Method and apparatus for estimating a position of a target

A position estimation apparatus is adapted to estimate the position of a target in the steps as will be set forth below. The target is observed four or more times by an image sensor during a time period in which the target and movable body unit move in those directions not parallel to each other. Acceleration is applied to an accelerator at least once at a time between the observation times. Two-dimensional angle information of the target's azimuth and elevation angles is detected from the image information of the target acquired by the image sensor at the time of observation. A coordinate system of the movable body unit is found in accordance with the position and attitude information of the movable body unit, and the two-dimensional angle information of the target is plotted on the coordinate system. Simultaneous equations are prepared by sequentially substituting the two-dimensional angle information of the target obtained through the observation into an equation of motion representing a regulator motion of the target initially entered on a position estimation apparatus. Parameters in the equation of motion is found from the simultaneous equations. The position of the target at a given time is estimated by substituting the parameters into the equation of motion and the given time into the latter equation.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to an apparatus mounted on a movable body 
unit which, in order to enable, for example, the movable body unit to 
approximate to a target, can estimate the position of the target and guide 
the movable body unit relative to the target and a method for estimating 
the position of a target. 
2. Description of the Related Art 
In recent times, a system has been developed so as to recover an object or 
objects left or thrown away by an unmanned space vehicle in the outer 
space. In order to enable a space vehicle which cannot be operated 
directly by an operator to be guided toward a target or object to be 
recovered, it is absolutely necessary that the target position be 
detected. 
However, no effective means has been found available up to this day, except 
for a now available radar system's range finding function as will be set 
forth below. According to the radar system, it is possible to, like other 
space vehicles or crafts, radiate an electromagnetic wave to the target, 
to receive an echo, to measure required angle and time information and to 
find a target's position from a result of measurement. In the radar system 
currently relied upon, however, a large antenna needs to be mounted 
outside the space vehicle, dissipating a greater electric power for 
electromagnetic wave radiation. It is not suitable to a space vehicle 
calling for a compact, lightweight and low dissipation power unit. 
This problem occurs not only in a rendezvous approach guidance of the space 
vehicle to the target but also in the approach guidance of a movable body 
unit to a regularly moving target, so long as the radar system is 
concerned. 
SUMMARY OF THE INVENTION 
Object of Invention 
It is an object of the present invention to provide a position estimation 
apparatus for accurately measuring the position of a target from a movable 
body unit, such as a space vehicle, calling for compactness, lightweight 
and low dissipation electric power, without inflicting any heavy burden on 
a sensor accuracy. 
According to the present invention, there is provided a position estimation 
apparatus mounted on a movable body unit to estimate a position in a given 
time of a target which moves regularly, which comprises: 
an accelerator for applying acceleration to the movable body unit; 
state detection unit for detecting position and attitude information of the 
movable body unit; 
an image sensor for acquiring the target as an image from the movable body 
unit; 
observation control unit for making four or more observations of the 
target, by said image sensor, during a period of time when the target and 
movable body unit are moved in those directions not parallel to each other 
and for applying acceleration by said accelerator to the moving body unit 
at least once at a point of time between the respective observations; 
an angle information detecting unit for detecting two-dimensional angle 
information of target's azimuth and elevation angles from the image 
information of the target acquired by the image sensor at the time of 
observation; 
a coordinate transformation unit for finding a coordinate system of the 
movable body un t at the time of observation in accordance with the 
information obtained by the state detection unit and for plotting, on the 
coordinate system, the two-dimensional angle information of the target 
which is obtained by the image sensor; and 
an arithmetic operation processing unit, initially stored with an equation 
of motion representing a regular motion of the target, for preparing 
simultaneous equations by sequentially substituting, into the equation of 
motion, the two-dimensional angle information of the target which is 
obtained through the observation, for finding parameters in the equation 
of motion from the simultaneous equations and for estimating a target 
position at a given time by substituting the parameters into the equation 
of motion and substituting given time data into the resultant equation of 
motion. 
It is another object of the present invention is to provide a position 
estimation method for accurately measuring the position of a target from a 
movable body unit, such as a space vehicle, calling for compactness, 
lightweight and low dissipation electric power, without inflicting any 
heavy burden on a sensor accuracy. 
