EP2796337B1 - Method for determining the track course of a track bound vehicle - Google Patents

Method for determining the track course of a track bound vehicle Download PDF

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Publication number
EP2796337B1
EP2796337B1 EP13164791.9A EP13164791A EP2796337B1 EP 2796337 B1 EP2796337 B1 EP 2796337B1 EP 13164791 A EP13164791 A EP 13164791A EP 2796337 B1 EP2796337 B1 EP 2796337B1
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Prior art keywords
track
curvature
value
error
probability
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German (de)
English (en)
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EP2796337A1 (fr
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Boubeker Belabbas
Anja Grosch
Oliver Heirich
Dr. Andreas Lehner
Dr. Thomas Strang
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Deutsches Zentrum fuer Luft und Raumfahrt eV
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Deutsches Zentrum fuer Luft und Raumfahrt eV
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B61—RAILWAYS
    • B61L—GUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
    • B61L25/00—Recording or indicating positions or identities of vehicles or trains or setting of track apparatus
    • B61L25/02—Indicating or recording positions or identities of vehicles or trains
    • B61L25/026—Relative localisation, e.g. using odometer
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B61—RAILWAYS
    • B61L—GUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
    • B61L2205/00—Communication or navigation systems for railway traffic
    • B61L2205/04—Satellite based navigation systems, e.g. global positioning system [GPS]

