# Patent

## Title
Method for determining a longitudinal vehicle velocity by compensating individual wheel speeds

## Abstract

A control system (24) for controlling a safety system (40) of an automotive vehicle includes a plurality of wheel speed sensors (30) generating a plurality of wheel velocity signals, a steering angle sensor (39) generating a steering actuator angle signal, a yaw rate sensor (28) generating a yaw rate signal, a lateral acceleration sensor (32) generating a lateral acceleration signal and a controller (26). The controller (26) generates a final reference vehicle velocity in response to the plurality of wheel speed signals, the steering angle signal, the yaw rate signal and the lateral acceleration signal. The controller (26) controls the safety system in response to the final reference vehicle velocity.

## Background
CROSS REFERENCE TO RELATED APPLICATIONS
The present invention claims priority to provisional application No. 60/450,248, filed on Feb. 26, 2003, filed simultaneously herewith, the disclosure of which is incorporated by reference.


BACKGROUND OF INVENTION
The present invention relates generally to dynamic control systems for automotive vehicles and, more specifically to a system that compensates wheel speed sensor signals to determine a vehicle reference velocity.
It is a well-known practice to control various operating dynamics of a motor vehicle to achieve active safety. Examples of active safety systems include traction control, yaw stability control and roll stability control systems. A more recent development has been to combine all the available subsystems to achieve better vehicle safety and dynamics performance. The effective operation of the various control systems requires high-accuracy and fast-response-times in the determination of the operating states of the vehicle, regardless of road conditions and driving conditions. Such vehicle operating states include the vehicle longitudinal, lateral and vertical velocities measured along the body-fixed longitudinal, lateral and vertical axes, the attitude of the vehicle body, and the travel course of the vehicle.
One piece of basic information that forms the afore-mentioned vehicle state estimation is the linear velocity of the rotating centers of the four wheels. For example, this information can be used to assess the wheel slip used in anti-brake-lock controls and traction controls and to estimate the longitudinal velocity of the vehicle. In order to obtain the linear corner velocities, the wheel speed sensors are used. The wheel speed sensors output the products of the wheel rotational speeds and the rolling radii. The wheel rotational speeds are directly measured and the rolling radii are assumed their nominal values. During dynamic maneuvers, the variations of the wheel normal loading will affect the rolling radii. Hence, the nominal rolling radii may not reflect the actual rolling radii and thus cause errors in the calculation of the wheel speeds.
It would, therefore be desirable to provide a more accurate way in which to determine the vehicle speed taking into consideration changes in rolling radii.
SUMMARY OF INVENTION
The present invention provides an improved determination of the individual wheel speeds. In the present invention the individual wheel speed calculations may be compensated for by learning the rolling radii of the wheels. Thus, a more accurate determination of the vehicle reference velocity or the longitudinal velocity may be determined.
In one aspect of the invention, a control system 24 for controlling a safety system 40 of an automotive vehicle includes a plurality of wheel speed sensors 30 generating a plurality of wheel velocity signals, a steering angle sensor 39 generating a steering actuator angle signal, a yaw rate sensor 28 generating a yaw rate signal, a lateral acceleration sensor 32 generating a lateral acceleration signal and a controller 26. The controller 26 generates a final reference vehicle velocity in response to the plurality of wheel speed signals, the steering angle signal, the yaw rate signal and the lateral acceleration signal. The controller 26 controls the safety system in response to the final reference vehicle velocity.
In a further aspect of the invention, a method of controlling a safety system for an automotive vehicle having a plurality of wheels includes determining a plurality of wheel velocities for the plurality of wheels, determining a preliminary longitudinal velocity of the vehicle from the plurality of wheel velocities, determining a plurality of correction factors for the plurality of wheel velocities for the plurality of wheels, determining a vehicle reference velocity in response to the plurality of correction factors, the plurality of wheel velocities and the preliminary longitudinal velocity, determining a lateral acceleration, determining a vehicle reference velocity correction factor in response to the lateral acceleration, determining a final reference velocity in response to the vehicle reference velocity correction factor and the vehicle reference velocity, and controlling the safety system in response to the final reference velocity.
Other advantages and features of the present invention will become apparent when viewed in light of the detailed description of the preferred embodiment when taken in conjunction with the attached drawings and appended claims.



BRIEF DESCRIPTION OF DRAWINGS
FIG. 1 is a top view of a motor vehicle illustrating various operating parameters of a vehicle experiencing a turning maneuver on a road surface.
FIG. 2 is a side view of a motor vehicle wheel illustrating various operating parameters of the wheel.
FIG. 3 is a block diagram showing a portion of a microprocessor interconnected to sensors and controlled devices, which may be included in a system according to the present invention.
FIG. 4 is a control system block diagram in accordance with the present invention.



