EP1056063B1 - Method and device for the determination of the traffic conditions of a roadsegment - Google Patents

Abstract

The method involves using a Kalman filter based on a model that can take into account the length of the traffic section and measured levels of traffic at the entry to and exit from the section. A transport-oriented model is selected in which a vector i formed contg. a correction value and a traffic level value for each of at least two segments using the length of the traffic sec and the sampled levels of traffic at the entry to and exit from the section. The vector is corrected using the Kalman filter to provide a precise estimate of the exit traffic level and of the traffic state. An Independent claim is also included for an arrangement for determining the traffic state of a section of traffic.

Description

The present invention relates to a method and a device according to the preamble of patent claim 1.

For automatic monitoring and control of road traffic, measuring devices are often used which measure the traffic volume or the number of vehicles that pass a measuring point within a certain period of time. Based on the resulting measurement results, however, only a useful statement about the locally occurring traffic intensity can be made. No information is possible about the state of the traffic in the traffic section lying in front of said measuring point.

A determination of the traffic condition is also possible on the basis of the measurement of the vehicle speed or speed trend. Due to the speed measurements, however, traffic disruptions can only be detected so late that appropriate traffic regulation measures can no longer counteract the disruption.

For monitoring a traffic section therefore serving at the entrance and exit of the traffic measurement sensor are provided. By comparing the measurement results of the two sensors can be made a statement about the traffic condition within the monitored traffic section. Since the measured traffic intensity shows strong fluctuations, which occur as stochastic disturbances around a "true" value, the measured values are filtered.

When filtering on the basis of classic low-pass, bandpass or high-pass filters, there are delays that prevent a quick statement of the traffic status from being made. It is known that measured values can be filtered with virtually no delay using a Kalman filter.

Kalman filters or so-called observers use a model and the input and output information of the object whose state is to be determined or tracked. As a general rule, the more object information can be determined more quickly and accurately, the more information the object will use for the model, which should correctly reflect the relationships between input and output variables. From [1] the use of a model is known that is based on the use of eight parameters, which are sometimes difficult to determine. Part of the parameters also depends on the weather. The results obtained in this system, despite the increased effort, therefore, deviate significantly from the results that can be ideally achieved.

The use of Kalman filters in a traffic surveillance system is known from US 5,801,943.

The present invention is therefore based on the object of specifying a method and a device for rapid determination of the state of a traffic section.

This object is achieved by the measures of claim 1. Advantageous embodiments of the invention are specified in further claims.

According to the invention, a Kalman filter with a model of the monitored traffic section is used. The advantageous choice of a simple model for the trouble-free case in conjunction with a Kalman filter KF, the traffic condition can be determined quickly and accurately. In particular, faults are detected almost instantaneously, whereby in each case the necessary measures (congestion warning, etc.) can be delivered quickly. Further advantages of the invention or the selected model will be explained below.

Models differ in their inputs and outputs and their interdependence, as well as in the choice of quantities that reflect the "internal state" of the model. For metrological reasons, there is a local and a time discretization of the continuous traffic. Measured values are only available at specific locations and at certain times (sampling times). According to the invention, a transport-oriented model is used for the state estimation. The monitored traffic section is accordingly considered as a transport medium which, like a conveyor belt, transports or passes elements or vehicles at a certain speed. To simplify, it is provided that all vehicles in the traffic section travel at a constant speed. Despite the simple structure of the transport model used, the method according to the invention with the aid of a Kalman filter makes it possible to quickly and reliably determine traffic disruptions and other parameters from strongly fluctuating measured values of the traffic volume q and the speed v.

What is essential is that the model used describes the conditions of an "ideal" road, which has an infinite capacity. This characteristic in particular makes it possible to detect disturbances very quickly and reliably, since measured values in the event of a fault differ greatly from the values "predicted" by the model. The model, however, is not suitable for the simulation of road traffic. The use of this model is therefore only useful in conjunction with a Kalman filter. Due to its linearity, however, the transport model is optimally suited for this purpose.

