Abstract:
Wheel speed values for each of four wheels are collected and statistically analyzed axle by axle for a difference which could indicate low tire pressure. Prior to analysis, and following reset of the system, calibration factors are determined for each axle to compensate for rolling radius variation, and are subsequently used to correct the percentage difference values for the two wheels on any one axle. When a sufficient number of values have been collected, a t 0  value is calculated for each axle according the paired t-test statistical method or a slight variation thereof The t 0  value for each axle is then compared to a respective empirical value based on a predetermined pressure loss. This comparison can provide the basis for a driver warning. Various types of filters can be used prior to calculating the t 0  values to eliminate data that may lead to improper deflation detection.

Description:
FIELD OF THE INVENTION 
     The invention relates to a method of detecting when the air pressure in a tire has fallen below a predetermined pressure level, based on the measured wheel speeds. 
     BACKGROUND OF THE INVENTION 
     The advent of anti-lock brake systems (ABS) and the placement of speed sensing devices at each of the wheels has sparked efforts to develop reliable methods for detecting tire deflation based on wheel speeds measured during driving. Theoretically, four equally inflated tires on a vehicle will have substantially the same rolling radius and will therefore each rotate at substantially the same speed during straight-line driving on a dry, flat and uniform surface. When a tire becomes deflated, its rolling radius is reduced and the wheel speed increases to compensate for the smaller radius. Numerous methods have been created that monitor the wheel speeds and detect variations that may be attributable to tire deflation. 
     A recurring problem associated with these deflation detection methods involves the ability to filter or eliminate the collection of faulty data points caused by a variety of factors such as built-in tire radius variations, vehicle maneuvering, road conditions and drive slip. Without eliminating or filtering out these faulty readings, the detection methods are prone to improper warnings of tire deflation or failure to detect actual tire deflation. False warnings are troublesome and annoying to drivers, while failure to detect deflation is dangerous and could result in tire blow-outs. Methods that accurately detect tire deflation while avoiding false detection have become the utmost priority. 
     Filtering or eliminating faulty data caused by drive slip has been a significant obstacle. Simply stated, a vehicle&#39;s driven wheels slip due to the torque being applied to the axle. This slippage results in higher wheel speeds for the driven wheels than for the non-driven wheels. For example, on a rear wheel drive vehicle travelling at highway speeds, the rear wheels may rotate approximately one percent faster than the non-driven front wheels. This one percent variation is unacceptably high in light of the small wheel speed variations (typically 0.1 percent to 0.5 percent) caused by an actual deflated tire. If faulty data is not filtered or eliminated, drive slip error can wash out the influence of tire pressure and thus severely degrade the ability to detect tire deflation. Drive slip becomes even more problematic during acceleration, uphill/downhill driving and driving on non-uniform surfaces (such as dirt, sand or gravel). 
     Several attempts have been made to filter or eliminate the effect of drive slip on collected data. U.S. Pat. No. 5,760,682, issued Jun. 2, 1998, applies an analysis of the variance (ANOVA) statistical technique to the data collected from all four wheel speeds. The statistical method incorporated provides more accurate results than the more common average value comparison methods (where the data collected for each wheel is simply averaged before being used in a comparison algorithm) typically used. Filters are used to eliminate data collected during acceleration/deceleration, uphill/downhill driving, tuning/cornering fluctuation and rough road driving, but drive slip occurring during straight-line driving would tend to fool the analysis of variance technique since it is not able to distinguish the increase in wheel speed due to drive slip from the increase in wheel speed due to tire deflation. A false detection may occur. 
     U.S. Pat. No. 5,578,984, issued Nov. 26, 1996, discloses a system where drive slip is learned and compensated for with a correction factor designated as the front/rear wheel ratio Z. Such a learning process is not robust since data resulting from such learning only applies to the surface on which it was learned. For example, if such learning occurred on dry asphalt, the resulting correction factor will be wrong for data collected while driving on wet asphalt. Additionally, if such learning occurred on a level road surface, the resulting correction factor will be wrong for data collected while driving uphill since uphill driving requires more power at the drive wheels, causing more drive slip. False detection or failure to detect may result. 