According to the present invention, there is provided a position estimation 
method for estimating a position in a given time of a target of a regular 
motion, on a position estimation apparatus, comprising the steps of: 
(1) entering into the position estimation apparatus an equation of motion 
representing the regular motion of the target; 
(2) setting observation times four or more times during a period of time 
when the target and a movable body unit move in those directions not 
parallel to each other; 
(3) applying acceleration to the movable body unit at least once during the 
period of time set by step (2); 
(4) acquiring the target as an image at the observation time set by step 
(2) and detecting two-dimensional angle information of the target's 
azimuth and elevation angles from the image information; 
(5) detecting position and attitude information of the movable body unit, 
finding a coordinate system of the movable body unit at the time of 
observation and plotting, on the coordinate system, the two-dimensional 
angle information of the target which is obtained by step (4); and 
(6) preparing simultaneous equations by sequentially substituting into the 
equation of motion the two-dimensional angle information at a respective 
time of observation obtained at step (5), finding parameters in the 
equation of motion from the simultaneous equations; and 
estimating a position in a given time of the target by substituting the 
parameters into the equation of motion and substituting the given time 
into the equation of motion. 
Additional objects and advantages of the invention will be set forth in the 
description which follows, and in part will be obvious from the 
description, or may be learned by practice of the invention. The objects 
and advantages of the invention may be realized and obtained by means of 
the instrumentalities and combinations particularly pointed out in the 
appended claims.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
An embodiment of the present invention will be explained below with 
reference to the accompanying drawings. 
FIG. 1 shows an arrangement of a position estimation apparatus according to 
the present invention. T and C denote a target and a chaser vehicle (space 
vehicle), respectively. The position estimation apparatus includes an 
image sensor 11, data processing unit 12, arithmetic operation processing 
unit 13, position sensor 14, attitude sensor 15, acceleration sensor 16 
and accelerator (for example, a thruster) 17 and is borne on the space 
vehicle C. 
The image sensor 11 acquires the target T as an image as indicated in FIG. 
2. The image data which is obtained at the image sensor 11 is sent to the 
data processing unit 12. The data processing unit 12 computes 
two-dimensional angle information, corresponding to the azimuth and 
elevation angles of the target T acquired as an image in the visual field 
of the sensor 11, from the image data. The angle information is sent to 
the arithmetic operation processing unit 13. 
The position sensor 14 is composed of, for example, a GPS (global 
positioning system) receiver. The GPS receiver receives GPS signals sent 
from a plurality of artificial satellites, matches received PN code 
information to PN code information initially prepared, demodulates the 
received data to calculate position information of, and distance 
information from, the respective satellite, and derives its own position 
information from both the information. The position information of the GPS 
receiver is sent to the arithmetic operation processing unit 13. 
The attitude sensor 15 is constructed of an inertial measurement unit a 
star sensor, earth sensor, sun sensor, etc. and detects a relative 
positional relation of a vehicle's own orbiting direction to the earth, to 
the stars, and to the sun. The attitude sensor 15 detects attitude 
information and delivers it to the arithmetic operation processing unit 
13. 
Based on a command coming from the arithmetic operation processing unit 13 
as will be set forth below, the thruster imparts acceleration, for 
example, to the vehicle. The acceleration sensor 16 detects the vehicle's 
acceleration by, for example, an accelerometer, etc. The acceleration 
information is sent to the arithmetic operation processing unit 13. 
The arithmetic operation processing unit 13 sets an acceleration time, as 
well as an observation time before and after the acceleration, in 
accordance with an observation command, such as a command from a 
corresponding earth station, accelerates the vehicle C at a time of 
acceleration and takes up, at a time of observation, two-dimensional angle 
information from the data processing unit 12, position information from 
the position sensor 14, attitude information from the attitude sensor 15 
and acceleration information from the acceleration sensor 16, all these 
information being associated with the target T. The unit 13 specifically 
identifies the vehicle's own position from the position and attitude 
information, generates a coordinate system from the vehicle's own attitude 
with the orbiting direction of the vehicle as a axis and plots the 
two-dimensional angle information coming from the data processing unit 12. 
The unit 13 implements a position estimation algorithm based on an 
initially entered equation of motion relating to the target T, that is, 
applies the equation of motion and the two-dimensional angle information 
with respective observation points plotted by coordinate transformation, 
evaluates a target's initial position and estimates the target's current 
position from the initial position above. 
The apparatus thus arranged will be explained below in connection with its 
operation principle. 