DETAILED DESCRIPTION
In the following figures the same reference numerals will be used to illustrate the same components.
Referring now to FIG. 1, various operating parameters and variables used by the present invention are illustrated as they relate to the application of the present invention to a ground based motor vehicle 10 having wheels 12, 14, 16, 18. Those skilled in the art will immediately recognize the basic physics represented by these illustrations, thereby making the adaptation to different types of vehicles easily within their reach. A lateral and longitudinal velocities of the center of gravity are denoted as Vx and Vy a yaw angular rate is denoted as ωx, a front wheel steering angle is denoted as δ, lateral acceleration is represented by ay, longitudinal acceleration is represented by ax.
Using those vehicle motion variables, the velocities of the vehicle at the four corner locations, where the wheels are attached to the vehicle, can be calculated in the following form which are projected along the body fixed longitudinal and lateral directions

Vlfx=Vx−ωztf, Vlfy=Vy+ωzlf

Vrfx=Vx+ωztf, Vrfy=Vy+ωzlf

Vlrx=Vx−ωztr, Vlry=Vy−ωzlr

Vrrx=Vx+ωztr, Vrry=Vy−ωzlr  (1)

where tf and tr are the half tracks for the front and rear axles, lf and lr are the distances between the center of gravity of the vehicle and the front and rear axles. The variables Vlf, Vrf, Vlr and Vrr are the linear velocities of the four corners along the wheel heading directions (left front, right front, left rear and right rear, respectively), which can be calculated as in the following

Vlf=Vlfx cos (δ)+Vlfy sin (δ)

Vrf=Vrfx cos (δ)+Vrfy sin (δ)

Vlr=Vlrx

Vrr=Vrrx  (2)

Referring now to FIG. 2, vehicle corner velocity along the wheel longitudinal direction is equal to the sum of the contact patch slip velocity vcp and the product of the wheel rotational rate ωwhl and its rolling radius r0.
Referring now to FIG. 3, stability control system 24 has a controller 26 used for receiving information from a number of sensors which may include a yaw rate sensor 28, speed sensors 30 (at each wheel), a lateral acceleration sensor 32, a roll rate sensor 34, a steering angle (hand wheel position) sensor 35, a longitudinal acceleration sensor 36, a pitch rate sensor 37, and steering angle position sensor 39. Steering angle position sensor 39 senses the position of the steered road wheels. Lateral acceleration, longitudinal acceleration, yaw rate, roll orientation and speed may also be obtained using a global positioning system (GPS). Based upon inputs from the sensors, controller 26 controls the safety system 40. Depending on the desired sensitivity, the type of safety system and various other factors, not all the sensors 28-39 may be used in a commercial embodiment. Other factors may be obtained from the sensors such as the surface mu and the vehicle side slip angle, β.
Roll rate sensor 34 and pitch rate sensor 37 may sense the roll condition to be used with a rollover control system as an extension of the present application.
Safety system 40 may be a number of types of safety systems including a roll stability control system, a yaw control system, antilock brakes, traction control, airbags, or active suspension system.
Safety system 40 if implemented may control a position of a front right wheel actuator, a front left wheel actuator, a rear left wheel actuator, or a right rear wheel actuator. Although, as described above, two or more of the actuators may be simultaneously controlled as one actuator. Based on the inputs from sensors 28 through 39, controller 26 determines the vehicle dynamic conditions and controls the safety system. Controller 26 may also use brake control coupled to front right brakes, front left brakes, rear left brakes, and right rear brakes to dynamically control the vehicle. By using brakes in addition to steering control some control benefits may be achieved. For example, yaw control and rollover control may be simultaneously accomplished.
Speed sensor 30 may be one of a variety of speed sensors known to those skilled in the art. For example, a suitable speed sensor may include a sensor at every wheel that is averaged by controller 26. As will be described below, the controller 26 translates the wheel speeds into the speed of the vehicle.
Referring now to FIG. 4, a method of operating a safety system using a corrected vehicle velocity is determined. In step 60 the wheel speed sensors are read. In one embodiment each wheel has a separate speed sensor.
The wheel speed sensor outputs usually are calibrated for providing the linear directional velocities Vlf, Vrf, Vlr and Vrr by multiplying the wheel rotational angular speeds with a nominal rolling radius of the wheels. The variables ωlf-sensor, ωrf-sensor, ωlr-sensor and ωrr-sensor are the wheel angular velocity at the left-front corner, right-front corner, left-rear corner and rear-right corner respectively. The nominal rolling radius (typically used in ABS) for calculating wheel speeds from the wheel rotational rates is r0. Thus, the linear directional velocities may be represented by:

vlf=ωlf-sensorr0

vrf=ωrf-sensorr0

vlr=ωlr-sensorr0

vrr=ωrr-sensorr0  (3)

