Dynamic monitoring of vehicle separation

A system for monitoring operation and location of a moving first vehicle relative to a second vehicle. A minimum separation distance between the first and second vehicles is estimated, based on the first vehicle velocity, and optionally on the second vehicle velocity, using location determination (LD) signals received from satellite-based transmitters from GPS, GLONASS and LEO satellites, or from ground-based signal sources such as LORAN signal towers, and using ranging signals from SONAR, RADAR or a similar system. The minimum separation distance is compared with the actual separation distance at selected times, and a vehicle driver is advised if the actual separation distance is too small, if the separation distance is decreasing too quickly, or if the second vehicle velocity is decreasing too quickly. The second vehicle may travel in the same traffic lane, in an adjacent lane, or on a road that intersects the road used by the first vehicle. Where the first and second vehicles travel on separate roads that will intersect, the system estimates whether the second vehicle will stop, or will be able to stop, at the intersection. The second vehicle may be a railroad car, such as a locomotive, or a road vehicle, such as an automobile, bus or truck. A maximum vehicle clear-view velocity, consistent with vehicle stopping within a selected distance, is estimated. Road conditions are estimated and compensated for in estimating the minimum separation distance and/or the maximum vehicle clear-view velocity.

FIELD OF THE INVENTION 
This invention relates to dynamic monitoring of a separation zone 
surrounding a moving vehicle, from which other vehicles are to be 
excluded. 
BACKGROUND OF THE INVENTION 
A moving vehicle, such as an automobile, truck, bus, motorcycle or railroad 
car, requires at least a minimum braking distance to stop after vehicle 
brakes are applied and an additional time and equivalent 
perception-reaction distance for the vehicle driver to perceive and/or 
react and to apply the brakes. Each of the braking distance and the 
perception-reaction distance increases with vehicle velocity and may be 
different for different vehicles and for different drivers. Where a first 
vehicle immediately follows a second vehicle in a traffic lane on a 
highway, expressway, street, lane or road ("road"), safe operation of the 
first vehicle requires keeping some distance between the first and second 
vehicles. Many drivers use an approximately fixed separation distance from 
the preceding vehicle, and this distance (often as small as two vehicle 
lengths) does not vary with vehicle velocity, with the type of vehicle, 
with road conditions or with the driver. 
Monitoring of vehicle velocities, vehicle spacings and the like, that 
control access to a specified zone, is disclosed in several U.S. patents. 
Most of these patents do not concern separation of two consecutive 
vehicles with reference to the individual velocities of the two vehicles. 
What is needed is a system for creating and subsequently monitoring a 
variable vehicle-to-vehicle buffer zone or separation distance whose 
location moves with the vehicle and whose size and/or character can change 
with vehicle velocities, with road conditions and with other variables. 
Preferably, the system should determine and take account of the velocities 
of each of the two vehicles and should permit receipt of information, 
received from a central station or elsewhere, that may affect 
determination of the size of the vehicle buffer zone. 
SUMMARY OF THE INVENTION 
These needs are met by the invention, which provides a system that uses 
location determination (LD) signals, ranging signals, road condition 
information and other information, received at the monitored vehicle, (1) 
to determine the present location and present velocity of the monitored 
vehicle and of the immediately preceding vehicle in the same road lane, 
(2) to determine a suitable minimum vehicle-to-vehicle separation distance 
for two vehicles traveling in the same road lane and to optionally display 
this distance, visually or audibly, to the driver, (3) to compare the 
minimum separation distance with the actual separation distance and to 
advise the driver if the monitored vehicle is too close to the immediately 
preceding vehicle, (4) to determine a maximum clear-view vehicle velocity, 
and (5) to take account of road conditions and other changing 
circumstances that may alter the minimum separation distance or maximum 
clear-view velocity. 
The monitored vehicle carries, or has attached thereto, an LD module that 
receives LD signals and estimates the present location and velocity of the 
LD module and that estimates the present location and present velocity of 
a vehicle, if any, that immediately precedes the monitored vehicle in the 
same road lane and moves in the same direction. The LD module may include 
a communications module that exchanges information with a central station.

DESCRIPTION OF BEST MODE OF THE INVENTION 
FIG. 1 illustrates one situation for practice of the invention. A monitored 
or first vehicle 11 moves in a traffic lane on a road, following an 
immediately preceding, second vehicle 41. The first vehicle 11 carries or 
has attached thereto a location determination (LD) module 13 that receives 
LD signals from two or more LD signal sources 17, 19, 21 and 23 and that 
analyzes these signals to determine the present location vector r(t;1) and 
the present velocity vector v(t;1) for the first vehicle as a function of 
time t. The LD module 13 may include an LD unit with an LD signal antenna 
14 and associated LD signal receiver/processor 15 that receive and analyze 
the LD signals. The LD signal sources may be satellite-based transmitters 
that are part of a Global Positioning System (GPS), a Global Orbiting 
Navigation Satellite System (GLONASS) or a Low Earth Orbit (LEO) system, 
such as the 66-satellite Motorola Iridium system. Alternatively, the LD 
signal sources may be part of a ground-based transmitter system, such as 
Loran, Tacan, Decca, Omega, JTIDS Relnav or an FM subcarrier system. 
Optionally, the LD module 13 includes a communications receiver or 
transceiver 25 (FIG. 2) that can exchange information with a central 
station 39 that is spaced apart from the vehicle 11. Optionally, the LD 
module 13 includes a visually perceptible display 29 and/or an audibly 
perceptible display 31, shown in FIG. 2, that present information for the 
driver of the first vehicle 11. Optionally, the LD module 13 includes a 
data/command entry module 33 (e.g., a keyboard or microphone) for entry of 
responses or supplementary information into the LD module. 
Optionally, the communications, control and display functionalities can be 
built into the vehicle 11 (for example, in the dashboard facing the 
vehicle operator) as OEM equipment, can be retrofitted into the vehicle 
and its computer system, or can be incorporated into software for a 
personal computer that is installed into or removable from the vehicle and 
that may have been originally intended to provide other vehicle-related 
functions, such as inside/outside temperature monitoring, radio 
entertainment, monitoring of fuel usage, and the like. These uses are 
discussed in the following in connection with the apparatus shown in FIG. 
2. 
The invention is used to determine and present a minimum separation 
distance d(t;1;2;sep) between the first vehicle 11 and the second vehicle 
41 that travels immediately ahead of the first vehicle in the same traffic 
lane of the road, as illustrated in FIG. 1. A minimum separation distance 
will depend upon the present velocity of the first vehicle and optionally 
upon the present velocity of the second vehicle 41 and/or on the road 
conditions, and may depend upon the number, ages and present health of any 
passengers that are traveling in the first vehicle and/or upon other 
relevant circumstances. 
FIG. 2 is a schematic view of an LD module 13, carried on the first vehicle 
11, suitable for monitoring and reacting to the vehicle-to-vehicle 
separation according to the invention. The apparatus 13 may include an LD 
signal antenna or sensor 14 and associated LD signal receiver/processor 15 
that receive and analyze LD signals from two or more LD signal sources and 
determine the present location vector r(t;1) and present velocity vector 
v(t;1) of a first vehicle. The LD module 13 also includes a range and 
(optional) range rate determination module 16, referred to for convenience 
as a "ranging" module, which may act cooperatively with, or be part of, 
the LD signal receiver/processor 15, that determines the separation 
distance d(t;1;2) between the first vehicle and a second vehicle that 
immediately precedes the first vehicle in the same traffic lane of the 
road. Optionally, the ranging module 16 determines a velocity vector 
v(t;2) of the second vehicle and/or a velocity difference vector 
.DELTA.v(t;1;2) of the first vehicle relative to the second vehicle. 