The apparatus acquires the target T as an image by the image sensor 11 and 
the vehicle receives the output data of the image sensor 11 and measures 
the azimuth and elevation angles of the target T thus acquired by the 
sensor 11. The apparatus detects the orbit and position of the vehicle C 
by the output data of the position sensor 14 and attitude sensor 15 and 
represents the vehicle's attitude, by the detection information, on the 
orbit coordinate system and plots the respective angle information of the 
target T on the orbit coordinate system with the velocity vector of the 
vehicle C as a reference. The information thus obtained is hereinafter 
referred to as measured angle information. 
The distance of the target T cannot always be estimated even if the 
aforementioned measured angle information is obtained. FIG. 3A shows the 
case where the distance of the target cannot be estimated and FIG. 3B 
shows the case where the distance of the target can be estimated. 
It is assumed that, as shown in FIG. 3A, the target T "on orbit" and 
vehicle C are moved in uniform motion in a direction parallel to the X 
axis on an X, Z coordinate system. At time t.sub.0, the target T is 
orbited at a location X.sub.T0 and the vehicle C at a location X.sub.C0. 
At time t.sub.1, the target T is orbited at a location X.sub.T1 and the 
vehicle C at a location X.sub.C1. In this case, the position and velocity 
of the target T cannot be estimated even if the measured angle information 
.phi..sub.0 and .phi..sub.1 of the target T are gained at those positions 
corresponding to times t.sub.0 and t.sub.1 of the vehicle C. It is, 
therefore, not possible to estimate their relative distance. 
In FIG. 3B, on the other hand, it is assumed that the vehicle C moves a 
distance Z.sub.1 from an orbiting position parallel to a Z-axis direction, 
when a time t.sub.1 is reached, to that position X.sub.C1 '. The distance 
Z.sub.1 represents a parallax. If the parallax Z.sub.1 and measured angle 
information .phi..sub.0 and .phi..sub.2 are used, it is possible to 
geometrically estimate the position and velocity of the target T and 
further to estimate a relative distance of the vehicle to the target T. 
However, the method for measuring or predicting the parallax Z.sub.1 will 
be in open loop relating to the position estimation of the target T. Thus 
the accuracy with which the parallax Z.sub.1 is measured or predicted is 
related directly to the position estimation error of the target T, failing 
to compensate for it with adequate accuracy in the current level of the 
sensor technique. This method sometimes encounters theoretical impossible 
conditions upon the estimation of the target's position and velocity or 
sometimes inflicts a heavy burden on the accuracy of the sensor even if it 
is possible to estimate the position and velocity of the target T. 
The present embodiment operates on a principle set forth below. 
Let it be assumed that the target T goes around the earth in circular orbit 
and that the vehicle C is guided into a visual range of the target T and 
moves in elliptic orbit relative to the orbit of the target T. It is thus 
assumed that the vehicle C and target T move in relative orbits as shown 
in FIG. 4. If, in this case, the vehicle C orbits in a range a or a range 
c, then the position of the target T can be positively estimated as set 
forth in connection with FIG. 3B because the vehicle's orbit is not 
parallel to the orbit of the target T. If, on the other hand, the vehicle 
C orbits in a range b, the orbits of the target T and vehicle C are 
substantially parallel to each other, failing to properly estimate the 
position of the target T as set forth in connection with FIG. 3A. Here, 
the position of the target T is estimated by finding an equation of motion 
of the target T in the range a with a time as a parameter and substituting 
a given time into the equation of motion. 
The position estimation method of the target T will be explained below with 
reference to FIG. 5. 
Let it be assumed that the target T and vehicle C are located in such a 
positional relation as shown in FIG. 5. By way of example, here, the 
coordinate axes X.sub.T and X.sub.C are set in those directions connecting 
the target T and vehicle C to the center P of the earth and the coordinate 
axes Y.sub.T and Y.sub.C are set in the orbiting directions of the target 
T and vehicle C and in those directions perpendicular to the coordinate 
axes X.sub.T and X.sub.C. The characters x.sub.C and y.sub.C show the 
coordinate of the vehicle C as seen from a (X.sub.T, Y.sub.T) coordinate 
in FIG. 5 and the characters x.sub.T and y.sub.T show the coordinate of 
the target T as seen from a (X.sub.C, Y.sub.C) coordinate system. In FIG. 
