Abstract:
A method of indirect tire pressure monitoring for indicating when a pneumatic tire on a wheel at one end of a motor vehicle axle is underpressurized relative to a pneumatic tire on a wheel at an opposite end of the axle while the vehicle is being driven on a road surface. ABS wheel sensors are used as inputs to a devoted processor for indirect tire pressure monitoring.

Description:
FIELD OF THE INVENTION 
       [0001]    This invention relates to motor vehicles that ride on pneumatic tires, and in particular it relates to a system and method using indirect measurement to indicate a difference in inflation pressure of pneumatic tires on wheels at opposite ends of an axle. 
       BACKGROUND OF THE INVENTION 
       [0002]    The increased presence of ABS systems on motor has led engineers to seek software methods for monitoring pneumatic tire pressure that use messages from the ABS controller because such methods can be highly cost effective due to the fact that each wheel is already equipped with a precision wheel speed sensor. The use of ABS wheel speed messages in methods for monitoring tire pressure are disclosed in various patents and other documents. 
         [0003]    In July, 2001, the United States Department of Transportation published a document “Tire Pressure Monitoring System, FMVSS No. 138”, summarizing ITPM (indirect tire pressure monitoring) project progress. That document represents that ITPM&#39;s can report tire underinflation when the tire pressure difference is greater than 20-30% of their placard pressure. This is due to the fact that the effective radius of a pneumatic tire decreases very slightly when a tire is underinflated by about 15 psi (pounds per square inch). 
       SUMMARY OF THE INVENTION 
       [0004]    The preferred embodiment of the invention utilizes a devoted processor to process data that is present in messages on a data bus conforming to SAE Standard J1939 in a motor vehicle such as a truck and to send an alert to the driver when the result of processing data for two tires on a common axle discloses that pressure in one has changed from the amount of change in the other by a certain amount while the vehicle is being driven. The messages include messages from ABS sensors. The calculations are made with a high degree of statistical confidence, such as 90% confidence. By the same token, a false alert is avoided with the same confidence. 
         [0005]    The processing is performed in the devoted processor by executing an algorithm that has been developed to be reasonably sensitive and reliable, with relatively high probability of giving a true alert indicative of a difference between pressure change in one tire relative to that in the other and/or uneven tire loading on opposite sides of the vehicle, and with relatively low probability of giving a false alert. 
         [0006]    This invention is suitable for use on various motor vehicles equipped with 4-wheel ABS systems, it has been developed to provide ITPM for large trucks whose GVW exceeds 4536 kg. with either single-wheel or dual-wheel drive axles and that may have relatively larger tires and higher pressures than typical of smaller vehicles. 
         [0007]    One general aspect of the invention relates to a method of indirect tire pressure monitoring for indicating when a pneumatic tire on a wheel at one end of a motor vehicle axle is underpressurized relative to a pneumatic tire on a wheel at an opposite end of the axle while the vehicle is being driven on a road surface. 
         [0008]    The method comprises repeatedly calculating difference between a current measurement of effective radius of each tire relative to a reference value for effective radius of the same tire and processing the calculated differences for each tire and comparing the calculated differences to each other. 
         [0009]    When the comparison of the calculated differences discloses that one of the calculated differences differs from that for the other by more than a defined amount, that disclosure is used to determine if an alert for indicating that one tire is too underpressurized relative to the other should be issued. 
         [0010]    Another general aspect relates to an indirect tire pressure monitoring system for indicating when a pneumatic tire on a wheel at one end of a motor vehicle axle is underpressurized relative to a pneumatic tire on a wheel at an opposite end of the axle while the vehicle is being driven on a road surface. 
         [0011]    The system comprises: a respective sensor at each wheel or at each side of wheel for dual wheel axis that supplies the same data to an ABS system of the vehicle and to a devoted processor for indirect tire pressure monitoring. 
         [0012]    The devoted processor is arranged to repeatedly execute an algorithm for calculating difference between a current measurement of effective radius of each tire relative to a reference value for effective radius of the same tire, to process the calculated differences for each tire and compare the calculated differences to each other. 
         [0013]    When the comparison of the calculated differences discloses that one of the calculated differences differs from that for the other by more than a defined amount, that disclosure is used to determine if an alert for indicating that one tire is too underpressurized relative to the other should be issued. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]      FIG. 1  is general schematic diagram of the inventive algorithm. 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0015]    The effective radius of a pneumatic tire can be written as r j =r j (p j ,v j ,T j ,l j ,x ij ,y kj ), j=1, 2, 3, 4, i,k=1, 2, 3, 4 . . . where j=1, 2, 3, 4 indicate front left, front right, rear left, rear right wheels, p j  is the pressure, T j  is the ambient temperature, v j  is wheel speed, l j  is load, x ij s are other factors which are virtually the same acting when acting on wheels on same axle while y kj s are factors which act differently on each wheel. Due to the complicated relationships and unpredictable factors that may arise during driving, this generalized function cannot be developed with sufficient specificity to enable individual tire pressure to be directly monitored. 
         [0016]    However, the following generalized functional relationship can be further developed in a way that enables indirect monitoring of tire pressure in each of a pair of tires: r j =r j0 +dr j  where r j0  is the effective radius of a pneumatic tire under a specified condition, such as the standard condition defined by the tire manufacturer. Examples of other specified conditions are the tire being under load on a vehicle, the tire being at a specified ambient temperature, such as room temperature for example, zero speed, etc. 
         [0017]    dr j  is the first order derivative which may be considered a small quantity compared with r j0  under normal and near-normal driving conditions. Higher order derivatives are quite small and can be ignored if desired for simplicity in developing an algorithm that can be executed by a processor. 
         [0018]    Because of manufacturing tolerances and vehicle-to-vehicle variations, r j0  for each wheel is likely to be slightly different. Effective radii of most truck tires are about 0.5 m. A 0.05% tolerance equates to 0.25×10 −3  m. 
         [0019]    Tests by one source have disclosed that a 10 PSI difference between the front tires will cause the effective radius to change about 0.8×10 −3  m on average, but with a rather large standard deviation, as will be more fully discussed later. Because the dimensions are of the same order of magnitude, the tolerance associated with them will strongly affect the measurement of the effective radius due to the pressure change. To avoid this, the inventors focus attention on dr j  instead of r j , directly. 
         [0020]    The derivative dr can be written as 
         [0000]    
       
