Method for determining protection levels when a vehicle is traveling with a GNSS-based localization system using a copula-based Bayesian framework

Abstract

Method for determining protection levels (7) during the journey of a vehicle with a GNSS-based localization system using a copula-based Bayesian framework, wherein a plurality of environment classes (10, 11) and a plurality of GNSS quality indicators (9) are predefined, and wherein for each environment class (10, 11) and each GNSS quality indicator (9) a copula model (15, 16, 17) is provided offline and stored in memory, comprising the following steps: a) Classifying the environment while driving based on the GNSS quality indicators (9) and determining to which environment class (10, 11) the environment belongs, b) Reading one of the copula models (15, 16, 17) corresponding to the determined environment class (10, 11) for the corresponding quality indicators (9) from memory, c) Extracting at least one likelihood function (1, 2, 3, 4, 12) from the read-out copula model (15, 16, 17) according to a quality indicator value (13), d) Determining a posterior distribution (6) for positional errors by multiplying the at least one likelihood function (1, 2, 3, 4, 12) based on Bayes' theorem with a prior distribution (5) for errors, and e) Determining Protection Levels (7) from the Posteriori Distribution (6) .

Description

State of the art

[0001] The present invention relates to a method for determining protection levels when driving a vehicle with a GNSS-supported localization system using a copula-based Bayesian framework. Furthermore, a control unit, a computer program, a machine-readable storage medium, and a localization system are specified. The invention can be applied in particular to GNSS-supported localization systems for automated or autonomous driving.

[0002] It is known that positioning and navigation on Earth and in the air can be achieved with a Global Navigation Satellite System (GNSS) by receiving navigation satellite signals. With the help of multi-frequency and multi-constellation reception, positions on Earth can be determined with centimeter accuracy. The quality of these positions depends on whether the required requirements, particularly accuracy, continuity, availability, and integrity, are met.

[0003] It can be stated that in safety-critical autonomous driving, integrity as well as positioning accuracy plays a very important role, since integrity ensures the reliability of positioning accuracy, and poor integrity monitoring can lead to catastrophic consequences in safety-critical environmental scenarios.

[0004] The term “integrity” was originally introduced for positioning and navigation in the air and can be described with regard to position errors using the following parameters: - AL (Alert Limit) describes a position error tolerance that must not be exceeded. Otherwise, a warning message is triggered. - TTA (Time to Alert) describes the maximum permissible time interval that may elapse from the AL being exceeded until the warning message is triggered. - IR (Integrity Risk) describes the probability that the position error exceeds the AL. - PE (Position Error) describes the deviation between the determined and the actual position. - PL (Protection Level) describes the position error at which the algorithm guarantees that it will not be exceeded undetected. - FA (False Alarm) describes the event in which a warning message is triggered without the AL being exceeded. - MI (Misleading Information) describes the event where the PL is smaller than the position error, and the PL and the position error are smaller than the AL. - HMI (Hazardously Misleading Information) describes the event where the PL is less than the position error and the AL, and the position error exceeds the AL.

[0005] The Protection Level (PL) parameter is the core for integrity monitoring, which can be output together with the position from the localization system and ensures that the entire system is safe if the position error is below the prescribed AL.

[0006] The known methods for determining protection levels were typically developed within the ABSA, GBAS, or SBAS concept for airborne positioning and navigation (e.g., Greer et al., 2007, Gratton et al., 2010, Zhu et al., 2018). Their standardized integrity algorithms were usually defined taking into account the reception conditions of flying aircraft. Therefore, they are not suitable for positioning and navigation on Earth for autonomous driving, given the many critical environmental conditions (e.g., in urban areas) and reception conditions (e.g., multipath reception). Furthermore, the methods developed within the ABSA, GBAS, or SBAS concept generally refer to single-frequency reception. In contrast, autonomous driving, as mentioned above, requires multi-frequency and multi-constellation reception.