5, .phi..sub.C (=.phi..sub.T +.delta.) represents the elevation angle of 
the vehicle side; .phi..sub.T, the elevation angle of the target side; R, 
a relative distance between the target T and the vehicle C; .delta., an 
earth's central angle formed between a line P-T and a line P-C, and 
.omega., a circumnavigation rate (an angular velocity: rad/sec.) of the 
target T with the earth as a center. It is to be noted that the target T 
has its presence recognized by the image sensor 11 as the azimuth and 
elevation angles, but that in FIG. 5 the azimuth angle is omitted for 
brevity in explanation. 
The elevation angle .phi..sub.T from the vehicle C to the target T is 
measured with the aforementioned coordinates so set. The coordinate system 
(X.sub.C, Y.sub.C) of the vehicle C can be estimated by the position 
sensor 14. The elevation angle which is found from the output data of the 
image sensor 11 is measured with the body of the vehicle C as a reference 
and hence it is necessary to, at that time, know what attitude the vehicle 
C assumes relative to the coordinate system (X.sub.C, Y.sub.C). The 
attitude is measured by the attitude sensor 15 and, by so doing, the 
vehicle's elevation in the visual field of the image sensor 11 is 
transformed to the elevation angle .phi..sub.T of the vehicle's coordinate 
system. The same thing is also done for the azimuth, though being not 
shown in FIG. 5. 
As will be seen from the above, the position of the target T with the 
vehicle C as a center can be expressed with the use of an equation of 
motion below. 
EQU X.sub.T =.PHI.(t, .omega.).multidot.X.sub.T0 (1) 
where 
EQU X.sub.T =(x.sub.T, y.sub.T, x.sub.T, y.sub.T) 
EQU X.sub.T0 =(x.sub.T0, y.sub.T0, x.sub.T0, y.sub.T0) 
where 
X, Y: the time differentiation (velocity) of x, y; 
X.sub.T0 : the initial position and velocity of the target T; 
.PHI.(t, .omega.): 4 rows.times.4 columns matrix; 
t: an elapsed time from X.sub.T0 ; and 
.omega.: a circumnavigation rate (angular velocity: rad/sec.). 
Equation (1) can be given below: 
##EQU1## 
If the initial state (the initial position and velocity) of the target T, 
that is, the unknown quantity of the equation above, is found, it is 
possible to estimate the position of the target T at a given time by 
substituting the given time into the equation. The estimation is made by a 
position estimation algorithm as set out below. 
Now suppose that the estimated initial value X.sub.T0 is a true initial 
value X.sub.T0 *. Then the estimation value .phi..sub.T * of the elevation 
angle .phi..sub.T becomes 
EQU .phi..sub.T *=arctan(x.sub.T */y.sub.T *) 
EQU x.sub.T *=x.sub.T (X.sub.T0 *, t, .omega.) 
EQU y.sub.T *=y.sub.T (Y.sub.T0 *, t, .omega.) 
in agreement with a corresponding observation point. Since, therefore, 
X.sub.T * is not obtained during a position estimation, it is estimated as 
X.sub.T0. Here, the elevation angle .phi..sub.T becomes 
EQU .phi..sub.T =arctan(x.sub.T /y.sub.T) 
and is calculated by the arithmetic operation processing unit 13 without 
using the image sensor 11. Using Equation (1), a calculation 
EQU X.sub.T =.PHI.(t, .omega.)X.sub.T0 
is made to find the elements x.sub.T, y.sub.T of X.sub.T. 
Then a difference .delta..phi. between the observed value and the 
estimation value is calculated by an equation given by: 
EQU .delta..phi.=.phi..sub.T *-.phi..sub.T (2) 
Given 
##EQU2## 
then Equation (2) can approximate to the following equation: 
EQU .delta..phi.=(.differential..phi./.differential.X)X.sub.T0, t, 
.omega..sup..multidot..delta.X (3) 
By observing the elevation angle .phi..sub.T (T= 1, 2, 3, 4) at respective 
times t.sub.1, t.sub.2, t.sub.3, t.sub.4 by these processings, it is 
possible to find an equation given below. 