         
           
             
               
                 dr 
                 j 
               
               = 
               
                 
                   
                     
                       ∂ 
                       
                         r 
                         j 
                       
                     
                     
                       ∂ 
                       
                         p 
                         j 
                       
                     
                   
                    
                   
                     dp 
                     j 
                   
                 
                 + 
                 
                   
                     
                       ∂ 
                       
                         r 
                         j 
                       
                     
                     
                       ∂ 
                       
                         T 
                         j 
                       
                     
                   
                    
                   
                     dT 
                     j 
                   
                 
                 + 
                 
                   
                     
                       ∂ 
                       
                         r 
                         j 
                       
                     
                     
                       ∂ 
                       
                         v 
                         j 
                       
                     
                   
                    
                   
                     dv 
                     j 
                   
                 
                 + 
                 
                   
                     
                       ∂ 
                       
                         r 
                         j 
                       
                     
                     
                       ∂ 
                       
                         l 
                         j 
                       
                     
                   
                    
                   
                     dl 
                     j 
                   
                 
                 + 
                 
                   
                     
                       ∂ 
                       
                         r 
                         j 
                       
                     
                     
                       ∂ 
                       
                         x 
                         ij 
                       
                     
                   
                    
                   
                     dx 
                     ij 
                   
                 
                 + 
                 
                   
                     
                       ∂ 
                       
                         r 
                         j 
                       
                     
                     
                       ∂ 
                       
                         y 
                         kj 
                       
                     
                   
                    
                   
                     dy 
                     kj 
                   
                 
               
             
             ; 
           
         
       
     
         [0000]    where j=1, 2, 3, 4 i,k=1, 2, 3, 4 . . . . 
         [0021]    Because x ij  are factors which are the same for each tire, the subscripts of j can be omitted. The same is true for ambient temperature, and hence the subscripts on T can also be omitted. 
         [0022]    This leaves: 
         [0000]    
       