     U.S. Pat. No. 4,876,528, issued Oct. 24, 1989, and U.S. Pat. No. 5,591,906, issued Jan. 7, 1997, disclose methods wherein angular velocities of two diagonally opposed wheels are added together and then compared (using various techniques) with the sum of the angular velocities of the other two diagonally opposed wheels. While this method should be resistant to drive slip error, there are other limitations associated with the formula, such as sensitivity to the diagonal component. For example, the front left wheel and rear right wheel could each only be slightly deflated (perhaps only ten percent), but the sum of that diagonal would appear the same as the case where only one of the wheels were significantly deflated (perhaps twenty-five percent). This results in undesired sensitivity since the objective is to detect twenty-five percent or greater deflation on one tire. Again, false detection may result. 
     Another problem with combining data from diagonally opposed wheels is discussed in U.S. Pat. No. 5,578,984. In many high performance sports cars, different sized tires are used for the front and rear axles. When this occurs, the critical threshold values used to detect deflation will be different for front and rear tires. Using diagonally opposed front and rear tires commingles the data so that the front and rear wheels can not be treated independently. 
     SUMMARY OF THE INVENTION 
     The present invention provides an improved method that substantially remedies the above-identified problems associated with attempts to eliminate error due to drive slip. Unlike the prior art methods that utilize data taken from all four tires in various combinations (i.e., comparing values from all four tires individually, opposing sets of diagonal tires or front tires and rear tires), the method of the present invention recognizes that utilizing combinations of data taken from all four tires cannot adequately prevent errors associated with drive slip. 
     As such, the present invention comprises a method for detecting a deflated tire wherein only the two wheels of one axle are considered at any one time to determine whether a tire is deflated. Since both wheels on a given axle rotate at substantially the same speed during straight-line driving, the comparison is inherently immune to drive slip and errors associated with using data from diagonally opposed tires. Even though the driven wheels tend to rotate faster than the non-driven wheels and may be larger than the non-driven wheels, the relative speed difference between the two driven wheels or the two non-driven wheels is zero. The present invention therefore analyzes the difference in speed between two wheels on a single axle to detect tire deflation. On the other hand, all four wheel speeds are still used together to detect rough road conditions and vehicle maneuvering conditions that provide other instances when false data should be filtered or eliminated. The result is a method of detecting a deflated tire that recognizes instances when data is faulty and should not be used, and additionally utilizes an algorithm that is inherently immune to drive slip error. 
     More specifically, the present invention is an improvement over U.S. Pat. No. 5,760,682, which is hereby incorporated by reference. In the present invention, a new statistical method suited for comparing data variability between two wheels replaces the ANOVA statistical analysis, which is suited for comparing data variability between all four wheels. The present invention utilizes a paired t-test statistical analysis, and more preferably a modification of the paired t-test, to consider data variability. Use of the modified paired t-test provides deflation detection that is more accurate and reliable than the previous ANOVA method which was already more accurate than calculations using the more common average value comparison methods. 
     The paired t-test is a statistical method applicable for use when data observation of two populations of interest is collected in pairs (i.e., data collected substantially simultaneously for the two wheels on a single axle). Each pair of observations is taken under substantially homogenous conditions, but these conditions may change from one pair of observations to the next. In the present invention, the paired t-test is run independently on pairs of wheel speed data taken from the front axle and pairs of wheel speed data taken from the rear axle. The paired t-test analyzes the differences between the paired data for each axle to provide independent to values for both axles. These to values are compared to predetermined upper and lower limits for each axle to determine whether the tires are properly inflated. The calculation of t 0  values according to the paired t-test is described in statistical texts. See for example, Hines and Montgomery, Probability and Statistics in Engineering and Management Science, pp. 312-313. The t 0  value is calculated as follows: 
     Let (X 11 ,X 21 ),(X 12 ,X 22 ), . . . ,(X 1n ,X 2n )be a set of n paired observations, where it is assumed that X 1 ˜N(μ 1 ,σ 1   2 ) and X 2 ˜N(μ 2 , σ 2   2 ). Define the differences between each pair of observations as D j =X 1j −X 2j ,j=1,2, . . . ,n. 
     The D j &#39;s are nonnally distributed with mean μ D =E(X 1 −X 2 )=E(X 1 )−E(X 2 )=μ 1 −μ 2  so testing hypotheses about equality of μ 1  and μ 2  can be accomplished by performing a one sample t-test on μ D . 
     Specifically, testing H 0 : μ 1 =μ 2  against H1:μ 1 ≠μ 2  is equivalent to testing 
     
       
           H   0 :μ D =0  
       
     
     
