∈ C y e i x 2 Ω i , where all constant parts that are not important for the optimization are neglected and the entire function has been multiplied by -2 to simplify the expressions. By multiplying the cost function by -2, the problem is transformed into a minimization problem, which will be the basis for the optimization. x ^ = arg min x c x .

[0046] The cost function c(x) can be visually represented by a graph, where each edge represents a term of the cost function and each node is a position to be optimized. An example of a graph, as found in the railway environment, is shown in the Fig. 1 The graph in the Fig. 1exhibits a discontinuity between poses x 5 and x 6. This is because, in a railway environment, it can happen that a train passes through a tunnel and then does not return for an extended period of time. The SLAM algorithm must therefore be able to combine data from multiple discontinuous measurement runs on the same track. These discontinuities motivate the preferential inclusion of absolute position measurements in the graph because they connect the poses from multiple measurement runs on the same track, even if the train always passes through the tunnel from the same direction. In addition, absolute measurements at the beginning and end of a tunnel help during optimization to reduce the overall position error in the tunnel when only relative information between different poses is available.

[0047] Examination of (8) shows that the MAP estimation of the trajectory is a weighted nonlinear least-squares problem. Within the scope of the present invention, the least-squares solution can be found using the Gauss-Newton method. This requires a linearization of the error functions for the a priori information ep (x), relative measurements e ij (x), and absolute measurements ei (x). The linearized version of these functions results from their Taylor series expansions around the operating point x*. e p l x = e p x ∗ + J p x − x ∗ e ij l x = e ij x ∗ + J ij x − x ∗ e i l x = e i x ∗ + J i x − x ∗ .

[0048] These include J p, J ij and J j the corresponding Jacobian matrices evaluated at the point x*, ie the Jacobian matrix results from J ij = ∇ x e ij x x = x * T Since the error functions are scalar, the Jacobian matrices are row vectors of dimension N, and the product with the vector Δx = xx* is a scalar. For the Gauss-Newton algorithm, the linearized error functions can be substituted into the cost function in (8). c 1 x = e p 1 x 2 Ω 0 + ∑ i j ∈ C z e ij 1 x 2 Ω ij + ∑ i ∈ C y e i 1 x 2 Ω i = c p x + c ij x + c i x .

[0049] The Gauss-Newton equations are obtained by setting the gradient of the cost function to zero with the linearized error functions in (11) ∇ x c 1 x = ∇ x c p x + ∇ x c ij x + ∇ x c i = 0 .

[0050] With the gradients of the individual parts of the cost function ∇ x c p x = 2 Ω 0 J p T e p x ∗ + 2 Ω 0 J p T J p x − x ∗ ∇ x c ij x = ∑ i j ∈ C z 2 Ω ij J ij T e ij x ∗ + 2 Ω ij J ij T J ij x − x ∗ ∇ x c i x = ∑ i ∈ C y 2 Ω i J i T e i x ∗ + 2 Ω i J i T J i x − x ∗ then an equation of the form − b = HΔx with the vector b = 2Ω 0 J p T e p x ∗ + ∑ i j ∈ C z 2Ω ij J ij T e ij x ∗ + ∑ i ∈ C y 2Ω i J i T e i x ∗ = b p + b r + b a and the Matrix H = 2Ω 0 J p T J p + ∑ i j ∈ C z 2Ω ij J ij T J ij + ∑ i ∈ C y 2Ω i J i T J i = H p + H r + H a .

[0051] To minimize the cost function, we can now solve for Δx and calculate the estimated value for x x ^ = x ∗ − H − 1 b .

[0052] This procedure is performed iteratively by setting x* = x̂ after each iteration until the estimate converges. Complexity considerations

[0053] The Matrix H, which must be inverted during optimization has the dimension N × N , where N is the number of nodes and thus the dimension of x. For large vectors x, this leads to high complexity, especially because the matrix H must be recalculated after each iteration step at the position of the new estimate x̂. In the simplest implementation, this would have a complexity of ( N 3< ). Fortunately, it can be shown that the matrix H is typically sparsely populated due to its construction. Relative measurements