         
           
             
               
                 dr 
                 j 
               
               = 
               
                 
                   
                     
                       ∂ 
                       
                         r 
                         j 
                       
                     
                     
                       ∂ 
                       
                         p 
                         j 
                       
                     
                   
                    
                   
                     dp 
                     j 
                   
                 
                 + 
                 
                   
                     
                       ∂ 
                       
                         r 
                         j 
                       
                     
                     
                       ∂ 
                       T 
                     
                   
                    
                   dT 
                 
                 + 
                 
                   
                     
                       ∂ 
                       
                         r 
                         j 
                       
                     
                     
                       ∂ 
                       
                         v 
                         j 
                       
                     
                   
                    
                   
                     dv 
                     j 
                   
                 
                 + 
                 
                   
                     
                       ∂ 
                       
                         r 
                         j 
                       
                     
                     
                       ∂ 
                       
                         l 
                         j 
                       
                     
                   
                    
                   
                     dl 
                     j 
                   
                 
                 + 
                 
                   
                     
                       ∂ 
                       
                         r 
                         j 
                       
                     
                     
                       ∂ 
                       
                         x 
                         i 
                       
                     
                   
                    
                   
                     dx 
                     j 
                   
                 
                 + 
                 
                   
                     
                       ∂ 
                       
                         r 
                         j 
                       
                     
                     
                       ∂ 
                       
                         y 
                         kl 
                       
                     
                   
                    
                   
                     dy 
                     kj 
                   
                 
               
             
             , 
           
         
       
     
         [0000]    where j=1, 2, 3, 4, i,k=1, 2, 3, 4 . . . . 
         [0023]    Many factors are uncontrollable during driving. To reduce these effects as much as possible, consider first the difference of derivatives of two front tires. (It is assumed that the loads on the front tires are same, although that may be not true for rear tires on uneven conditions): 
         [0000]    
       
         
           
             
               
                 dr 
                 1 
               
               - 
               
                 dr 
                 2 
               
             
             = 
             
               
                 ( 
                 
                   
                     
                       
                         ∂ 
                         
                           r 
                           1 
                         
                       
                       
                         ∂ 
                         
                           p 
                           1 
                         
                       
                     
                      
                     
                       dp 
                       1 
                     
                   
                   - 
                   
                     
                       
                         ∂ 
                         
                           r 
                           2 
                         
                       
                       
                         ∂ 
                         
                           p 
                           2 
                         
                       
                     
                      
                     
                       dp 
                       2 
                     
                   
                 
                 ) 
               
               + 
               
                 
                   ( 
                   
                     
                       
                         ∂ 
                         
                           r 
                           1 
                         
                       
                       
                         ∂ 
                         T 
                       
                     
                     - 
                     
                       
                         ∂ 
                         
                           r 
                           2 
                         
                       
                       
                         ∂ 
                         T 
                       
                     
                   
                   ) 
                 
                  
                 dT 
               
               + 
               
                 ( 
                 
                   
                     
                       
                         ∂ 
                         
                           r 
                           1 
                         
                       
                       
                         ∂ 
                         
                           v 
                           1 
                         
                       
                     
                      
                     
                       dv 
                       1 
                     
                   
                   - 
                   
                     
                       
                         ∂ 
                         
                           r 
                           2 
                         
                       
                       
                         ∂ 
                         
                           v 
                           2 
                         
                       
                     
                      
                     
                       dv 
                       2 
                     
                   
                 
                 ) 
               
               + 
               
                 
                   ( 
                   
                     
                       
                         ∂ 
                         
                           r 
                           1 
                         
                       
                       
                         ∂ 
                         l 
                       
                     
                     - 
                     
                       
                         ∂ 
                         
                           r 
                           2 
                         
                       
                       
                         ∂ 
                         l 
                       
                     
                   
                   ) 
                 
                  
                 dl 
               
               + 
               
                 
                   ( 
                   
                     
                       
                         ∂ 
                         
                           r 
                           1 
                         
                       
                       
                         ∂ 
                         
                           x 
                           i 
                         
                       
                     
                     - 
                     
                       
                         ∂ 
                         
                           r 
                           2 
                         
                       
                       