##EQU3## 
Here, .delta.X is composed by Equation (4) for unknown parameters (any 
parameters, if known, are zeros each) of .delta.x.sub.0, .delta.y.sub.0, 
.delta.x.sub.0, .delta.y.sub.0. Of those elements of the matrix, an 
element corresponding to .delta.X is selected to compose a matrix P. For 
.delta..phi., those elements necessary to find .delta.X are taken out to 
given 
EQU .delta..phi.=P(X.sub.0, t.sub.1, t.sub.2, t.sub.3, t.sub.4).delta.X (5) 
Since the unknown parameter of Equation (5) is .delta.X, 
EQU .delta.X=P.sup.-1 (X.sub.0, t.sub.1, t.sub.2, t.sub.3, 
t.sub.4).delta..phi.(6) 
As set forth earlier, it is necessary to impart a motion to the vehicle C 
in P.sup.-1 non-singular form and the vehicle C is accelerated by the 
accelerator 17 in the presence of P.sup.-1, the acceleration control of 
which will be set forth below with reference to FIG. 6. 
Upon comparing a target's true orbit and a prediction orbit before position 
estimation regarding to the relative position between the target T and the 
vehicle C, both have a similarity relation as shown in FIG. 6, that is, 
elevation direction information (the same thing can be said for the 
azimuth information) acquired by the image sensor 11 offers the same 
elevation angle whether the target T is located at a position 1 on the 
true orbit x or at a position 1' on the prediction orbit x' before 
position estimation. In this case, a vector .delta.X may take any 
quantities for the vector .delta..phi. in Equation (4) on the algorithm, 
meaning that p.sup.-1 is not present. 
However, an angle difference .delta..phi. is generated when a comparison is 
made between measured angle information (the elevation angle when the 
target T is at a position 2 on the true orbit x) obtained by applying 
acceleration to the vehicle C, for example, at a location 3 in FIG. 6 and 
measuring a corresponding angle after lapse of a certain period of time 
and measured angle information (the elevation angle when the target T is a 
position 2' on a prediction orbit X' before position estimation) obtained 
by applying the same acceleration as set out above to the vehicle C at a 
location 3' on a prediction orbit before position estimation and analyzing 
a corresponding angle after the lapse of the same period of time as set 
out above. 
In view of such a phenomena as set out above, it is possible to acquire the 
presence of P.sup.-1 by performing such control as shown in FIG. 7. In 
FIG. 7, M.sub.1 to M.sub.4 mean the obtaining of measured angle 
information by the vehicle C and t.sub.M1 to t.sub.M4 represent a timing 
for obtaining measured information. In FIG. 7, reference letter a 
represents the magnitude of acceleration under the action of the 
accelerator 17 and h, the generation time of the acceleration a. The 
feature of this control comprises starting the acceleration generation of 
the accelerator 17 at time t.sub.F0 in a range between the times t.sub.M1 
and t.sub.M2 and stopping the accelerator 17 at time t.sub.F1 between 
them. Based on the measured angle information obtained at the observation 
time t.sub.M1 before the start of the acceleration generator, and at 
respective observation times t.sub.M2, t.sub.M3, and t.sub.M4 after 
stopping the acceleration generation, it is possible to find such four of 
angle difference of Equation (2) that make P non-singular, then it is 
possible to acquire P.sup.-1 for finding the initial unknown state of the 
target T by computing Equations (1) to (6). 
The control at times t.sub.M1 to t.sub.M4, t.sub.F0, t.sub.F1 as shown in 
FIG. 7, if being implemented on an actual orbit, can be represented as 
shown, for example, in FIG. 8. With the center-of-gravity position of the 
vehicle C as an origin 0, the vehicle C is so guided that the target T 
moves on the orbit x as shown in FIG. 8, where t.sub.0 represents an 
initial time; t.sub.F0 to t.sub.F1, a period at which acceleration is 
generated; t.sub.M1 to t.sub.M4, times at which measured angle information 
is acquired; and G.sub.1 to G.sub.8, respective targeting positions as 
milestones at which the vehicle C is guided into closest proximity to the 
target T. 
Assume that, in FIG. 8, the target T is moved into closest proximity to the 
vehicle C at time t.sub.0 at a location G.sub.1 (a location 352 km from an 
origin 0) with the center-of-gravity position of the vehicle as the origin 
0. The location G.sub.1 can be roughly estimated through the observation 
from ground stations. A first angle measurement is carried out at time 
t.sub.M1 at which the target T is on orbit not parallel to that on which 
the vehicle C moves. A second closest proximity point G.sub.2 (a location 
280 km from the origin 0) can also be roughly estimated by the observation 
from ground stations. Now acceleration is applied to the vehicle C at a 
time interval between prediction times t.sub.F0 and t.sub.F1 at which the 
target T will move past the location G.sub.2. Subsequent angle 
measurements are made at time t.sub.M2, t.sub.M3, t.sub.M4 at which the 
target T moves on orbit not parallel to that on which the vehicle C moves. 
