System for estimating vehicle body speed and road surface friction coefficient

A system for a wheeled vehicle includes sensors for determining wheel speed, wheel load and wheel longitudinal driving or braking force of each wheel, and an estimating or controlling unit for estimating a vehicle body speed and/or a road surface friction coefficient from sensor output signals. The estimating unit determines a coordinate pair of a wheel speed value and a longitudinal force coefficient value for each wheel, and plots the coordinate pairs of the individual wheels as a set of points in a plane rectangular coordinate axis. The unit determines a regression line closely fit to the point set and obtains the estimates of the vehicle body speed and friction coefficient from the intercept of the regression line on the coordinate axis of the wheel speed and the slope of the regression line.

BACKGROUND OF THE INVENTION 
The present invention relates to a system and a process for estimating a 
vehicle body speed and/or a road surface friction coefficient of a wheeled 
vehicle. 
Estimation of vehicle body speed and road surface friction coefficient is 
required in a anti-skid brake control system (or wheel slip brake control 
system) for automatically controlling the braking force to prevent wheel 
locking on braking, a traction control system for preventing the spinning 
of drive wheels due to excess driving power and a vehicle directional 
behavior control system for reducing a deviation of an actual vehicle 
motion variable such as a vehicle yaw rate from a desired value by 
controlling the braking forces of left and right wheels individually. The 
following are some conventional examples for estimating the vehicle body 
speed or friction condition. Some are put to practical use. 
As to the estimation of the vehicle body speed, there are at least three 
conventional examples. 
The first conventional example is often used in a traction control system 
for a two wheel drive vehicle. The non-driving wheels of the two wheel 
drive vehicle are exempt from acceleration slip (or driving slip). 
Therefore, this conventional example regards the wheel speed of the 
non-driving wheels as the vehicle body speed during the traction control 
operation. 
The second conventional example is for an anti-skid brake control system. 
The system first eliminates a slip by temporarily removing the braking 
force of a specified wheel and then takes the wheel speed of the specified 
wheel as the vehicle body speed. 
The third conventional example is arranged to sense the longitudinal 
acceleration of the vehicle, and determine the vehicle body speed by 
integrating the sensed longitudinal acceleration. 
As to the estimation of the friction coefficient, there are known three 
conventional examples. 
The first conventional example is disclosed in Japanese Patent Provisional 
Publication No. 7-132787. This system applies a light braking force on a 
specified wheel to detect a relationship between the braking force and 
slip during the light braking, and estimates the road surface friction 
coefficient by predicting a variation characteristic of the friction 
coefficient with respect to the slip rate. 
The second conventional example is disclosed in Japanese Patent Provisional 
Publication No. 6-286630. This system is arranged to determine a 
relationship between the road surface friction coefficient and a certain 
sensed variable strongly correlated to the friction coefficient by 
learning with a neural network, and estimate the friction coefficient from 
the sensed variable during movement of the vehicle. 
The third conventional example is disclosed in Japanese Patent Provisional 
Publication No. 7-101258. This system is arranged to determine a driving 
torque difference between the left and right drive wheels from a 
differential limiting torque of a limited slip differential, and to 
estimate the road friction coefficient according to a predicted 
characteristic of the road surface friction coefficient with respect to 
the slip rate, predicted from the torque difference and a wheel speed 
difference between the left and right drive wheels. 
However, the first conventional vehicle body speed estimating technique is 
not applicable to a four wheel drive vehicle having no non-driving wheels. 
Moreover, this technique is unable to estimate the vehicle body speed 
during braking because the brakes are applied to all the wheels and none 
of the wheel speeds represents the vehicle body speed. 
In the second conventional body speed estimating technique, the removal of 
the braking force to the specified wheel tend to incur undesired hunting 
and make the estimate of vehicle body speed unstable. As a result, the 
anti-skid control based on the estimate is less stable, and the control 
accuracy is poorer. 
In the third conventional body speed estimating technique, a drift of the G 
sensor for sensing the vehicle longitudinal acceleration lowers the 
accuracy of the vehicle body speed estimation, and the road surface 
inclination exerts undesirable influence on the output of the G sensor. 
The first conventional friction estimating technique is unable to estimate 
the friction coefficient during brake application to all the wheels due to 
lack of ability of predicting a variation of the road friction coefficient 
with respect to the slip rate. 
The second conventional friction estimating technique requires a long time 
for the learning operation of the neural network and the design of the 
neural network architecture is not easy. 
The third conventional friction estimating technique is incompetent for 
estimation of the friction coefficient during braking, and hence the 
application is limited. This technique takes no account of load transfer 
during vehicle motion, and this affects the estimation accuracy. 
SUMMARY OF THE INVENTION 
It is therefore an object of the present invention to provide new 
estimating system and process of wider application and higher accuracy. 
According to the present invention, a system for estimating an unknown 
vehicle operating variable such as a vehicle body speed or a road surface 
friction parameter includes at least a sensor group and an estimating unit 
or controller. The sensor group is for sensing vehicle operating 
conditions required to determine values of a wheel speed, a wheel load and 
a wheel longitudinal driving or braking force of each of monitored wheels 
which are at least two of road wheels of the vehicle. The estimating unit 
or controller is for estimating the vehicle operating variable from the 
wheel speed, load and longitudinal force. 
This estimating system is applicable no matter whether 2WD or 4WD. This 
estimating system can always function properly whether the brake is 
applied or not. This system can improve the accuracy and stability in 
estimation and vehicle control by eliminating the need for temporal 
braking operation or temporal releasing operation. This system is 
advantageous in estimating speed and structure as compared to the neural 
network technique.

DETAILED DESCRIPTION OF THE INVENTION 
FIG. 1 shows a vehicle operating variable estimating system according to 
one embodiment of the present invention. In this embodiment, the 
estimating system is incorporated in a brake control system for a vehicle. 
A vehicle shown in FIG. 1 comprises a set of road wheels, a power or drive 
system, a brake system and a suspension system. 
The wheel set of this example includes left and right front wheels 1 and 2 
and left and right rear wheels 3 and 4. 