       
           H   1 :μ D ≠0  
       
     
     The appropriate test statistic for the above equation is          t   0     =       D   _         S   D     /     n                                
     where          D   _     =         ∑     j   =   1     n          D   j       n                            
     and          S   D     =             ∑     j   =   1     n          D   j   2       -     [         (       ∑     j   =   1     n          D   j       )     2     /   n     ]         n   -   1                                
     are the sample mean difference and standard deviation of the differences, respectively. 
     According to the preferred embodiment of the present invention, t 0  is calculated using a somewhat modified formulation of the t 0  equation. The modified t 0  equation is used to simplify the mathematics, making the calculations faster in a simple microcontroller where multiplication and division functions require more time than simple logic or addition operations, and where advanced math functions, such as the calculation of square roots, are not possible. The modified to equation uses an estimated standard deviation value S D  described in statistical texts. See for example, Hines and Montgomery, Probability and Statistics in Engineering and Management Science, p. 584. The estimated standard deviation value is calculated as follows: 
     The relationship between the range, R, of k samples from a normal population with known parameters and the standard deviation of that population is needed. Since R is a random variable, the quantity W=R/S D , called the relative range, is also a random variable. The parameters of the distribution of W have been determined for any sample size n R  (designated as n in the statistical text, but designated herein as n R  to eliminate confusion). The mean distribution of W is called d 2 , and is tabulated for various n R  in the above-mentioned statistical text. 
     Let R i  be the range of the ith sample, and let          R   _     =       1   k            ∑     i   -   1     k          R   i                                
     be the average range. 
     Then an estimate of S D  would be          S   D     =         R   _       d   2       .                            
     This estimate works well for two reasons. First, the data range R is small because the data has been screened against abrupt changes caused by vehicle maneuvering. Additionally, the number of data samples k gathered by the wheel speed sensors is very high. 
     The modified paired t-test of the preferred invention also utilizes an interpolating look-up table to supply the value {square root over (n)}. Since simple microprocessors cannot compute this value directly, yet the range of inputs and outputs is clearly defined, accuracy is maintained and the calculation is simplified by interpolating the {square root over (n)} using the following table: 
     
       
         
               
               
               
             
               
               
               
             
           
               
                   
                   
               
               
                   
                 n 
                 square root 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 2500 
                 50 
               
               
                   
                 3600 
                 60 
               
               
                   
                 6400 
                 80 
               
               
                   
                 10000 
                 100 
               
               
                   
                 19600 
                 140 
               
               
                   
                   
               
             
          
         
       
     
     By using an estimated standard deviation value and an interpolated {square root over (n)} value to calculate to, the modified paired t-test provides an algorithm that can be utilized with a relatively inexpensive embedded integer processor or microcontroller, as opposed to the more expensive and slower floating-point processors required in many other prior art deflation detection methods using complex algorithms. Since the modified paired t-test algorithm does not require calculation of any square roots or multiplications to a power higher than two, an integer processor is more than suitable to perform the required calculations. It should be noted, however, that the present invention can be practiced using a floating point processor and the standard paired t-test as opposed to the faster, simpler and less expensive method used in the preferred embodiment. 
     To calculate the to value, the normalized percentage difference in wheel speed between the two wheels on the respective front and rear axles is used. The normalized percentage difference in wheel speed for the respective axles can be written as:          NORM   1     =       (       V   1     -     V   2       )       V   ref                              
     
       
         
           
             
               NORM 
               2 
             
             = 
             
               
                 ( 
                 
                   
                     V 
                     3 
                   
                   - 
                   
                     V 
                     4 
                   
                 
                 ) 
               
               
                 V 
                 ref 
               
             
           
         
                 
         
             
         
      