Notice that the wheels have different rolling radii than r0. Hence, in order to accurately calculate the actual linear velocities at the four corners, correction factors need to be added. The individual correction factors are denoted as Klf, Krf, Klr and Krr for the left-front, right-front, left-rear and rear-right corners, respectively. Thus, the linear directional velocities may then be represented by:

vlf=Klfωlf-sensorr0

vrf=Krfωrf-sensorr0

vlr=Klrωlr-sensorr0

vrr=Krrωrr-sensorr0   (4)

Notice also that the wheels experience not only the rotational motion but also the linear sliding motion, or longitudinal slip. The slip is caused by the relative motion between the wheel and the road at the contact patch (CP). The longitudinal velocities of the relative motions at the contact patches are denoted as vcp-lf, vcp-rf, vcp-lr and vcp-rr, then the vehicle corner velocities can be expressed as the sums of two speeds as in the following

Vlf=vcp-lf+vlf

Vrf=vcp-rf+vrf

Vlr=vcp-lr+vlr

Vrr=vcp-rr+vrr  (5)

The longitudinal and lateral velocities of the vehicle may be determined in step 62 from the sensors, or they may be calculated as in Ford disclosure 201-1057 filed simultaneously herewith, or even a rough estimation by averaging certain variables calculated from wheel speeds. This may be a rough estimate or average but, as mentioned above, does not take into consideration the rolling radius or other factors. Consider

Vy=Vx tan (β)  (6)

where β is the vehicle side slip angle Vy is the lateral velocity of the vehicle and Vx is the longitudinal velocity of the vehicle. In step 64, the front steering angle 8 is determined. Then, the individual correction factors Klf, Krf, Klr and Krr for each wheel can be calculated in step 66 as 



  
    
      
        
          
            
              
                κ
                lf
              
              =
              
                
                  
                    
                      
                        V
                        x
                      
                      ⁡
                      
                        [
                        
                          
                            cos
                            ⁡
                            
                              (
                              δ
                              )
                            
                          
                          +
                          
                            
                              tan
                              ⁡
                              
                                (
                                β
                                )
                              
                            
                            ⁢
                            
                               
                            
                            ⁢
                            
                              sin
                              ⁡
                              
                                (
                                δ
                                )
                              
                            
                          
                        
                        ]
                      
                    
                    +
                    
                      
                        ω
                        z
                      
                      ⁡
                      
                        [
                        
                          
                            
                              l
                              f
                            
                            ⁢
                            
                               
                            
                            ⁢
                            
                              sin
                              ⁡
                              
                                (
                                δ
                                )
                              
                            
                          
                          -
                          
                            
                              t
                              f
                            
                            ⁢
                            
                               
                            
                            ⁢
                            
                              cos
                              ⁡
                              
                                (
                                δ
                                )
                              
                            
                          
                        
                        ]
                      
                    
                  
                  
                    
                      ω
                      
                        lf
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
                -
              
            
          
        
        
          
            
              
                 
              
              ⁢
              
                
                  v
                  
                    cp
                    -
                    lf
                  
                
                
                  
                    ω
                    
                      lf
                      -
                      sensor
                    
                  
                  ⁢
                  
                    r
                    0
                  
                
              
            
          
        
        
          
            
              
                κ
                rf
              
              =
              
                
                  
                    
                      
                        V
                        x
                      
                      ⁡
                      
                        [
                        
                          
                            cos
                            ⁡
                            
                              (
                              δ
                              )
                            
                          
                          +
                          
                            
                              tan
                              ⁡
                              
                                (
                                β
                                )
                              
                            
                            ⁢
                            
                               
                            
                            ⁢
                            
                              sin
                              ⁡
                              
                                (
                                δ
                                )
                              
                            
                          
                        
                        ]
                      
                    
                    +
                    
                      
                        ω
                        z
                      
                      ⁡
                      
                        [
                        
                          
                            
                              l
                              f
                            
                            ⁢
                            
                               
                            
                            ⁢
                            
                              sin
                              ⁡
                              
                                (
                                δ
                                )
                              
                            
                          
                          +
                          
                            
                              t
                              f
                            
                            ⁢
                            
                               
                            