The power system of the vehicle includes at least an engine 5, an automatic 
transmission 6 and a differential 7 of a type having no differential 
limiting function. Power from the engine 5 is transmitted through the 
transmission 6 and the differential 7 to the rear wheels 3 and 4. In this 
example, the rear wheels 3 and 4 are driving wheels, and the front wheels 
1 and 2 are non-driving wheels on a non-powered axle. 
The brake system of this example is a hydraulic brake system including four 
wheel cylinders 8.about.11 each provided for a unique one of the four road 
wheels 1.about.4. In accordance with a driver's pedal effort on a brake 
pedal 12, a brake master cylinder 13 displaces brake hydraulic fluid under 
pressure to a brake fluid pressure control actuator (or hydraulic 
modulator) 14. The brake fluid pressure control actuator 14 supplies a 
brake fluid pressure with or without pressure modulation to each wheel 
cylinder 8.about.11. In the example shown in FIG. 1, the brake fluid 
pressure control actuator 14 has four outlet ports respectively and 
individually connected to the four wheel cylinders 8.about.11. 
An engine speed sensor (or engine revolution sensor) 15 senses an engine 
speed Ne (in terms of the number of revolutions per unit time). A throttle 
position sensor 16 senses an engine throttle opening (degree) TVO. An 
engine controller 17 controls the engine 5 in accordance with engine and 
vehicle operating conditions sensed by a sensor group including the engine 
speed sensor 15 and the throttle position sensor 16. The vehicle of this 
example further includes a transmission controller 18 for controlling the 
automatic transmission 6 in accordance with various input information 
items. 
A brake controller 19 shown in FIG. 1 controls individual brake fluid 
pressures P1.about.P4 destined for the wheel cylinders 8.about.11 by 
controlling the brake fluid pressure control actuator 14. In addition, the 
brake controller 19 estimates an unknown vehicle operating variable such 
as a vehicle body speed Vx(now) and a road surface friction coefficient 
.mu. for a wheel slip brake control (or anti-skid brake control). In this 
example, the brake controller 19 can serve as an estimating unit, and the 
brake fluid pressure control actuator 14 can serve as a vehicle control 
actuator for controlling a behavior of the vehicle in response to a 
control signal of the brake controller 19. 
Brake fluid pressure sensors 20.about.23 sense the respective brake fluid 
pressures P.sub.1 .about.P.sub.4 supplied to the wheel cylinders 
8.about.11. In this example, the brake fluid pressure sensors 20.about.23 
serve as brake sensors for sensing individual braking conditions of the 
wheels 1.about.4. 
Wheel speed sensors 24.about.27 sense the wheel speeds VW.sub.1 
.about.VW.sub.4 of the respective wheels 1.about.4. 
Signals from these sensors 20.about.23 and 24.about.27 are inputted to the 
brake controller 19. The brake controller 19 further receives the signals 
indicative of the engine speed Ne and the throttle opening TVO from the 
engine controller 17, and a transmission condition signal indicative of a 
selected gear position g from the transmission controller 18. These 
components supply information on actual operating conditions of the 
vehicle's drive or power system inclusive of the engine 5, to the brake 
controller 19, and can serve as a drive system condition sensor. 
Lateral acceleration sensor 28, longitudinal acceleration sensor 29 and yaw 
rate sensor 30 are mounted at the center of gravity of the vehicle body, 
and arranged to sense lateral acceleration Y.sub.G, longitudinal 
acceleration X.sub.G and yaw rate (d/dt).phi. of the vehicle. The sensed 
vehicle motion variables Y.sub.G, X.sub.G and (d/dt).phi. are inputted to 
the brake controller 19. 
A steering angle sensor 31 senses a steering wheel angle .theta. and 
supplies the sensed angle .theta. to the brake controller 19. 
Suspension stroke sensors 32 sense suspension stroke quantities L.sub.1 
.about.L.sub.4 of the four wheels 1.about.4, and supplies the sensed 
stroke quantities L.sub.1 .about.L.sub.4 to the brake controller 19. These 
sensors 32 serve as suspension condition sensors for sensing individual 
suspension conditions (L.sub.1 .about.L.sub.4) of the four wheels 
1.about.4. 
In response to these input data items, the brake controller 19 performs a 
program of FIG. 2 for estimating the vehicle body speed Vx(now) and the 
road surface friction coefficient .mu., and further performs a wheel slip 
control procedure as mentioned later in accordance with the results of the 
estimation. 
The estimation of FIG. 2 is based on the following principle. 
As shown in FIG. 3A, the road friction coefficient .mu. (i.e., the wheel's 
longitudinal braking or driving force) varies in dependence on the wheel 
slip rate S as shown by a solid line on a high friction road surface, and 
as shown by a one dot chain line on a low friction surface. Despite a 
conspicuous difference in maximum .mu..sub.max, both characteristics have 
similar tendencies. 
This relationship holds valid in a braking region where S.gtoreq.-So as 
well as in an accelerating region where S.ltoreq.So, as known in the art. 
FIG. 3B shows a two dimensional rectangular coordinate system having a 
horizontal axis representing a wheel speed VW and a vertical axis 
representing a longitudinal (braking or driving) force F per unit wheel 
load. The data pair (or coordinate pair) of the wheel speed VW.sub.1 
.about.VW.sub.4 and the per-unit-load longitudinal force F.sub.1 
.about.F.sub.4 of each wheel 1.about.4 determines the position of a point 
in a plane defined by this coordinate system. In FIG. 3B, there are four 
of the points plotted by the four coordinate pairs of the four wheels 
1.about.4. In a region where the wheel slip rate S is equal to or smaller 
than a predetermined slip rate value So and the relationship between the 
friction coefficient and slip rate can be safely regarded as linear, these 
four points approximately collinear and lie on, or closely near, a 
straight line shown by a solid line in FIG. 3B. 
This straight line intersects the horizontal axis or wheel speed (VW) axis 
of the plane coordinate system at an intercept point. The intercept of the 
straight line on the horizontal axis represents a vehicle body speed Vx. 