A significant advantage of the method according to the invention is that all the parameters of the model result in a simple manner from the geometric arrangement of the measuring points. A complex identification of model parameters is thus eliminated. In particular, the parameters of the model used do not depend on weather influences such as moisture or smoothness, which makes adaptation to different environmental conditions superfluous.

Fig. 1

ein Verkehrsmodell mit Ein- und Ausgangsgrössen q1, q2,

Fig. 2

das Verkehrsmodell gemäss Fig. 1 für einen Verkehrsabschnitt, den Fahrzeuge mit einer bestimmten Gruppenlaufzeit durchfahren,

Fig. 3

den Verlauf der Verkehrsstärke q2 am Ausgang des Verkehrsabschnittes als Reaktion eines synthetischen Verlaufs der Verkehrsstärke q1 am Eingang des Verkehrsabschnittes für das kontinuierliche Modell,

Fig. 4

das Verkehrsmodell mit virtueller Ein- und Ausfahrt,

Fig. 5

das verwendete Kalman-Filter KF mit einem erweiterten diskreten Modell MOD,

Fig. 6

den Verlauf der Verkehrsstärke q2 am Ausgang des Verkehrsabschnittes als Reaktion eines synthetischen Verlaufs der Verkehrsstärke q1 am Eingang des Verkehrsabschnittes für das diskrete Modell und

Fig. 7

den vom Kalman-Filter KF geschätzten Verlauf der Verkehrsstärke q2_e (verzögerungsfreie Glättung von q2) sowie die Verkehrsstärke q2_d auf den virtuellen Ein- und Ausfahrten beim Auftreten einer Störung (Wert q2_d durch das Kalman-Filter KF geschätzt, wird mit q2_de bezeichnet).

The invention will be explained in more detail with reference to a drawing, for example. Showing:

Fig. 1

a traffic model with input and output variables q1, q2,

Fig. 2

the traffic model according to FIG. 1 for a traffic section which vehicles travel through with a specific group delay,

Fig. 3

the course of the traffic volume q2 at the exit of the traffic section in response to a synthetic course of the traffic volume q1 at the entrance of the traffic section for the continuous model,

Fig. 4

the traffic model with virtual entry and exit,

Fig. 5

the Kalman filter KF used with an extended discrete model MOD,

Fig. 6

the course of the traffic volume q2 at the exit of the traffic section in response to a synthetic course of the traffic volume q1 at the entrance of the traffic section for the discrete model and

Fig. 7

estimated by the Kalman filter KF course of traffic q2 _e (smooth smoothing of q2) and the traffic q2 _d on the virtual entrances and exits at the occurrence of a disturbance (value q2 _d estimated by the Kalman filter KF, with q2 _de designated).

Initially, the terms used are listed in tabular form: table description unit importance l _s km Length of a traffic section bounded by two measuring points T _L s Running time of the vehicles through the traffic section T _s s Interval, sampling period v; v ₀ km / h Speed; constant speed v1 km / h Speed at the entrance of the traffic section v2 km / h Speed at the exit of the traffic section q Fz / Ts Vehicle strength (vehicles per measurement period) q1 Vehicles / Ts Vehicle strength at the entrance of the model (measured) q2 Fz / Ts Vehicle strength at the exit of the model (measured) A, B, C matrix Description of the model G matrix Input matrix for process faults q2 _m Fz / Ts Vehicle strength calculated according to model (m: model) q2 _e Fz / Ts vehicle strength estimated by the Kalman filter (e: estimated) q2 _de Fz / Ts estimated deviation of the traffic volume (d: difference) x (k) vector internal state vector of the Kalman filter at step k x _e (k) vector Estimate of the int. State vector of the Kalman filter at step k n - Number of segments of the traffic section p Fz / Ts process noise s Fz / Ts sensor noise

1 shows a traffic model corresponding to a traffic segment, to which the traffic volume q1 measured at the entrance of the traffic segment is fed as input parameter and the speed v1 measured at the entrance of the traffic segment as well as the course constant length I _{s of} the traffic segment. The model provides an output q 2 _m , which, taking into account the calculated running time T _{L of} the vehicles Fz, indicates the traffic volume at the exit of the traffic section. For the sake of simplification, it is assumed that all vehicles in the section travel at the same constant speed v1.