The ranging module 16 may use range determination apparatus disclosed in 
U.S. Pat. No. 5,379,045, issued to Gilbert, Kersey and Janky for "SATPS 
Mapping Angle Orientation Calibrator", or in U.S. Pat. No. 5,568,152, 
issued to Janky, Loomis and Schipper for "Integrated Image Transfer For 
Remote Target Location", both incorporated by reference herein. Each of 
these two patents discloses methods and apparatus for determining the 
angular direction to and/or the distance to a remote, visible object 
relative to an LD unit, such as a GPS unit including a GPS signal antenna 
and GPS signal receiver/processor. Alternatively, the ranging module 16 
may use any other suitable range determination apparatus, such as a 
conventional automated rangefinder and time-based range sampler. 
Alternatively, the LD module 13 may include a speedometer/odometer with a 
wheel revolution sensor mounted on a vehicle wheel, a local magnetic field 
sensor with time-based sensor sampler (disclosed in U.S. Pat. No. 
3,860,869 and 4,743,913, issued to Parks and to Takai), or the like. 
A preferred alternative for the ranging module 16 is a SONAR system, which 
can determine a distance and a closure rate and even an object size, 
between a vehicle and an object spaced apart from the vehicle. A SONAR 
(sound navigation and ranging) system transmits sonic or supersonic waves 
and determines time of arrival of the return waves (reflected from a 
visible object) to determine distance to the reflecting object, analogous 
to a radar system. SONAR waves normally have a carrier frequency of 10-50 
kHz (equivalent wavelength=0.66-3.3 cm) but may have a higher carrier 
frequency. The directional pattern of the transmitter/receiver can be used 
to determine a heading angle for the object, and the return wave pattern 
can be used in some circumstances to estimate the effective reflecting 
area of the object. By comparing two consecutive range measurements from 
return waves, a range rate or closure rate for the object can be 
estimated. 
Alternatively, a side-looking or conventional RADAR system can be used for 
a ranging module 16. The operating principles of RADAR are well known and 
are discussed by M. J. Skolnick in Radar Handbook, Second Edition, 1990. 
The LD module 13 estimates a minimum separation distance d(t;1;2;sep) 
between the first and second vehicles, based on the magnitude, 
v(t;1)=.vertline.v(t;1).vertline., of the first vehicle velocity vector, 
and compares the separation distances d(t;1;2) and d(t;1;2;sep), as 
discussed in the following. Alternatively, the LD module 13 determines the 
minimum separation distance d(t;1;2;sep) based on the magnitudes, v(t;1) 
and v(t;2), of the velocity vectors of the first and second vehicles, as 
discussed in the following. Road conditions may be taken into account in 
estimating the minimum separation distance d(t;1;2;sep). 
The LD module 13 also includes a comparator 35 that computes difference 
functions, such as .DELTA.(t;1;2)=d(t;1;2;sep)-d(t;1;2), and determines if 
this difference function is (i) greater than or equal to zero or (ii) less 
than zero. If .DELTA.(t;1;2).gtoreq.0, the operator of the first vehicle 
is advised, using a visually perceptible display 29 or an audibly 
perceptible display 31, of this condition and can take appropriate action. 
Optionally, the comparator module 35 also determines the time rate of 
change, .differential..DELTA.(t;1;2)/.differential.t, of the difference 
function .DELTA.(t;1;2). If .DELTA.(t;1;2)&lt;0 but 
.differential..DELTA.(t;1;2)/.differential.t is greater than or equal to a 
selected positive threshold rate v1, the driver of the first vehicle 11 is 
advised that the separation distance d(t;1;2) is decreasing and will soon 
become less than the minimum separation distance; the driver can take 
appropriate action. Optionally, the comparator 35 compares the present 
vehicle velocity with a computed maximum vehicle velocity. 
A visual display 29, illustrated in FIG. 2, that is part of the LD module 
13, is connected to the LD signal receiver/processor 15 and may visually 
advise the driver of the first vehicle 11 to which the LD module 13 is 
attached of any or all of the following information on a visual display 
screen: (1) a map of the relevant part of the road and the present 
separation distance d(t;1;2), preferably in a contrasting color or 
cross-hatched area; (2) the first vehicle's present location vector r(t;1) 
and/or velocity vector v(t;1); (3) the second vehicle's present location 
vector r(t;2) and/or velocity vector v(t;2); (4) a difference 
.DELTA.(t;1;2)=d(t;1;2;sep)-d(t;1;2) between the minimum separation 
distance and the actual separation distance for the first and second 
vehicles; and (5) relevant information concerning road conditions or 
special circumstances that are present. These road conditions include, but 
are not limited to, road surface conditions, local weather conditions and 
whether the vehicle is operating in daylight or in the nighttime. 
An audible display 31, illustrated in FIG. 2, that is part of the LD module 
13, is connected to the LD signal receiver 15 and may audibly advise the 
driver of the first vehicle 11 to which the LD module 13 is attached of 
any or all of the same information as set forth for the visual display 29. 
Visual or audible display of the restricted activity time interval may be 
repeated at periodic intervals, such as once every 15-180 sec, before the 
beginning of this buffer activation time interval. The visual display 29 
or audible display 31 optionally includes a keyboard, microphone or other 
data/command entry device 33 that can be used to enter relevant 
information or a request for display of particular information related to 
determination of the minimum separation distance. 
The LD module also includes a power module 37 and an input/output ("I/O") 
module 38 (a collection of I/O ports) that can exchange signals with a 
supplementary service module 51, also illustrated in FIG. 2. 
The supplementary service module 51 (optional) includes an I/O module 53, a 
central processing unit ("CPU") 55 for an on-board computer, and a ROM 
unit 57, RAM unit 59, floppy drive unit 61, hard drive unit 63 and flash 
memory unit 65 (optional) that serve the CPU. The supplementary service 
module 51 optionally includes a visual display 67 and a data/command entry 
device 69, such as a keyboard, light pen pressure pen or touch screen, 
that is used to enter a command or a request for information or relevant 
data requested by the CPU. The supplementary service module 51 optionally 
includes an audible display 71, such as a loudspeaker, and an audible 
data/command entry device 73, such as a microphone with or without voice 
recognition capability (hardware or software). The supplementary service 
module 51 optionally includes a CD ROM player 75, an AM/FM receiver 77, a 
fuel usage monitor 78 and/or inside/outside temperature monitor 79. The 
supplementary service module 51 can be as small as 10 cm.times.17 
cm.times.2.5 cm, as are the Toshiba Libretto, Philips Velo and other 
notebook computers now available in the market place and may exercise 
control through an electronic control monitor 80. These notebook examples 
are given to illustrate existing technology that permits reduction in size 
of the service module 51 and/or the LD signal module to a size that can 
easily be positioned in a vehicle dashboard, or elsewhere if desired. The 
LD signal module 13 and/or the supplementary module 51 can be OEM 
electronics equipment for the vehicle or can be redesigned and/or 
repackaged for rertofitting into the vehicle 11, as desired. The 
supplementary service module 51 may provide one or more additional 
functions, such as navigation, entertainment, temperature and fuel usage 
monitoring, in addition to the function of monitoring minimum vehicle 
separation distances and/or maximum vehicle velocities. The CPU 55, ROM, 
RAM, FD, HD and/or flash memory may be part of the LD signal 
receiver/processor 15 or may be part of a separate computer. 