On the other hand, the straight line is inclined, and the gradient of the 
straight line with respect to the horizontal wheel speed (VW) axis 
represents a driving stiffness k of the vehicle. The driving stiffness k 
corresponds to the gradient of the rise of the road surface friction 
coefficient .mu. with respect to the horizontal slip rate (S) axis of FIG. 
3A. 
Comparison between the solid line curve and two dot chain line curve in 
FIG. 3A shows that there exists a relationship between the driving 
stiffness k and the maximum road surface friction coefficient .mu..sub.max 
as shown in FIG. 4. The maximum road surface friction coefficient 
.mu..sub.max is a parameter indicating the absolute degree of difficulty 
of (or resistance against) slippage on a road surface. (Hereinafter, the 
maximum road surface friction coefficient .mu..sub.max is also called a 
friction coefficient .mu..) 
From the gradient or slope (i.e. the driving stiffness k) of the inclined 
straight line of FIG. 3B with respect to the wheel speed (VW) axis, it is 
possible to estimate the friction coefficient .mu. indicative of the 
absolute degree of friction (or difficulty of slippage). 
Therefore, the estimating system according to this embodiment first 
determines the coordinate pair of the wheel speed VW.sub.1 .about.VW.sub.4 
and per-unit-load longitudinal force F.sub.1 .about.F.sub.4 for each wheel 
which remains in the linearity region where the degree of slip is 
relatively small; then finds a straight line (or regression line) 
representative of points corresponding to the determined coordinate pairs 
in the plane coordinate system as shown in FIG. 3B; and finally estimates 
the vehicle body speed Vx and the road surface friction coefficient .mu. 
in the above-mentioned manner. 
The program of FIG. 2 shows a process for estimating the vehicle body speed 
Vx and the friction coefficient .mu.. The estimating system starts 
executing the estimating program at a start of the engine 5. The 
estimating system first performs a step I for initialization, and then 
repeats a cycle of process steps A.about.F. 
Step A 
The first process step A is a process or program section for calculating 
the individual wheel speeds of the four wheels 1.about.4. The wheel speed 
determining step A of this example evaluates the wheel speed of each wheel 
by the following first and second sub-steps or operations A1 and A2. 
A1. Reading of Sensed Wheel Speeds 
The brake controller (or estimating unit) 19 of the estimating system reads 
the sensed individual wheel speed values VW.sub.1 .about.VW.sub.4 supplied 
from the wheel speed sensors 24.about.27 for the four wheels 1.about.4. 
A2. Filtration of Sensed Wheel Speeds 
The brake controller 19 determines filtered wheel speed values VW.sub.f1 
.about.VW.sub.f4 by passing the sensed wheel speed values VW.sub.1 
.about.VW.sub.4 through a filter of first order lag to remove noise. The 
filtered wheel speed values VW.sub.fi are given by; 
EQU VW.sub.fi =[1/(1+Tw.multidot.s)]VW.sub.i (1) 
where i is any whole number from 1 to 4, Tw is a time constant of the first 
order lag, and s is a Laplace operator (or a complex variable used in the 
Laplace transform). 
Step B 
The estimating system computes the individual vertical wheel loads W.sub.1 
.about.W.sub.4 of the vehicle wheels 1.about.4 by the following four 
sub-steps B1.about.B4. 
B1. Reading of Sensed Lateral and Longitudinal Accelerations 
The brake controller 19 reads the sensed lateral acceleration Y.sub.G and 
the sensed longitudinal acceleration X.sub.G from the sensors 28 and 29. 
B2. Filtration of Sensed Lateral and Longitudinal Accelerations 
This sub-step includes filtering operations for determining filtered 
lateral and longitudinal accelerations Y.sub.Gf and X.sub.Gf by passing 
the sensed lateral and longitudinal accelerations Y.sub.G and X.sub.G, 
respectively, through filters of first order lag, designed to take 
consideration of a delay in load transfer due to suspension strokes. The 
filtered lateral and longitudinal accelerations Y.sub.Gf and X.sub.Gf are 
expressed as; 
EQU Y.sub.Gf =[1/(1+T.sub.Y .multidot.s)]Y.sub.G (2) 
EQU X.sub.Gf =[1/(1+T.sub.X .multidot.s)]X.sub.G (3) 
where T.sub.Y is a time constant of the first order lag for the lateral 
acceleration, T.sub.X is a time constant of the first order lag for the 
longitudinal acceleration, and s is the Laplace operator. 
B3. Calculation of Load Transfer Quantities 
This sub-step calculates load variations .DELTA.W.sub.1 
.about..DELTA.W.sub.4 from the filtered lateral acceleration Y.sub.Gf and 
the filtered longitudinal acceleration X.sub.Gf according to the following 
equations. 
EQU .DELTA.W.sub.1 =K.sub.x .multidot.X.sub.Gf -K.sub.YF .multidot.Y.sub.Gf(4) 
EQU .DELTA.W.sub.2 =K.sub.x .multidot.X.sub.Gf +K.sub.YF .multidot.Y.sub.Gf(5) 
EQU .DELTA.W.sub.3 =-K.sub.x .multidot.X.sub.Gf -K.sub.YR .multidot.Y.sub.Gf(6) 
EQU .DELTA.W.sub.4 =-K.sub.x .multidot.X.sub.Gf +K.sub.YR .multidot.Y.sub.Gf(7) 
where K.sub.x, K.sub.YF and K.sub.YR are constants determined by the wheel 
base, height of the center of gravity, tread and roll stiffness 
distribution of the vehicle. 
B4. Calculation of Individual Wheel Loads 
This sub-step is for determining the individual wheel loads W.sub.1 
.about.W.sub.4 of the four wheels 1.about.4 according to the following 
equations (8) by using initial wheel loads W0.sub.1 .about.W0.sub.4 
preliminarily stored in a memory section, and the individual load 
variations .DELTA.W.sub.1 .about..DELTA.W.sub.4. 
EQU W.sub.i =W0.sub.i +.DELTA.W.sub.i (8) 
where i is any whole number from 1 to 4. 
