Abstract:
A method and an apparatus for monitoring an operating state of at least one tire of a vehicle are provided. The monitored operating state may be, for example, the air pressure of the tire. One tire state variable that represents the current operating state of the tire, and one calibration variable that represents the target tire state of the tire, are taken into consideration in the monitoring. The monitoring is accomplished in different monitoring modes, i.e., the particular monitoring mode employed is determined as a function of at least one driving state variable representing the driving state. In an example embodiment, for a given driving state variable, the vehicle speed is selected as the differentiation criterion for the different monitoring modes.

Description:
FIELD OF THE INVENTION 
   The present invention relates to a method and an apparatus for monitoring an operating state of at least one tire of a vehicle. 
   BACKGROUND INFORMATION 
   The tires of a vehicle are among the systems most critical to driving safety during operation of the vehicle. A sudden pressure decrease, which regularly occurs as an indication of tire damage, can result in limited road adhesion and, in some cases, can render the vehicle no longer controllable. At high speeds, in particular, tire pressure losses can therefore have an extremely devastating effect. Prompt detection of a defective tire can thus make a considerable contribution to driving safety. 
   Systems which monitor the state of a tire, in particular the air pressure, are known in the art. In addition to direct determination of the air pressure of a tire, the rotation speeds of the wheels can be employed in order to determine a change in tire pressure. For example, changes in the rotation speeds of individual wheels can be sensed and used to demonstrate a change in the operating state of the tires. 
   Published German patent documents DE 36 10 116 and DE 32 36 520 describe monitoring systems which indicate the tire state in the context of specific operating states (traveling straight ahead without deceleration or acceleration). These documents also describe a normalization of the rotation speeds to the respective vehicle speed. 
   For indirect-measurement tire-pressure monitoring systems, the use of differences in wheel rotation speeds of individual wheels for tire state detection is known, for example, from European Patent 0 291 217. In such systems, pressure losses can be ascertained by way of the deviation in wheel speeds in the context of a reduced tire circumference. 
   Published German Patent Application 199 44 391 describes the adaptation of a calibration value serving to monitor tire pressure. In this method, a recalibration of the tire pressure system is performed on the basis of a modified operating state of the tire, the old value being overwritten. 
   SUMMARY OF THE INVENTION 
   The present invention provides a method and an apparatus with which an operating state of at least one tire of a vehicle can be monitored. The monitored operating state may be, for example, the air pressure of the tire. Provision is further made that, one tire state variable that represents the current operating state of the tire, and one calibration variable that represents the target tire state of the tire, are taken into consideration in the monitoring. In accordance with the present invention, the monitoring is accomplished in different monitoring modes. The particular monitoring mode employed is determined as a function of at least one driving state variable representing the driving state. 
   In an example embodiment of the present invention, the monitoring mode is selected as a function of a comparison of the driving state variable to a definable limit value. For example, the vehicle speed can be compared to a given speed, the monitoring mode being changed if the given speed is exceeded. The present invention provides two monitoring modes, a transition from the first monitoring mode (in which the monitoring normally begins) into the second monitoring mode taking place as a function of the comparison. In addition to the exceedance of the defined limit value, the behavior over time of the exceedance of the limit value is also monitored for the comparison. As a result of the comparison, the transition into the second monitoring mode is performed only if the exceedance of the limit value persists for a definable period of time. In a further embodiment of the invention, it is provided that no further comparison is performed after the change into the second monitoring mode has taken place. As a result, no further change in the monitoring mode is provided for. 
   In an example embodiment, provision is made for selecting the vehicle speed, as a differentiation criterion between the individual monitoring modes, as the driving state variable. This makes possible a monitoring process adapted to the instantaneous driving state. 
   In accordance with the present invention, provision is made for equipping each monitoring mode with at least one calibration mode. Provision is further made for each calibration mode to contain at least one calibration variable. It is thus possible to achieve, within the individual monitoring modes, fine gradations that permit accurate identification and monitoring of the operating state of the tire. In order to adapt the determination of the calibration variables as closely as possible to the actual operation of the vehicle, the calibration variables are determined as a function of a series of parameters. At least one tire state variable, one driving state variable, one calibration request, and/or the monitoring mode, for example, are included in the determination of the calibration variable. It is thus possible to eliminate spikes or brief disturbances from the determination by taking an average of several tire state variables in the determination of the calibration variables. 