The change of the traffic volume q is thus described in analogy to the transport of material (for example sand) on a conveyor belt moving at a constant speed v. The material appears after a time delay, which depends on the transport speed and the length of the conveyor belt, unchanged at the delivery location. There are no transit time differences of the transported material particles. Therefore, the vehicles F1, F2 and F3 appear according to the idealized model shown in Fig. 1 without transit time differences, in the same mutual distance at the exit of the traffic section.

A transport process of this kind corresponds to the partial differential equation (1): $$\frac{\partial q\left(s,,t\right)}{\partial t}=-v\frac{\partial q\left(s,,t\right)}{\partial s}$$

exakt der Verlauf von q1, d.h. es gilt: q2(t) = q1 (t-T_L).At a constant speed v thus repeats at the end of the conveyor belt after the runtime: $$T_L=\frac{l_s}{{\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">v</figure-callout>}}_0}$$

exactly the course of q1, ie the following applies: q2 (t) = q1 (tT _L ).

However, this situation does not do justice to the behavior of the vehicles, since the vehicles which are measured in a time interval do not have the same speed and consequently, as shown in FIG. 2, pass the second measuring cross section after different transit times.

The intended use of a Kalman filter also requires a description of the process in the form of an ordinary and not a partial differential equation containing partial derivatives of an unknown function with multiple variables (for the difference between ordinary and partial differential equations see [3], page 435) ,

According to the invention, one obtains an ordinary differential equation by considering only discrete locations in the traffic section. For this purpose, the traffic segment is subdivided into n segments s1, s2,..., S _n whose inner limits do not have sensors or measuring sensors. In each of these segments, the speed is assumed to be constant.

If one describes the behavior of one of the n subsegments by a discrete delay of the first order, then the entire segment behaves like a delay element le whose time constant reads as follows: $$T_{\mathit{le}}=\frac{T_L}{n}=\frac{l_s}{n{\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">v</figure-callout>}}_0}$$

The larger the number n of the segments, the more accurately the behavior can be described. The transport process is thus mapped by placing n 1st order delays in a row: $$\frac{dq1.\left(t\right)}{dt}=\frac{n}{T_L}\left(q{1}_{i-1}\left(t\right)-q1.\left(t\right)\right).$$

As a result of this measure, location discretization takes place for selected segments s1, s2,... (See FIG. 1), as a result of which an ordinary differential equation is achieved. The first value of the chain q _{1, 0} is the value q1 at the input q1; the last value of the string q _{1, n} is identical to the value q2 at the output of the model.

$$q2=\tilde{C}\begin{array}{}\end{array}x$$

If the values q _{1, l are combined} to form a state vector X describing the internal state of the system, the system of differential equations can be specified in the form of a state. A system consisting of four segments has the following representation with T _le = 4 / T _L : $$\dot{x}=\tilde{A}\begin{array}{}\end{array}x+\tilde{B}\begin{array}{}\end{array}q1.$$

$$q2=\tilde{C}\begin{array}{}\end{array}x$$

The individual matrices are as follows: $$\tilde{A}=\left[\begin{array}{cccc}-\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="T\; le"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">T\; </figure-callout>}}_{\mathit{le}}}& 0& 0& 0\\ \frac{1}{T_{\mathit{le}}}& -\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="T\; le"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">T\; </figure-callout>}}_{\mathit{le}}}& 0& 0\\ 0& \frac{1}{T_{\mathit{le}}}& -\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="T\; le"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">T\; </figure-callout>}}_{\mathit{le}}}& 0\\ 0& 0& \frac{1}{T_{\mathit{le}}}& -\frac{1}{T_{\mathit{le}}}\end{array}\right].\tilde{B}=\left[\begin{array}{c}\frac{1}{{\mathrm{<figure-callout\; id="0"\; label="T\; le"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">T\; </figure-callout>}}_{\mathit{le}}}\\ 0\\ 0\\ 0\end{array}\right].\tilde{C}=\left[\begin{array}{cccc}0& 0& 0& 1\end{array}\right]$$