     
     where V ref  represents the velocity of the vehicle. 
     Theoretically, the percentage difference in wheel speed between two wheels on any one axle should be zero if the tires are equally inflated and the vehicle is travelling in a straight line on a level surface over a period of time. Due to built-in variations, however, it cannot be assumed that the rolling radii of different tires are exactly the same, nor can it be assumed that the rolling radius of each tire is constant over time. 
     In order to correct for these disparities, a correction factor MOD j  is determined by taking the mean of the NORM j  values during a calibration mode. As used herein and in the figures and appended claims, the use of the subscript“j” to modify a variable means that the variable is measured or calculated for both axles individually. MOD j  simply represents the normally existing percent difference attributable to inherent disparities between the two tires on an axle. To correct the respective NORM j  values for use during tire inflation monitoring, the following equations are used:          NORM   i1     =         (       V   i1     -     V   i2       )       V   iref       -     MOD   1                              
     and          NORM   i2     =         (       V   i3     -     V   i4       )       V   iref       -     MOD   2                              
     As used herein and in the appended claims, the use of the subscript “i” to modify a variable means that the variable is measured or calculated repeatedly for each data set collected in the sample n. Note that the correction of percentage difference values does not affect the result of the paired t-test, nor the t 0  value. 
     To further distinguish the wheel speed difference caused by pressure loss from differences caused by other sources, a dynamic filtering process is used to exclude wheel speed data collected during various vehicle maneuvers. For that purpose, the algorithm according to the invention includes (1) wheel acceleration and deceleration filtering, (2) turning fluctuation filtering, and (3) rough road filtering at the ABS sampling period level. Additionally, a cornering detection routine is effective over a certain number of sampling periods, for example ten. For cornering, the difference between the linear speeds at the center of the right and left side wheels is proportional to vehicle speed and inversely proportional to cornering radius:            V   1     -     V   2       =       V   ref          l   r                              
     where r is the cornering radius and I is the track width. Wheel speed differences under this driving condition cannot be used to identify pressure loss due to the corruption by cornering. The algorithm identifies cornering by recognizing similar wheel speed difference patterns at both the front and the rear axles, and excludes the data collected under these conditions from entering the detection process. The equation can be simplified and manipulated as follows:            (       V   1     -     V   2       )       V   ref       =     l   r                            
     The left side of this equation is simply NORM j  such that          NORM   j     =     l   r                            
     and          1   r     =       NORM   j     l                            
     1/r is recognized as the curvature and can be compared to predetermined curvature values “B” and “C” that represent the values of curvature beyond which the vehicle is judged to be in a significant curve. The “B” and “C” values are chosen to be small enough that the algorithm can detect a vehicle negotiating an actual turn (so that data during such situations can be ignored). On the other hand, a value that is too small will determine that the vehicle is negotiating a turn when in fact the driver is simply making normal course corrections while driving straight (thus reducing the amount of “good” data that is usable for deflation detection). 
     Other features and advantages of the invention will become apparent to those skilled in the art upon review of the following detailed description, claims, and drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1A and 1B represent a flow chart of a preferred method according to the invention. 
     FIG. 2 shows a more detailed flow chart of the calculation of to. 
    