                            ⁢
                            
                              cos
                              ⁡
                              
                                (
                                δ
                                )
                              
                            
                          
                        
                        ]
                      
                    
                  
                  
                    
                      ω
                      
                        rf
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
                -
              
            
          
        
        
          
            
              
                 
              
              ⁢
              
                
                  v
                  
                    cp
                    -
                    rf
                  
                
                
                  
                    ω
                    
                      rf
                      -
                      sensor
                    
                  
                  ⁢
                  
                    r
                    0
                  
                
              
            
          
        
        
          
            
              
                κ
                lr
              
              =
              
                
                  
                    
                      V
                      x
                    
                    -
                    
                      
                        ω
                        z
                      
                      ⁢
                      
                        t
                        r
                      
                    
                  
                  
                    
                      ω
                      
                        lr
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
                -
                
                  
                    v
                    
                      cp
                      -
                      lr
                    
                  
                  
                    
                      ω
                      
                        lr
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
              
            
          
        
        
          
            
              
                κ
                rr
              
              =
              
                
                  
                    
                      V
                      x
                    
                    +
                    
                      
                        ω
                        z
                      
                      ⁢
                      
                        t
                        r
                      
                    
                  
                  
                    
                      ω
                      
                        rr
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
                -
                
                  
                    v
                    
                      cp
                      -
                      rr
                    
                  
                  
                    
                      ω
                      
                        rr
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
              
            
          
        
      
    
    
      
        (
        7
        )
      
    
  




The product term tan (β) sin (δ) is negligible in comparison to cos (δ), hence equation (7) may be further simplified to the following, which is independent of the vehicle side slip angle β



  
    
      
        
          
            
              
                κ
                lf
              
              ≈
              
                
                  
                    
                      
                        V
                        x
                      
                      ⁢
                      
                         
                      
                      ⁢
                      
                        cos
                        ⁡
                        
                          (
                          δ
                          )
                        
                      
                    
                    +
                    
                      
                        ω
                        z
                      
                      ⁡
                      
                        [
                        
                          
                            
                              l
                              f
                            
                            ⁢
                            
                               
                            
                            ⁢
                            
                              sin
                              ⁡
                              
                                (
                                δ
                                )
                              
                            
                          
                          -
                          
                            
                              t
                              f
                            
                            ⁢
                            
                               
                            
                            ⁢
                            
                              cos
                              ⁡
                              
                                (
                                δ
                                )
                              
                            
                          
                        
                        ]
                      
                    
                  
                  
                    
                      ω
                      
                        lf
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
                -
                
                  
                    v
                    
                      cp
                      -
                      lf
                    
                  
                  
                    
                      ω
                      
                        lf
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
              
            
          
        
        
          
            
              
                κ
                rf
              
              ≈
              
                
                  
                    
                      
                        V
                        x
                      
                      ⁢
                      
                         
                      
                      ⁢
                      
                        cos
                        ⁡
                        
                          (
                          δ
                          )
                        
                      
                    
                    +
                    
                      
                        ω
                        z
                      
                      ⁡
                      
                        [
                        
                          
                            
                              l
                              f
                            
                            ⁢
                            
                               
                            
                            ⁢
                            
                              sin
                              ⁡
                              
                                (
                                δ
                                )
                              
                            
                          
                          +
                          
                            
                              t
                              f
                            
                            ⁢
                            
                               
                            
                            ⁢
                            
                              cos
                              ⁡
                              
                                (
                                δ
                                )
                              
                            
                          
                        
                        ]
                      
                    
                  
                  
                    
                      ω
                      
                        rf
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
                -
                
                  
                    v
                    
                      cp
                      -
                      rf
                    
                  
                  
                    
                      ω
                      
                        rf
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
              
            
          
        
        
          
            
              
                κ
                lr
              
              =
              
                
                  
                    
                      V
                      x
                    
                    -
                    
                      
                        ω
                        z
                      
                      ⁢
                      
                        t
                        r
                      
                    
                  
                  
                    
                      ω
                      
                        lr
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
                -
                
                  
                    v
                    
                      cp
                      -
                      lr
                    
                  
                  
                    
                      ω
                      
                        lr
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
              
            
          
        
        
          
            
              
                κ
                rr
              
              =
              
                
                  
                    
                      V
                      x
                    
                    +
                    
                      
                        ω
                        z
                      
                      ⁢
                      
                        t
                        r
                      
                    
                  
                  
                    
                      ω
                      
                        rr
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
                -
                
                  
                    v
                    
                      cp
                      -
                      rr
                    
                  
                  