In Fig. 3, the traffic intensity q2 is shown in response to a synthetic history of q1 for n = 4 segments (or delays, respectively). It can be seen that now some of the vehicles arrive already before the time T _L , while another part due to a slightly lower speed requires more time (see Fig. 2).

The selected model is now suitable for the description of the transport process and thus the undisturbed traffic in a traffic section. This shape is also very suitable for a Kalman filter because it is linear in the state quantities. The model serves as a building block for a traffic section with two measuring points. With the help of this module, it is easy to set up models for arbitrarily complex topologies that have entrances, exits, branches and merges.

The measured values are available as time-discrete values for a specific measuring interval (sampling time Ts). Therefore, the discrete version of the model that results from the continuous model is chosen as follows (matrix C does not change): $$A:=e^{{\tilde{A}}_1{T}_s}={\displaystyle \underset{i=0}{\overset{\infty }{\Sigma }}}\frac{\left(\tilde{A}{T}_s\right)}{i!}.\begin{array}{}\end{array}B={\displaystyle \underset{0}{\overset{T_S}{\int }}}A\left(\mathit{\tau }\right)\mathit{d\tau }\tilde{B}$$

von der gemessenen Geschwindigkeit abhängen und somit nicht konstant sind. Die Diskretisierung kontinuierlicher Systeme ist u.a. auch aus [4], Seiten 74-80, Kapitel 3.1 (Diskretisierung der Regelstrecke) bekannt. Für das diskrete Modell gelten somit die Gleichungen : $$x\left(k+1\right)=A\left(k\right)x_e\left(k\right)+B\left(k\right)q1\left(k\right),$$

$$q{2}_m\left(k\right)=C_{1}x\left(k\right)+D\left(k\right)q1\left(k\right)\mathrm{.}$$

The infinite series converges very quickly due to the faculty in the denominator, so that no very high computing power is necessary. However, the discretization needs to be redone every measurement interval k since the matrices $$\tilde{A}.\tilde{B}$$

depend on the measured speed and are therefore not constant. The discretization of continuous systems is also known from [4], pages 74-80, chapter 3.1 (discretization of the controlled system). The equations thus apply to the discrete model: $$x\left(k+1\right)=A\left(k\right)x_e\left(k\right)+B\left(k\right)q1\left(k\right).$$

$$q{2}_m\left(k\right)={\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">C</figure-callout>}}_{1}x\left(k\right)+D\left(k\right)q1\left(k\right)\mathrm{,}$$

For simplification, the sampling step k has been written as an index. The index k identifies the interval for the time t $${\mathit{kT}}_s\le t<\left(k+1\right)T_s$$

According to the invention, all values are assumed to be constant in one interval, which makes a simple calculation possible. It should be noted, however, that the parameters of the process model are not constant. After each sampling interval T _S , a new value results for the speed v1 measured at the entrance of the traffic section, with which, as assumed, all vehicles in the monitored section travel.

The deviations between the predictive values of the model q2 _m and the actually measured values q2 are corrected by the Kalman filter, which calculates the estimates q2 _e , in the undisturbed case. However, if there are errors that were not taken into account in the modeling, the Kalman filter also returns erroneous values. The accident is now taken into account by extending the model, as shown in FIG. 4, to virtual entrances and exits to a "parking space with infinite capacity".

The traffic flows on the virtual exits, which are designated q2 _d , are a measure of the effects of a fault that has occurred. The Kalman filter estimates the values q2 _d (value q2 _de ).