The communications signals used by the transceiver 25 for exchange of 
inquiries and information between an LD module 13 and a central station 39 
may be part of an analog cellular system (such as AMPS or NAMPS), a 
digital cellular system (such as IS-54 or IS-95), a cellular digital 
packet data system, a personal communications services (PCS) system, a 
Digital European Cordless Telecommunications (DECT) system, a radiopaging 
system, a nationwide wireless network, a conventional land mobile radio 
system, radio data networks (such as ARDIS and RAM Mobile Data), 
Metricom's Ricochet Micro Cellular Data Network, a radiofrequency or 
infrared WAN, an analog or digital microwave relay system, a geostationary 
satellite system, or a low earth orbit (LEO) system, among others. These 
communication systems are summarized by S. D. Elliott and D. J. Dailey in 
Wireless Communications for Intelligent Transportation Systems, Artech 
House, Boston, 1995, pp. 11-32, and are discussed in greater detail in the 
remainder of this book. The communications signals may also be part of a 
Group Special Mobile (GSM) pan-European system, as discussed by D. M. 
Balston and C. Watson in Cellular Radio Systems, ed. by D. M. Balston and 
R. C. V. Macario, Artech House, Boston, 1993, pp. 153-206. 
Table 1 includes data taken from a Skid Chart compiled by Michael J. 
Shepston & Associates, Traffic Accident Reconstruction, Cave Creek, Ariz. 
85331. Table 1 provides estimates of perception-reaction distance 
(conservatively assuming a driver perception-reaction time of 1.5 sec. at 
any velocity), braking distance and total stopping distance (sum of 
columns 2 and 3) for a passenger vehicle initially traveling at various 
velocities, as gathered and analyzed by various highway monitoring groups. 
The Total Stopping Distance set forth in Table 1 represents a suitable 
separation distance for two vehicles traveling in the same lane and in the 
same direction on dry pavement. The results set forth in Table 1 may be 
modified by taking account of road surface condition (dry, slightly wet, 
wet/saturated, snow, ice, sleet, etc.) on braking distance. 
TABLE 1 
______________________________________ 
Representative Vehicle Stopping Distances 
Vehicle Percep-React 
Braking Total Stopping 
Velocity Distance Distance Distance 
______________________________________ 
10 (m.p.h.) 
22 (feet) 5 (feet) 27 (feet) 
20 44 19 63 
30 66 43 109 
40 88 76 164 
50 110 119 229 
60 132 172 304 
70 154 234 388 
80 176 305 481 
90 198 386 584 
______________________________________ 
A general model for vehicle deceleration upon braking assumes that loss of 
vehicle velocity v is proportional to a pth power of velocity, viz. 
EQU dv/dt=-K'.multidot.v.sup.p, (1) 
where K' and p are parameters that should be determined by measurement. 
Assuming that p.noteq.+1 (a special case), this model has the following 
solutions for velocity and linear displacement. 
EQU v(t)={v0.sup.1-p -(1-p)K(t-t0)}.sup.1/(1-p), (2) 
EQU v(t=t0)=v0, (3) 
EQU x(t)=x0+(1/K(2-p)){v0.sup.2-p -{v0.sup.1-p -(1-p)K(t-t0)}.sup.(2-p)/(1-p) 
},(4) 
EQU x(t=0)=x0. (5) 
If vehicle braking is applied at t=t0, the vehicle will come to a stop at 
the end of a time interval of length 
EQU .DELTA.t(brake;v0)=t(stop)-t0=(v0).sup.1-p /K(1-p), (6) 
and the braking distance will be 
EQU .DELTA.x(brake;v0)=x(stop)-x0=(v0).sup.2-p /K(2-p). (7) 
If kinetic energy is assumed to be lost at a constant rate throughout the 
braking interval, p=-1 and the braking distance .DELTA.x(brake) is 
proportional to v0.sup.3. If momentum is assumed to be lost at a constant 
rate throughout the braking interval, p=0 and the braking distance 
.DELTA.x(brake) is proportional to v0.sup.2. 
Most tabular estimates of braking distance, including the results presented 
in Table 1, appear to incorporate the assumption that p=0. It is 
preferable, where possible, to estimate the value of the parameters p and 
K using measurements on a given vehicle. For example, if the braking 
distance .DELTA.x(brake;v0) is known for two distinct non-zero initial 
velocities v0' and v0", the parameter p may be estimated using the 
equation 
EQU p=log.sub.a {.DELTA.x(brake;v0')/.DELTA.x(brake;v0")}/log.sub.a 
{v0'/v0"},(8) 
where a is any real number greater than 1.0, such as a=2, 
a=e.apprxeq.2.718282 and a=10. Using this estimate, one can easily verify 
that p.apprxeq.0 is assumed for the results presented in Table 1. 
These considerations can be used to provide an arguably more realistic 
determination of minimum separation distance, using knowledge of the 
velocities v(t;1) and v(t;2) for the first and second vehicles. Assume 
that the first vehicle 11 is traveling at a present velocity v(t;1), 
behind a second vehicle 41 that is traveling at a present velocity v(t;2) 
in the same traffic lane and that is proceeding in the same direction, as 
illustrated in FIG. 1. At a given time, taken to be t=t0=0 for ease of 
notation, the brakes on the second vehicle 41 are abruptly applied, and 
the second vehicle comes to a stop after traveling an additional distance 
.DELTA.x(brake;v20), due solely to vehicle braking. Here, v10 and v20 are 
the initial velocities of the respective first and second vehicles 11 and 
41. Perception-reaction time for the second vehicle 41 is ignored here, 
because the driver of the first vehicle 11 will only react after the 
driver observes that the second vehicle is braking. However, the driver of 
the first vehicle 11 will have a non-zero perception-reaction time. 
.DELTA.t(percep;1). During the time interval 0&lt;t&lt;.DELTA.t(percep;1) the 
first vehicle 11 will travel a distance 
EQU .DELTA.x1(percep;v10)=v10.multidot..DELTA.t(percep;1). (9) 
From Eq. (2), the second vehicle 41 is estimated come to a complete stop at 
a time 
EQU .DELTA.t2=.DELTA.t(brake;v20)=(v20).sup.1-p /K(1-p), (10) 
after traveling an additional braking distance 
EQU .DELTA.x2(brake)=(v20).sup.2-p /K(2-p). (11) 
The first vehicle 11 is estimated to come to a complete stop at a time 
EQU .DELTA.t1=.DELTA.t1(brake;v10)+.DELTA.t1(percep;1)=(v10).sup.1-p 
/K(1-p)+.DELTA.t(percep;1), (12) 
after traveling an additional total stopping distance of 
EQU .DELTA.x1=(v10).sup.2-p /K(2-p)+v10.multidot..DELTA.t(percep;1).(13) 
The difference 
EQU d=.DELTA.x1-.DELTA.x2=(v10).sup.2-p /K(2-p)-(v20).sup.2-p 
/K(2-p)+v10.multidot..DELTA.t(percep;1), (14) 
if non-negative, is the minimum separation distance that is appropriate for 
this situation. At any time t before the second vehicle 41 begins braking, 
the "initial" velocities v10 and v20 are the present velocities v(t;1) and 
v(t;2) for the two vehicles, and the minimum separation distance 
d(t;1;2;sep) between the two vehicles becomes 
EQU d(t;1;2;sep)=.DELTA.x1(t)-.DELTA.x2(t)={(v(t;1)).sup.2-p -(v(t;2)).sup.2-p 
}/K(2-p)+v(t;1).multidot..DELTA.t(percep;1). (15) 
The parameters p and K for the first vehicle and for the second vehicle may 
differ. If the parameter p=0 for both vehicles, Eq. (15) becomes 
EQU d(t;1;2;sep)={(v(t;1)).sup.2 -(v(t;2)).sup.2 
}/2K+v(t;1).multidot..DELTA.t(percep;1). (15') 
Equation (13) or (14) may be implemented to provide adaptive cruise control 
for appropriate separation of the first vehicle 11 from another vehicle 41 
traveling ahead of the first vehicle in the same lane. In a pessimistic 
approach, the term -(v20).sup.2-p /K(2-p) is ignored, and Eq. (13) is used 
to determine the minimum first vehicle-to-second vehicle separation 
distance d(t;1;2;sep). In a less pessimistic, more realistic approach, Eq. 