Definitions

  • the invention is related to a method for determining the track course of a track bound vehicle.
  • a track bound vehicle can be for example a train or another vehicle in railroad traffic. Further, it can be any other vehicle which is bound to a track, meaning the vehicle is not able to leave this track under ordinary conditions.
  • inertial sensors For this purpose, it is known to use inertial sensors.
  • a drawback when using inertial sensors is that no method is known in order to determine the reliability of a determination of the position of the vehicle based on their function. For applications which are relevant to safety, for example in railroad traffic, this information is required.
  • the inventive method for determining the track course of a track bound vehicle comprises the following method steps:
  • the inventive method can be used for a plurality of applications which will be described in more detail later.
  • the first and second wrong decision probability can be identical or differ from each other.
  • first and second error distribution in particular for each user sensor are determined each by a long time measurement in a static laboratory environment meaning that the conditions which might influence the function of the sensors are kept constant in this environment so that the exact error distribution of the sensor or sensors used can be determined. It is preferred that the first and the second error distribution are estimated.
  • the quality of the performed curvature determination is determined in terms of a wrong decision probability.
  • Standard curvatures in railroad traffic can be for example 0.4x10 ⁇ (-3) l/m for a radius of 2.5km til 5.26x10 ⁇ (-3) l/m for a radius of 190m.
  • a decision between the first estimated curvature k ⁇ 1 and the second estimated curvature value k ⁇ 2 is taken such that the value leading to the lowest wrong decision probability is chosen.
  • the minimum distance between k1 and k2 is obtained such that the reliability requirements (Pfa and Pmd) are just fulfilled. That is for any k3>k2, the probability of miss-detection is smaller than the required on: Pmd(k3) ⁇ Pmd(k2)
  • a further possible application of the inventive method is to determine a minimum difference between two standard curvatures which is required to be able to distinguish between them with a predefined wrong decision probability. For example it might follow from the inventive method that a minimum difference of 0.45x10 -3 l/m is necessary in order to fulfill the predefined wrong decision probability 10 -5 at a velocity of 36.72km/h.
  • the wrong decision probability can be a value between 10 -4 and 10 -6 .
  • a further possible application of the inventive method is that a minimum speed can be specified for the vehicle for passing a switch which is required in order to be able to determine the correct function of the switch with a predefined wrong decision probability.
  • a minimum speed can be specified for the vehicle for passing a switch which is required in order to be able to determine the correct function of the switch with a predefined wrong decision probability.
  • the track curvature of the track bound vehicle is measured by at least one sensor in or at the track bound vehicle.
  • the inventive method can be used as a subsidiary system which is part of an overall system (for example a system for localizing a vehicle in a map).
  • an overall system for example a system for localizing a vehicle in a map.
  • a curvature of the track course of the vehicle is determined. If this is done only in one snap-shot it is possible to reduce the number of possible positions of the vehicle in a map to all these positions which have the specified curvature. As an alternative it is possible to determine a plurality of subsequent curvatures, meaning that a plurality of curvatures of the vehicle is recorded over time. These recorded curvatures can be compared to the curvatures on a map so that it is possible to precisely identify the track course of the vehicle on the map.
  • the inventive method can be used in order to determine sensor errors, so that the sensor can be calibrated.
  • the track curvature is determined by using the above described sensors in particular based on three different methods which will be described later in more detail.
  • each of these three curvature determination methods can result in a different minimum detectable curvature difference and a different vehicle speed dependency. For example, one method might result in lower required vehicle speeds which are necessary in order to be able to fulfill a required predefined wrong decision probability at different standard curvatures while another method might require higher speeds for the same preconditions. Since the performance order of the three methods is not constant over speed, it is preferred to switch between the three curvature determination methods depending on the speed and sensor quality. For example, if automotive grade sensors are used, it might be beneficial to use method 2 for 0-45km/h and method 3 for higher speeds ( Figure 10 ).
  • this curvature determination method for a first speed range which allows the vehicle to travel with lower speeds at given curvatures and wrong decision probabilities while a second (and possibly third) different curvature determination method is used for another speed range in which this other curvature determination method allows the vehicle to travel with lower speed in order to achieve the same results.
  • each method it is further possible to adapt the weight of each method depending on the camber of a track (namely the rotation around an x-axis running parallel to the longitudinal direction of the vehicle). It is further possible to choose the weight of each method based on an ascending or descending slope of the track (namely a rotation around the y-axis of the vehicle).
  • Fig. 1 shows qualitatively the expected error distribution p k ( k ⁇ ) of a curvature determination error.
  • the error distribution is used as an input for a threshold test, which for example can result in a minimum required curvature difference between two tracks.
  • a first threshold T 1 is defined in the first error distribution (see Fig. 2 ).
  • the probability of false alert is marked with P fa in Fig. 2 .
  • the probability of misdetection is marked with P md in Fig. 3 .Since both probabilities characterize the allowed decision error for either curvature one or two, they could be considered equal and can be called probability of wrong decision.
  • Fig. 4 shows some examples of these MDCD values, whereby three different curvature determination methods and inertial sensors of very high quality have been used.
  • the curvature difference minima shown in Fig. 4 have been calculated based on a wrong decision probability of 10 -5 and tactical grade sensors. They are further dependent on the speed of the vehicle.
