Method for determining the course of another vehicle

A method for determining the course of another vehicle in relation to one's own vehicle by measuring the position of the other vehicle in relation to one's own vehicle with a transmitter/receiver system, such as a radar system permits course determination both on straight and on bend segments. According to the method, the side location of the other vehicle and one's own vehicle is determined at a position where the other vehicle is level with one's own vehicle, by moving the front vehicle backwards in time and/or moving the rear vehicle forwards in time, on the basis of position measurements of the position of the other vehicle. The side location of the other vehicle is compared with the side location of one's own vehicle, by which a measure of the discrepancy between the course of the other vehicle and the course of one's own vehicle is obtained. According to the invention, the position where the other vehicle is level with one's own vehicle may be determined on the basis of the inertial speed vector of the other vehicle at one or more points in time.

FIELD OF THE INVENTION 
The present invention relates to a method for determining the course of 
another vehicle in relation to one's own vehicle by measuring the position 
of the other vehicle in relation to one's own vehicle by a 
transmitter/receiver system, such as a radar system, including the 
following steps being carried out: 
a) the position of the other vehicle is determined by position 
measurements, 
b) on the basis of position measurements carried out in accordance with 
step a), the side location of the other vehicle and one's own vehicle is 
determined at a position where the other vehicle is level with one's own 
vehicle, by moving the front vehicle backwards in time and/or moving the 
rear vehicle forwards in time, 
c) the side location at the position determined in accordance with step b) 
is compared with the side location of one's own vehicle, and 
d) the difference in the side locations in accordance with step c) between 
one's own vehicle and the other vehicle is used as a measure of the 
discrepancy between the course of the other vehicle and the course of 
one's own vehicle. 
BACKGROUND OF THE INVENTION 
In order to increase road safety, intensive work is being carried out 
towards finding systems which improve safety. In this connection, it has 
been proposed, among other things, to use radar technology in cars, 
so-called car radar. In a cruise control system, the car radar can help 
the driver to keep a sufficient distance from the vehicle in front, can 
warn of vehicles approaching from behind, and, in a further perspective, 
can form part of a more general collision-prevention system. One problem 
in this connection is that of determining the course of the cars in front. 
Straight sections ahead can be monitored relatively easily. The problems 
become greater when a vehicle in front is going into and following a bend. 
The system should be able to follow the vehicle regardless of the 
curvature of the road. A method of the type mentioned in the first 
paragraph of the description is already known from the U.S. Pat. No. 
5,249,157. 
For use in cruise control systems, it is important that the system also 
functions when the distance in relation to the vehicle in front remains 
constant, i.e. when the closing speed=0, and in situations with short 
increasing distances. The method according to the cited U.S. Pat. No. 
5,249,157 crucially makes use of prediction of the "intercept time" as 
determined by the ratio between the distance separating the vehicles and 
the closing speed. A disadvantage of this known method is that the 
"intercept time" cannot be determined when the closing speed is zero, 
which is a common situation with cruise control systems. 
A study of the road network shows that, over large parts of their length, 
the majority of roads can be approximated with great accuracy to straight 
and circular segments. Bends which do not have circular segments are 
considered awkward to negotiate, since the driver's handling of the 
steering wheel has to be corrected through the bend, and they are 
therefore uncommon. A circular bend segment can be defined in a known 
manner as having a constant center of curvature and a constant radius of 
curvature. By contrast, other parts of the road, including straight 
segments, cannot be defined in this way. 
The curvature of a bend is a measure of the rate at which the tangent 
vector changes direction. The curvature is therefore expressed by second 
derivatives (accelerations), where transversal accelerations (angular 
accelerations and magnitudes derived therefrom) are especially important. 
Angular accelerations determined from angle measurements are generally 
very noisy signals. This is especially the case if radar sensors are used. 