                         ∂ 
                         
                           x 
                           i 
                         
                       
                     
                   
                   ) 
                 
                  
                 
                   dx 
                   i 
                 
               
               + 
               
                 ( 
                 
                   
                     
                       
                         ∂ 
                         
                           r 
                           1 
                         
                       
                       
                         ∂ 
                         
                           y 
                           
                             k 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                     
                      
                     
                       dy 
                       
                         k 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                   - 
                   
                     
                       
                         ∂ 
                         
                           r 
                           2 
                         
                       
                       
                         ∂ 
                         
                           y 
                           
                             k 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                     
                      
                     
                       dy 
                       
                         k 
                          
                         
                             
                         
                          
                         2 
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
         [0000]    where i,k=1, 2, 3, 4 . . . . 
         [0024]    The same model tires should have similar behavior with small tolerances for load, temperature, and other factors so that these effects will be second order of small quantities and can be neglected when the first order contributions are considered, thereby leaving: 
         [0000]    
       
         
           
             
               
                 dr 
                 1 
               
               - 
               
                 dr 
                 2 
               
             
             = 
             
               
                 ( 
                 
                   
                     
                       
                         ∂ 
                         
                           r 
                           1 
                         
                       
                       
                         ∂ 
                         
                           p 
                           1 
                         
                       
                     
                      
                     
                       dp 
                       1 
                     
                   
                   - 
                   
                     
                       
                         ∂ 
                         
                           r 
                           2 
                         
                       
                       
                         ∂ 
                         
                           p 
                           2 
                         
                       
                     
                      
                     
                       dp 
                       2 
                     
                   
                 
                 ) 
               
               + 
               
                 ( 
                 
                   
                     
                       
                         ∂ 
                         
                           r 
                           1 
                         
                       
                       
                         ∂ 
                         
                           v 
                           1 
                         
                       
                     
                      
                     
                       dv 
                       1 
                     
                   
                   - 
                   
                     
                       
                         ∂ 
                         
                           r 
                           2 
                         
                       
                       
                         ∂ 
                         
                           v 
                           2 
                         
                       
                     
                      
                     
                       dv 
                       2 
                     
                   
                 
                 ) 
               
               + 
               
                 ( 
                 
                   
                     
                       
                         ∂ 
                         
                           r 
                           1 
                         
                       
                       
                         ∂ 
                         
                           y 
                           
                             k 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                       
                     
                      
                     
                       dy 
                       
                         k 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                   - 
                   
                     
                       
                         ∂ 
                         
                           r 
                           2 
                         
                       
                       
                         ∂ 
                         
                           y 
                           
                             k 
                              
                             
                                 
                             
                              
                             2 
                           
                         
                       
                     
                      
                     
                       dy 
                       
                         k 
                          
                         
                             
                         
                          
                         2 
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
         [0000]    where k=1, 2, 3, 4, . . . . 
         [0025]    The contribution of the second term during normal driving should be a small second order quantity (both 
         [0000]    
       
         
           
             
               ∂ 
               
                 r 
                 i 
               
             
             
               ∂ 
               
                 v 
                 i 
               
             
           
         
       
     
         [0000]    and dr j  are first order quantities) that can be neglected. Even on curve driving, it can also be considered as a second order small quantity. If a vehicle&#39;s width is a, the curvature of the road is R, a first wheel (Wheel  1 ) is on the inside of the curve and a second wheel (Wheel  2 ) is on the outside, v 1  and v 2  will not be much different. Therefore, we can consider 
         [0000]    
       
         
           
             
               
                 
                   ∂ 
                   
                     r 
                     1 
                   
                 
                 
                   ∂ 
                   
                     v 
                     1 
                   
                 
               
               ≈ 
               
                 
                   ∂ 
                   
                     r 
                     2 
                   
                 
                 
                   ∂ 
                   
                     v 
                     2 
                   
                 
               
             
             , 
           
         
       
     
         [0000]    and can write the function as 
         [0000]    
       
         
           
             
               
                 ∂ 
                 
                   r 
                   1 
                 
               
               
                 ∂ 
                 
                   v 
                   1 
                 
               
             
              
             
               
                 ( 
                 
                   
                     dv 
                     1 
                   
                   - 
                   
                     dv 
                     2 
                   
                 
                 ) 
               
               . 
             