   With the driving state variable, for example the vehicle speed, a calibration adapted to the modified physical behavior of the tire at high speeds, for example, can be taken into account. The calibration request moreover allows a calibration to be performed in controlled fashion when permitted by the driving situation. 
   In an example embodiment of the present invention, the determination of the calibration variable is performed as a function of the number of tire state variables acquired, and the monitoring mode. Provision is made in particular, in this context, for determining a calibration variable of a first kind and/or a calibration variable of a second kind, depending on the defined number of tire state variables that have entered into the determination. An example embodiment provides for the calibration variable to be determined as the average of the number of tire state variables that have entered into the determination. 
   In accordance with the present invention, the determination of the calibration variable of the first kind is performed until the prerequisite for creation of the calibration variable of the second kind. Provision is additionally made for further determination of the calibration variable to be terminated when the calibration variable of the second kind has been created. However, the determination of a new calibration variable may be performed again if a calibration request is identified. 
   The dependence of the monitoring operation on the monitoring mode represents a further example embodiment of the invention. Here, a tire state variable which represents the current tire state is determined, and is referred to the calibration variable of the monitoring mode. From the comparison, associated therewith, of the two variables, a malfunction is identified if the difference goes outside a defined range, i.e., beyond a defined threshold value. In an example embodiment of the present invention, the defined range or the threshold value is selected as a function of at least one driving state variable, for example the vehicle speed. As a result, nonlinear or only locally linear correlations between rolling circumference and vehicle speed can also be taken into account. Alternatively or simultaneously, however, the monitoring can also be selected as a function of the number of tire state variables used for determination of the calibration variable. The advantage of this embodiment lies in the fact that the threshold values have different sensitivities as a result of the modification. A large number of tire state variables in the context of determination of the calibration variable thus reduces the variability of the tire state variables that is sensed, thereby permitting more-sensitive monitoring. 
   In accordance with the present invention, the monitoring of the tire state is accomplished by way of a tire state variable representing the tire state, the tire state variable being created on the basis of wheel rotation speeds. The determination of the tire state variable is ascertained by creating a difference between the wheel speeds at at least two wheels in each case. Provision is made here, in particular, for creating the difference in wheel speeds at the wheels of one axle and/or at the diagonally located wheels. In addition to this, however, the possibility also exists of determining the tire state variable by creating a difference between the sums of the wheel rotation speeds at the wheels of the front axle and of the rear axle. It is also possible, however, to determine the tire state variable as the difference between the sums of the wheel rotation speeds at the wheels of the left and of the right side of the vehicle. In a further embodiment, provision is moreover made for normalizing the created differences to the vehicle speed. Provision is furthermore made for ascertaining the wheel rotation speed by way of a wheel dynamics variable representing the wheel rotation speed. 
   In accordance with the present invention, the calibration request may be accomplished at a defined point in time. The point in time can be determined by way of a command initiated by the driver, or automatically by detecting a tire change or an operation of adding air to the tire. 
   The present invention may provide that upon detection of a malfunction, i.e., upon occurrence of a pressure loss in a tire, the driver is informed thereof acoustically and/or optically. It is furthermore possible, upon detection of a malfunction, to activate a braking system present in the vehicle and/or an active steering system, in such a way that the vehicle&#39;s reaction counteracts the cause of the malfunction. Dangerous driving situations resulting from a pressure loss in the tires can thus be compensated for or mitigated. 
   In a further example embodiment of the invention, the fact that the definable limit value has been exceeded by the driving state variable during a defined time is interpreted as a prerequisite for a tire state in which a plastic deformation of the tire is occurring. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows, in a block diagram, the acquisition of operating variables that are necessary for monitoring of the tire state, and the processing of the read-in values and forwarding of a detected malfunction. 
       FIG. 2  depicts in a flow-chart the initialization and determination of the calibration variables. 
       FIG. 3  depicts in a flow-chart the sequence of monitoring the tire air pressure. 
       FIG. 4  depicts in a flow-chart the procedure of a further exemplary embodiment of the present invention. 
       FIG. 5  depicts in a flow-chart the operation of monitoring attainment of a high-speed range. 
   