Step C 
The step C is a program section for determining the longitudinal driving or 
braking forces of the four wheels 1.about.4 by the following twelve 
sub-steps C1.about.C12. 
C1. Reading of Sensed Wheel Speeds 
The brake controller 19 reads the sensed individual wheel speeds VW.sub.1 
.about.VW.sub.4 from the wheel speed sensors 24.about.27 for the four 
wheels 1.about.4. 
C2. Calculation of Angular Speeds and Angular Accelerations of Wheels 
The second sub-step is to calculate the rotational angular speeds (or spin 
velocities) .omega..sub.1 .about..omega..sub.4, and angular accelerations 
(d/dt).omega..sub.1 .about.(d/dt).omega..sub.4 of the wheels 1.about.4 
according to the following equations by using the sensed individual wheel 
speeds VW.sub.1 .about.VW.sub.4 and a wheel rolling radius R. 
EQU .omega..sub.i =VW.sub.i /R (9) 
EQU (d/dt).omega..sub.i =s.multidot..omega..sub.i (10) 
where i is any whole number from 1 to 4, and s is the Laplace operator. 
C3. Reading of Engine Speed and Throttle Opening 
The brake controller 19 reads the engine speed Ne (rpm) sensed by the 
sensor 15, and the engine throttle opening (degree) TVO sensed by the 
sensor 16 via the engine controller 17. 
C4. Calculation of Engine Output Torque 
From the engine speed Ne and the throttle opening TVO obtained by the 
previous sub-step, the brake controller 19 determines an engine output 
torque Te according to a map which, in this example, corresponds to engine 
operating characteristics shown in FIG. 5. 
C5. Calculation of Transmission Ratio 
The brake controller 19 reads the gear position signal indicative of the 
selected gear position g of the automatic transmission 6 from the 
transmission controller 18, and determines the transmission ratio (or 
speed ratio) .lambda. in accordance with the gear position signal. 
C6. Calculation of Axle Driving Torque 
The brake controller 19 calculates an axle driving torque TD transmitted 
toward the driving wheels (i.e. the rear wheels 3 and 4 in this example) 
by multiplication of the engine output torque Te and the transmission 
ratio .lambda.. That is; T.sub.D =Te.multidot..lambda.. 
C7. Calculation of Individual Driving Torques 
The axle driving torque T.sub.D is divided by the differential 7 between 
the left and right driving wheels 3 and 4. The differential 7 of this 
example is a standard differential as distinguished from a limited slip 
differential. The differential 7 of the standard type equally divides the 
input driving torque T.sub.D between the left and right driving wheels 3 
and 4. The wheel driving torques T.sub.D3 and T.sub.D4 of the left and 
right driving wheels 3 and 4 are given by; T.sub.D3 =T.sub.D4 =T.sub.D /2. 
The drive system of this example does not transmit engine power to the 
front wheels 1 and 2. Therefore, the driving torques T.sub.D1 and T.sub.D2 
of the non-driving wheels 1 and 2 are given by; T.sub.D1 =T.sub.D2 =0. 
C8. Reading of Brake Fluid Pressures 
From the brake fluid pressure sensors 20.about.23 provided, respectively, 
in the brake hydraulic circuits for the wheels 1.about.4, the brake 
controller 19 reads the sensed individual brake fluid pressures P.sub.1 
.about.P.sub.4 supplied to the wheel cylinders 8.about.11. 
C9. Calculation of Individual Braking Torques 
The brake controller 19 calculates the individual wheel braking torques 
T.sub.B1 .about.T.sub.B4 of the wheels 1.about.4 by multiplying each of 
the sensed brake pressures P.sub.1 .about.P.sub.4 by a corresponding one 
of constants K.sub.B1 .about.K.sub.B4 determined by design specification 
data items of the brake system. 
EQU T.sub.Bi =K.sub.Bi .multidot.P.sub.i (11) 
where i is any whole number from 1 to 4, and K.sub.Bi are constants each 
determined by brake pad material, a pad area, a rotor diameter and other 
items of a unique one of the wheels 1.about.4. 
C10. Calculation of Individual Wheel Torques 
The brake controller 19 calculates individual wheel torques T.sub.1 
.about.T.sub.4 of the wheels 1.about.4 by subtracting the braking torque 
T.sub.B1 .about.T.sub.B4 from the driving torque T.sub.D1 .about.T.sub.D4 
for each wheel. 
EQU T.sub.i =T.sub.Di -T.sub.Bi (12) 
where i is any whole number from 1 to 4. 
C11. Calculation of Individual Longitudinal Forces 
From the calculated individual wheel torques T.sub.1 .about.T.sub.4, and 
individual angular accelerations (d/dt).omega..sub.1 
.about.(d/dt).omega..sub.4, the brake controller 19 calculates the 
individual longitudinal (driving or braking) forces F.sub.1 .about.F.sub.4 
of the wheels 1.about.4 by using an equation of wheel rotational motion. 
That is; 
EQU F.sub.i =[T.sub.i -I.multidot.(d/dt).omega..sub.i ]/R (13) 
where i is any whole number from 1 to 4, I is the moment of inertia of each 
wheel, and R is the rolling radius of the wheels. 
C12. Filtration of Individual Longitudinal Forces 
This sub-step is for reducing noises by filtering the calculated individual 
longitudinal forces F.sub.1 .about.F.sub.4 with a first order lag filter 
approximately similar in effect to the filter of the second sub-step A2 of 
the step A. The resulting filtered individual longitudinal forces F.sub.f1 
.about.F.sub.f4 are; 
EQU F.sub.fi =[1/(1+T.sub.F .multidot.s)]F.sub.i (14) 
where i is any whole number from 1 to 4, T.sub.F is a time constant of the 
first order lag, and s is the Laplace operator. 
Step D 
The step D is a section for determining a per-unit-wheel-load longitudinal 
force (or longitudinal force coefficient) of each wheel 1.about.4 by the 
following three sub-steps D1, D2 and D3. 