In the method according to the U.S. patent referred to above, the angular 
acceleration is determined in accordance with the above as a second 
derivative. Consequently, advantageous methods for course determination 
should function on curving roads, and yet not use angular accelerations, 
and, taking into consideration non-circular road sections, including 
straight sections, should not use expressions for radii of curvature. 
When holding speed with respect to a vehicle in front, the distance is 
constant. If both vehicles lie simultaneously within a circular bend 
segment, the vehicle in front is additionally observed at a constant 
angle, and it therefore has a relative movement equal to zero both in 
terms of distance and in terms of angle. For this reason, observing only 
the relative movement when following at constant speed does not permit to 
distinguish between circular bend segments and straight roads. 
SUMMARY OF THE INVENTION 
The object of the present invention is to provide a method for determining 
the course of another vehicle, which does not have the shortcomings 
discussed above and found in the known systems. 
The invention is based on using, for the purpose of course determination, 
the inertial speed vector of the other vehicle, i.e. its speed vector over 
ground. The method is characterized in that the position where the other 
vehicle is level with one's own vehicle is determined on the basis of the 
other vehicle's inertial speed vector (speed vector over ground) at one or 
more points in time. The components of this inertial speed vector can be 
determined, in a manner familiar to one skilled in the art, by means of 
the relative movement in terms of distance and angle being corrected with 
the speed and rotation of one's own vehicle. The rotation can be measured 
by a sensor which measures angular velocity, a so-called yaw rate sensor. 
On straight roads the other vehicle has no inertial speed component 
transverse to the direction of movement of one's own vehicle. This is not 
the case with a bend. In order to identify the beginning and ending of 
bends, changes in the inertial transversal velocity of the vehicle in 
front can advantageously be detected. 
In an advantageous method for course determination, the side location of 
the other vehicle, when it is level with one's own vehicle, is determined 
by extending the inertial speed vector of the other vehicle in the 
direction of one's own vehicle to a length which is a certain proportion k 
of the distance between one's own vehicle and the other vehicle. 
For an arc of a circle, the tangents at the end points of the arc intersect 
each other outside the midpoint of the bend. This applies also to a line 
section. Thus, the above-mentioned proportion is 0.5 for arcs of circles 
and straight lines. If the vehicles are moving along a circular bend 
segment, the method gives side locations which are equivalent to side 
locations obtained by calculations based on knowledge of the center of 
curvature and radius of curvature. However, the present method does not 
make use of such knowledge. The proportion k can be determined 
continuously on the basis of current measurements and earlier measurements 
of the other vehicle's inertial speed vector and distance. This provides, 
for example, the possibility of special values for k when the entry into, 
and exit from, bends have been identified. According to an advantageous 
method based on point identification in accordance with the above, the 
proportion is constant. A particularly advantageous method is obtained in 
this respect when the proportion k is a constant in the range 
0.4.ltoreq.k.ltoreq.0.6. The range includes k=0.5, which is the correct 
value for circular and rectilinear bend segments. 
According to a further advantageous method, the position where the vehicle 
in front and one's own vehicle are level can be determined by time 
integration in two directions, where one direction, the x direction, 
corresponds to the direction of movement of one's own vehicle, and the 
other direction corresponds to a direction at right angles to the 
direction of movement of one's own vehicle, i.e. the y direction or 
lateral direction. The method is characterized in that, on the basis of 
position measurements which have been carried out, the inertial speed 
vector of the other vehicle is determined during a period of time 
corresponding to at least the time gap between the other vehicle and one's 
own vehicle, and the other vehicle and one's own vehicle are moved level 
with each other by means of performing time integration in the 
longitudinal direction, until the other vehicle is situated level with 
one's own vehicle, and at the same time performing integration in the 
transverse direction, where the longitudinal direction corresponds to the 
direction of travel of one's own vehicle, and the transverse direction 
corresponds to a direction at right angles to the direction of travel. 
This method does not require that the road be approximated to consist of 
straight and circular segments, but instead the method is completely 
independent of the curvature of the road. 