   DETAILED DESCRIPTION 
     FIG. 1  shows an exemplary embodiment for monitoring of a vehicle having four tires. An adaptation of the example to a vehicle having additional tires is certainly possible, but not necessary for presentation of the example. For acquisition of the monitoring parameters necessary for monitoring, each wheel equipped with a tire possesses a wheel rotation speed sensor ( 130  through  136 ) for ascertaining the wheel rotation speed. From these wheel rotation speed sensors ( 130  through  136 ), the wheel rotation speed variables v VR  ( 140 ), v VL  ( 142 ), v HR  ( 144 ), and v HL  ( 146 ), which represent the wheel rotation speeds, are forwarded to central monitoring unit  100 . To complete the driving-dynamics variables for monitoring, monitoring unit  100  reads out of a corresponding system  138  a variable v car  ( 148 ) representing the vehicle speed. In block  150 , tire state variables Δv A , ΔV D  which represent the tire state of the wheels are ascertained from these read-in values. 
   An initialization, which can be accomplished manually by the driver and/or automatically, for example by a calibration request generator  110 , in the context of a tire change or an operation adding air to the tire, causes a flag F I  ( 115 ) to be set, i.e., flag F I  changes from the value 0 to the value 1. A further exemplified embodiment shows, however, that in addition to continuous setting of the flag, a brief setting of flag F I  ( 115 ) is sufficient for initialization of the calibration operation. 
   In block  150 , because flag F I  ( 115 ) is set, calibration values are created from the tire state variables as a function of the read-in vehicle speed variable v car  ( 148 ). Only wheel speed variables ( 140  through  146 ) that are suitable for the purpose are used, however, to ascertain the tire state variables. Certain driving situations are conceivable—for example heavy braking/acceleration, cornering, or an ABSR/ESP control action—that do not supply tire state variables suitable for evaluation. To filter such driving situations out of the monitoring process and the determination of calibration variables, a driving observation module  120  is used; this detects the corresponding driving situations and sets a flag F M  ( 125 ) if monitoring and calibration are to be briefly discontinued. 
   Since the tires have different physical properties depending on the rotational velocity of the wheel, various speed ranges are set up. This can be done, for example, using the index B as shown in the following table: 
   
     
       
             
             
             
           
         
             
                 
                 
             
             
                 
               Index B 
               Speed Range V B  [km/h] 
             
             
                 
                 
             
           
           
             
                 
               1 
                0-50 
             
             
                 
               2 
                51-100 
             
             
                 
               3 
               101-150 
             
             
                 
               4 
               151-200 
             
             
                 
               5 
               201-250 
             
             
                 
                 
             
           
        
       
     