                    
                      ω
                      
                        rr
                        -
                        sensor
                      
                    
                    ⁢
                    
                      r
                      0
                    
                  
                
              
            
          
        
      
    
    
      
        (
        8
        )
      
    
  




In the case of small wheel longitudinal slip ratios, the longitudinal velocities vcp-lf, vcp-rf, vcp-lr and vcp-rr of the relative motions at the contact patches are close to zero, and equation (8) can be further simplified as the following 



  
    
      
        
          
            
              
                κ
                lf
              
              ≈
              
                
                  
                    
                      V
                      x
                    
                    ⁢
                    
                       
                    
                    ⁢
                    
                      cos
                      ⁡
                      
                        (
                        δ
                        )
                      
                    
                  
                  +
                  
                    
                      ω
                      z
                    
                    ⁡
                    
                      [
                      
                        
                          
                            l
                            f
                          
                          ⁢
                          
                             
                          
                          ⁢
                          
                            sin
                            ⁡
                            
                              (
                              δ
                              )
                            
                          
                        
                        -
                        
                          
                            t
                            f
                          
                          ⁢
                          
                             
                          
                          ⁢
                          
                            cos
                            ⁡
                            
                              (
                              δ
                              )
                            
                          
                        
                      
                      ]
                    
                  
                
                
                  
                    ω
                    
                      lf
                      -
                      sensor
                    
                  
                  ⁢
                  
                    r
                    0
                  
                
              
            
          
        
        
          
            
              
                κ
                rf
              
              ≈
              
                
                  
                    
                      V
                      x
                    
                    ⁢
                    
                       
                    
                    ⁢
                    
                      cos
                      ⁡
                      
                        (
                        δ
                        )
                      
                    
                  
                  +
                  
                    
                      ω
                      z
                    
                    ⁡
                    
                      [
                      
                        
                          
                            l
                            f
                          
                          ⁢
                          
                             
                          
                          ⁢
                          
                            sin
                            ⁡
                            
                              (
                              δ
                              )
                            
                          
                        
                        +
                        
                          
                            t
                            f
                          
                          ⁢
                          
                             
                          
                          ⁢
                          
                            cos
                            ⁡
                            
                              (
                              δ
                              )
                            
                          
                        
                      
                      ]
                    
                  
                
                
                  
                    ω
                    
                      rf
                      -
                      sensor
                    
                  
                  ⁢
                  
                    r
                    0
                  
                
              
            
          
        
        
          
            
              
                κ
                lr
              
              =
              
                
                  
                    V
                    x
                  
                  -
                  
                    
                      ω
                      z
                    
                    ⁢
                    
                      t
                      r
                    
                  
                
                
                  
                    ω
                    
                      lr
                      -
                      sensor
                    
                  
                  ⁢
                  
                    r
                    0
                  
                
              
            
          
        
        
          
            
              
                κ
                rr
              
              =
              
                
                  
                    V
                    x
                  
                  +
                  
                    
                      ω
                      z
                    
                    ⁢
                    
                      t
                      r
                    
                  
                
                
                  
                    ω
                    
                      rr
                      -
                      sensor
                    
                  
                  ⁢
                  
                    r
                    0
                  
                
              
            
          
        
      
    
    
      
        (
        9
        )
      
    
  




The digital value of the above wheel speed individual correction factors Klf, Krf, Klr and Krr at the time instant t=kΔT are

Klfk, Krfk, Klrk and Krrk,

then learning algorithms can be used to calculate the average correction factors. The correction factors are determined using an iterative process that is updated every N calculation samples in the following learning example. Notice that this is a conditional computation which is conducted only if the wheel's longitudinal slip ratios are small. 



  
    
      
        
          
            START
          
          
            
               
            
          
        
        
          
            if
          
          
            
              k
              <
              N
            
          
        
        
          
            
               
            
          
          
            
              
                
                  κ
                  _
                
                
                  lf
                  
                    k
                    +
                    1
                  
                
              
              =
              
                
                  
                    κ
                    _
                  
                  
                    lf
                    k
                  
                
                +
                
                  
                    κ
                    
                      lf
                      
                        k
                        +
                        1
                      
                    
                  
                  N
                
              
            
          
        
        
          
            
               
            
          
          
            
              
                
                  κ
                  _
                
                
                  rf
                  
                    k
                    +
                    1
                  
                
              
              =
              
                
                  
                    κ
                    _
                  
                  
                    rf
                    k
                  
                
                +
                
                  
                    κ
                    
                      rf
                      
                        k
                        +
                        1
                      
                    
                  
                  N
                
              
            