Since the model, as mentioned above, has an unlimited capacity, it can not be deduced from the input information q1 and the measured value q2 to the value q2 _d . Since the Kalman filter can only make optimal estimates based on a model, the q2 _d value must also be taken into account by the model. Since the model is designed for trouble-free operation, it is consequently assumed that the initial value of q2 _{d is} equal to zero and then behaves as follows from sample period to sample period: q2 _d (k + 1) = q2 _d (k). Therefore, as modeled, the model does not provide any disturbance, so that the value q2d is constant or can be changed with each interval k only by the Kalman filter KF (q2 _d (k + 1) = q2 _d (k) + corr _KF (k)). For this purpose, the state vector x provided for four segments s1, s2, s3, s4 is expanded as follows: $$x\left(k\right)=\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\\ x_d\end{array}\right].\begin{array}{}\end{array}{x}_e\left(k\right)=\left[\begin{array}{c}{x}_{1e}\\ x_{2e}\\ x_{3e}\\ x_{4e}\\ x_{\mathit{de}}\end{array}\right]$$

In the undisturbed case, no virtual traffic flows (see FIG. 4) occur. If malfunctions occur, the Kalman filter can compare measured values and estimated values of the model via the virtual traffic flows. The vector x (k) is corrected by the Kalman filter KF (see Fig. 5), whereby the vector x _e (k) with corrected values x _1e , ..., x _4e and x _de arises. The corrected (internal) state values x _4e plus x _de and x _de thus correspond to the estimates q2e and q2 _{de of} the Kalman filter KF. The values q2 _de are an immediate measure of the degree of interference that has occurred in the monitored section (see FIG. 7).

$$q2{*}_m\left(k\right)=C\left(k\right)x\left(k\right)+D\left(k\right)q1\left(k\right)+s\left(k\right)\cong q2\left(k\right)$$

The basis of the Kalman filter KF shown in FIG. 5 is the extended discrete model MOD described above, which satisfies the conditions in the ideal state. In order to adapt to the real conditions, it is additionally assumed that process and sensor disturbances p and s are effective at the points shown in FIG. 5 as follows (assumption D (k) = [0]): $$x\left(k+1\right)=A\left(k\right)x\left(k\right)+B\left(k\right)q1\left(k\right)+G\left(k\right)p\left(k\right).$$

$$q2{*}_m\left(k\right)=C\left(k\right)x\left(k\right)+D\left(k\right)q1\left(k\right)+s\left(k\right)\cong q2\left(k\right)$$

minimiert. Der "wahre" Zustandsvektor ist nicht bekannt. Man verwendet deshalb x_e(k) als Schätzwert für den unbekannten Zustandsvektor x(k).The corrected model value q2 * _m (k) thus corresponds to the value q2 (k) actually measured in the interval k. The assumed disturbances result from the traffic process and correspond to the form of a frequency-independent noise with a gaussian distributed amplitude spectrum. If one observes measured progressions of the traffic volume q, one recognizes that the strong fluctuations are quite good as a noise process to represent a mean value. The Kalman filter KF is an optimal filter that estimates the variance of the estimation error $$x_{\mathit{err}}\left(k\right)\cong x\left(k\right)-x_e\left(k\right)$$

minimized. The "true" state vector is unknown. It is therefore used x _e (k) as an estimate for the unknown state vector x (k).

entsteht, gibt an, wie sich die (unbekannten) Störgrössen auf die internen Zustandsgrössen des Prozesses verteilen. Im einfachsten Fall nimmt man an, dass diese Störgrössen gleichmässig auf alle internen Zustandsgrossen einwirken. Durch die Matrix G(k) wird daher angegeben wo nicht aber mit welcher Intensität die Störgrössen auf das Modell einwirken. Die Intensität der Störungen wird durch die nachstehend beschriebenen Kovarianzmatrizen Q und R beschrieben. Sofern zum Beispiel drei Zustandsgrössen und zwei Störgrössen vorhanden sind und die erste Störgrösse nur auf die erste Zustandsgrösse und die zweite Störgrösse nur auf die beiden folgenden Zustandsgrössen einwirkt, würde dieser Sachverhalt mit einer Matrix G(k) der nachstehend angegebenen Form berücksichtigt: $$\tilde{G}=\left[\begin{array}{c}10\\ 01\\ 01\end{array}\right]\Rightarrow G\left(k\right)$$