   
   However, other subdivisions adapted to the particular vehicle are also conceivable. It is furthermore possible to make the speed ranges variable during operation of the vehicle. 
   Since the behavior of the tires also changes along with the tire properties, it is necessary to ascertain separate calibration variables for each speed range. In the context of monitoring the operating state of the tires, the vehicle speed variable v car  ( 148 ) is therefore employed in order to allocate the corresponding calibration variable. 
   The calibration variables ascertained in the individual speed ranges, as well as the number n of tire state variables taken into account in that context, are stored in a memory  155  and read out as necessary. If a malfunction is identified in the course of the monitoring, the driver can be informed thereof. This can be accomplished both optically and acoustically via a corresponding indicator  170 . It is also conceivable, on the basis of the detected malfunction, for a system  190  located in the vehicle, which counteracts the possible impairments of driving behavior resulting from the tire pressure loss by way of a corresponding control action  180 , to be activated. Present-day systems that can perform this are, for example, an ABS, ESP, or an active steering system. 
   The flow chart in  FIG. 2  describes one possible program sequence for ascertaining the calibration variables that are required as reference values for monitoring the tire state, e.g., the tire air pressure. In a first step  200  the calibration request is queried. This is done by querying flag F I  ( 115 ). If an unset flag F I  ( 115 ) is detected, i.e., F I =0, the program terminates execution. If, however, a set flag F I  ( 115 ) (i.e., F I =1) indicates that a calibration request has been made by the driver or on the basis of automatic detection, then in the next step  205  the flags F KB , which represent a successful determination of a calibration variable for speed range V B  by way of a set flag F KB =1, are set to a value of 0 for all indices B. In step  210 , execution pass variable n B  and calibration variables Kal AB  for single-axle monitoring and Kal DB  for diagonal monitoring are also set to 0 for all indices B. For determination of the current speed range V B , in step  215  vehicle speed variable v car  ( 148 ), representing the vehicle speed, is read in. A comparison of vehicle speed variable v car  ( 148 ) to the previously subdivided speed ranges V B  allows a determination of the range in which the vehicle is located. This comparison yields the associated value of index B that is used for further determination of the calibration variable. If it is found by way of execution pass variable n B  that the current execution pass for ascertaining the calibration variable is the first one, i.e., if n B =0, the value of index B belonging to the current speed range V B  is then stored in a variable Z K . This allows identification of the calibration variable that has been determined, and allocation thereof to the associated speed range. Step  220  then checks whether the current speed range V B  matches the range in which the calibration is to be performed. This is done by comparing the value of B determined in step  215  to the variable Z K . This comparison thus allows identification of a switchover into a different speed range brought about by a change in vehicle speed v car  ( 148 ). At the same time, the existence of an already determined calibration variable of the second kind for speed range V B  is queried by way of flag KB. As already described, a set flag F KB =1 indicates the presence of a calibration variable of the second kind in the corresponding speed range V B . If the decision upon combination of the two comparisons
 
B=Z K 
 
and
 
F KB =0
 
is negative, then in step  225  the allocation
 
 Z K =B
 
is made, in order to adapt variable Z K  to the current speed range with the value of index B. After this allocation in step  225 , step  210  starts a new cycle for determining the calibration variable. In the event of a positive outcome of the comparison in step  220 , the program proceeds with the next step  230 . Here the wheel rotation speeds v VR  ( 140 ), v VL  ( 142 ), V HR  ( 144 ) and v HL  ( 146 ) are read in. If the vehicle is in a driving situation that does not permit determination of a tire state variable suitable for evaluation, flag F M  ( 125 ) is then set, i.e., F M =1. Because this flag F M  ( 125 ) is set, in step  235  execution branches to step  240  of the flow chart, in which the allocation
 
Z K =B
 
is made in order to adapt variable Z K  to the current speed range of index B. Once the allocation Z K =B has been made in step  240 , the program loops back to step  215 .
 
   If an impermissible driving situation was not identified, however, i.e., if F M =0, then in step  245  the equations
 
Δν A :={(ν VL +ν VR )−(ν HL +ν HR )}/ν car •
 
Δν D :={(ν VL +ν HR )−(ν VR +ν HL )}/ν car 
 
are used to ascertain the wheel state variables, which are determined on both a single-axle (Δv A ) and diagonal basis (Δv D ) for wheel rotation speed variables v VR  ( 140 ), v VL  ( 142 ), v HR  ( 144 ), and v HL  ( 146 ), normalized to the vehicle speed v car  ( 148 ). Also in step  245 , the execution pass variable n B  is incremented:
 
  n   B   =n   B +1.
 