          
        
        
          
            
               
            
          
          
            
              
                
                  κ
                  _
                
                
                  lr
                  
                    k
                    +
                    1
                  
                
              
              =
              
                
                  
                    κ
                    _
                  
                  
                    lr
                    k
                  
                
                +
                
                  
                    κ
                    
                      lr
                      
                        k
                        +
                        1
                      
                    
                  
                  N
                
              
            
          
        
        
          
            
               
            
          
          
            
              
                
                  κ
                  _
                
                
                  rr
                  
                    k
                    +
                    1
                  
                
              
              =
              
                
                  
                    κ
                    _
                  
                  
                    rr
                    k
                  
                
                +
                
                  
                    κ
                    
                      rr
                      
                        k
                        +
                        1
                      
                    
                  
                  N
                
              
            
          
        
        
          
            
               
            
          
          
            
              k
              =
              
                k
                +
                1
              
            
          
        
        
          
            elseif
          
          
            
              k
              =
              N
            
          
        
        
          
            
               
            
          
          
            
              k
              =
              0
            
          
        
        
          
            
               
            
          
          
            
              
                
                  κ
                  _
                
                lf
              
              =
              
                
                  κ
                  _
                
                
                  lf
                  
                    N
                    +
                    1
                  
                
              
            
          
        
        
          
            
               
            
          
          
            
              
                
                  κ
                  _
                
                rf
              
              =
              
                
                  κ
                  _
                
                
                  rf
                  
                    N
                    +
                    1
                  
                
              
            
          
        
        
          
            
               
            
          
          
            
              
                
                  κ
                  _
                
                lr
              
              =
              
                
                  κ
                  _
                
                
                  lr
                  
                    N
                    +
                    1
                  
                
              
            
          
        
        
          
            
               
            
          
          
            
              
                
                  κ
                  _
                
                rr
              
              =
              
                
                  κ
                  _
                
                
                  rr
                  
                    N
                    +
                    1
                  
                
              
            
          
        
        
          
            
               
            
          
          
            
              go
              ⁢
              
                 
              
              ⁢
              to
              ⁢
              
                 
              
              ⁢
              START
            
          
        
      
    
    
      
        (
        10
        )
      
    
  




Using the above learning algorithm, corrected wheel speeds at each wheel can be determined in step 66 based upon the learned correction factor.

{circumflex over (v)}lfk={overscore (K)}lfr0ωlf-sensork

{circumflex over (v)}rfk={overscore (K)}rfr0ωrf-sensork

{circumflex over (v)}lrk={overscore (K)}lrr0ωlr-sensork

{circumflex over (v)}rrk={overscore (K)}rrr0ωrr-sensork  (11)

Notice that the above learning algorithm only corrects the individual wheel speeds. There are cases when the average rolling radii of the four wheels are reduced together due to vehicle loading change. Feeding back the above corrected wheel speeds to the algorithms used in vehicle dynamics control will provide a vehicle reference velocity

{circumflex over (V)}ref

in step 70 which needs to be further calibrated against the available vehicle longitudinal acceleration sensor signal.

Consider that the actual vehicle reference velocity is

Vref=K{circumflex over (V)}ref   (12)

where K is the global correction factor due to the total vehicle loading. K is usually a slow time varying parameters

K{dot over({circumflex over (V)})}ref=ax−gθy  (13)

where θy is the vehicle pitch angle generated from a pitch angle sensor or calculated from the pitch rate sensor signal.

In step 72, the longitudinal acceleration ax is determined. Then, the following variables are defined 



  
    
      
        
          
            
              
                
                  V
                  ⋒
                
                =
                
                  [
                  
                    
                      
                        
                          
                            v
                            ⋒
                          
                          
                            ref
                            1
                          
                        
                      
                    
                    
                      
                        
                          
                            v
                            ⋒
                          
                          
                            ref
                            2
                          
                        
                      
                    
                    
                      
                        ⋮
                      
                    
                    
                      
                        
                          
                            v
                            ⋒
                          
                          
                            ref
                            N
                          
                        
                      
                    
                  
                  ]
                
              
              ,
            
          
          
            
              
                
                  A
                  x
                
                =
                
                  [
                  
                    
                      
                        
                          a
                          
                            x
                            1
                          
                        
                      
                    
                    
                      
                        
                          a
                          
                            x
                            2
                          
                        
                      
                    
                    
                      
                        ⋮
                      
                    
                    
                      
                        
                          a
                          
                            x
                            N
                          
                        
                      
                    
                  
                  ]
                
              
              ,
            
          
          
            
              