The matrix G (k), which just like the matrices A (k), B (k) by discretization $$\tilde{G}\Rightarrow G\left(k\right)$$

arises, indicates how the (unknown) disturbances are distributed among the internal state variables of the process. In the simplest case, it is assumed that these disturbances act uniformly on all internal state variables. The matrix G (k) therefore indicates where, but not with what intensity, the disturbing variables act on the model. The intensity of the perturbations is described by the covariance matrices Q and R described below. If, for example, three state variables and two disturbance variables are present and the first disturbance variable acts only on the first state variable and the second disturbance variable only on the two following state variables, this situation would be considered with a matrix G (k) of the form given below: $$\tilde{G}=\left[\begin{array}{c}10\\ 01\\ 01\end{array}\right]\Rightarrow G\left(k\right)$$

According to the invention, the matrix G (k) is selected in such a way that process disturbances p influence all variables of the state vector x (k) in the same way.

The control parameters of the Kalman filter KF are the covariance matrices Q and R of the (assumed) noise processes which act on the process itself or on the measured values output by the sensors. The matrix Q describes the intensity of the process disturbances p. The matrix R describes the intensity of the sensor disturbances s. Although the matrices Q and R may theoretically be time-variant, it is assumed that the fluctuations in the measured values are independent of the traffic situation and thus independent of time. The matrices Q and R thus assume constant values. The elements of the matrices Q and R are the design parameters of the Kalman filter KF, with which the settling time and susceptibility of the Kalman filter KF are set.

und $$x\left(0\right)=0$$

sind folgende Gleichungen zu berechnen. Man unterscheidet zwischen den Gleichungen zur Bestimmung der optimalen Schätzwerte und den Gleichungen zur Berechnung des Folgezustandes.With the initialization values $$\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">P</figure-callout>}\left(0\right)=\mathrm{<figure-callout\; id="0"\; label="G"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">G</figure-callout>}\left(0\right){\mathit{<figure-callout\; id="0"\; label="QG\; T"\; filenames="imgf0003.png,imgf0004.png"\; state="\{\{state\}\}">QG\; </figure-callout>}}^T\left(0\right)$$

and $$x\left(0\right)=0$$

the following equations have to be calculated. A distinction is made between the equations for determining the optimal estimates and the equations for calculating the subsequent state.

$$P_e\left(k\right)=\left(I-L\left(k\right)C_1\right)P\left(k\right),$$

$$x_e\left(k\right)=x\left(k\right)+L\left(k\right)\left(q2\left(k\right)-C_{1}x\left(k\right)-D\left(k\right)q1\left(k\right)\right)$$

$$q{2}_e\left(k\right)=C_1{x}_e\left(k\right)+D\left(k\right)q1\left(k\right)$$

The equations for determining the optimal estimates are as follows (I is the unit matrix): $$L\left(k\right)=P\left(k\right)C_1^T({\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">C</figure-callout>}}_{1}P\left(k\right)C_1^T+R{)}^{-1}.$$

$$P_e\left(k\right)=\left(I-L\left(\mathrm{<figure-callout\; id="1"\; label="k\; \; C"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k\; </figure-callout>},\right)C_{}{}_1\right)P\left(k\right).$$

$$x_e\left(k\right)=x\left(k\right)+L\left(k\right)\left(q2\left(k\right)-{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">C</figure-callout>}}_{1}x\left(k\right)-D\left(k\right)q1\left(k\right)\right)$$

$$q{2}_e\left(k\right)={\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">C</figure-callout>}}_1{x}_e\left(k\right)+D\left(k\right)q1\left(k\right)$$

$$P\left(k+1\right)=A\left(k\right)P_e\left(k\right)A^T\left(k\right)+G\left(k\right){\mathit{QG}}^T\left(k\right)$$

The equations for calculating the subsequent state are as follows: $$x\left(k+1\right)=A\left(k\right)x_e\left(k\right)+B\left(k\right)q1\left(k\right).$$

$$P\left(k+1\right)=A\left(k\right)P_e\left(k\right)A^T\left(k\right)+G\left(k\right){\mathit{QG}}^T\left(k\right)$$

The above equations are calculated for each sampling step. The order in which the equations are calculated must not be reversed, as the results are partly dependent on each other.