   The wheel state variables Δv A  and Δv D  ascertained in this fashion are then used, in step  250 , to ascertain calibration variables Kal AB  and Kal DB , using 
         Kal   AB     =       Kal   AB     +         Kal   AB     -     Δ   ⁢           ⁢     v   AB           n   B             
     and     
         Kal   DB     =       Kal   DB     +         Kal   DB     -     Δ   ⁢           ⁢     v   AB           n   B             
 
   In order to define a calibration variable of the first kind, in step  255  a minimum number n min  is defined which must be reached or exceeded by execution pass variable n B  in order to reach step  260 . If, on the other hand, at this point in time fewer tire state variables than the required number have entered into the determination of the calibration variable of the first kind, the algorithm is then continued with step  240 . In addition to a minimum number n min  for all speed ranges V B , in another example embodiment it is also conceivable to define, using n min , B , a separate minimum number for each individual speed range V B . 
   If it is found in step  255  that a sufficient number of tire state variables have entered into the determination of the calibration variable of the first kind, in step  260  calibration variables Kal AB  and Kal DB  are stored in memory  155 . For determination of a calibration variable of the second kind, step  265  checks, by a comparison to execution pass variable n B , whether the maximum number n max  of tire state variables that have entered into the determination of the calibration variable has been reached or exceeded. By analogy with the comment regarding minimum number n min , an example embodiment is also possible for maximum number n max  in which, using n max , B , a separate maximum number can be defined for each individual speed range V B . The values according to the table below can be used as an example for the minimum and maximum numbers n min  and n max : 
   
     
       
             
             
             
           
         
             
                 
                 
             
             
                 
               n min   
               n max   
             
             
                 
                 
             
           
           
             
                 
               250 
               5000 
             
             
                 
                 
             
           
        
       
     
   
   If the result of the check in step  265  is negative, i.e., if fewer tire state variables than the maximum number have been used for ascertaining the calibration variable, the algorithm is then continued in step  240 . If, however, it is found in step  265  that a sufficient number of tire state variables (n B ≧n max ) have entered into the determination of the calibration variable, this calibration variable of the second kind then constitutes the comparison variable for the corresponding speed range V B  until the next identification of a calibration request F I =1. In the comparison to the calibration variable of the first kind, the calibration variable is no longer modified in a further execution pass without a calibration request. This is indicated by the fact that in step  270 , flag F KB  belonging to the corresponding speed range V B  is set, i.e., F KB =1. Step  275  then queries whether one of the flags F KB  for all indices B is still unset. Since this would indicate a missing calibration variable of the second kind, a positive decision in step  275  moves execution to step  240  for further processing. If, however, flags F KB  are set for all indices B, then in step  280  flag F I  ( 155 ) is deleted, i.e., reset F I =0. This reset is forwarded to block  110  in order to make possible another calibration request by the driver or on the basis of automatic detection. The program is then terminated, before being restarted either at regular time intervals or on the basis of a calibration request. 
   One possible algorithm for monitoring tire states, e.g., tire air pressures, is depicted with reference to a flow chart in FIG.  3 . Once the algorithm has been started, in step  300  flag F M  ( 125 ) is queried. If it is found here that flag F M ( 125 ) is set, i.e., F M =1, meaning the vehicle is in a driving situation that is unsuitable for evaluation of a tire state variable, the algorithm is immediately terminated. If an unset flag F M  ( 125 ) is found, however, then in step  310  the vehicle speed variable v car  ( 148 ) representing the vehicle speed is read in. By comparing vehicle speed variable v car  ( 148 ) to the previously subdivided speed ranges V B , it is possible to determine the range in which the vehicle is currently located. This comparison yields the associated value of index B, which defines the monitoring range and is used for further monitoring. In the next step  320 , calibration variables Kal AB  and Kal DB  and execution pass variable n B , in addition to wheel rotation speed variables v VR  ( 140 ), v VL  ( 142 ), v HR  ( 144 ) and v HL  ( 146 ), are read out of memory  155 . The check as to whether calibration variables exist in the current speed range V B  is then performed in step  330 . The existence of the calibration variables for speed range V B  can be queried explicitly, for example, by making the comparisons
 
 Kal   DB ≠0
 
and
 
 Kal   DB ≠0
 
   If both calibration variables have a value of 0, the algorithm is terminated until the next start instruction. If the comparison in step  330  is positive, however, then in step  340  the single-axle Δv A  and diagonal Δv D  tire state variables are ascertained using
 