(14) is used to determine the minimum separation distance d(t;1;2;sep) 
between the two vehicles 11 and 41. Whichever approach (Eq. (13) or Eq. 
(14)) is used, the minimum separation distance d(t;1;2;sep) is computed, 
displayed visually or audibly (optional), and compared with the present 
separation distance d(t;1;2). 
The quantity d(t;1;2) is computed approximately periodically, for example, 
once every 1-5 seconds, using the preceding analysis and the measured 
present values of vehicle velocities, v(t;1) and v(t;2), and this minimum 
separation distance is compared with the measured present separation 
distance d(t;1;2) between the two vehicles. If the difference 
EQU .DELTA.(t;1,2)=d(t;1;2;sep)-d(t;1;2) (16) 
is non-negative, or if the difference .DELTA.(t;1;2) is negative but is 
increasing at greater than a selected threshold rate v1, 
EQU .differential..DELTA.(t;1;2)/.differential.t&gt;v1, (17) 
(i) the driver of the first vehicle 11 is advised to increase the 
separation distance d(t;1;2) between the first and second vehicles, or to 
decrease the velocity v(t;1) of the first vehicle; or (ii) the system 
automatically applies the brakes at the first vehicle to increase the 
actual separation distance d(t;1;2). If the difference .DELTA.(t;1;2) is 
negative and its time derivative does not satisfy Eq. (17), the system 
continues to monitor the relevant variables. 
In the unlikely event that the parameter p=+1, the solutions for velocity 
and linear displacement, analogous to Eqs. (2) and (4), become 
EQU v(t)=v0exp{-K(t-t0)}, (18) 
EQU x(t)=x0+(v0/K){1-exp{-K(t-t0)}}. (19) 
The minimum separation distance d(t;1;2;sep) becomes 
EQU d(t;1;2;sep)={v(t;1)-v(t;2)}(v(t;1)/K)+v(t;1).multidot..DELTA.t(percep;1),( 
20) 
by analogy with Eq. (15). 
The formalism developed in Eqs. (1)-(7) can also be used to estimate when 
the second vehicle is decelerating rapidly without the second vehicle's 
brake light indicating such deceleration. A change in velocity of the 
second vehicle may be estimated by the relation 
EQU .differential.v(t;2)/.differential.t=.differential..sup.2 
d(t;1;2)/.differential.t.sup.2 +.differential.v(t;1)/.differential.t,(21) 
where the first term on the left is computed using the system's measurement 
of the separation distance d(t;1;2) and the second term on the left is 
computed using velocity measurements made by the LD unit 13 attached to 
the first vehicle. If the relation 
EQU .differential.v(t;2)/.differential.t.ltoreq.-v2, (22) 
where v2(&gt;0) is a selected threshold acceleration value, such as 5 
meter/sec.sup.2, the system concludes that the second vehicle is 
decelerating rapidly, independent of whether the second vehicle brake 
lights appear. If Eq. (22) is satisfied, the system can either (i) advise 
the driver of the first vehicle that the second vehicle is now 
decelerating rapidly and allow the first vehicle driver to quickly respond 
or (ii) automatically apply the brakes of the first vehicle to reduce the 
velocity of the first vehicle toward zero, without waiting for the first 
vehicle driver to apply the brakes. 
The preceding formalism can also be used to estimate a maximum clear-view 
vehicle velocity v(t;D;max) that is consistent with stopping a vehicle 
within a selected clear-view stopping distance D, which may be a 
vehicle-to-vehicle separation distance or a representative visual distance 
where the vehicle is operated in heavy fog or under other inclement 
weather conditions that severely reduce visibility. Equation (13) may be 
re-expressed in the form 
EQU (v(t;1)).sup.2-p /K(2-p)+v(t;1).multidot..DELTA.t(percep;1)-D.ltoreq.0.(23) 
If the parameter p=0, corresponding to constant momentum loss during 
braking, Eq. (23) becomes a quadratic equation, 
EQU (v(t;1)).sup.2 /2K+v(t;1).multidot..DELTA.t(percep;1)-D.ltoreq.0,(24) 
which has a solution 
EQU v(t;1;max)=K{[.DELTA.t(percep;1).sup.2 +2D/K].sup.1/2 
.+-..DELTA.t(percep;1)}. (25) 
If the parameter p=-1, corresponding to constant loss of energy during 
braking, Eq. (23) becomes a cubic relation 
EQU (v(t;1)).sup.3 /3K+v(t;1).multidot..DELTA.t(percep;1)-D=0, (26) 
which has at least one real root and is solvable analytically. If the 
parameter p has some value other than p=0 or p=1, the maximum velocity 
v(t;1;max) may be estimated using a numerical equation solver that is 
incorporated in the software or hardware of the LD signal 
receiver/processor 15. A simple, and often sufficiently accurate, upper 
bound for the maximum vehicle clear-view velocity v(t;1;max) can be 
obtained by dropping either the first or the second term on the left in 
Eq. (23) to obtain 
EQU v(t;1;max).ltoreq.min{[(2-p).multidot.K.multidot.d].sup.-(2-p),D/.DELTA.t(p 
ercep;1)}. (27) 
FIG. 3 illustrates an alternative embodiment, in which a first range/range 
rate determination module or "ranging" module 81, preferably a SONAR or 
RADAR transceiver, is mounted on the first vehicle 11 to illuminate a 
preceding second vehicle 41 or other object located to the front of the 
first vehicle. A second ranging module 83 is mounted toward the right side 
on the first vehicle 11 to illuminate vehicles located to the right of the 
first vehicle, such as a third vehicle 43 traveling in an adjacent 
parallel traffic lane on the road 12 in the same or opposite direction as 
the first vehicle for illustrative purposes. A third ranging module 85 is 
mounted toward the left side of the first vehicle 11 to illuminate 
vehicles located to the left of the first vehicle, such as a fourth 
vehicle 45 that is approaching an intersection 49 along an intersecting 
road 50 that the first vehicle will also soon pass through. In this 
embodiment, the system preferably includes an electronically perceptible 
map showing all roads and lanes of roads in a region where the first 
vehicle 11 operates. The second ranging module 83 and/or the third ranging 
module 85 can optionally be deleted, but preferably both of these modules 
are included in the system, to provide information on vehicles to the 
right and to the left of the first vehicle 11. The first ranging module 81 
and/or the second ranging module 83 and/or the third ranging module 55 may 
be, but need not be, part of the LD module 13. 