           
         
       
     
         [0026]    According to the standard WdK (German Rubber Enterprise Association) 
         [0000]    
       
         
           
             
               
                 ∂ 
                 
                   r 
                   1 
                 
               
               
                 ∂ 
                 
                   v 
                   1 
                 
               
             
             ≈ 
             
               0.0001 
               * 
               
                 r 
                 1 
               
             
           
         
       
     
         [0000]    (m/(km/h)), usually d(v 1 −v 2 )&lt;10 −2  mile/h on curve driving, is small so that the contribution will be on the order of 10 −6  m, a small second order quantity that can be neglected. However, the curve driving itself causes much bigger “effective radius” change, to be discussed later. The third term can usually be filtered out unless some factors last for a long period, also to be discussed later. 
         [0027]    Discussion now focuses on the first term. 
         [0028]    Under normal condition, 
         [0000]    
       
         
           
             
               
                 p 
                 1 
               
               ≅ 
               
                 p 
                 2 
               
             
             , 
             
               
                 
                   dp 
                   1 
                 
                 ≅ 
                 
                   dp 
                   2 
                 
               
               = 
               0 
             
             , 
             
               
                 
                   ∂ 
                   
                     r 
                     1 
                   
                 
                 
                   ∂ 
                   
                     p 
                     1 
                   
                 
               
               = 
               
                 
                   ∂ 
                   
                     r 
                     2 
                   
                 
                 
                   ∂ 
                   
                     p 
                     2 
                   
                 
               
             
             , 
           
         
       
     
         [0000]    making the first term of the right side of the above equation equal to 0. 
         [0029]    If tire pressure changes such that dp 1 ≠dp 2  and 
         [0000]    
       
         
           
             
               
                 ∂ 
                 
                   r 
                   1 
                 
               
               
                 ∂ 
                 
                   p 
                   1 
                 
               
             
             ≠ 
             
               
                 ∂ 
                 
                   r 
                   2 
                 
               
               
                 ∂ 
                 
                   p 
                   2 
                 
               
             
           
         
       
     
         [0000]    (if dp 1 , dp 2  have a significant difference) 
         [0000]    
       
         
           
             
               
                 dr 
                 1 
               
               - 
               
                 dr 
                 2 
               
             
             = 
             
               
                 
                   
                     ∂ 
                     
                       r 
                       1 
                     
                   
                   
                     ∂ 
                     
                       p 
                       1 
                     
                   
                 
                  
                 
                   dp 
                   1 
                 
               
               - 
               
                 
                   
                     ∂ 
                     
                       r 
                       2 
                     
                   
                   
                     ∂ 
                     
                       p 
                       2 
                     
                   
                 
                  
                 
                   
                     dp 
                     2 
                   
                   . 
                 
               
             
           
         
       
     
         [0030]    Should one tire leak (assume right front) and the other is normal (left front): 
         [0000]    
       
         
           
             
               
                 dr 
                 1 
               
               - 
               
                 dr 
                 2 
               
             
             = 
             
               
                 - 
                 
                   
                     ∂ 
                     
                       r 
                       2 
                     
                   
                   
                     ∂ 
                     
                       p 
                       2 
                     
                   
                 
               
                
               
                 dp 
                 2 
               
             
           
         
       
     
         [0000]    and because 
         [0000]    
       
         
           
             
               
                 ∂ 
                 
                   r 
                   1 
                 
               
               
                 ∂ 
                 
                   p 
                   1 
                 
               
             
             , 
             
               
                 ∂ 
                 
                   r 
                   2 
                 
               
               
                 ∂ 
                 
                   p 
                   2 
                 
               
             
           
         
       
     