Δν A :={(ν VL +ν VR )−(ν HL +ν HR )}/ν car •
 
Δν D :={(ν VL +ν HR )−(ν VR +ν HL )}/ν car 
 
based on wheel rotation speed variables v VR  ( 140 ), v VL  ( 142 ), v HR  ( 144 ) and v HL  ( 146 ) determined in step  320  and normalized to vehicle speed v car  ( 148 ). If however, only one calibration variable Kal AB  or Kal DB  is set to 0 in step  330 , the associated tire state variable is not determined.
 
   Before the calibration variables are compared to the tire state variables that have been ascertained, the permissible defined threshold values SW AB  and SW DB  must be adapted to the number of tire state variables serving as basis for the calibration variable. More specifically, the less sensitive (i.e. higher) threshold values must be, the smaller the number of tire state variables serving as basis for the calibration variables. In the present example embodiment, therefore, in step  350  the threshold values are ascertained as a function of the number n B  of tire state variables that have entered into the calibration. Using the equations
 
 SW   AB   =SW   AB *(1 +SW   F )
 
and
 
 SW   DB   =SW   DB *(1 +SW   F )
 
for example, the threshold values can be modified by the factor SW F  as a function of the number n B . One possible allocation of the modification factor in relation to the number n B  is shown by the following table:
 
   
     
       
             
             
             
           
             
             
             
           
         
             
                 
                 
             
             
                 
               n B  ≧ 
               Factor SW F   
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
                 
               250 
               1/10  
             
             
                 
               500 
               5/100 
             
             
                 
               1000 
               2/100 
             
             
                 
               2000 
               1/100 
             
             
                 
               3300 
               3/500 
             
             
                 
               5000 
               1/500 
             
             
                 
                 
             
           
        
       
     
   
   For example, a number 2000&gt;n B &gt;1000 means a modification of the threshold values by a factor of 1.02. For finer gradations, it is possible to select additional subdivisions or an entirely different allocation. The dependence of the threshold value on the number of tire state variables included in the determination of the calibration variable is not, however, the only conceivable dependence. In a further example embodiment, the threshold values are modified as a function of the vehicle speed v car  ( 148 ) and the speed range V B . 
   The threshold values SW AB  and SW DB  ascertained in step  350  are then used in step  360  to determine the deviation of the ascertained tire state variables Δv A  or Δv D  from calibration variables Kal AB  and Kal DB . This is done by checking whether the equations
 
| Kal   AB −Δν AB   |&lt;SW   AB 
 
or
 
| Kal   DB −Δν DB   |&lt;SW   DB 
 
are satisfied. If so, the algorithm is terminated with no further consequences. If one of the deviations goes beyond the threshold value, the wheel that is exhibiting a tire pressure loss can be deduced in step  370 , based on a synopsis of the deviations. In step  380 , the algorithm completes the monitoring cycle with an error message  160  to an acoustic and/or optical indicator  170  which informs the driver of the tire pressure loss, and a suitable activation  180  of a system  190  for compensating for the threat of a loss of driving stability.
 
   In addition to the monitoring of tire pressure in speed ranges using incompletely performed calibration values, a further example embodiment of the present invention may utilize extrapolation of calibration values for those speed ranges for which a complete calibration has not yet been performed. To achieve this, in the program sequence shown in  FIG. 3 , after wheel rotation speed variables v VR  ( 140 ), v VL  ( 142 ), v HR  ( 144 ) and V HL  ( 146 ) as well as calibration variables Kal AB  and Kal DB  and execution pass variable n B  have been read in from memory  155 , a further program section illustrated in  FIG. 4  is executed. In this program section, step  400  first checks, using F KB =1, whether a complete calibration has been performed, and a corresponding calibration value Kal AB  or Kal DB  exists, in the current speed range B in which the vehicle is located. If it is found that a complete calibration has already been accomplished, program execution continues with step  330  in FIG.  3 . If a complete calibration has not yet been performed, however, step  410  then checks, with F K(B−1) =1, whether a calibration value from a complete calibration is available for speed range B−1 located below speed range B. If so, a calibration data set Kal AB  and Kal DB  for speed range B is extrapolated from calibration data set Kal A(B−1)  and Kal D(B−1)  for speed range B−1. This is done by first, in step  420 , creating the difference between the current vehicle speed v car  ( 148 ) and the maximum limit speed for speed range B−1, using: 
    Δ v=|v   car −max. limit speed of range B−1| 
   Δv being an indication of the deviation of the current vehicle speed v car  ( 148 ) from the next-lower speed range. As a function of this deviation and in conjunction with the calibration values from speed range B−1, calibration values for speed range B are generated using
 