[0007] Although the well-known ARAIM concept (Blanch et al., 2007) was developed with multi-frequency and multi-constellation reception in mind to provide information on degraded GNSS satellites and is more robust than the ABSA, GBAS, or SBAS concepts in terms of lower ionospheric propagation delay due to multi-frequency reception and higher measurement redundancy due to multi-constellation reception, it appears difficult to implement this concept in the process of determining protection levels for positioning and navigation on Earth. In this context, the following challenges exist in particular: The use of non-ionospheric (IF) measurements is known to increase the magnitude of errors that are not correlated between frequencies, such as thermal noise, multipath effects, or certain distortions. In a typical road environment, this can lead to large position uncertainties.

[0008] In addition, aviation GNSS receivers typically perform pseudorange phase smoothing for 100 seconds to reduce noise and multipath. This approach cannot be used in automotive applications, as carrier phase tracking is unlikely to be reliably maintained for very long due to environmental conditions.

[0009] Furthermore, for most planned applications in the automotive industry, a more stringent AL and TTA are expected than in aerospace (typically AL in the range of 0.5 to 10 meters and TTA in the range of 1 second), without necessarily requiring a less stringent integrity risk (IR). This means that the typical scale of the ARAIM concept may result in an overly large PL.

[0010] It is therefore desirable to develop a method for determining protection levels in the context of positioning and navigation on Earth that can be used not only for multi-frequency and multi-constellation reception, but also for determining a robust protection level under critical environmental conditions. This is particularly important for autonomous driving, because autonomous driving places particularly high demands on the security and integrity / correctness of positioning information, in addition to positioning accuracy. Disclosure of the invention

[0011] A method for determining protection levels when driving a vehicle with a GNSS-supported localization system using a copula-based Bayesian framework contributes to this, wherein a plurality of environment classes and a plurality of GNSS quality indicators are predefined, and wherein for each environment class and each GNSS quality indicator, a copula model is provided offline and stored in a memory, comprising the following steps: a) Classifying the environment during travel based on the GNSS quality indicators and determining to which environment class the environment belongs, b) Reading a copula model corresponding to the determined environment class for the corresponding quality indicators from the memory, c) Extracting at least one likelihood function from the extracted copula model according to a quality indicator value, d) determining a posterior distribution for errors by multiplying the at least one likelihood function based on Bayes’ theorem with a prior distribution for position errors, and e) Determining protection levels from the posterior distribution.

[0012] The described method is particularly suitable for autonomous driving. Autonomous driving here refers in particular to the movement of vehicles, mobile robots, and driverless transport systems that operate largely autonomously using a GNSS receiver and based on global navigation satellite systems (GNSS). It is particularly advantageous if a self-driving vehicle is equipped with a localization system for implementing the described method. The localization system can be a GNSS-based or a GNSS and INS-based localization system that detects GNSS satellites in its field of view, receives GNSS signals, and can position based on the received GNSS signals.

[0013] It can be provided that the described method is executed epochally or regularly. An epoch here refers in particular to a time interval in which a currently determined position is valid or until a currently determined position is updated. This can mean that the described method is executed once each time the position is updated, thus the currently determined protection level can be output together with the currently determined position. This can also mean that all parameters relevant for position determination, such as Dilution of Precision (DOP) or the number of available GNSS signals in the field of view, are updated once in an epoch.

[0014] Although the steps are listed here with letters a) to e) in a specific order, it is not necessary to always follow this order. For example, the individual steps can be repeated independently of one another many times and / or, if repeated, partially omitted. It is possible that the steps are performed at least partially at different times.

[0015] The key idea of ​​the invention is to provide copula models based on the training data acquired through test measurements and / or simulations offline in advance and to store them in a memory. A copula model describes the statistical relationship between ranked data sets. A copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniformly distributed over the interval [0, 1] (Schmidt, T. (2007). Coping with copulas. Copulas-Form theory to application in finance, 3-34). The copula models provided offline can be read from the memory during the online drive of a vehicle according to step b) and used to generate likelihood functions according to step c).Thus, protection levels during online travel according to steps d) and e) can be determined using the posterior distribution, which is determined by multiplying the likelihood functions by a prior distribution based on Bayes' theorem. In step d), the errors can be the deviations of all variables output by the GNSS-based localization system, e.g., position errors, speed errors, and / or orientation errors. In step e), the protection levels can be determined based on a target integrity risk from the posterior distribution.