The position where the other vehicle is level with one's own vehicle can 
advantageously be determined using several variants of the same basic 
principle, for example with one variant being used for relatively short 
distances and another for relatively long distances. It is also possible 
to weigh together calculations which have been made in accordance with two 
different variants. In this context, relatively short distances can be 
taken as distances up to the order of magnitude of a hundred meters, while 
relatively long distances can be taken as distances of about a hundred 
meters and upwards.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT(S) 
The car radar 4 shown in FIG. 1 comprises an aerial 6, a transmitter part 7 
and a receiver part 8. The aerial 6 is preferably mounted at the front of 
the vehicle and includes for example, of a mechanically scanning reflector 
aerial of the Cassegrain type. The transmitter part includes a 
linearization circuit 9 and an oscillator 10. The oscillator preferably 
generates a signal in the gigahertz range, for example 77 GHz, which 
signal is conveyed to the aerial 6 via a directional coupler 11 and a 
circulator 12. A reflected signal received by the aerial is conveyed via 
the circulator 12 to a mixer 13 where the received signal is mixed with 
the transmitted signal. After amplification 14, filtering 15 and signal 
processing 16, the distance r and the direction a with respect to the 
vehicle in front, in accordance with the definition below, can be 
obtained, among other things, in accordance with known radar principles, 
as can information, if so required, on the relative speed of the vehicle 
in front. 
A first method according to the present invention, using side location 
determination by identification of a point between one's own vehicle and 
the other vehicle, is described below with reference to FIGS. 2 and 3. 
In FIG. 2, a first vehicle 23, referred to hereinafter as one's own vehicle 
or the host vehicle, is situated in a bend section 22 together with 
another vehicle 25, which in this case is in front. The first vehicle 23 
is provided with a car radar according to the block diagram shown 
schematically in FIG. 1. The distance between the two vehicles has been 
designated by r, and .alpha. designates the direction to the front vehicle 
25 in relation to the direction of travel of the host vehicle 23. The 
transverse distance with respect to the vehicle in front, i.e. the 
difference in the lateral direction, has been designated by d. A Cartesian 
system of coordinates is assigned to the host vehicle 23, with the x axis 
lying in the direction of travel of the host vehicle. It is assumed that 
the position and speed of the vehicle in front are known through 
measurement principles described above. 
From the front vehicle 25, a line 26 is drawn straight back (in the 
direction of the tangent) to a point 27 at the same distance a/2 from the 
front vehicle 25 and one's own vehicle 23. It is evident from FIG. 2 that 
the point 27 has the same side location relative to one's own vehicle as 
to a front vehicle which has been moved backwards in time along a circular 
bend segment. The difference in side location between the vehicles can be 
determined in this way. For bend segments of small curvature, which is 
usually the case, the distance r between the vehicles is approximately 
equal to a (r.apprxeq.a). 
For an arc of a circle, as illustrated in FIG. 2, the tangents at the end 
points of the arc intersect each other outside the midpoint of the bend. 
The proportion k of the distance between one's own vehicle and another 
vehicle is in this case equal to 0.5. 
The following analysis with reference to FIG. 3 gives a necessary condition 
for the equations for bends having a certain constant proportion k, where 
the tangents at the end points A, B of an arbitrary bend section 42 
intersect each other at a point C which divides the distance between the 
end points into parts whose lengths have a ratio of (1-k) to k. 
Assume that the bend section is given by y=f(x). Select units so that one 
end point A of the bend section 42 is at the origin (0,0). By changing 
over to the function g(x)=f(x)-x*f'(0), the analysis can be reduced to the 
case where the tangential direction at the origin is horizontal. Assume 
further that the function g and its derivative g' are such small sums that 
the distance along the bend y=g(x) can be approximated to the distance 
along the x axis. 