The signal flow in the Kalman filter KF according to the invention is shown in FIG. For each interval, the products are added from input value q1 (k) times matrix B (k) and estimated state vector x _e (k) times matrix A (k) in addition stage ADD1. After the time shift, the sum yields the new uncorrected internal state vector x (k) which is multiplied by the matrix C ₁ = [00011], whereby the sum of the values x ₄ plus x _{d is} formed (q 2 _m = x ₄ + x _d ). Then, based on the difference stage DIFF, the difference between the traffic volume q2 _m (k) newly determined by the model and the actually measured traffic volume q2 (k) (at the exit of the traffic segment) is formed. The resulting difference (q2 _m (k) - q2 (k)) is multiplied by the Kalman matrix L (k), whereby values are formed with which the state vector x (k) is corrected by the adder ADD3 or in the estimated State vector x _e (k) is converted. The estimated values x4 _e and x _de are read out using the matrices C ₁ = [00011] and C ₂ = [0000-1]. Based on C ₁ , the sum of the estimated values x4 _e and x _{de is} formed, which yields the estimated value q2 _e (k). As already mentioned, the matrices C ₁ and C _{2 are} constant. The last element of the matrix C ₂ is negative, in order to get a positive value for q2 _de (k). Of course, all arithmetic operations can be performed by a computer system known to those skilled in the art (eg: processor, signal processor).

7 shows the course of the traffic force q2 _e estimated by the Kalman filter KF and the estimated traffic volume q2 _de on the virtual entry and exit, influenced by a disturbance that occurs at a time t1 and during the time T _dist up to one Time t2 stops. Until the time t1, the vehicles can pass the traffic section unhindered, so that the at the entrance and exit determined traffic levels neglecting the transit time differences to the value q1. At time t1, a disturbance occurs through a bottleneck in the transport section, which can happen _dist traffic only with the reduced traffic volume q2. In order to be able to take appropriate corrective and safety measures in good time, the malfunction in the traffic control center must be recognized immediately. In FIG. 7, a course typical for the measured quantities q1 and q2 is additionally indicated. It can be seen that the measured variables q1, q2 have large statistical fluctuations even in the undisturbed case and that the effect of a disturbance within the traffic segment can only be determined after a considerable delay. The device according to the invention and the method by which input and output variables q1, q2 are processed on the basis of the Kalman filter KF now make it possible to record the occurrence of the disturbance virtually instantaneously. Immediately after the fault has occurred, the value q2 _{de runs} high. This corresponds to an increase in the estimated traffic volume q2 _de on the approach to the virtual parking lot. After cancellation of the disturbance at the time t2, the traffic volume q2 _de increases again from the virtual parking space back into the quadrilateral section and then falls back to zero as soon as the traffic volumes q1 and q2 at the entrance and exit of the traffic section are equalized. By comparing the estimated traffic volumes q2 _de between the virtual parking lot and the monitored traffic segment with positive and negative threshold values thp; thm can therefore be quickly determined in each case whether a fault has occurred or has been canceled.

The threshold values are selected according to the size of the disturbance to be detected. Preferably, several threshold values are provided which correspond to the states "slight traffic obstruction", "viscous traffic" or "traffic jam". Upon the occurrence of the appropriate conditions, therefore, the appropriate measures (e.g., congestion) may be initialized.