 Kal   B   =f ( Kal   B−1   , Δv ).
 
   One possible allocation of the calibration values can be made using
 
 Kal   AB   =Kal   A(B−1) *(1 +Kal   F )
 
and
 
 Kal   DB   =Kal   D(B−1) *(1 +Kal   F );
 
the modification of the calibration variables Kal F  as a function of Δv can be performed, for example, in accordance with the following table:
 
   
     
       
             
             
             
           
         
             
                 
                 
             
             
                 
               Deviation (km/h) 
               Factor Kal F   
             
             
                 
                 
             
           
           
             
                 
                0 &lt; Δv ≦ 5 
               2/100 
             
             
                 
                5 &lt; Δv ≦ 10 
               5/100 
             
             
                 
               10 &lt; Δv ≦ 20 
               1/00  
             
             
                 
               20 &lt; Δv ≦ 30 
               2/10  
             
             
                 
               30 &lt; Δv ≦ 40 
               5/10  
             
             
                 
                 
             
           
        
       
     
   
   If it is found in step  410  that a complete calibration has not been performed in speed range B−1, then in step  440  a corresponding query is made for speed range B+1. If flag F K(B+1)  is not set, the monitoring is discontinued. If, however, F K(B+1) =1 indicates detection of a complete calibration in speed range B+1, then in accordance with the procedure in steps  420  and  430 , the deviation of the current vehicle speed v car  ( 148 ) from the next-higher speed range B+1 is ascertained in step  450  using
 
Δ v=|v   car −min. limit speed of range B+1|.
 
   This is followed in step  460  by an extrapolation of the calibration values for speed range B using
 
 Kal   B   =f ( Kal   B+1   ,Δv ).
 
   As explained above in connection with step  430 , one possible allocation of the calibration values involves the use of
 
 Kal   AB   =Kal   A(B+1) *(1 +Kal   F )
 
and
 
 Kal   DB   =Kal   D(B+1) *(1 +Kal   F ).
 
   The modifications of the calibration variable Kal F  can be performed in accordance with the table presented above. 
   Step  470  then checks for the existence of calibration variables in the calibration data set of the current speed range V B . If both calibration variables have the value 0, the algorithm is terminated until the next start instruction. If the result of the comparison in step  470  is positive, however, then in step  480  the single-axle tire state variable Δv A  and diagonal tire state variable Δv D  are ascertained, similarly to step  340 , using 
    Δν A :={(ν VL +ν VR )−(ν HL +ν HR )}/ν car •
 
Δν D :={(ν VL +ν HR )−(ν VR +ν HL )}/ν car 
 
based on wheel rotation speed variables v VR  ( 140 ), v VL  ( 142 ), v HR  ( 144 ) and v HL  ( 146 ) determined in step  320  and normalized to vehicle speed v car  ( 148 ). If, however, in step  470  a calibration variable Kal AB  or Kal DB  is set to 0, the associated tire state variable is not ascertained.
 