D1. Retrieval of Wheel Load Dependent Nonlinearity Compensation Coefficient 
The actual wheel longitudinal force F increases monotonically as the wheel 
load increases. However, the relationship deviates from an exact 
proportionality as shown by a solid line in FIG. 6. Therefore, this 
estimating system employs a nonlinearity compensation coefficient f.sub.w 
to compensate for the deviation from an ideal linearity shown by a broken 
line in FIG. 6. 
FIG. 7 shows a characteristic of the nonlinearity compensation coefficient 
f.sub.w with respect to the wheel load (W) in this example. The 
characteristic is preliminarily stored in the memory section. In 
accordance with a map corresponding to this characteristic, the brake 
controller 19 retrieves a value of the nonlinearity compensation 
coefficient f.sub.w1 .about.f.sub.w4 corresponding to the wheel load 
W.sub.1 .about.W.sub.4 for each wheel 1.about.4. In the example shown in 
FIG. 7, the compensation coefficient fw is equal to or smaller than one 
and greater than zero, and not linear. The compensation coefficient 
f.sub.w decreases monotonically as the wheel load W increases. 
D2. Retrieval of Wheel Slip Dependent Nonlinearity Compensation Coefficient 
FIG. 8 shows, by a solid line, the longitudinal force F increasing 
monotonically with increase in the wheel slip rate S. This relationship is 
also deviant from the ideal proportionality. Therefore, the estimating 
system of this example figures in a nonlinearity compensation coefficient 
f.sub.s to compensate for the deviation from the ideal linearity shown by 
a broken line in FIG. 8. 
FIG. 9 shows a characteristic of the nonlinearity compensation coefficient 
f.sub.s with respect to the wheel slip (S) in this example. The 
characteristic is preliminarily stored in the memory section. In 
accordance with a map corresponding to this characteristic, the estimating 
system retrieves a value of the nonlinearity compensation coefficient 
f.sub.s1 .about.f.sub.s4 corresponding to a value of the wheel slip rate S 
for each wheel 1.about.4. 
In this example, the estimating system calculates the individual wheel slip 
rates S at the step F after the step D, and the wheel slip rates of the 
current cycle are undecided at the time of the step D. Therefore, the 
estimating system of this example retrieves values of the nonlinearity 
compensation coefficients f.sub.si by using the previous values S.sub.i 
(n-1) of the wheel slip rates obtained in the previous operating cycle. 
D3. Calculation of Per-Unit-Load Longitudinal Forces 
By using the values of the nonlinearity compensation coefficients f.sub.w1 
.about.f.sub.w4 and f.sub.s1 .about.f.sub.s4, the values of the individual 
wheel loads W.sub.1 .about.W.sub.4 obtained in the fourth sub-step B4 of 
the second step B, and the values of the filtered individual longitudinal 
forces F.sub.f1 .about.F.sub.f4, the brake controller 19 calculates the 
per-unit-wheel-load longitudinal force F.sub.w1 .about.F.sub.w4 for each 
wheel by: 
EQU F.sub.wi =F.sub.fi /(W.sub.i .multidot.f.sub.wi .multidot.f.sub.si)(15) 
where i is any whole number from 1 to 4. 
Step E 
This step is for estimating the vehicle body speed and the road surface 
friction coefficient by the following seven sub-steps E1.about.E7. 
E1. Reading of Filtered Wheel Speeds 
The brake controller 19 reads the filtered individual wheel speeds 
VW.sub.f1 .about.VW.sub.f4 determined by the second sub-step A2 of the 
first step A. 
E2. Reading of Sensed Steering Angle and Yaw Rate 
The brake controller 19 reads the vehicle yaw rate (d/dt).phi. sensed by 
the sensor 30, and the steering wheel angle .theta. sensed by the sensor 
31 shown in FIG. 1. 
E3. Calculation of Wheel Travel Speed Modification Quantities 
In a cornering operation of the vehicle, there arise differences among the 
wheels in wheel travel speed that is the wheel speed at zero wheel slip. 
For correction for these differences, the brake controller 19 calculates 
wheel travel speed modification quantities .DELTA.VI.sub.1 
.about..DELTA.VI.sub.4 from the sensed yaw rate (d/dt).phi., the sensed 
steering wheel angle .theta. and the sensed lateral acceleration Y.sub.G 
obtained by the sub-step B1, for example, by using functions f.sub.v1 
.about.f.sub.v4 which are determined, respectively, for the wheels 
1.about.4, by the wheel base, treads and position of the center of 
gravity. 
In this example, the brake controller 19 calculates the wheel travel speed 
modification quantities .DELTA.VI.sub.1 .about..DELTA.VI.sub.4 from the 
sensed yaw rate (d/dt).phi., the sensed steering wheel angle .theta. and 
the sensed lateral acceleration Y.sub.G and the sensed longitudinal 
acceleration X.sub.G obtained by the sub-step B1, by using the following 
equation: 
EQU .DELTA.VI.sub.1 =V.sub.L .multidot..theta..sub.F {.beta..sub.F 
-(.theta..sub.F /2)}-(T.sub.F /2)(d/dt).phi. (15A-1) 
EQU .DELTA.VI.sub.2 =V.sub.L .multidot..theta..sub.F {.beta..sub.F 
-(.theta..sub.F /2)}+(T.sub.F /2)(d/dt).phi. (15A-2) 
EQU .DELTA.VI.sub.3 =-(T.sub.R/ 2)(d/dt).phi. (15A-3) 
EQU .DELTA.VI.sub.4 =(T.sub.R /2)(d/dt).phi. (15A-4) 
In these equations, V.sub.L is a longitudinal speed of the vehicle, 
.beta..sub.F is a side slip angle of the vehicle body at the middle of the 
front axle, .theta..sub.F is a front wheel steer angle, T.sub.F is a front 
tread between the front wheels 1 and 2, and T.sub.R is a rear tread 
between the rear wheels 3 and 4. The longitudinal speed V.sub.L is 
determined from the longitudinal acceleration X.sub.G. The side slip angle 
.beta..sub.F is determined from the direction of motion of the vehicle 
determined from the lateral and longitudinal accelerations Y.sub.G and 
X.sub.G, and the direction determined from the steering wheel angle sensed 
by the steering angle sensor 31. 