                Θ
                y
              
              =
              
                [
                
                  
                    
                      
                        θ
                        
                          y
                          1
                        
                      
                    
                  
                  
                    
                      
                        θ
                        
                          y
                          2
                        
                      
                    
                  
                  
                    
                      ⋮
                    
                  
                  
                    
                      
                        θ
                        
                          y
                          N
                        
                      
                    
                  
                
                ]
              
            
          
        
      
    
    
      
        (
        14
        )
      
    
  




Then a least square computation of the correction factor due to loading can be determined in step 74 as the following:

{circumflex over (K)}=inv({circumflex over (V)}T{circumflex over (V)}){circumflex over (V)}T[Ax−gΘy]  (15)

or in the following form 



  
    
      
        
          K
          ^
        
        =
        
          
            
              ∑
              
                k
                =
                
                  M
                  +
                  1
                
              
              
                M
                +
                N
              
            
            ⁢
            
              
                
                  v
                  ⋒
                
                
                  ref
                  k
                
              
              ⁡
              
                (
                
                  
                    a
                    
                      x
                      k
                    
                  
                  -
                  
                    g
                    ⁢
                    
                       
                    
                    ⁢
                    
                      θ
                      
                        y
                        k
                      
                    
                  
                
                )
              
            
          
          
            
              ∑
              
                k
                =
                
                  M
                  +
                  1
                
              
              
                M
                +
                N
              
            
            ⁢
            
              
                v
                ⋒
              
              
                ref
                k
              
              2
            
          
        
      
    
    
      
        (
        16
        )
      
    
  




Notice that the global correction factor

{circumflex over (K)}

is updated every N computational samples when the wheels have small longitudinal slip ratios. The digital implementation of equation (16) can be obtained as in the following where Vk+1 is the updated reference velocity determined in step 76. 



  
    
      START
    
    
      
         
      
    
  
  
    
      if
    
    
      
        k
        <
        N
      
    
  
  
    
      
         
      
    
    
      
        
          A
          
            k
            +
            1
          
        
        =
        
          
            A
            k
          
          +
          
            
              
                v
                ⋒
              
              
                ref
                
                  k
                  +
                  1
                
              
            
            ⁢
            
               
            
            ⁢
            
              (
              
                
                  a
                  
                    x
                    
                      k
                      +
                      1
                    
                  
                
                -
                
                  g
                  ⁢
                  
                     
                  
                  ⁢
                  
                    θ
                    
                      y
                      
                        k
                        +
                        1
                      
                    
                  
                
              
              )
            
          
        
      
    
  
  
    
      
         
      
    
    
      
        
          V
          
            k
            +
            1
          
        
        =
        
          
            V
            k
          
          +
          
            
              
                v
                ⋒
              
              
                ref
                
                  k
                  +
                  1
                
              
            
            ⁢
            
              
                v
                ⋒
              
              
                ref
                
                  k
                  +
                  1
                
              
            
          
        
      
    
  
  
    
      
         
      
    
    
      
        k
        =
        
          k
          +
          1
        
      
    
  
  
    
      elseif
    
    
      
        k
        =
        N
      
    
  
  
    
      
         
      
    
    
      
        
          κ
          ^
        
        =
        
          
            A
            
              N
              +
              1
            
          
          
            V
            
              N
              +
              1
            
          
        
      
    
  
  
    
      
         
      
    
    
      
        k
        =
        0
      
    
  
  
    
      
         
      
    
    
      
        go
        ⁢
        
           
        
        ⁢
        to
        ⁢
        
           
        
        ⁢
        START
      
    
  




The final corrected wheel speed sensor signals may be corrected by the aforementioned factors can also be obtained as the following:

{circumflex over (v)}lfk={circumflex over (K)}{overscore (K)}lfr0ωlf-sensork

{circumflex over (v)}rfk={circumflex over (K)}{overscore (K)}rfr0ωrf-sensork

{circumflex over (v)}lrk={circumflex over (K)}{overscore (K)}lrr0ωlr-sensork

{circumflex over (v)}rrk={circumflex over (K)}{overscore (K)}rrr0ωrr-sensork  (17)

Once the corrected final vehicle reference velocity is determined, the safety system 40 may be controlled using the compensated velocity values.
While particular embodiments of the invention have been shown and described, numerous variations and alternate embodiments will occur to those skilled in the art. Accordingly, it is intended that the invention be limited only in terms of the appended claims.