    
     Before one embodiment of the invention is explained in detail, it is to be understood that the invention is not limited in its application to the details of construction and the arrangements of the components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of being practiced or being carried out in various ways. Also, it is understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including” and “comprising” and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The flow chart represented in FIGS. 1A,  1 B and  2  outlines a simplified rendition of a computer program that can be used to practice the method according to the present invention. Throughout the program, wheel speeds are read in from the wheel speed sensors at each of the four wheels at regular sampling intervals. These wheel speed values, which are used to calculate normalized percentage difference in wheel speed as described above, are used both in a calibration procedure, wherein built-in variations are determined, and the ensuing t 0  calculations, wherein inflation is checked. When deflation is detected, it is assumed that the driver will take remedial action to render the tire pressures uniform. On doing this, he can reset the system by pushing a reset button. This can be done any time re-calibration is desired, such as after a wheel alignment or fitting new tires. 
     Whenever the system is reset, the various flags and counters used in the program are initialized (block  10 ). Setting the calibration flag (f_cal=1) indicates that the reset button has been pushed and the calibration is to proceed. Setting the warning light flag (f_wlt=1) turns on the warning light setting. The brake light switch flag (f_bls=0) indicates lack of brake pressure. This switch is wired in parallel with the brake lights. The tire inflation monitoring counter (hereinafter TIM counter), which counts the total number n of data pairs used for either calibration or monitoring tire inflation, is set to zero (i_tim=0). Likewise, the maneuver counter, which is a loop counter operating in conjunction with the TIM counter, is set to zero (i_man=0). 
     Following initialization, reading of wheel speeds V 1 , V 2 , V 3  and V 4 , begins (block  12 ). As each set of four values is read, the calibration and warning light flags are checked (block  14 ). If both are set, this is clear indication that the program is starting the calibration loop. The warning light is turned off (block  16 ), the modification factors MOD j  are set at 0 (block  18 ) and the maneuver and TIM sums are cleared (block  20 ). If the warning light flag is set and the system is not in calibration (block  22 ), this is a clear indication that low tire pressure has been detected. The program returns to block  12  and continues to read in wheel speeds until the system is reset. It is now up to the driver to put air in the tires and reset the system. 
     If the warning light is off (answer “no” in block  22 , or as a result of the warning light being cleared in block  16 ), then the wheel speed values are run through several filtering steps to eliminate values which cannot be used for a reliable calibration or tire inflation check. Block  24  checks for ABS failure, which is determined externally by the ABS control module so that the ABS shuts down, and automatic regulation of brake pressure is eliminated. Block  26  checks for presence of a spare tire, which is detected when one wheel speed is significantly faster than other wheel speeds. If either of the above checks is positive, the tire inflation monitoring step is bypassed and the program returns to block  12  for the next set of wheel speed data. 
     If the above checks are negative, filtering continues. Block  28  filters out wheel speeds which occur when the vehicle is moving especially slow (below 10 kph) or especially fast (above 200 kph). Block  30  checks for braking, and disregards values when the brake light switch is on. If braking is not present, the wheel speed values are checked for abrupt positive or negative changes (block  32 ), which would indicate non-steady behavior or wheel noise that can be caused, for example, by large bumps in the road. Block  32  only accepts wheel speed values when dv/dt is within limits which correspond to limits of wheel acceleration and deceleration. Block  33  checks for wheel spin-up which is an extreme form of acceleration in the drive wheels that may occur, for example, when a driver uses excessive throttle input on a slippery surface (e.g., ice or snow-covered roads). Wheel spin-up may be detected in block  32 , but due to the large potential for “bad” data caused by spin-up, a second check is run in block  33 . A comparison is made between each of the driven wheels and each of the undriven wheels. If the difference between any drive wheel and any undriven wheel is greater than “X”, the data is not allowed to pass. “X” is a value larger than any observed drive slip, but is small enough to detect spin-up as quickly as possible. 
     Referring now to FIG. 1B, following the preliminary filtering of FIG. 1A, the normalized percentage difference in wheel speed between the left and right wheel of each axle is calculated in block  34  and is represented as NORM i1  for the front axle and NORM i2  for the rear axle. Note that if the calibration loop has not yet been completed, the modification factor for each axle MOD j  is still set at 0. Following correction, the normalized axle percentage differences are added to the respective maneuver sums MAN SUM j  (block  36 ) and the maneuver counter is incremented (block  38 ). The maneuver loop is a ten-loop cycle which is run at all times to check if the vehicle is in a maneuver. When ten loops are completed (block  40 ), MAN SUM j  equals the sum of ten NORM j  values. MAXIMUM NORM j  represents the largest of these ten NORM j  values and MINIMUM NORM j  represents the smallest of these ten NORM j  values. The MAXIMUM NORM j  and MINIMUM NORM j  values are stored in block  41 . 
     A maneuver check is performed (block  42 ), wherein the ten NORM j  values are compared with fixed values “B” and “C” to determine whether the vehicle is cornering. If the NORM j  values fall outside the predetermined range between “B” and “C”, the vehicle is in a turn and the program proceeds to block  50 , which is described below. If the NORM j  values fall within the predetermined range between “B” and “C”, the maneuver sums for each axle are added to the tire inflation monitoring sums TIM SUM j  (block  46 ). Next, the RANGE SUM j  is updated by adding the range from the most recent data (block  47 ). The RANGE SUM j  value represents the value {overscore (R)} used to calculate the estimated standard deviation (as described above) and the (MAXIMUM NORM j −MINIMUM NORM j ) value represents R i . With the RANGE SUM j  value updated, the TIM counter is incremented by 10 (block  48 ), signifying that ten more data pairs have been entered. Following this incrementing of the TIM sum and TIM counter, the program proceeds to block  50 . 