E4. Calculation of Modified Wheel Speeds 
The brake controller 19 determines modified wheel speeds VW.sub.1 
'.about.VW.sub.4 ' by modifying the filtered wheel speeds VW.sub.f1 
.about.VW.sub.f4 by the modification quantities .DELTA.VI.sub.1 
.about..DELTA.VI.sub.4. That is; 
EQU VW.sub.i '=VW.sub.fi -.DELTA.VI.sub.i (16) 
where i is any one of 1.about.4. 
E5. Reading of Wheel Selecting Flags 
The brake controller 19 reads four wheel selecting flags FLAG.sub.1 
.about.FLAG.sub.4 for the wheels 1.about.4. In this example, the wheel 
selecting flags FLAG.sub.1 .about.FLAG.sub.4 are determined in the next 
step F. The estimating system of this example, therefore, uses the 
previous values of the wheel selecting flags FLAG.sub.1 .about.FLAG.sub.4 
determined in the previous operating cycle. 
E6. Estimation of Vehicle Body Speed and Road Surface Friction Coefficient 
The brake controller 19 checks each of the wheel selecting flag (or 
condition code) FLAG.sub.1 .about.FLAG.sub.4 of each wheel 1.about.4 to 
determine whether the flag is equal to 1 or not. Thus, the set of the 
wheels 1.about.4 is divided into a selected subset and an unselected 
subset. Each of the wheels 1.about.4 is an element of the selected subset 
if its selecting flag is one, and an element of the unselected subset if 
its flag is zero. The brake controller 19 forms a numerical data pair of 
the values of the modified wheel speed VW.sub.i ' and the per-unit-load 
longitudinal force F.sub.wi for each wheel of the selected subset. As 
shown in FIG. 10, the numerical data pair of each wheel of the selected 
subset is plotted as a point in the plane of the two dimensional 
coordinate system having the first (horizontal) coordinate axis 
representing the first variable and the second (vertical) coordinate axis 
representing the second variable. In this example, the first variable is 
the modified wheel speed VW', and the horizontal axis has calibrations for 
measuring the modified wheel speed VW'. The second variable is the 
per-unit-load longitudinal force Fw, and the second (vertical) coordinate 
axis has calibrations for the per-unit-load longitudinal force Fw. 
Then, the estimating system finds a straight or curved regression line (or 
regression curve) representing the points plotted in the coordinate 
system. In the example of FIG. 10, the regression function is linear, and 
the regression line is a straight line. 
As mentioned before with reference to FIG. 3, the wheel speed value at the 
intercept point at which the linear regression line intersects the 
horizontal axis represents the vehicle body speed Vx. The inclination 
angle between the regression line and the horizontal axis (determined by 
the regression coefficient) represents the vehicle's driving stiffness k 
from which the estimating system can estimate the road surface friction 
coefficient .mu. as shown in FIG. 4. From these parameters of the 
regression function, the estimating system estimates the vehicle body 
speed Vx and the road surface friction coefficient .mu.. 
In this example, the estimating system determines the vehicle body speed Vx 
and driving stiffness k by using the known least squares method. The 
driving stiffness k and vehicle body speed Vx are expressed as; 
EQU k=[n.SIGMA.(VW.sub.i '.times.F.sub.wi)-.SIGMA.VW.sub.i 
'.times..SIGMA.F.sub.wi ]/[n.SIGMA.(VW.sub.i ').sup.2 -(.SIGMA.VW.sub.i 
').sup.2 ] (17) 
EQU Vx=[.SIGMA.VW.sub.i '.multidot..SIGMA.(VW.sub.i 
'.times.F.sub.wi)-.SIGMA.(VW.sub.i ').sup.2 .multidot..SIGMA.F.sub.wi 
]/[n.SIGMA.(VW.sub.i '.times.F.sub.wi)-.SIGMA.VW.sub.i 
'.times..SIGMA.F.sub.wi ] (18) 
In these equations, i is any one of 1.about.4. 
E7. Estimation Delay Correction of Vehicle Body Speed 
Each of the thus-calculated driving stiffness k and vehicle body speed Vx 
involves a delay of dead time caused by the operations for filtering the 
sensed wheel speeds and calculated longitudinal forces, so that there 
arises a slight shift between the result of the calculation and the actual 
current value. The estimating system of this example employs the driving 
stiffness k calculated by the equation (17) without modification because 
the driving stiffness k is not a rapidly changing variable and the dead 
time delay offers no practical problem. However, the estimating system 
corrects the calculated vehicle body speed Vx in the following manner. 
As shown in FIG. 11, the calculated vehicle body speed Vx(n) resulting from 
the calculation of the equation (18) is delayed with respect to a current 
vehicle body speed Vx(now) by a dead time delay td caused by the filtering 
operations. 
On the assumption that the time rate of change (d/dt)Vx(n) of the vehicle 
body speed is constant as shown by a broken line in FIG. 11, the 
estimating system of this example calculates the current vehicle body 
speed Vx(now) and the time rate of change (d/dt)Vx(n) of the vehicle body 
speed by the following equations; 
EQU Vx(now)=Vx(n)+td.multidot.(d/dt)Vx(n) (19) 
EQU (d/dt)Vx(n)=[(Vx(n)-Vx(n-1)]/ts (20) 
where ts is a sampling period. 
Step F 
The sixth process step F is a wheel selecting step to rule out the wheel 
speed data and per-unit-load longitudinal force data tending to aggravate 
the error in estimation of the vehicle body speed and road friction 
parameter. The step F includes the following three sub-steps F1, F2 and 
F3. 
F1. Calculation of Wheel Travel Speeds 
From the vehicle body speed Vx obtained by the seventh sub-step E7 of the 
step E and the wheel travel speed modification quantities .DELTA.VI.sub.1 
.about..DELTA.VI.sub.4 of the wheels 1.about.4 obtained by the third 
sub-step E3 of the step E, the brake controller 19 calculates the 
individual wheel travel speeds VI.sub.1 .about.VI.sub.4 by; 
EQU VI.sub.i =Vx+.DELTA.VI.sub.i (21) 
where i is any whole number from 1 to 4. 