[0054] The previous section briefly explained the general idea of ​​the graph-based SLAM approach. To clarify some preferred aspects of the invention, this section will describe the relative observations and how they can be obtained in more detail. 1) Odometer edges: As shown in the example graph in the Fig. 1 As shown, there is an edge between consecutive nodes, provided they were created during the same run or series of measurements. The measurements zi,j For example, the edges between consecutive nodes are obtained from an odometer. On railways, the odometer can typically be determined by integrating the speed of a wheel speed sensor or Doppler radar. 2) Detection of a loop closure or a previously recorded reference point:In addition to edges based on odometer measurements, edges between non-consecutive nodes are also preferably considered here. An edge between two non-consecutive nodes can be introduced when a loop closure is detected. A loop closure should be detected when a train revisits a position or reference point on the track. The advantage of a loop closure edge is that it connects newly added nodes with older nodes already present in the graph. Roughly speaking, this connection between new and old nodes "bounds" the overall trajectory and can therefore, if enough loop closures are detected, significantly improve the estimated trajectory compared to the odometer alone.

[0055] As previously mentioned, a core aspect of the present invention relates to the manner in which loop inclusions are detected, or rather, how reference points acquired in previous measurement series are detected in subsequent measurement series. In particular, it is proposed here to detect loop inclusions by creating a local map of the magnetic field (also known as a local magnetic field signature) in its surroundings for each newly added node. How these local maps can be created will be explained in more detail in the next section. Initially, it is sufficient to know that a local map is preferably a function that takes a one-dimensional position as input and returns the corresponding magnetic field vector at this position. Since the map is "local," the input position is preferably relative to the position of the corresponding reference point. With this local map, the detection of the

[0056] Loop closure should preferably be done in three steps when a new node is added Search for the set of indices all nodes located within a predefined search radius R LC around the newly created node Compare the magnetic field that is generated on the last d LC meters of the route around the new junction was recorded, with the local maps of all junctions on and find the position where it best fits each local map Add an edge between the current node and a node in if the similarity between the current magnetic field and the local map is above a defined threshold T LC . The relative dimensions of the edge are given by the position where the current magnetic field best fits the local map, where the dimensions describe the distance between the points.

[0057] The following explains how the similarity can be determined and how the local maps can be constructed.

[0058] 3) Local maps:To create a local map or a local magnetic field signature, the magnetic field measurement results and the train speed during these measurements can be stored in a buffer. The train speed is also measured, e.g., using a wheel speed sensor. From this buffer, a local map can then be calculated each time a new node is created. To calculate the map, the measured speed can first be integrated backward in time, starting with the most recent available measurement. By integrating the speed, the relative position of each magnetic field measurement is also assigned to the position of the newly created node. In a second step, the magnetic data can be interpolated to an equidistant position grid.This interpolation is advantageous because the relative position from the velocity integration depends on the train's speed during the measurements, and therefore the magnetic field data are not equally spaced in the spatial domain, which can affect further processing. An example of a magnetic map and the measurement of the relative position is shown in the . Fig. 2 The length L map of the map can can be freely chosen. However, initial studies have shown that setting the length to a few hundred meters is advantageous. If the maps are too long, the error in the relative position caused by integrating the measured train speed becomes too large. The choice of map length is a compromise between maximizing the number of loop closures between the nodes and the accuracy and reliability of the loop closure.

[0059] 4) Detector:Using the local maps from the previous section, a loop closure detector can now be implemented. The detector proposed here is essentially a correlator. When a new node is created, its local map can be created and stored together with the node. Subsequently, a piece of the map with length L sig, which is called a magnetic signature or magnetic field signature. The signature can, for example, be cut out at the beginning of the card. In general, the equation L map > L sig must be fulfilled, since the entire signature should be compared with the local maps of the other nodes to obtain good and reliable results.

[0060] To detect a loop closure, the local map of each candidate node included in the index set contained in the map are compared with the signature of the newly created node. The comparison is preferably based on a correlation coefficient. If the map is longer than the signature, the correlation coefficient can be evaluated for all possible positions of the signature in the local map by "sliding" the signature across the map. For the detector, only the highest value of the correlation coefficient and the relative position at which it was calculated are stored. After the comparison has been performed for all candidate nodes, a loop closure can be detected if the stored maximum coefficient is above the threshold. T LC. For each detected loop closure, a relative measurement edge is inserted between the corresponding candidate node and the newly created node. The measurements zi,jThe inserted edge corresponds to the position in the local map where the maximum coefficient was observed. Attention should be paid to the correct sign here, as the sign depends on the direction of the edge and the definition of the relative position. If the local map and the signature were recorded during journeys with different directions of travel, the map or the signature must be adjusted accordingly. Evaluation

[0061] This section evaluates the proposed approach using measurement data collected using Deutsche Bahn's advanced TrainLab. The measurements were taken on the line between Göttingen and Kassel at speeds of up to 100 km / h. The magnetic field was measured using a low-cost magnetometer from KMX, and the train speed was determined using a wheel encoder from Deuta. The evaluation uses data from three runs on a track section approximately 3 km long. During the three runs, the train always crossed the track from the same direction, which is not strictly necessary for the proposed approach. This means that the dataset is discontinuous, and GNSS measurements were used at the beginning and end of the track section to align the coordinate systems of the different runs.GNSS data were only used at the beginning and end, as this corresponds to a tunnel scenario.