  • the horizontal lines indicate the standard curvatures which are used in German railroad traffic (and their differences). The end of each of these horizontal lines indicates the maximum speed on these tracks. Therefore, the right, upper area shows vehicle speeds which are higher than the allowed German maximum speed on the respective track and hence, they are not relevant.
  • the inventive method can also be applied for determining the position of the vehicle in a three dimensional space. In this case additional sensors will be necessary since a three dimensional position cannot be determined by using the described three sensors.
  • a more complex error model can be used for example by assuming that the bias of the sensors is defective meaning that it is not constant over a time. The same applies to the scale factor of the sensors.
  • the two main methods are map matching and dead reckoning system.
  • the former obtains an absolute 3D position estimating using GNSS and additional sensors for each epoch and matches this position with the track map. This could be done by choosing the closest point in the track as the best estimate.
  • the second approach the movement of the train relatively to a reference point is estimated incorporating all available sensors. Hence the position within the map is directly known. This approach can provide a more accurate and reliable solution since no intermediate solution is computed.
  • Train localization/navigation using GNSS and IMU has been investigated by many different authors some of them providing novel and promising techniques using Bayesian filters [6].
  • An ideal accelerometer would directly sense m ( t ) but in a non ideal case, the measured acceleration or turn rate is decomposed into a proportional part (proportional to a scaling factor s f ) and a time dependent drift part b ( t ) .
  • the offset b 0 stays constant during each run and is corrected by an initial calibration of the sensors.
  • the sampling noise is assumed to be Gaussian distributed with zero-mean and a variance ⁇ m 2 .
  • the first one uses a generator of the Ito-diffusion process defined by the stochastic differential equation and derive a partial differential equation, so called Kolmogorov Forward Equation or Fokker Planck Equation. Its solution is a transition probability density function of the solution process (see [4] and [3]).
  • the second method takes advantage of the fact that the process solution is Gaussian distributed, if the initial state densities can be assumed to be also Gaussian distributed. Hence, it is sufficient to investigate the evolution of the corresponding expectation and variance of the transition density function. In the section below, we apply the second concept and discuss the results.
  • ⁇ ⁇ t ⁇ 0 t ⁇ 0 r e l - r ⁇ d B l , 1 d ⁇ r .
  • ⁇ ⁇ ( t ) is function of B t ,1 , we kept the cross products as non necessarily zero terms.
  • s ( t ) being the curvilinear abscissa representing the length of the arc represented by the track from a reference position to a current point.
  • Equation (11) can be expressed in terms of ⁇ rather than ⁇ and observing that
  • Second method ⁇ 2 Here, we observe a ratio between a normally distributed random variable and a folded normal distribution (the absolute value of a normally distributed random variable). In the case of a ratio between two independent, normally distributed random variables with zero mean, the distribution of the ratio follows a Cauchy distribution.
  • One possibility is to exclude the samples of a CT ( t ),
  • the area to exclude using a pretest should not be too large for one reason essentially: the exclusion reduces the availability of the test statistics (for each sample falling in the excluded area, the corresponding test statistics is set as unavailable). But the closer the exclusion bounds are to zero, the wider the distribution of the test statistics and therefore the smaller the minimum detectable curvature difference (MDCD).
  • H a ⁇ T ⁇ ⁇ p K ⁇
  • GNSS is not longer available, the velocity is drifting from its initial value considering a coasting using along track accelerometer.
  • the localization problem consists of determining the track segment ID, the direction of displacement and the curvilinear abscissa on the track segment.
  • a track segment is defined as a path between two switches.
  • velocity fixes a coasting with the inertial unit based on along track, cross track accelerometers and a heading rate gyro using the characteristics defined in Table 2.
  • the coasting time is not longer than 1 second when at least 5 satellites are visible which is generally the case. But in some cases (long tunnels or in the general case of bad satellite visibility or when the satellite signals are blocked or reflected by a strong multipath environment) the coasting time could be last much longer (up to several minutes).
  • the error in the information is stationary and can be overbounded by a Gaussian distribution for a non zero required integrity risk. This overbound remains constant assuming the error is a stationary process.
  • the MDCD is a function of the velocity of the train. Intuitively the larger the velocity of the train, the smaller the dispersion of the test statistic.
  • the MDCD curves cross at a speed of approximately 50 [km/h]. This suggests a velocity based test selection: below 50 [km/h] we use ⁇ 2 to make our decision and above this limit, we use ⁇ 3 which performs better.
  • a more efficient strategy could consist of defining a weighted combination of both test statistics enabling even lower MDCD. However, this is beyond the scope of this paper.
  • the expectation and the variance of the Gaussian overbound of the sensor errors are analytically expressed and the test statistics after pretreatment of the random denominators (exclusion of an interval around zero to prevent heavy tailed distributions) are investigated using Monte Carlo simulations.
  • the minimum detectable curvatures difference is determined for three different classes of IMUs, namely consumer, automotive and tactical grade.
  • the resulting MDCD curves have been compared to standard curvatures and their performance have been assessed.
  • ⁇ 1 in addition to being unavailable a large part of the time (exclusion of the high density around zero of the cross track acceleration) provides when a bad performance.
  • ⁇ 2 and ⁇ 3 show best results with a maximum availability when the train is moving. A performance crossover can be observed for the consumer and automotive grade IMUs. That is ⁇ 3 can outperform ⁇ 2 when the velocity of the train is larger than 50 km/h.
  • ⁇ 3 depends on the cross track acceleration which is difficult to sense in a more realistic dynamic scenarios (for a non-perfect horizontal plan of motion, for which the gravity vector may introduce a component in cross track direction).
  • ⁇ 2 shows a real improvement as it can be reliably used for a large range of velocities. Furthermore, it has a dependency on the heading rate rather than on the accelerations which makes it more robust to realistic scenarios (non-perfect horizontal displacements).
  • V ⁇ t ⁇ E ⁇ t ⁇ ⁇ 2