F2. Calculation of Wheel Slip Rates 
From the sensed individual wheel speeds VW.sub.1 .about.VW.sub.4 obtained 
by the first sub-step A1 of the step A, and the individual wheel travel 
speeds VI.sub.1 .about.VI.sub.4 obtained by the preceding sub-step, the 
brake controller 19 calculates the individual wheel slip rates S.sub.1 
.about.S.sub.4 of the wheels 1.about.4 by; 
EQU S.sub.i =[(VW.sub.i -VI.sub.i)/VI.sub.i ].times.100% (22) 
where i is any whole number from 1 to 4. 
F3. Setting of Wheel Selecting Flags 
As mentioned before with reference to FIG. 3A, the road surface friction 
coefficient .mu. (the wheel longitudinal force) varies linearly with 
increase in the wheel slip rate S in the linear region where the slip rate 
S is equal to or lower than the predetermined level So. The estimation of 
the vehicle body speed and road surface friction parameter is accurate 
when the estimation is based on data on the operating conditions of the 
wheels which are in the linear region. 
To maintain the accuracy, the estimating system of this example excludes 
the data of each wheel by setting the wheel selecting flag to zero if the 
absolute value of the wheel slip rate S of the given wheel exceeds the 
preset level So. In this sub-step, the brake controller 19 sets the wheel 
selecting flag (or condition code) FLAG.sub.1 .about.FLAG.sub.4 of each 
wheel to one if the absolute value of the wheel slip rate S of that wheel 
is equal to or lower than the predetermined value So 
(.vertline.S.vertline..ltoreq.So). The wheel selecting flag FLAG.sub.1 
.about.FLAG.sub.4 of each wheel is set to zero if the absolute value of 
the wheel slip rate S of that wheel is greater than the predetermined 
value So (.vertline.S.vertline.&gt;So). 
The wheel selecting flags FLAG.sub.1 .about.FLAG.sub.4 are checked in the 
fifth sub-step E5 of the step E, and each of the wheels 1.about.4 is 
entered in either of the selected subset and the unselected subset. Each 
wheel cannot belong to both subsets simultaneously. Each of the selected 
and unselected subsets is the complement of the other in the wheel set. 
The estimating system estimates the vehicle body speed and friction 
parameter using the data of the selected subset and disregarding the data 
of the unselected subset. In the example shown in FIG. 10, the cardinal 
number of the selected subset is four and the unselected subset is empty. 
In the thus-constructed estimating system, the brake controller (or 
estimating unit) 19 selects the wheels not slipping excessively by 
checking the wheel selecting flags FLAG.sub.1 .about.FLAG.sub.4, and finds 
a straight line of regression best fit to a set of points determined by 
the data pair of the wheel speed VW.sub.i ' and the per-unit-load 
longitudinal force F.sub.wi of each of the selected wheels in the 
rectangular plane coordinate system as shown in FIG. 10. Then, the brake 
controller 19 determines the driving stiffness k and the vehicle body 
speed Vx from the slope and intercept of the straight line, and determines 
the absolute road surface friction coefficient .mu. from the driving 
stiffness by using the map corresponding to the characteristic shown in 
FIG. 4. 
By using the thus-estimated vehicle body speed Vx and road friction 
coefficient .mu., the brake controller 19 of this example performs the 
anti skid brake control of a known type by sending brake control signals 
indicative of desired brake fluid pressures for the individual wheels 
1.about.4 to the brake fluid control actuator 14. In response to the 
control signals, the brake fluid control actuator 14 controls the brake 
fluid pressures P1.about.P4 individually so as to reduce the deviation 
from the desired value. In this way, the brake control system can prevent 
the wheel locking during braking, and attain the highest braking 
efficiency. 
The estimation system according to the illustrated embodiment of the 
present invention can properly estimate the vehicle body speed and road 
surface friction coefficient at all times, irrespective of whether the 
vehicle is a two wheel drive type or a four wheel drive type, and 
irrespective of whether the brakes are being applied or not. 
The estimating system does require neither a temporary braking operation 
nor a temporary brake releasing operation for a specified wheel. 
Therefore, the result of the estimation is free from undesired hunting, 
the accuracy in the estimation is high and the anti skid brake control 
performance is improved. 
Moreover, the estimating system according to the embodiment of the present 
invention is advantageous in speed of estimation and structure of the 
system as compared with the estimating system of the neural network type. 
Without the need for a sensor susceptible to an undesired drift, the 
estimating system according to the embodiment is simple, uncostly and 
accurate. 
The selection of the wheels by checking the wheel slip rate can improve the 
accuracy of the estimation. With the slip level So set equal to the upper 
limit of the slip rate in the linear range for selecting the wheels, the 
estimating system can improve the accuracy of estimation by collecting all 
the appropriate data, and removing the inappropriate data of wheels 
slipping in the nonlinear region. 
The estimating system of this embodiment calculates the longitudinal 
driving or braking force in the eleventh sub-step C11 of the step C, from 
the wheel torque Ti and the wheel angular acceleration (d/dt).omega. 
according to the equation obtained by applying the Newton's second law to 
a rotational system of a wheel. Therefore, the system can avoid the 
complexity, difficulty and inaccuracy involved in the technique of 
directly sensing the wheel longitudinal force. 
The estimating system of this embodiment employs at least one drive or 
power system condition sensor, such the engine speed sensor 15, and the 
throttle position sensor 16, to determine the wheel driving torques 
T.sub.Di, and the brake condition sensors in the form of the brake 
pressure sensors 20.about.23 to determine the wheel braking torques 
T.sub.Bi. The estimating unit in the form of the brake controller 19 
determines the wheel torques T.sub.i by subtracting the braking torque 
from the driving torque. The brake controller 19 can readily determine the 
engine torque Te by using the map as shown in FIG. 5, the calculation of 
the transmission ratio .lambda. is easy, and the brake pressure sensors 
20.about.23 can readily sense the brake pressures. Therefore, the 
estimating system according to the illustrated embodiment can compute the 
wheel torques T.sub.i without difficulty and without increasing the cost. 