The second ranging module 83 estimates the distance d(t;1;3), closure rate 
.differential.d(t;1;3)/.differential.t, bearing or observation angle 
.phi.(t;1;3) and bearing angle rate 
.differential..phi.(t;1;3)/.differential.t between the first vehicle 11 
and the third vehicle 43 ("V3") and determines two-dimensional location 
coordinates (.DELTA.x13(t),.DELTA.y13(t)) of the third vehicle 43, 
relative to the first vehicle 11 ("V1") and relative to the moving 
xy-coordinate frame shown in FIG. 3, using the relations 
EQU .DELTA.x13(t)=d(t;1;3) cos .phi.(t;1;3), (28) 
EQU .DELTA.y13(t)=d(t;1;3) sin .phi.(t;1;3), (29) 
EQU d(t;1;3)={.DELTA.x13(t).sup.2 +.DELTA.y13(t).sup.2 }.sup.1/2,(30) 
where the bearing angle .phi.(t;1;3) is measured positive in a 
counterclockwise direction. 
After the closure rate .differential.d(t;1;3)/.differential.t and the 
bearing angle rate .differential..phi.(t;1;3)/.differential.t are measured 
or otherwise determined, the rates of change of the relative coordinates 
are determined by the relations 
EQU .differential..DELTA.x13/.differential.t= cos 
.phi.(t;1;3).differential.d/.differential.t-d(t;1;3) sin 
.phi.(t;1;3).differential..phi./.differential.t, (31) 
EQU .differential..DELTA.y13/.differential.t= sin 
.phi.(t;1;3).differential.d/.differential.t+d(t;1;3) cos 
.phi.(t;1;3).differential..phi./.differential.t. (32) 
The time derivative .differential..DELTA.x13/.differential.t is examined, 
and the following standards are applied: 
EQU if .differential..DELTA.x13/.differential.t.ltoreq.-v(t;1),(33A) 
V3 is approaching V1 (moving in the opposite direction) or V3 is 
stationary; 
EQU if -v(t;1)&lt;.differential..DELTA.x13/.differential.t.ltoreq.0,(33B) 
V1 is overtaking V3 and moving in the same direction, if V3 is ahead of V1, 
and V3 is overtaking V1, if V1 is ahead of V3; 
EQU if .differential..DELTA.x13/.differential.t&gt;0 (33C) 
and V1 and V3 are moving in the same direction; V3 is moving faster, if V3 
is ahead of V1. The time derivative 
.differential..DELTA.y13/.differential.t is examined, and the following 
standards are applied: 
EQU if .differential..DELTA.y13/.differential.t&lt;-v.sub.y1, (34A) 
V3 is likely changing its traffic lane toward the V1 lane; 
EQU if -v.sub.y1 
.ltoreq..differential..DELTA.y13/.differential.t.ltoreq.v.sub.y2,(34B) 
V3 is likely not changing its traffic lane or is stationary; 
EQU if .differential..DELTA.y13/.differential.t&gt;v.sub.y2, (34C) 
V3 is likely changing its traffic lane away from the V1 lane. Small 
velocity thresholds v.sub.y1 and v.sub.y2, such as v.sub.y1 =0.2 
meter/sec.sup.2 and v.sub.y2 =0.3 meter/sec.sup.2, are used in the 
conditions (34A), (34B) and (34C) to compensate for a small amount of 
vehicle "wander" within a lane that occurs and to compensate for a small 
movement of the third vehicle V3 to the right or to the left as V3 
negotiates a right or left curve in the present V3 traffic lane. 
The first, second and third velocity ranges set forth in Eqs. (33A), (33B) 
and (33C) may be changed modestly to reflect the particular circumstances 
of the situation represented in FIG. 3 for the first and third vehicles. 
Similarly, the first, second and third velocity ranges set forth in Eqs. 
(34A), (34B) and (34C) may be changed modestly to reflect the particular 
circumstances of the situation represented in FIG. 3 for the first and 
third vehicles. It is preferable that the first, second and third velocity 
ranges chosen for the variable .differential..DELTA.x13/.differential.t be 
substantially non-overlapping, in order to avoid ambiguity in assignment 
of this variable to precisely one of these ranges; and that the first, 
second and third velocity ranges chosen for the variable 
.differential..DELTA.y13/.differential.t be substantially non-overlapping, 
in order to avoid ambiguity in assignment of this variable to precisely 
one of these ranges. 
The driver of the first vehicle 11 should be specially concerned if 
condition (34A) is present, indicating that the third vehicle 43 may be 
moving toward, or changing into, the first vehicle's lane. The driver of 
the first vehicle 11 would also be specially concerned if condition (33B) 
is satisfied and the time derivative 
.differential..DELTA.x13/.differential.t is rapidly decreasing toward the 
value -v(t;1), indicating that the third vehicle 43 is rapidly 
decelerating, possibly to avoid an obstruction 14 or collision in the V3 
traffic lane; the third vehicle 43 may abruptly move into the V1 traffic 
lane to avoid the obstruction 14 or collision. If 
.differential..DELTA.x13/.differential.t .apprxeq.-v(t;1), a subset of 
condition (33A), and condition (34B) is also present, it is likely that 
the third vehicle 43 or other object illuminated by the second RRD module 
83 is stationary. 
The second ranging module 83 can also be used to provide a "window" for the 
driver of the first vehicle 11 into a blind spot, such as a space to the 
right or and behind the first vehicle, where another vehicle V3' may be 
traveling. in the same direction as the first vehicle. For the vehicle 
V3', if the condition (33B) is satisfied, the vehicle V3' is overtaking 
the first vehicle 11 from the rear, but in a lane adjacent to the first 
vehicle traffic lane. In this instance, the driver of the first vehicle 11 
should be advised, visually or audibly, that another vehicle is traveling 
in an adjacent lane and may be hidden from the first vehicle driver's 
present view. 
The third ranging module 85 estimates the distance d(t;1;4), closure rate 
.differential.d(t;1;4)/.differential.t, bearing angle .phi.(t;1;4) and 
bearing angle rate .differential..phi.(t;1;4)/.differential.t between the 
first vehicle 11 and an object 45 and determines two-dimensional location 
coordinates (.DELTA.x14(t),.DELTA.y14(t)) of the fourth vehicle 45, 
relative to the first vehicle 11 (V1) and relative to the moving 
xy-coordinate frame shown in FIG. 3, using the relations 
EQU .DELTA.x14(t)=d(t;1;4) cos .phi.(t;1;4), (35) 
EQU .DELTA.y14(t)=d(t;1;4) sin .phi.(t;1;4), (36) 
EQU d(t;1;4)={.DELTA.x14(t).sup.2 +.DELTA.y14(t).sup.2 }.sup.1/2,(37) 
where the bearing angle .phi.(t;1;4) is measured positive in a 
counterclockwise direction. The rates of change of the relative 
coordinates (.DELTA.x14,.DELTA.y14) are determined by the relations 
EQU .differential..DELTA.x14/.differential.t= cos 
.phi.(t;1;4).differential.d/.differential.t-d(t;1;4) sin 
.phi.(t;1;4).differential..phi./.differential.t, (38) 
EQU .differential..DELTA.y14/.differential.t= sin 
.phi.(t;1;4).differential.d/.differential.t+d(t;1;4) cos 
.phi.(t;1;4).differential..phi./.differential.t. (39) 
The system refers to its electronic map whenever another vehicle or other 
object 45 is determined to be present by a ranging module. Here, the 
system recognizes the presence of an object 45 that is located on or near 
a road 50 that intersects the road 12 traveled by the first vehicle 11 at 
an intersection 49 at an angle .PHI.. If the object 45 is a moving 
vehicle, the measured or computed rates of change of the relative 
coordinates, become 
EQU .differential..DELTA.x14/.differential.t=v(t;4) cos 
.PSI.(t;1;4)-v(t;1),(40) 
EQU .differential..DELTA.y14/.differential.t=v(t;4) sin .PSI.(t;1;4),(41) 
where the velocity v(t;4) and the heading angle .PSI.(t;1;4) of the object 
45 relative to the first vehicle 11 are not yet known. The system 
estimates the fourth vehicle velocity v(t;4) by computing the quantity 
EQU {(.differential..DELTA.x14/.differential.t+v(t;1)).sup.2 
+(.differential..DELTA.y14/.differential.t).sup.2 }.sup.1/2 
=v(t;4).sup.2,(42) 
and computes the heading angle .PSI.(t;1;4) by computing the quantity 
EQU {.differential..DELTA.y14/.differential.t}/{.differential..DELTA.x14/.diffe 
rential.t+v(t;1)}.apprxeq. tan .PSI.(t;1;4). (43) 
If the quantity v(t;4).sup.2 computed in Eq. (37) is substantially greater 
than zero, the system concludes that the object 45 is a moving vehicle V4 
and is not stationary. If the quantity tan .PSI.(t;1;4) computed in Eq. 