## Claims

1. A control system for controlling a safety system of an automotive vehicle comprising:
a plurality of wheel speed sensors generating a plurality of wheel velocity signals; 
a steering angle sensor generating a steering actuator angle signal; 
a yaw rate sensor generating a yaw rate signal; 
a lateral acceleration sensor generating a lateral acceleration signal; and 
a controller coupled to the plurality of wheel speed sensors, the steering actuator angle sensor, the yaw rate sensor, the lateral acceleration sensor, said controller generating a final reference vehicle velocity in response to the plurality of wheel velocity signals, the steering angle signal, the yaw rate signal and the lateral acceleration signal, said controller controlling the safety system in response to the final reference vehicle velocity.

2. A control system as recited in claim 1 wherein the safety system comprises a rollover control system.

3. A control system as recited in claim 1 wherein the safety system comprises a yaw control system.

4. A control system as recited in claim 1 wherein the safety system comprises an antilock brake system.

5. A control system as recited in claim 1 wherein the final reference vehicle velocity is determined in response to a learning function.

6. A control system for an automotive vehicle comprising:
a plurality of wheel speed sensors generating a plurality of wheel velocity signals; 
a lateral acceleration sensor generating a lateral acceleration signal; 
a safety system; and 
a controller coupled to the plurality of wheel speed sensors, the lateral acceleration sensor and the safety system, said controller determining a preliminary longitudinal velocity of the vehicle from the plurality of wheel velocity signals, determining a plurality of correction factors for the plurality of wheel velocity signals, determining a vehicle reference velocity in response to the plurality of correction factors, the plurality of wheel velocities and the preliminary longitudinal velocity, determining a vehicle reference velocity correction factor in response to the lateral acceleration, determining a final reference velocity in response to the velocity correction factor and the vehicle reference velocity, said controller controlling the safety system in response to the final reference vehicle velocity.

7. A control system as recited in claim 1 wherein the safety system comprises a rollover control system.

8. A control system as recited in claim 1 wherein the safety system comprises a yaw control system.

9. A control system as recited in claim 1 wherein the safety system comprises an antilock brake system.

10. A control system as recited in claim 1 wherein determining a plurality of correction factors is performed using a learning function.

11. A control system as recited in claim 1 wherein the learning function averages N correction factors, where N is an integer.

12. A control system as recited in claim 1 further comprising said controller determining a nominal rolling radius,
wherein the wheel velocity is a function of vehicle speed.

13. A method of controlling a safety system for an automotive vehicle having a plurality of wheels comprising:
determining a plurality of wheel velocities for the plurality of wheels; 
determining a preliminary longitudinal velocity of the vehicle from the plurality of wheel velocities; 
determining a plurality of correction factors for the plurality of wheel velocities for the plurality of wheels; 
determining a vehicle reference velocity in response to the plurality of correction factors, the plurality of wheel velocities and the preliminary longitudinal velocity; 
determining a lateral acceleration; 
determining a vehicle reference velocity correction factor in response to the lateral acceleration; 
determining a final reference velocity in response to the vehicle reference velocity correction factor and the vehicle reference velocity; and 
controlling the safety system in response to the final reference velocity.

14. A method as recited in claim 13 further comprising determining a yaw rate determining a plurality of preliminary lateral velocity of the vehicle from the plurality of wheel speeds and the yaw rate.

15. A method as recited in claim 13 further comprising determining a front steering angle, wherein determining a plurality of correction factors are determined in response to the front steering angle.

16. A method as recited in claim 13 wherein said safety system comprises at least one selected from a rollover stability control system, a yaw control system, a traction control system or an antilock brake control system.

17. A method as recited in claim 13 further comprising using a learning function in the step of determining a plurality of correction factors.

18. A method of controlling a safety system for an automotive vehicle having a plurality of wheels comprising:
determining a plurality of wheel velocities for the plurality of wheels; 
determining a yaw rate; 
determining a preliminary longitudinal velocity of the vehicle from the plurality of wheel velocities and the yaw rate; 
determining a front steering angle; 
determining a plurality of correction factors for the plurality of preliminary wheel speeds in response to the front steering angle; 
determining a vehicle reference velocity in response to the plurality of correction factors and the plurality of correction factors and the preliminary longitudinal velocity.

19. A method as recited in claim 18 further comprising determining a lateral acceleration;
determining a velocity correction factor in response to the lateral acceleration; and 
determining a final reference velocity in response to the velocity correction factor and the vehicle reference velocity.

20. A method as recited in claim 18 further comprising using a learning function in the step of determining a plurality of correction factors.

21. A method as recited in claim 18 wherein said safety system comprises at least one selected from a rollover stability control system, a yaw control system, a traction control system or an antilock brake control system.