The processing from Equations (1) to (6) is implemented using measured 
angle information before and after acceleration, obtaining P.sup.-1. It is 
thus possible to find the initial state (initial position and velocity) of 
the target T at the location G.sub.1. 
The same processing is repeated at the location G.sub.2 and the following 
so as to find the initial state of the target T. As the relative position 
of the vehicle C to the target T becomes nearer to each other, it is 
possible to increase the accuracy with which the position of the target T 
is estimated. Eventually, a value X.sub.T0 * corresponding to a true 
position of the target T becomes 
EQU X.sub.T0 *=X.sub.T0 +.delta.X 
In actual practice, it is not sufficient at all time to complete the 
evaluation of X.sub.T0 * in a single computation. Given that 
EQU (X.sub.T0).sub.N+1 =(X.sub.T0).sub.N +.delta.X.sub.N 
(provided, N=1, 2, 3, . . . ) (7) 
the calculation of Equations (1) to (6) is repeatedly performed until the 
absolute value .vertline..delta..phi..vertline. of .delta..phi. becomes 
sufficiently small and a result of computation, that is, 
(X.sub.T0).sub.N+1, is interpreted as being equal to X.sub.T0 *. The 
aforementioned position estimation algorithm, upon being arranged, will be 
given below. 
##STR1## 
The aforementioned position estimation algorithm is stored in the 
arithmetic operation processing unit 13. Now the operation of the 
apparatus as shown in FIG. 1 will be explained below with reference to 
FIG. 9. 
The equation of motion of the target T--Equation (1)--is entered in the 
position estimation algorithm at step a. Then step b sets the observation 
time, number of times of observations, M, and acceleration generation 
timing. 
Step c finds target's two-dimensional angle information (azimuth and 
elevation measurements) from the output data of the image sensor 11 when 
an observation time is reached at which the vehicle C moves into a visual 
range of the target T and, at the same time, finds position and attitude 
information of the vehicle C. Step d prepares a coordinate system of the 
vehicle C from the position and attitude information and subjects the 
two-dimensional angle information of the target T to a coordinate 
transformation. At step e, two-dimensional angle information (estimation 
value) corresponding to the two-dimensional angle information subjected to 
the coordinate transformation is analytically evaluated based o the 
target's equation of motion to take a difference with respect to an 
associated measured value. At step f, it is determined whether or not an 
acceleration generation time set at step b is reached during a period of 
time at which M number of times of observations is not reached. When M 
number of times of observations is reached, step g applies acceleration to 
the vehicle C at that time and detects it. 
After steps a to e are repeated M number of times at step h, step i enters 
a result of M observations into the position estimation algorithm and 
estimates the state of the target T at time t.sub.0. Step j computes the 
position of the target T at a desired time with the use of the analytical 
equation of motion of the target T. 
The aforementioned position estimation apparatus can estimate the position 
of a target T at a given time in spite of using the image sensor 11 having 
no range finding function in particular. If calculated values of 
parameters are updated through a continuous observation, an accurate 
position estimation can be performed as the vehicle C comes nearer to the 
target T. Since the image sensor 11 only is mounted outside the vehicle C, 
there is almost no restriction on the mounting of any external device. The 
mere use of the image sensor 11 as an external device ensures a very small 
dissipation power and hence a compact light-weight vehicle C. 
The present invention is not restricted to the aforementioned embodiment 
and can be applied to, for example, a self-propelled robot capable of, for 
example, avoiding a hindrance by radiating an electromagnetic wave and an 
automobile's alarm device capable of estimating where an approaching 
automobile diagonally from behind is run upon a change from one traffic 
line to another on the road, that is, upon the indication of a direction 
by a direction indicator and sounding a buzzer if it is run in a dangerous 
area on the road. Various changes or modifications of the present 
invention can be made without departing from the spirit and scope of the 
present invention. 
Additional advantages and modifications w 11 readily occur to those skilled 
in the art. Therefore, the invention in its broader aspects is not limited 
to the specific details, representative devices, and illustrated examples 
shown and described. Accordingly, various modifications may be made 
without departing from the spirit or scope of the genera inventive concept 
as defined by the appended claims and their equivalents.