(42) is approximately equal to the known tangent value tan .PHI. for the 
intersecting road 50, the system concludes that the object 45 is likely a 
vehicle V4 traveling at a velocity of 
v(t;4)=.+-..vertline.v(t;4).vertline. along the intersecting road 50, away 
from or toward the intersection 49, where the plus sign (+) or the minus 
sign (-) is chosen according as 
EQU .differential..DELTA.y14/.differential.t&gt;0 (plus sign: away from)(44A) 
or 
EQU .differential..DELTA.y14/.differential.t&lt;0 (minus sign: toward).(44B) 
Where the quantity v(t;4).sup.2 computed in Eq. (34) is substantially zero, 
the system concludes that the object 45 is likely stationary and ignores 
its presence. Where the tangent value tan .PSI.(t;1;4) computed in Eq. 
(43) does not satisfy 
EQU tan .PSI.(t;1;3).apprxeq. tan .phi., (45) 
the system concludes that the fourth vehicle 45 is not moving on the 
(nearest) intersecting road 50; the system may or may not ignore the 
fourth vehicle 45 in this situation. 
If v(t;4).sup.2 is substantially greater than zero and Eq. (45) is 
satisfied, the system estimates v(t;4), using Eqs. (42), (44A) and (44B). 
Only situations where v(t;4)&lt;0 are of interest here. The system then 
estimates the distances, D(t;1;49) and D(t;4;49), between the first 
vehicle 11 and the intersection 49 and between the fourth vehicle 45 and 
the intersection 49, respectively. The system also estimates the total 
stopping distances, d(t;v(t;1);stop) and d(t;v(t;4);stop), for the 
respective first and fourth vehicles, using Eq. (13) or some other 
suitable estimate. If the distance D(t;4;49) satisfies the inequality 
EQU D(t;4;49)-d(t;v(t;4);stop)&gt;0, (46) 
the system concludes that the fourth vehicle 45 still has time to slow down 
for, or stop at, the intersection 49, and the system continues to monitor 
the location and velocity of the fourth vehicle. If the distance D(t;4;49) 
satisfies the inequality 
EQU D(t;4;49)-d(t;v(t;4);stop).ltoreq.0, (47) 
the system concludes that the fourth vehicle does not have sufficient time 
to significantly slow down for, or stop at, the intersection 49. 
The system then optionally estimates the time interval length .DELTA.t1 
required for the first vehicle to reach and "clear" (pass through) the 
intersection 49, using a relation such as 
EQU .DELTA.t1=D(t;1;49)/v(t;1)+.DELTA.t(clear), (48) 
where .DELTA.t(clear) is a selected time interval length, such as 1-3 sec. 
The system also optionally estimates the time interval length .DELTA.t4 
required for the fourth vehicle 45 to reach the intersection 49, using a 
relation such as 
EQU .DELTA.t4=D(t;4;49)/.vertline.v(t;4).vertline.. (49) 
The system optionally computes .DELTA.t1-.DELTA.t4. If this quantity is 
negative, or if the preceding development of the time interval lengths 
.DELTA.t1 and .DELTA.t4 is not included in the logic, the system 
immediately either (1) advises the driver of the first vehicle 11 that the 
fourth vehicle cannot or will not stop at the intersection 49 so that this 
driver can quickly respond or (2) automatically applies the brakes of the 
first vehicle to attempt to stop the first vehicle before the first 
vehicle reaches the intersection 49. 
This last embodiment can also be applied to an intersection of a road 12 
with railroad tracks 50, where the vehicle 45 is a locomotive or other 
railroad car in a moving train. In this situation, it is prudent to assume 
that the locomotive 45 will not stop; and the central question becomes 
whether the first vehicle 11 can reach and "clear" the intersection before 
the locomotive 45 reaches this intersection. If the road-railroad track 
intersection 49 has an associated rail crossing control mechanism, such as 
one or more gates that descend and block the flow of automobile traffic 
when a train approaches, another question that must be answered is whether 
the first vehicle 11 can "clear" the intersection 49 before the rail 
crossing control mechanism is activated and blocks the flow of auto 
traffic. This sort of information is best built into the LD module 13 so 
that the LD module can (1) identify the location and the road-rail 
intersection, (2) call up details from its library to determine what is 
the safety time interval (in advance of arrival of the locomotive) used 
for activating the railroad crossing mechanism, and (3) determine if the 
first vehicle can "clear" this intersection before the railroad crossing 
control mechanism is activated. 
FIG. 4 is a flow chart of a suitable procedure for implementing the 
vehicle-to-vehicle separation distance embodiment of the invention, using 
only the observed velocity v(t;1) of the first vehicle, or using the 
observed velocities v(t;1) and v(t;2) of the first and second vehicles, 
for the situation shown in FIG. 1. A system to practice the first 
embodiment of the invention will provide either the Total Stopping 
Distance in column 4 of Table 1, or the Perception-Reaction Distance and 
the Braking Distance set forth in columns 2 and 3, as a function of 
vehicle velocity. The system will further: (1) estimate and monitor the 
velocity magnitudes v(t;1)=.vertline.v(t;1).vertline. and 
v(t;2)=.vertline.v(t;2).vertline. of the first vehicle 11 and (optionally) 
second vehicle 41 as functions of time t, step 91 in the flow chart shown 
in FIG. 4; (2) estimate and monitor the actual separation distance 
d(t;1;2) between the first vehicle and a second vehicle, if any is 
visible, that moves immediately ahead of the first vehicle on the road in 
the same lane and in the same direction, in step 92; (3) estimate a 
minimum separation distance d(t;1;2;sep) between the first and second 
vehicles, based on the velocity v(t;1) and, optionally, on the velocity 
v(t;2), using interpolations between entries in a table, such as Table 1, 
where necessary, in step 93; (4) compute a separation distance difference 
.DELTA.(t;1;2)=d(t;1;2;sep)-d(t;1;2), in step 94; (5) determine if 
.DELTA.(t;1;2).gtoreq.0, in step 95; (6) if .DELTA.(t;1;2).gtoreq.. . . 0, 
(i) advise the operator of the first vehicle that .DELTA.(t;1;2).gtoreq.0, 
or (ii) apply the first vehicle brakes, in step 96; (7) if 
.DELTA.(t;1;2)&lt;0, determine whether the rate of change with time, 
.differential..DELTA.(t;1;2), of .DELTA.(t;1;2) is positive and is greater 
than a first selected threshold rate v1, in step 97; (8) if the answer to 
the question in step 97 is "no," continue with step 91, or continue to 
step 101; (9) if the answer to the question in step 97 is "yes," (i) 
advise the operator of the first vehicle that .DELTA.(t;1;2) will soon 
become positive, or (ii) apply the first vehicle brakes, in step 98; (10) 
estimate the time derivative .differential.v(t;2)/.differential.t for the 
second vehicle, in step 101; (11) determine if the time derivative 
.differential.v(t;2)/.differential.t is less than a (negative) second 
selected threshold rate -v2, in step 102; (12) if the answer to the 
question in step 102 is "no," continue with step 91; (13) if the answer to 
the question in step 102 is "yes," (i) advise the first vehicle driver 
that the second vehicle is decelerating rapidly or (ii) apply the first 
vehicle brakes, in step 103. 