[0016] The invention has the advantage that the protection levels are implemented independently of variances.

[0017] When providing the copula models, it can be planned that the copula models are modeled with the training data, taking into account different environmental conditions and GNSS quality indicators. It is possible to classify the environmental conditions into different environmental classes, so that at least one copula model can be provided for each environmental class. It is also possible to predefine multiple GNSS quality indicators, so that a copula model can be provided for each environmental class and for each GNSS quality indicator.

[0018] A GNSS quality indicator characterises the quality of the position estimation situation for positioning algorithms and can be specified as a number between zero and a positive real number (see Fig. 2). Zero represents very poor quality, and a positive real number represents very good quality. A GNSS quality indicator refers to key signals or key variables of a GNSS that can be measured or calculated online.

[0019] A GNSS quality indicator can be Dilution of Precision (DOP). DOP is a quality measure of the available GNSS signals under line-of-sight conditions and describes how well the GNSS satellites that transmitted these available GNSS signals are suited for positioning at a location, in their relative positions. A GNSS quality indicator can also be the number of available GNSS signals in the field of view. Since at least four GNSS signals are typically required for positioning, at least five GNSS signals for integrity monitoring, and at least six GNSS signals for identifying defective GNSS satellites, the number of available GNSS signals is also extremely relevant for positioning quality.

[0020] As mentioned at the beginning, positioning on Earth is strongly influenced by environmental conditions. It can be planned that environmental conditions are classified both during the offline modeling of the copula models and, according to step a), during the online determination of protection levels.

[0021] Depending on the multipath effect caused by obstacles to GNSS signal propagation, environmental conditions may be classified into different classes: an open environment class, an urban environment class, and a critical environment class. The open environment class may include scenarios such as driving on open land, highways, etc., where there are almost no obstacles. The urban environment class may include scenarios such as driving in urban canyons, where there are numerous buildings that prevent GNSS signal propagation and / or reflect GNSS signals, and multipath must be taken into account. The critical environment may include scenarios such as driving on a multi-level road with multiple lanes stacked on top of each other.

[0022] During online travel, both the DOP and the number of available GNSS signals are typically output along with the specific position. This means that the GNSS quality indicators can be measured and / or calculated online. It is also possible to (pre-)determine both the DOP and the number of available GNSS signals in a field of view based on location, time, and movement patterns for the provision of the copula models. This is because each GNSS system has a large number of GNSS satellites (e.g., Galileo with 28 satellites, GPS with 24 satellites) that are evenly distributed in the sky or in orbit and move according to a movement pattern. This means that only certain GNSS signals from certain GNSS satellites can be received at a specific location at a specific time interval. For this purpose, the movement patterns are publicly accessible and can be downloaded (e.g., from the International GNSS Service (ISG)).

[0023] It is preferred to provide a copula model with the following steps: i) Providing training data collected through test measurements and / or simulations, ii) Classifying the training data into the environment classes, iii) providing an empirical copula for each environment class and each quality indicator, and iv) Fitting an analytical copula model to the empirical copula.

[0024] It is possible for the training data to be acquired from measurements in the real field and / or from simulated test data. The simulated test data can, for example, be generated by a GNSS signal generator capable of accounting for multipath propagation, i.e., the different environment classes.

[0025] It is preferred if in step c) the at least one likelihood function is extracted from the copula model with the following sub-steps: 1) Extracting a conditional distribution of position errors from the copula model, and 2) Obtaining at least one likelihood function from the conditional distribution according to the various GNSS quality indicators.

[0026] It is also preferred if, in sub-step 1), the conditional distribution is provided from the training data acquired by test measurements and / or simulations.

[0027] It is further preferred if in step d) the prior distribution is defined based on the training data and using a parametric distribution.

[0028] It is particularly preferred if in step d) the posterior distribution for position errors is determined for each epoch.