The tangent at the bend section's other end point B=(x, y), where x&gt;0 and 
y=g(x), will intersect the x axis (=the tangent at the other end point, 
origin) at the point C=((1-k)*x, 0). If g(x)=0 identically, i.e. the bend 
AB, is a straight line, this is complied with irrespective of the value of 
k. Otherwise, according to the triangle BCD, where D=(x, 0) and the line 
CD has the length k*x, BD/CD=g(x)/(k*x)=g'(x). 
This relation, which applies for all values of x, gives the differential 
equation 
EQU g'(x)/g(x)=1/k*1/x 
with the solution 
1n.vertline.g(x).vertline.=(1/k)*1n.vertline.x.vertline.+C, i.e. 
EQU g(x)=(.+-.) exp(C)*x.sup.1/k 
k=0.5 gives a parabolic curve with constant second derivative, i.e. a small 
angle approximation of an arc of a circle having constant curvature. This 
is a necessary condition in the case where k=0.5. It is easy to see that 
this is also sufficient. 
The bends for which it holds true that the tangents at the end points of an 
arbitrary bend section intersect each other outside the middle of the bend 
section, are therefore (small angle approximations of) bends of constant 
curvature (including straight lines which have 0 curvature). This 
characterization of bends of constant curvature does not exploit the fact 
that the value of a radius of curvature is known. 
For bend segments where the curvature increases with the road distance 
covered, k is &lt;1/2 and not constant over the bend segment, but instead can 
also depend, for example, on the distance between the points (the 
vehicles). An example of such a bend is a so-called clothoid (Cornu 
spiral; see Struik, Differential Geometry, Addison-Wesley 1950, p 201), 
where the curvature increases with the arc length from the point of 
symmetry. Such a bend can be approximated locally to a third degree bend, 
and can be considered as a transition bend between a straight line section 
and a bend. In the same way, k&gt;1/2 when the curvature decreases with the 
road distance covered. An advantageous method for side location 
determination can therefore use k&lt;1/2, for example when the entry into a 
bend is detected, and can use k&gt;1/2, for example when transition from a 
bend to a straight road is detected, the distance also being used in the 
determination of the instantaneous k value. 
The integration principle illustrated in FIG. 4 builds on the relationship 
that 
EQU road=time integral of speed=sum of v(t)*dt! 
The figure shows how a displacement backwards in time from a first point 31 
to a second point 32 along a stretch of road can be divided into two 
components 33 and 34. The component 33 corresponds to a displacement 
backwardly in the x direction, while the component 34 corresponds to a 
displacement backwardly in the y direction, where the y direction 
corresponds to displacement in the lateral direction, and the x direction 
corresponds to a displacement at right angles to the lateral displacement. 
By observing the transversal and longitudinal speeds of the vehicle in 
front for a period of time, the vehicle in front can thus be moved 
backwardly in the x direction until it is situated level with one's own 
vehicle. Integration in the length corresponding to the y direction gives 
the side location. The integration principle in accordance with the above 
can be applied irrespective of the curvature of the road. 
Since one's own vehicle does not have any fixed system, but instead its own 
system of coordinates which is turned with the movements of the vehicle, 
correction should be made for the movements of one's own vehicle. In the 
integration (=summation), the speeds are therefore resolved depending on 
how one's own vehicle has turned since the speeds were measured. This 
turning is given as the time integral of the signal from the yaw rate 
sensor of one's own vehicle. The resolution can often be performed using 
so-called small angle approximations, i.e. using the approximations 
sin(x)=x and cos(x)=1. 
The invention has been described above for radar frequencies, but it is not 
in any way limited to this range, and instead completely different 
frequency ranges are conceivable, including the laser frequency range. In 
the exemplary embodiments discussed above, the vehicle in front has been 
moved backwardly in time throughout. It is possible, for example, at least 
in certain applications, for one's own vehicle to be moved forwardly in 
time or for both the vehicles to be moved in time to a position where they 
are situated level.