         [0000]    are not constants, dr 1 −dr 2  is not a linear function of dp 2 . 
         [0031]    Thus far the discussion has focused on the effective radius change due to physical factors. It is necessary to consider another factor: the effective radius change due to calculation. That happens on curve driving. It is not decided by the physical factor as mentioned in the second term, but is decided by kinetic calculation by the formula for curve driving. 
         [0032]    Let φ be the angle of the curve, and a be the distance between the two front steering wheels. The inside wheel travels the distance is Rφ and outside wheel travels the distance is (R+a)φ. The contribution due to curve driving will be: 
         [0000]    
       
         
           
             
               
                 
                   dr 
                   1 
                 
                 - 
                 
                   dr 
                   2 
                 
               
               
                 r 
                 2 
               
             
             ≅ 
             
               a 
               R 
             
           
         
       
     
         [0033]    Usually the width a is about 2.5 m, and so if we set curvature of the driving curve as 2500 m., a/R is about 0.1%, or the difference is 0.5×10 −3  m. 
         [0034]    The measurement of dr 1 −dr 2  is important to the algorithm. 
         [0035]    dr j  is the difference between the current effective radius of a tire (with the tire either cold or warm) and the effective radius of the tire when first put into service on the vehicle, typically as a new tire. The meaning of j is given in Paragraph [0015]. 
         [0036]    dr o  is the difference between the current effective radius of a tire and the effective radius that is first calculated after a limited amount of time has elapsed upon the vehicle being first driven after having been parked for an amount of time sufficient to allow the tires to assume substantially ambient temperature. The limited amount of time corresponds to a warm-up time for the tires and is typically preset (15 minutes for example), but can be determined on the basis of certain conditions. dr j  is used as a reference to decide if a significant pressure leak during the parking period. It can give a quick alert. The threshold is bigger than that using dr j . 
         [0037]    The high resolution wheel speed data has the precision of 1/256 km/h (0.004 km/h). At a vehicle speed of 40 km/h, the relative error will be 0.01% (for each wheel, this is only the measurement error, we have not included the physical error for the tire yet, but it will be discussed later), or the order of the 0.05×10 −3  m. Testing has disclosed that the value of dr 1 −dr 2  when one tire is 10 PSI low, is about 0.28×10 −3  m. 
         [0038]    However, testing has disclosed that during driving, the variation in the effective radius of a tire is significant. For example the standard deviation has been seen to have a range from about 1.5×10 −3  m. to about 4.0×10 −3  m., and that makes it difficult to pick up useful information. The inventive algorithm however functions to extract the useful information with a reasonably high degree of confidence in accuracy of the extracted information. Moreover, the algorithm can be used in a circumstance where the tires have slightly different initial radii. 
         [0039]      FIG. 1  shows a system  10  that performs the method. System  10  comprises five sub-systems: CAN communication  12 , Radius Calculation  14 , Filtering  16 , New Tire  18 , and Algorithm  20 . 
         [0040]    The method comprises reading speed of each wheel from the associated ABS wheel speed sensor and vehicle speed (sub-system, or sub-method  12 ), calculating the effective radius of each tire (sub-system or sub-method  14 ), removing noise from the input data (sub-system or sub-method  16 ), calculating an effective radius for a newly installed tire (sub-system or sub-method  18 ), and judging the tire pressure condition and determining the alert level that is displayed to the driver (sun-system or sub-method  20 ). 
         [0041]    The Radius Calculation sub-system  14  performs a sub-method of calculating the effective radii as described above. 
         [0042]    The Filtering sub-system  16  performs five functions: removing bad messages, removing low speed messages, removing curve driving messages, removing noises, and controlling the deviations. If a calculated effective radius is greater than 0.6 m or less than 0.4 m, the calculation is discarded. If the vehicle speed is less than 25 km/h, the calculation is also discarded because an ABS signal is typically not sufficiently accurate at low speed for the inventive algorithm to produce an accurate result with a high degree of probability. Because the messages from J1939 have absolute precision, the relative error will be five times greater at a vehicle speed of 24 km/h (15 mph) than at a vehicle speed of 112 km/h (70 mph). For example, the wheel relative speed has a resolution of 1/16 (km/h), it has the relative error of 0.05% at 112 mk/h (70 mph) and 0.25% at 24 km/h (15 mph). 
         [0043]    When 
         [0000]    
       
         
           
             
               
                  
                 
                   
                     