In addition, different road sections can be interconnected. The models of different road sections can be simply lined up, whereby for each model again length, output and input quantities of the traffic section concerned are to be considered. Measured values at the output of a traffic segment can therefore be used simultaneously as input variables for the subsequent traffic segment. By connecting several sections of traffic a delay-free smoothing effect comes to bear.

On the basis of the gained knowledge about traffic volumes, the expected travel times can be calculated quickly and precisely. As a result, optimum itineraries can be determined for road users.

bibliography

1. [1] Michael Cremer, The Traffic Flow on Expressways, Springer Verlag, Berlin 1979
2. [2] Kai Müller, Draft of Robust Regulations, Teubner Verlag, Stuttgart 1996
3. [3] Lothar Papula, Mathematics for Engineers and Scientists, Vieweg Verlag, Wiesbaden 1997, 8th edition
4. [4] Jürgen Ackermann, Abtastregelung, Springer Verlag, 3rd edition, Berlin 1988

Claims (5)

1. Method for determining the traffic conditions within a road segment using a Kalman filter based on a model, by means of which the length l_s of the road segment as well as the traffic volumes q1 and/or q2 measured at the entry and exit of the road segment are taken into account, with
   a transport-oriented model being selected, in which a vector x(k) containing a correction value (x_d ) as well as a traffic volume value (x1; ...; x _n ) for each segment (s1; ...; s_n) in each instance is formed for at least two segments (s1; ...; s_n ) of the road segment on the basis of the length l_s as well as the traffic volume q1 measured at the entry of the road segment and the vehicle speed v1(k) in scanning intervals, said vector x(k) being corrected by comparison with the traffic volume q2 measured at the exit of the road segment on the basis of the Kalman filter, with the corrected vector x_e (k) comprising more precise estimated values q2 _e for the traffic volume at the exit of the road segment and a estimated value q2 _de for a difference traffic volume q2 _d representing the internal condition of the road segment.
2. Method according to claim 1,
   characterised in that
   a new vector x(k+1) is calculated on the basis of new matrices A(k) and B(k) of the extended traffic model determined as a function of the speed v1(k) for each scanning interval k, as follows: $$\mathrm{x}\left(\mathrm{k}\mathrm{+}\mathrm{1}\right)\mathrm{=}\mathrm{A}\left(\mathrm{k}\right){\mathrm{x}}_{\mathrm{e}}\left(\mathrm{k}\right)\mathrm{+}\mathrm{B}\left(\mathrm{k}\right)\mathrm{q}\mathrm{1}\left(\mathrm{k}\right)\mathrm{,}$$

   

   
   with the old vector x(k) being carried over into the corrected vector x _e by means of the Kalman Filter (KF): $$x\left(k\right)=\left[\begin{array}{c}{x}_1\\ x_2\\ \dots \\ x_n\\ x_d\end{array}\right]\Rightarrow \begin{array}{}\end{array}{x}_e\left(k\right)=\left[\begin{array}{c}{x}_{1e}\\ x_{2e}\\ \dots \\ x_{\mathit{ne}}\\ x_{\mathit{de}}\end{array}\right],$$

   

   
   by multiplying the difference between the measured value q2(k) and the sum of the values x _n (k) and x _d (k) with a Kalman matrix L(k) newly determined for each scanning interval.
3. Method according to claim 1 or 2,
   characterised in that
   the estimated values q2 _de for the difference traffic volumes q2 _d
   representing the inner condition of the road segment are compared with at least one threshold value thp; thm, a condition change being determined within the road segment after said threshold value has been exceeded.
4. Method according to claim 3,
   characterised in that
   gradual reductions and/or increases in the capacity of the road segment are determined as a function of the polarity and amplitude of the estimated values q2 _de and measures for informing the parties involved in the traffic and/or for controlling the traffic are taken as a function thereof.
5. Method according to one of claims 1 to 4,
   characterised in that
   a number of road segments are linked in a model and are monitored by a Kalman Filter and/or that travel times and/or optimal traffic routes are calculated as a function of the determined conditions.

Images