FIG. 5 is a flow chart of a suitable procedure for implementing the 
vehicle-to-vehicle separation distance embodiment of the invention, using 
the observed velocities v(t;1) and v(t;3) of the first vehicle (V1) and 
third vehicle (V3), for the situation shown in FIG. 3. In this embodiment: 
(1) the system estimates and monitors the first vehicle-third vehicle 
closure rate components .differential..DELTA.x13/.differential.t and 
.differential..DELTA.y13/.differential.t (Eqs. (31) and (32)), in step 
111; (2) the system determines, in steps 113, 115 and 117, whether the 
first component .differential..DELTA.x13/.differential.t lies in a first 
x-range, in a second x-range or in a third x-range, as set forth in Eqs. 
(33A), (33B) and (33C), respectively; (3) if 
.differential..DELTA.x13/.differential.t lies in the first x-range, the 
system optionally advises the driver (of the first vehicle 11) that the 
third vehicle is approaching V1 from the opposite direction or is 
stationary, in step 119; (4) if .differential..DELTA.x13/.differential.t 
lies in the second x-range, the system, in step 121, optionally advises 
the driver that the first vehicle is overtaking the third vehicle from 
behind and moving in the same direction, if the third vehicle is ahead of 
the first vehicle, or that the third vehicle is overtaking the first 
vehicle from behind, if the first vehicle is ahead of the third vehicle; 
(5) if .differential..DELTA.x13/.differential.t lies in the third x-range, 
the system, in step 123, optionally advises the driver that the third 
vehicle is ahead of and is moving faster than the first vehicle, or the 
first vehicle is ahead of and moving faster than the third vehicle; the 
system then continues, from step 119 or 121 or 123, to step 125; (6) the 
system determines, in steps 125, 127 and 129, whether the second component 
.differential..DELTA.y13/.differential.t lies in a first y-range, in a 
second y-range or in a third y-range, as set forth in Eqs. (34A), (34B) 
and (34C), respectively; (7) if .differential..DELTA.y13/.differential.t 
lies the first y-range, the system optionally advises the driver that the 
third vehicle is likely changing its traffic lane and moving toward the 
first vehicle traffic lane, in step 131; (8) if 
.differential..DELTA.y13/.differential.t lies in the second y-range, the 
system optionally advises the driver that the third vehicle is likely not 
changing its traffic lane, in step 133; and (9) if 
.differential..DELTA.y13/.differential.t lies in the third y-range, the 
system optionally advises the driver that the third vehicle is likely 
changing its traffic lane away from the first vehicle traffic lane, in 
step 135; the system then returns to step 111 or some other suitable 
return step, from step 131 or 133 or 135. 
Because the first, second and third x-ranges are exhaustive and mutually 
exclusive, one of the steps 113, 115 and 117 may be deleted. For example, 
if step 117 is eliminated, the system will pass directly from step 115 to 
step 123, if the answer to the question in step 115 is "yes." Because the 
first, second and third y-ranges are exhaustive and mutually exclusive, 
one of the steps 125, 127 and 129 may be deleted. For example, if step 129 
is eliminated, the system will pass directly from step 127 to step 135, if 
the answer to the question in step 127 is "yes." 
FIG. 6 is a flow chart of a suitable procedure for implementing the 
vehicle-to-vehicle separation distance embodiment of the invention, using 
the observed velocities v(t;1) and v(t;4) of the first vehicle (V1) and 
fourth vehicle (V4), for the situation shown in FIG. 3. In this 
embodiment: (1) the system estimates and monitors the first vehicle-object 
closure rate components, .differential..DELTA.x14/.differential.t and 
.differential..DELTA.y14/.differential.t, the first vehicle velocity 
v(t;1) and the object velocity magnitude .vertline.v(t;4).vertline., in 
step 141; (2) the system estimates and monitors the object heading angle 
.PSI.(t;1;4), in step 143; (3) the system determines whether the object 
velocity magnitude .vertline.v(t;4).vertline. is approximately zero, in 
step 145; (4) if the answer to the question in step (3) is "yes," the 
system concludes that the object is approximately stationary, in step 147 
(optional), and the system returns to step 141; (5) if the answer to the 
question in step 145 is "no," the system determines whether the heading 
angle .PSI.(t;1;4) is approximately equal to the heading angle .PHI. for 
the intersecting road, in step 149; (6) if the answer to the question in 
step 145 is "no," the system concludes that the object 45 is not traveling 
on the intersecting road 50, in step 151 (optional), and the system 
returns to step 141; (7) if the answer to the question in step 149 is 
"yes," the system estimates and monitors the velocity v(t;4) of the moving 
object or fourth vehicle, in step 153; (8) in step 155, the system 
estimates and monitors the distances D(t;1;49) and D(t;4;49) of the first 
and fourth vehicles from the intersection 49; (9) in step 157, the system 
estimates and monitors the fourth vehicle stopping distance 
d(t;v(t;4);stop); (10) in step 159, the system determines whether 
d(t;v(t;4);stop)-D(t;4;49)&gt;0; (11) if the answer to the question in step 
159 is "yes," the system returns to step 153 or to step 141; (12) if the 
answer to the question in step 159 is "no," the system optionally 
determines, in step 161, whether the first vehicle can reach and "clear" 
the intersection before the fourth vehicle arrives at the intersection; 
(13) if the answer to the question in step 161 is "yes," the system 
advises the driver (of the first vehicle) to continue through the 
intersection at present velocity, in step 163, and returns to either step 
153 or to step 141; this assumes, of course, that the first vehicle is not 
required to stop at a stop sign or traffic control light at the 
intersection; (14) if the answer to the question in step 161 is "no," the 
system either (i) advises the driver that the fourth vehicle cannot or 
will not stop at the intersection, or (ii) automatically applies the 
brakes to the first vehicle to bring this vehicle to a stop at or before 
this vehicle reaches the intersection; the system then optionally returns 
to step 141. 