[0029] In contrast to the known methods for determining protection levels, which are based either on the estimated variance from a parameter estimation process or on the GNSS residuals from RAIM, the described method is carried out independently of the estimated variance but on the GNSS quality indicators. The quality indicators are key signals or key system variables that can be measured and / or calculated online and characterize the quality of the position estimation situation for the positioning algorithm.

[0030] For this purpose, Bayes' theorem is used to determine a posterior distribution for position errors at each epoch by multiplying a plurality of likelihood functions with a prior. The likelihood functions are obtained from the conditional probability distribution of the position error (from the training data) for various GNSS quality indicators. One of the main advantages of the invention, especially compared to known methods, is the use of a copula to generate the likelihood functions. This makes it possible to obtain a reliable likelihood function and, consequently, to directly derive the posterior distribution. By directly deriving the posterior distribution, robust protection levels can be determined, thus reducing the probability of an HMI problem.

[0031] It is preferred if a control device for the GNSS receiver is configured to carry out the described method.

[0032] It is also preferred if a computer program is used to carry out a method described here. In other words, this particularly relates to a computer program (product) comprising instructions that, when executed by a computer, cause the computer to carry out a method described here.

[0033] It is also preferred if a machine-readable storage medium is used on which the computer program proposed here is stored. The machine-readable storage medium is usually a computer-readable data carrier.

[0034] It is particularly preferred if the localization system for a vehicle is set up to carry out a method described here.

[0035] The solution presented here and its technical environment are explained in more detail below with reference to the figures. It should be noted that the invention is not intended to be limited by the exemplary embodiments shown. In particular, unless explicitly stated otherwise, it is also possible to extract partial aspects of the facts explained in the figures and combine them with other components and / or findings from other figures and / or the present description. It shows schematically: Fig. 1: an example function graph for likelihood functions, prior distribution and posterior distribution, Fig. 2: Extracting a likelihood function from a copula model according to a quality indicator value, Fig. 3: a block diagram for providing copula models, and Fig. 4: a block diagram of a described method.

[0036] Fig. 1 and Fig. 2 show the mathematical functions used in the described method and the associated data, and are explained together here so that the invention becomes more understandable at the data level.

[0037] Fig. 1 shows a function graph in which the likelihood function P(Qi1|dx) 1, the likelihood function P(Qi2|dx) 2, the likelihood function P(Qi3|dx) 3, the likelihood function P(Qi4|dx) 4, the prior distribution 5 and the posterior distribution 6 are compared with each other and distributed over the dx-axis 8 corresponding to the position error.

[0038] In order to obtain the protection levels 7 during the online journey, the respective likelihood functions 1, 2, 3, 4 are first multiplied with the prior distribution 5 based on Bayes’ theorem, which results in the posterior distribution 6, whose two limits, as in Fig. 1, correspond to the protection levels 7 to be determined.

[0039] Each likelihood function 1, 2, 3, 4 is assigned a quality indicator (not shown). For example, in the online run, the extracted likelihood function 12, as shown in Fig. 2, are extracted from the corresponding copula model (not shown) according to a quality indicator value 13. In Fig. 2 also shows that a quality indicator 9 is scaled from zero to thirty-five.

[0040] Fig. 3 schematically shows a sequence of a method presented here for providing copula models 15, 16, 17. The illustrated order of substeps i), ii), iii), and iv) with blocks 210, 220, 230, and 240 is merely exemplary. In block 210, training data acquired through test measurements and / or simulations is provided. In block 220, the provided training data is classified into the different environment classes 10, 11. In block 230, an empirical copula between quality indicators 9 and position errors is provided for each class 10, 11. In block 240, an analytical copula model is adapted to the empirical copula in order to provide the copula models 15, 16, 17.