     At block  50 , the MAN SUM j  is cleared and at block  52 , the maneuver counter is reset. Block  54  then checks whether calibration is still underway, i.e., whether the calibration flag is still set to f_cal=1. Calibration following a reset requires 6000 filtered wheel speed readings. Thus, if the calibration flag remains set at f_cal=1, block  56  asks whether 6000 loops have been completed (i_tim=6000). If no, the program returns to block  12  where additional wheel speeds are read in, and the sequence is repeated until 6000 data pairs have been entered. Once the 6000 loops for calibration are completed, the modification factors MOD j , are calculated for each axle (block  58 ). MOD j  is simply the mean NORM i  values for each axle as seen from the calculation in block  58 . Recall that n is simply the current value of the TIM counter, i_tim. The TIM sums are cleared in block  60  because data collected to this point has been for calibration, and tire inflation monitoring has not yet begun. Finally, the calibration flag is set to zero and the TIM counter is reset (block  62 ). The program then returns to block  12  where new wheel speed values are read in and the program proceeds as described above. 
     The next time the program reaches block  54 , the calibration flag is set at f_cal=0 (this was done at block  62 ), indicating that calibration is complete and tire inflation monitoring is ready to begin. The program then proceeds to block  64 . First, a lower limit is calculated, representing a t 0  value below which both tires on a single axle are considered normally inflated with certainty. Lower limits are calculated individually for both the front and rear axle, thereby isolating the axles from one another and eliminating problems normally associated with drive slip and different size wheels or tires. The lower limit is a function of i_tim (the total number n of data pairs entered) and can be interpolated from a stored look-up table or alternatively can be calculated as will be described below. Next, an upper limit is calculated, representing a t 0  value above which a tire on a single axle is determined to be deflated with certainty (block  66 ). Again, separate upper limits for the front and rear axle are calculated to isolate the axles. Like the lower limit, the upper limit is a function of i_tim and can be interpolated from a stored look-up table or alternatively can be calculated. 
     In the case of a look-up table, experimental values for the upper and lower limits can be determined by driving the vehicle with deflated tires of varying degree. Corresponding to values can be determined, tabulated and stored in the microprocessor. The designer can choose the upper and lower limits for each axle in accordance with the desired sensitivity of deflation detection. Alternatively, if the exact change in rolling radius due to tire deflation is known (either by design or experimental means), the corresponding value of {overscore (D)} j  can be calculated. S D  can then be determined experimentally based on vehicle testing (to find standard deviation or “noise” caused by factors such as suspension tuning, tire stiffness, and choice of wheel speed sensors) and upper and lower limits for t 0  values can be calculated and stored in the microprocessor. 
     The actual t 0  value for each axle is now calculated (block  68 , which is detailed in FIG. 2) according to the modified paired t-test described in the summary, i.e., by the calculation:          t   0     =         D   _     j         S   D     /     n                                
     where              D   _     j     =           ∑     i   =   1     n          NORM     i                 j         n     =       TIM                   SUM   j       n         ,                                  S   D     =       RANGE                   SUM   j           d   2        k                               
     wherein d 2  is a constant (supplied from a statistical table, in this case d 2 =3.078 since n R =10)and          k   =     n   10       ,                          
     and {square root over (n)} is interpolated from a table stored in the microprocessor. Recall that n is simply the current value of the TIM counter, i_tim, at the point that to is being calculated. 
     Implementation of the to calculation may be simplified even more. For example, FIG. 2 shows that D j  and S D  both contain “n” in the denominator. Thus t 0  can be represented as            t   0     =           ∑     i   =   1     n          NORM     i                 j           RANGE                   SUM   j              n     ×   c       ,                          
     where “c” equals “d 2 /10.”Furthermore, “c” need not be used at all since this is a constant gain and may be simply incorporated (pre-processed) into the upper and lower limit in blocks  64  and  66 , resulting in an even simpler calculation. 
     The to value for each axle is then compared to the upper limit (block  70 , shown in FIG.  1 B). If at block  70 , the to value for an axle is greater than the upper limit, then a tire on that axle is determined to be deflated with certainty, in which case, a warning light is activated (block  72 ). The TIM sums are cleared (block  78 ) and the program returns to block  12 . Wheel speed values will continue to be read in, but will not be used in this sub-routine. If the t 0  value for an axle is less than or equal to the upper limit, then the t 0  value is compared to the lower limit (block  74 ). If t 0  for an axle is less than the lower limit, then the tires on that axle are determined to be normally inflated with certainty. The TIM counter is cleared (block  76 ) and the TIM sums are cleared (block  78 ). Note that if t 0  is greater than the lower limit and less than the upper limit (a NO answer at block  74 ), the program returns to block  12  and data continues to be accumulated (resulting in more data pairs, n) until either the upper threshold or the lower threshold is crossed, respectively indicating either deflation with certainty or proper inflation with certainty. 
     While not shown in the figures, the program could include an option wherein the tire inflation monitoring subroutine continues after the warning light is activated in block  72 . If t 0  later returns to a value less than the lower limit, the deflated tire has been properly serviced by the user and assumes its proper inflation level. When the t 0  value becomes less than the lower limit, the low tire pressure warning light is cleared (f_wlt=0) automatically and the driver need not manually reset the system. 
     Various features of the invention are set forth in the following claims.