The system may also take account of the weather conditions and road 
conditions in which a vehicle operates. The preceding discussion will 
apply to a road that is dry or damp but may need to be modified for a road 
that is wet or is covered with snow or ice. For a road that is wet, snowy 
or icy, Eq. (1) may need to be modified, by adding a fraction f of the dry 
road stopping distance to the total distance required to bring the vehicle 
to a stop. For a snowy or icy road, this fraction f may be larger than 1 
so that the stopping distance for such road conditions is more than twice 
the stopping distance for a dry road. If the fraction f can be measured or 
estimated, the stopping distance can be increased by the fraction f by 
reducing the coefficient K(dry road) in Eq. (1), for example, by replacing 
this coefficient by the coefficient 
EQU K(non-dry)=K(dry)/(1+f). (45) 
Use of a coefficient K(non-dry), as in Eq. (45), will increase the stopping 
distance of each of two consecutive vehicles and will increase the minimum 
stopping distance between the two vehicles. If the stopping distance for a 
wet, snowy or icy road cannot be modeled using a fractional increase 
relative to the dry road stopping distance, the non-dry stopping distance 
may need to be measured for different conditions and incorporated in an 
on-vehicle table. 
Local road conditions can be estimated by an optical, infrared or other 
road condition sensor 171, mounted on a front or rear or side portion of 
the vehicle 11, that examines a small adjacent portion 12P of the road 
along which the vehicle passes, as illustrated in FIG. 7. Optionally, the 
sensor 171 can measure reflected light provided by a light source that 
uses an automatic light-sensing aperture, such as is now used on 
auto-exposure cameras available from Canon, Minolta, Pentax, Olympus and 
others. 
The sensor 171 estimates the condition of the road portion 12P (which 
changes as the vehicle moves) and passes this information to the LD signal 
receiver/processor 15 for determination of minimum vehicle stopping 
distance or maximum vehicle clear-view velocity according to the preceding 
developments. If the sensor 171 uses a reflected light value RL, the 
sensor may determine whether the road is dry/damp, wet, snowy or icy, 
using the following algorithm, which is graphically illustrated in FIG. 8 
for various road conditions. Note that RL is (usually) much higher for a 
snow-covered road than for other road conditions. 
______________________________________ 
if 0 &lt; RL &lt; RL(1), 
road is dry/damp; 
(46A) 
if RL(1) &lt; RL &lt; RL(2), 
road is probably wet; 
(46B) 
if RL(2) &lt; RL &lt; RL(3), 
road is probably icy; 
(46C) 
if RL &gt; RL(4), road is snow-covered; 
(46D) 
______________________________________ 
where the parameters RL(j) (j=1, 2, 3, 4) are selected numerical values 
that have been determined empirically for the type of road on which the 
vehicle now moves. The LD signal receiver/processor 15 can receive and 
analyze the road condition information from the sensor and apply the 
appropriate value of the parameter K(dry) or K(non-dry) within a few 
milliseconds, before the vehicle has traveled more than, say, 30 cm along 
the road. Thus the vehicle 11 receives and acts upon real time information 
concerning local road conditions in determining the minimum 
vehicle-to-vehicle separation distance or the maximum vehicle velocity. 
Alternatively, a vehicle driver or passenger can enter the local road 
conditions manually into the LD module 13, for use in determining the 
appropriate value for the parameter K. 
Preferably, the sensor 171 is adaptively trained on roads with differing 
conditions so that, after training, the sensor can reliably distinguish a 
dry or damp road, a wet road, an ice-covered road and a snow-covered road. 
Preferably, the sensor 171 is trained on various road surfaces, where the 
reflected light parameter RL may differ from one road to another for the 
same road conditions (for example, dry road versus dry road). 
Distinguishing between a wet road and an icy road for a given road segment 
may not be necessary if the coefficients K(non-dry) discussed above are 
quantitatively similar for these two conditions, or if a vehicle stopping 
is qualitatively similar for these two conditions. 
FIG. 9 illustrates, in more detail, apparatus 181 suitable for monitoring 
road conditions. A light source 183 produces ultraviolet, visible and/or 
infrared light or other suitable electromagnetic radiation, and a lens 
system 185 (optional) captures and directs a beam 187 of this light toward 
a portion 12P of a road 12 adjacent to a moving vehicle on which the 
apparatus 181 is carried. Preferably, the light beam 187 is not directed 
perpendicularly at the road portion 12P but is directed at a selected 
incidence angle .theta. that is substantially greater than 0.degree. and 
is substantially less than 90.degree.. The beam 187 of light is specularly 
and diffusely reflected from the road portion 12P, and part or all of the 
reflected light beam 187R is received by a light sensor 171 and used to 
estimate the condition of the road portion 12P illuminated by the light 
beam. The intensity of the reflected light beam 187R received by the 
sensor 171, or other relevant information obtained from receipt of the 
light beam, is delivered to, and processed by, the LD module 13 to 
estimate the local road conditions, as indicated by the response of the 
road portion 12P. For example, the intensity I(rcv) of the reflected light 
beam 187R can be divided by a reference light beam intensity I(ref) to 
form a ratio 
EQU r(rcv)=I(rcv)/I(ref), (47) 
and the ratio r(rcv) can be used as the reflected light value RL to 
estimate the road conditions as in Eqs. (46A)-(46D). Alternatively, an 
intensity difference 
EQU d(rcv)=I(ref)-I(rcv) (48) 
can be formed and used as the reflected light value RL to estimate the road 
conditions as in Eqs. (46A)-(46D). 
If heavy fog or another visibility-reducing atmosphere is present, the 
light sensor 171 may sense a sharply reduced intensity of the reflected 
light beam 187R, or perhaps no light intensity at all. The light sensor 
and the LD module are arranged to recognize the presence of this situation 
and (optionally) to estimate and display a maximum clear-view vehicle 
velocity for the vehicle under these conditions, as discussed in the 
preceding. The ratio r(rcv), defined in Eq. (47), or the difference 
d(rcv), defined in Eq. (48), can be used to estimate light-absorbing 
characteristics of the ambient atmosphere and/or the maximum distance of 
visibility from the vehicle. 
Presence of a visibility-reducing atmosphere should be distinguished from a 
situation in which the light beam source 183 and/or the light beam sensor 
171 are malfunctioning. Optionally, a selected small portion 187P of the 
light beam 187 is split off by a light beam splitter 191 and is delivered 
to a second light beam sensor 193 as unreflected light. Information 
gleaned from receipt of the selected portion 187P of the light beam is 
also delivered to the LD module 13 for processing. Preferably, the 
selected portion 187P of the light beam 187 is delivered to the second 
light sensor 193 through a tube (optionally evacuated) or other light beam 
delivery means 195 that does not permit entry therein of any 
visibility-reducing atmosphere that may be present outside the vehicle. 
Thus, presence of a visibility-reducing atmosphere does not interfere with 
receipt of the selected portion 187P of the light beam by the second 
sensor 193. 
If the second light beam sensor 193 does not register receipt of any light 
when this light beam monitoring sub-system 190 is activated, the system 
concludes that the light beam source 183 and/or the second light beam 
sensor 193 is malfunctioning. Optionally, the second light sensor 193 can 
coincide with the first light sensor 171, by allowing at most one of the 
reflected light beam 189 and the selected light beam portion 187P to be 
received at any time. For example, activation of this light beam 
monitoring sub-system may alternate with activation of the sub-system that 
receives and monitors the reflected light beam 187R. If the light beam 
monitoring sub-system 190 indicates that the light source 183 and the 
light sensor 193 (or 171) is operating properly, the LD module 13 treats 
the information it receives from the light sensor 171 as correct and acts 
accordingly. If the light beam monitoring sub-system 190 indicates that 
the light source 183 and/or the light sensor 193 (or 171) is not operating 
properly, optionally, the LD module can treat the information it receives 
from the light sensor 171 as possibly inaccurate and may process this 
information differently, or may ignore this information.