                       ω 
                       1 
                     
                     - 
                     
                       ω 
                       2 
                     
                   
                   
                     
                       ω 
                       1 
                     
                     + 
                     
                       ω 
                       2 
                     
                   
                 
                  
               
               &gt; 
               0.0005 
             
             , 
             
               
                  
                 
                   
                     
                       ω 
                       3 
                     
                     - 
                     
                       ω 
                       4 
                     
                   
                   
                     
                       ω 
                       3 
                     
                     + 
                     
                       ω 
                       4 
                     
                   
                 
                  
               
               &gt; 
               0.0005 
             
             , 
           
         
       
     
         [0000]    and (ω 1 −ω 2 )(ω 3 −ω 4 )≧0 are true, the vehicle is on curve driving, and the calculations are also discarded. 0.0005 is from the example discussed earlier. 
         [0044]    In the calculation performed by the New Tire sub-system  18 , the algorithm uses the mean value of 2560 calculations of effective radius to obtain the reference value for effective radius that is used by the algorithm once the tires have warmed up. During the normal indirect monitoring process, the algorithm use an average from 256 calculations. The standard deviation of the effective radius from test record is about 0.0015 m-0.0040 m. To ensure with a 95% confidence level that the error range of abs(dr 1 −dr 2 ) is less than 0.00028 m (from the analysis of test data), we should have at least 256 calculations that can be averaged each time that the current effective radius is being calculated. 
         [0045]    The New Tire sub-system  18  saves the initial radii for tires when first installed on the vehicle. 
         [0046]    The Algorithm sub-system  20  judges the tire conditions. 
         [0047]    Assign a parameter AL as an alert level, and a parameter CR as the maximum allowable difference between allowed (in this example 0.00028 m, 95% confidence level from certain empirically obtained test data) 
         [0048]    While the initial values of AL, CR are set to be zero, a value of CR is entered at the beginning of execution of the algorithm. 
         [0049]    The algorithm sets a value for AL based on the result of calculating dr 1 −dr 2 . 
         [0050]    If dr 1 −dr 2 &lt;−CR, and AL is zero, AL remains at zero, but if AL had been greater than zero, its value would be decremented by one, and if AL had been less than zero, its value would be incremented by one. 
         [0051]    If dr 1 −dr 2 &lt;CR, and AL is zero, AL remains at zero, but if AL had been greater than zero, its value would be incremented by one, and if AL had been less than zero, its value would be decremented by one. 
         [0052]    Whenever the absolute value of AL reaches a predetermined value, an alert is given to indicate that the calculated rate of change of effective radius for one tire differs from that for the other tire by an amount that indicates with high probability that one tire is sufficiently underpressurized to deserve attention. 
         [0053]    The algorithm uses the change of effective radius (dr 1 , dr 2 ) as the basic variable instead of the effective radius. By comparing the change of effective radius on left and right side on the same axle (single wheel, or equivalent effective radius for dual wheels), this algorithm removes the influence of tire wear, and manufacturing tolerances for new tires. Most of the effective radius change caused by those factors, and others like speed, evenness of load, temperature, road condition, etc., act on both sides of the same axle are essentially canceled out. Any difference caused by these factors can be considered as second order small quantity, and omitted in most cases by comparing only the first order quantity, i.e., change in the effective radius caused by pressure changes and/or uneven tire loading. 
         [0054]    The devoted processor collects ABS wheel speed data and removes the influence of noise, curve driving, and low speed operation so as to allow only data with high probability of being accurate to be used in the calculation of effective tire radius. By using the effective radius of the tire when first put into service on the vehicle as the reference value during warm-up periods, the influence of changes that are occurring as the tires are becoming warmer is avoided. 
         [0055]    Once the tires have warmed up, the effective radii calculated substantially at the completion of the warm-up period are subsequently used as the reference values, being used each time until the vehicle&#39;s engine is turned off. When a tire is changed, a signal can be given to the devoted processor, such as by a push button switch, to cause the algorithm to calculate the initial effective radius for that tire. 
         [0056]    While a presently preferred embodiment of the invention has been illustrated and described, it should be appreciated that principles of the invention apply to all embodiments falling within the scope of the following claims.