[0062] In the Fig. 3 The final graph after the three runs is shown. As can be seen, despite the distance traveled of approximately 9 km, the graph has only 166 nodes. A node was only created when the train had traveled 50 m compared to the last node according to the odometer. The sparseness of the nodes can be achieved because local maps are used, which densely represent the magnetic field between the nodes. The improvement in the position error of the SLAM algorithm compared to the pure unaided odometer is shown in the Fig. 4shown. After optimization, the error is usually less than 10 m, whereas the pure odometer (odometer) has errors of up to 60 m. In the measured data, the wheel diameter was well calibrated, so the odometer error was very small, which is why the wheel diameter was reduced by one centimeter during evaluation in order to obtain larger errors in the odometer and to check whether the optimization still produced good results. It should also be mentioned that the odometer seems to be working quite well here. With ETCS, the odometer error after 3 km may be up to 5 m + 5% x 3000 m = 155 m. For an accurate representation of the magnetic field over longer distances, the pure odometer measurement is therefore not suitable.

[0063] To create the desired magnetic map, additional processing is required, as the graph only contains a node every 50 m. Therefore, for mapping purposes, interpolation between nodes can be performed to obtain the positions of individual magnetic field measurements for which no node was created. Due to the low dynamic and acceleration capabilities of a train, it can be assumed that linear interpolation should be sufficient in this case.

[0064] To complete the evaluation, a train was simulated traveling twice, forwards and backwards, on the same approximately 5 km long route. The magnetic field map used for the simulation was measured using the BRB between Augsburg and Friedberg. To simulate the measurements, the map value was taken at the train's current position and noise was added. Compared to the measured data, the simulated dataset is continuous (in the sense that the train position does not jump from one journey to the next) and therefore no external information is required to perform SLAM, i.e., no GNSS is needed. Only the first node was anchored to its position to fix the coordinate system, as is common in the SLAM procedure.

[0065] In the Fig. 5 and 6The graph and the resulting position error are shown. It can be seen that only 362 nodes are needed to cover the almost 20 km of data. The graph also shows that the different journeys are now connected via an odometer edge, as the train decelerates at the end of the route and then begins to travel in the opposite direction. The odometer in the simulation has a systematic error, which leads to a position error of several hundred meters. As shown in the Fig. 6As can be seen, the use of the graph-based SLAM method can significantly reduce the odometer error. This is achieved by loop closures that connect nodes created at the beginning of the dataset with nodes created towards the end. This connects nodes with low uncertainty with nodes with high uncertainty. The introduction of these connections makes it possible to correct the positions of nodes created with an odometer position that already has a large error.

[0066] This work was carried out within the framework of a grant from the Initiative and Networking Fund of the Hermann von Helmholtz Association of German Research Centres (contract number ZT-I-PF-5-49 ("Ubiquitous Spatio-Temporal Learning for Future Mobility (ULearn4Mobility)"). BIBLIOGRAPHY

[0067] [1] G. Grisetti, R. Kümmerle, C. Stachniss, and W. Burgard, "A Tutorial on Graph-Based SLAM," IEEE Intelligent Transportation Systems Magazine, vol. 2, no. 4, pp. 31-43, 2010. [2] J. Jung, J. Choi, T. Oh, and H. Myung, "Indoor Magnetic Pose Graph SLAM with Robust Back-End," in Robot Intelligence Technology and Applications 5. Springer International Publishing, 2019, pp. 153-163.