The use of the wheel load dependent nonlinearity compensating coefficient 
f.sub.w shown in FIG. 7 and/or the wheel slip dependent nonlinearity 
compensating coefficient f.sub.s shown in FIG. 9 can further improve the 
accuracy of estimation. 
The filtering operation for the sensed wheel speed in the sub-step A2 of 
the step A, and the filtering operation for the longitudinal force in the 
sub-step C12 can further improve the accuracy of estimation by removing 
noise. 
The estimation delay correction of the vehicle body speed in the sub-step 
E7 can improve the accuracy in estimating the vehicle body speed. 
In the present invention, it is possible to replace the step B by the 
following modified step B'. 
Step B' 
B'1 Calculation of Suspension Stroke Quantities and Suspension Stroke Speed 
The brake controller 19 reads the suspension stroke quantities L.sub.1 
.about.L.sub.4 sensed by the group of the suspension stroke sensors 32 of 
the individual wheels 1.about.4, and calculates the suspension stroke 
speeds (d/dt)L.sub.1 .about.(d/dt)L.sub.4 by; 
EQU (d/dt)L.sub.i =[(L.sub.i (n)-L.sub.i (n-1)]/ts (23) 
where L.sub.i (n) are current values of the sensed suspension stroke 
quantities, L.sub.i (n-1) are previous values of the sensed suspension 
quantities, ts is an operating cycle, and i is any whole number from 1 to 
4. 
B'2 Calculation of Spring Related Wheel Load Components 
From the individual suspension stroke quantities L.sub.1 .about.L.sub.4 of 
the wheels 1.about.4, the brake controller 19 determines individual spring 
related wheel load components W.sub.L1 .about.W.sub.L4 by information 
retrieval using the characteristic of the spring related wheel load 
component W.sub.L versus the suspension stroke quantity L as shown in FIG. 
12. 
B'3 Calculation of Shock Related Wheel Load Components 
From the individual suspension stroke speeds (d/dt)L.sub.1 
.about.(d/dt)L.sub.4 of the wheels 1.about.4, the brake controller 19 
determines individual shock (or damper) related wheel load components 
W.sub.S1 .about.W.sub.S4 by information retrieval using the characteristic 
of the shock related wheel load component Ws versus the suspension stroke 
speed (d/dt)L as shown in FIG. 13. 
B'4 Calculation of Wheel Loads 
The brake controller 19 determines the individual wheel loads W.sub.1 
.about.W.sub.4 of the wheels 1.about.4 by addition of each of the spring 
related load components W.sub.L1 .about.W.sub.L4 and a corresponding one 
of the shock related load components W.sub.S1 .about.W.sub.S4. 
By this step B', the estimating system according to the present invention 
can determine the individual wheel loads readily, uncostly and reliably 
while the vehicle is in motion. 
In the present invention, it is possible to replace the step D by the 
following modified step D'. 
Step D' 
As shown in FIG. 14A, the characteristic of the road surface friction 
coefficient .mu. with respect to the wheel slip rate S is influenced by 
the wheel side slip angle .beta.. The road surface friction coefficient 
.mu. (the longitudinal driving or braking force) decreases as the wheel 
side slip angle .beta. increases. The step D' is designed to compensate 
for this influence. 
D1. Retrieval of Wheel Load Dependent Nonlinearity Compensation Coefficient 
The first sub-step of the step D' is the same as the first sub-step D1 of 
the step D. 
D2. Retrieval of Wheel Slip Dependent Nonlinearity Compensation Coefficient 
The second sub-step of the step D' is the same as the second sub-step D2 of 
the step D. 
D'2a Retrieval of Side Slip Dependent Compensation Coefficient 
The estimating system of this example employs a predetermined side slip 
dependent compensating coefficient f.sub.B shown in FIG. 14B for 
compensating for the influence of the wheel side slip angle .beta. on the 
wheel longitudinal driving or braking force. The side slip dependent 
compensating coefficient f.sub.B is a function of the wheel side slip 
angle .beta.. This function is preliminarily determined by the 
characteristics of tires of the wheels. 
The individual wheel side slip angles .beta..sub.1 .about..beta..sub.4 of 
the wheels 1.about.4 are determined from the vehicle body speed Vx (the 
previous value of Vx), the lateral acceleration Y.sub.G, the yaw rate 
(d/dt).phi. and the steering wheel angle .theta.. From the individual 
wheel side slip angles .beta..sub.1 .about..beta..sub.4, the brake 
controller 19 determines individual side slip dependent compensating 
coefficients f.sub.B1 .about.f.sub.B4, respectively, corresponding to the 
wheel side slip angles .beta..sub.1 .about..beta..sub.4 by information 
retrieval using the map corresponding to the characteristic of FIG. 14B. 
As shown in FIG. 14B, the side slip dependent coefficient f.sub.B 
decreases from 1 toward zero as the wheel side slip angle .beta. 
increases. 
D'3. Calculation of Per-Unit-Load Longitudinal Forces 
By using the values of the compensation coefficients f.sub.W1 
.about.f.sub.W4, f.sub.S1 .about.f.sub.S4 and f.sub.B1 .about.f.sub.B4, 
the values of the individual wheel loads W.sub.1 .about.W.sub.4 obtained 
in the fourth sub-step B4 of the second step B (or the sub-step B'4 of the 
step B'), and the filtered individual longitudinal forces F.sub.f1 
.about.F.sub.f4, the brake controller 19 calculates the 
per-unit-wheel-load longitudinal forces F.sub.w1 .about.F.sub.w4 for the 
wheels by: 
EQU F.sub.wi =F.sub.fi /(W.sub.i .multidot.f.sub.Wi .multidot.f.sub.Si 
.multidot.f.sub.Bi) (24) 
where i is any whole number from 1 to 4. 
The use of the side slip dependent compensating coefficients further 
improves the accuracy of estimation by reducing the error caused by the 
influence of the side slip angle. 
In the illustrated example, each of the engine controller 17, transmission 
controller 18 and brake controller 19 comprises an onboard computer.