[0041] Fig.4 shows a schematic and exemplary block diagram of the described method for determining protection levels using a copula-supported Bayesian framework, wherein a plurality of environment classes and a plurality of GNSS quality indicators are given, and wherein a copula model 15, 16, 17 is provided offline for each environment class and each GNSS quality indicator and stored in a memory (not shown). The method steps a), b), c), d) and e) are carried out epoch by epoch during the journey (i.e., online). The illustrated order of the method steps a), b), c), d) and e) with block 110, arrows 120, blocks 130, 140 and 150 is merely exemplary. In block 110, the environment during the journey is classified based on the GNSS quality indicators 9 and the environment class to which the environment belongs is determined, whereby online data 14 such as GNSS signal data, sensor data are recorded.At arrows 120, a copula model 15, 16, or 17 corresponding to the determined environment class is read from the memory. In block 130, at least one likelihood function 1, 2, 3, 4, 12 is extracted from the read copula model 15, 16, or 17 according to a quality indicator value 13. In the two blocks 140, a posterior distribution 6 for position errors is determined. In the first block 140, the prior distribution 5 is defined based on the training data and using a parametric distribution, and then in the second block 140, the at least one likelihood function 1, 2, 3, 4, 12 is multiplied by a prior distribution 5 for position errors based on Bayes' theorem. In block 150, protection levels 7 are determined from the posterior distribution 6 based on a target integrity risk. QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited non-patent literature

[0000] Greer et al., 2007, Gratton et al., 2010, Zhu et al., 2018

[0006] Blanch et al., 2007

[0007] Schmidt, T. (2007). Coping with copulas. Copulas-Form theory to application in finance, 3-34

[0015]

Claims

[1] Method for determining protection levels (7) when driving a vehicle with a GNSS-supported localization system using a copula-supported Bayesian framework, wherein a plurality of environment classes (10, 11) and a plurality of GNSS quality indicators (9) are predefined, and wherein for each environment class (10, 11) and each GNSS quality indicator (9) a copula model (15, 16, 17) is provided offline and stored in a memory, comprising the following steps: a) Classifying the environment during travel based on the GNSS quality indicators (9) and determining to which environment class (10, 11) the environment belongs, b) reading a copula model (15, 16, 17) corresponding to the determined environment class (10, 11) for the corresponding quality indicators (9) from the memory, c) extracting at least one likelihood function (1, 2, 3, 4, 12) from the read copula model (15, 16, 17) according to a quality indicator value (13), d) determining a posterior distribution (6) for errors by multiplying the at least one likelihood function (1, 2, 3, 4, 12) based on Bayes’ theorem with a prior distribution (5) for position errors, and e) Determining protection levels (7) from the posterior distribution (6) [2] Method according to claim 1, wherein a copula model (15, 16, 17) is provided with the following steps: i) Providing training data collected through test measurements and / or simulations, ii) Classifying the training data into the environment classes (10, 11), iii) providing an empirical copula for each environment class (10, 11) and each quality indicator (9), and iv) Fitting an analytical copula model (15, 16, 17) to the empirical copula. [3] Method according to claim 1 or 2, wherein in step c) the at least one likelihood function is extracted from the copula model (15, 16, 17) with the following substeps: 1) Extracting a conditional distribution of position errors from the copula model (15, 16, 17), and 2) Determining at least one likelihood function (1, 2, 3, 4) from the conditional distribution according to the various GNSS quality indicators (9). [4] Method according to claim 3, wherein in sub-step 1) the conditional distribution is provided from the training data acquired by test measurements and / or simulations. [5] Method according to one of the preceding claims, wherein in step d) the prior distribution (5) is defined based on the training data and using a parametric distribution. [6] Method according to one of the preceding claims, wherein in step d) the posterior distribution (6) for errors is determined for each epoch. [7] Method according to one of the preceding claims, wherein the errors affect all quantities output by the GNSS-based localization system. [8] Method according to one of the preceding claims, wherein the errors are position errors, speed errors and / or alignment errors. [9] Control device which is arranged to carry out a method according to one of the preceding claims. [10] Computer program for carrying out a method according to one of the preceding claims 1 to 8. [11] Machine-readable storage medium on which the computer program according to claim 10 is stored [12] Localization system for a vehicle, arranged to carry out a method according to one of claims 1 to 8.

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