   In the context of monitoring using extrapolated calibration variables, an adaptive adaptation of the threshold values as a function of the speed deviation Δv can additionally be performed, as shown in step  490 . For example, using
 
 SW   AB   =SW   AB *(1 +SW   F )
 
and
 
 SW   DB   =SW   DB *(1 +SW   F ),
 
the corresponding threshold values can be assigned a correction factor SW F  that can be selected as a function of Δv. The table below represents one possible allocation:
 
   
     
       
             
             
             
           
         
             
                 
                 
             
             
                 
               Deviation km/h 
               Factor SW F   
             
             
                 
                 
             
           
           
             
                 
                0 &lt; Δv ≦ 5 
               2/100 
             
             
                 
                5 &lt; Δv ≦ 10 
               5/100 
             
             
                 
               10 &lt; Δv ≦ 20 
               1/00  
             
             
                 
               20 &lt; Δv ≦ 30 
               2/10  
             
             
                 
               30 &lt; Δv ≦ 40 
               5/10  
             
             
                 
                 
             
           
        
       
     
   
   Once the modified threshold values for the extrapolated calibration variables have been ascertained, monitoring is continued with step  360  as depicted in FIG.  3 . 
     FIG. 5  depicts a further example embodiment in which exceedance of a limit value by a driving state variable indicates a change in a monitoring mode. The change in monitoring mode generates a calibration request ( 115 ) and, optionally, the algorithm described in  FIG. 2  is started immediately thereafter. 
   In the example embodiment shown in  FIG. 5 , step  500  first queries whether a high-speed range has already been attained at earlier points in time during vehicle operation. This can be determined, for example, if a flag F H  is set, i.e., F H =1. If a set flag F H  is detected, the algorithm shown in  FIG. 5  is terminated. Otherwise, in step  510 , limit values SW G  and SW t  are read in from memory  155 . Limit value SW G  represents a vehicle speed value that, when exceeded the first time by a new tire, results in an irreversible one-time plastic deformation (spreading) of the tire. In order for a deformation of the tire to be observed, however, the tire must be driven for a defined time SW t  above vehicle speed SW G . Both variables are specific to the tire, and can be updated in memory  155 , for example, by way of an external update or an automatic detection of the tire or of a tire change. In addition to the reading in of values SW G  and SW t , an internal timer is started (t=0) in step  510 . In the next step  520 , the instantaneous vehicle speed v car  ( 148 ) is read in. In step  530  this instantaneous vehicle speed v car  ( 148 ) is compared to limit value SW G . If the instantaneous vehicle speed v car  ( 148 ) is below limit value SW G , the algorithm is terminated. If v car  ( 148 ) exceeds SW G , however, then in step  540  the behavior over time of the exceedance is checked. If it is found that the tire has not yet been driven for sufficient time at the corresponding speed, the algorithm continues to execute with step  520 . If, however, the tire has been operated for a defined time above the stipulated speed limit value SW G , i.e., if the comparison t&gt;SW t  gave a positive result, then in step  550  flags F H  and F I  ( 115 ) are set, and are stored in memory  155 . A set flag F H =1 indicates that the tires have experienced a plastic deformation. A set flag F I =1 moreover makes possible a restart of the calibration algorithm that was presented in a previous exemplified embodiment. Optionally, in step  560 , subsequent to step  550 , initiation of the calibration algorithm (e.g., in accordance with the example embodiment of  FIG. 2 ) can then also be enabled before the algorithm shown in  FIG. 5  is complete. 
   The case of a single new tire plays a critical role in the consideration of the irreversible one-time plastic deformation of new tires when a speed threshold is exceeded. If, for example, a spare tire is mounted on a vehicle that already has three previously broken-in tires, the calibration operation must be restarted, since otherwise the deformation of the new tire after exceedance of the speed threshold value would cause the spare tire to roll more slowly. The calibration operation can be restarted on the one hand manually by the driver of the vehicle, but also automatically by resetting flag F I , i.e., F I =0. This can be done, for example, by manual deletion of flag F I  ( 115 ) by the mechanic or the driver upon replacement of the tire. Another possibility is that replacement of a tire is detected automatically and causes a reset of flag F I  ( 115 ). 
   The algorithms presented in the example embodiments set forth above can be started for monitoring at regular intervals, or on the basis of a deliberate action by the driver.