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Navigation (AREA)

Claims (8)

  1. Procédé pour déterminer le parcours d'un véhicule guidé sur rails, le procédé comprenant les étapes suivantes :
    a) définir une première distribution d'erreur d'une erreur de détermination de courbure correspondant à une pluralité de courbures de la voie mesurées de façon erronée autour d'une première valeur de courbure estimée k̂ 1,
    b) définir un premier seuil T1 selon une première probabilité prédéfinie de fausse décision, de sorte que toute courbure de la voie mesurée au-delà de ce seuil est classée comme n'étant pas la première valeur de courbure estimée k̂ 1,
    c) définir une deuxième distribution d'erreurs d'une erreur de détermination de courbure correspondant à une pluralité de courbures de la voie mesurées de façon erronée autour d'une deuxième valeur de courbure estimée k̂ 2, la première valeur de courbure estimée k̂ 1 étant plus petite que la deuxième valeur de courbure estimée k̂ 2,
    d) définir un deuxième seuil T2 selon une deuxième probabilité prédéfinie de fausse décision, de sorte que toute courbure de la voie mesurée au-dessous de ce seuil est classée comme n'étant pas la deuxième valeur de courbure estimée k̂ 2, le deuxième seuil T2 étant positionné à cette extrémité de la deuxième distribution d'erreurs tournée vers la première distribution d'erreurs,
    e) de sorte que la distance entre la première et la deuxième valeurs de courbure estimées k̂ 1 et k̂ 2 peut être spécifiée de façon fiable lorsque T1 = T2 ou que T1 < T2 est satisfait,
    f) mesurer une courbure de voie du véhicule guidé sur rails, de sorte que la valeur de courbure mesurée est considérée comme étant k̂ 1 si elle est < T1 et est considérée comme étant k̂ 2 si elle est > T2, de sorte que si la valeur mesurée est identique à T1 et à T2, la décision de définir si elle est T1 ou T2 est prise sur la base d'une préférence de système prédéfini.
  2. Procédé selon la revendication 1, caractérisé en ce que la première et la deuxième distributions d'erreurs sont déterminées, chacune, par une mesure sur une longue durée, dans un environnement de laboratoire statique, en particulier une mesure à long terme à entrée nulle, laquelle est utilisée pour déterminer les paramètres d'erreur requis.
  3. Procédé selon les revendications 1 ou 2, caractérisé en ce que selon la précondition que la voie peut seulement présenter des courbures prédéterminées discrètes, en particulier des courbures standard dans le trafic ferroviaire, la qualité de la détermination de la courbure réalisée est déterminée en termes de probabilité de fausse décision, de qualité de capteur et de vitesse du véhicule.
  4. Procédé selon les revendications 1 à 3, caractérisé en ce qu'une décision entre la première valeur de courbure estimée k̂ 1 et la deuxième valeur de courbure estimée k̂ 2 est prise de telle façon que la valeur conduisant à la probabilité de fausse décision la plus basse est choisie.
  5. Procédé selon les revendications 1 à 4, caractérisé en ce qu'une différence minimale entre deux courbures est déterminée de telle sorte que cette décision satisfasse des exigences de fiabilité prédéfinies, par exemple, une probabilité de fausse décision.
  6. Procédé selon les revendications 1 à 5, caractérisé en ce qu'une vitesse minimale est déterminée pour le véhicule en vue de passer par un aiguillage qui est requis afin de pouvoir déterminer le fonctionnement correct de l'aiguillage avec une probabilité de fausse décision prédéfinie.
  7. Procédé selon les revendications 1 à 6, caractérisé en ce que la courbure de la voie du véhicule guidé sur rails est mesurée par au moins deux capteurs dans le, ou au niveau du, véhicule guidé sur rails, en particulier par trois capteurs exclusivement inertiels, à savoir un capteur d'accélération latérale, un capteur d'accélération longitudinale et un capteur de vitesse ou gyroscope.
  8. Procédé selon les revendications 1 à 7, caractérisé en ce que, lorsque la courbure de la voie est connue, le procédé de l'invention est utilisé afin de déterminer les erreurs des capteurs et, en conséquence, de calibrer les capteurs.
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EP3499271A1 (fr) * 2017-12-18 2019-06-19 Siemens Aktiengesellschaft Détermination d'une position d'un véhicule
CN111854776B (zh) * 2019-04-30 2024-04-16 北京京东乾石科技有限公司 导航的处理方法、装置、设备及存储介质
CN111866709B (zh) * 2020-06-29 2022-05-17 重庆邮电大学 一种面向运动目标的室内Wi-Fi定位误差界估计方法
CN112531683A (zh) * 2020-11-19 2021-03-19 国网湖北省电力有限公司电力科学研究院 一种基于奥恩斯坦-乌伦贝克过程求解的配网线路负荷预测方法
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CN107664994A (zh) * 2016-07-29 2018-02-06 通用汽车环球科技运作有限责任公司 用于自主驾驶合并管理的系统和方法

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