Claims

1. A method for magnetic field-based detection of a reference point when carrying out several series of measurements to create a magnetic field map for a rail network, the method comprising the following steps: - carrying out a first series of measurements to determine a magnetic field at several reference points within a predetermined section of the rail network, wherein at each of the reference points the magnetic field is detected using a magnetic field sensor and the position of the reference point is detected using an odometer, wherein at each reference point a local magnetic field signature is recorded and stored in a database, and each local magnetic field signature represents the local magnetic field in the area around the reference point, wherein the magnetic field signatures recorded during the first series of measurements have a length l sig1- carrying out a second series of measurements to determine the magnetic field at several reference points within the specified section of the rail network, wherein at each of the reference points the magnetic field is detected using the magnetic field sensor and the position of the reference point is detected using an odometer, wherein a local magnetic field signature is recorded for each reference point, and each local magnetic field signature represents the local magnetic field in the area around the reference point, wherein the magnetic field signatures recorded during the second series of measurements have a length l sig2- comparing at least one magnetic field signature recorded during the second series of measurements or a section of this magnetic field signature with the magnetic field signatures recorded during the first series of measurements; and - detecting the identity between a reference point recorded within the second series of measurements and a reference point already recorded in the first series of measurements, provided that the magnetic field signature or the section of the magnetic field signature has a minimum similarity to the reference point from the second series of measurements with the magnetic field signature of the reference point from the first series of measurements.

2. Method according to claim 1, characterized in thatthe method comprises the following steps: - comparing a section of a magnetic field signature recorded during the second series of measurements with the magnetic field signatures recorded during the first series of measurements, wherein the section of the magnetic field signature recorded during the second series of measurements has a length l section and where l section < l sig2 applies; where - during the comparison of the section of the signature recorded during the second series of measurements with the magnetic field signatures recorded during the first series of measurements, a successive comparison of said section with mutually shifted sections of a magnetic field signature recorded during the first series of measurements is carried out.

3. Method according to claim 2, characterized in that l section maximum 75% of l sig2 is that preferably l section maximum 50% of l sig2 and that particularly preferred l section maximum 25% of l sig2amounts.

4. Method according to one of claims 1 to 3, characterized in that at least one local magnetic field signature within the first series of measurements and / or within the second series of measurements represents the magnetic field in a range of 100 m to 500 m, preferably in a range of 200 to 400 m, wherein the range includes the associated reference point.

5. Method according to one of claims 1 to 4, characterized in that the recording of at least one local magnetic field signature is carried out by detecting the magnetic field in the vicinity of a reference point with a measuring frequency of ≥ 10 Hz or ≥ 30 Hz or ≥ 50 Hz, preferably with a measuring frequency of ≥ 100 Hz and particularly preferably with a measuring frequency of ≥ 200 Hz.

6. Method according to one of claims 1 to 5, characterized in thatthe comparison of at least one magnetic field signature recorded during the second series of measurements with the magnetic field signature recorded during the first series of measurements is carried out based on a correlation calculation.

7. Method according to claim 6, characterized in that a correlation coefficient is calculated in each case to determine the similarity of a magnetic field signature recorded during the second series of measurements with several magnetic field signatures recorded during the first series of measurements, wherein the correlation coefficient with the largest value is compared with a predetermined correlation limit and an identity between a reference point recorded during the second series of measurements and a reference point recorded during the first series of measurements is detected if the correlation coefficient with the largest value exceeds the predetermined correlation limit.

8. Method according to one of claims 1 to 7, characterized in thatthe comparison of the reference point recorded during the second series of measurements with the reference points recorded during the first series of measurements is carried out selectively, so that the comparison is only carried out with selected reference points for which there is an increased probability of the reference points being identical.

9. Method according to one of claims 1 to 8, characterized in that the values ​​of the recorded local magnetic field signatures are interpolated.

10. Method according to one of claims 1 to 9, characterized in that the odometer comprises a speed sensor designed to detect the speed of a wheel of a rail vehicle and / or a Doppler radar sensor designed to measure the speed of the rail vehicle.

11. A method for creating a magnetic field map for a section of track within a rail network, the method comprising the following steps: - creating a magnetic field map for a section of track using a graph-based method for simultaneous positioning and map creation, SLAM, - detecting reference points that have already been recorded in previous measurement series using one of the methods according to claims 1 to 10.

12. Method according to claim 11, characterized in that an edge is added within the SLAM graph between a reference point from the second series of measurements and a reference point from the first series of measurements, provided that an identity between these reference points has been detected.

13. A method for determining the position of a rail vehicle within a rail network, wherein the rail vehicle has a magnetic field sensor and the method comprises the following steps: - creating a magnetic field map for a section of track within a rail network according to one of claims 11 or 12; - detecting a magnetic field using the magnetic field sensor; - comparing the magnetic field with the magnetic field map; and - determining the position of the rail vehicle within the rail network as a function of the detected magnetic field and the magnetic field map.

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