Tire pneumatic pressure estimating apparatus

• US 5,753,809 A
• Filed: 08/02/1996
• Issued: 05/19/1998
• Est. Priority Date: 08/04/1995
• Status: Expired due to Term

• Current Assignee: Nippondenso Co., Ltd. (DENSO Corporation)
• Original Assignee: Nippondenso Co., Ltd. (DENSO Corporation)
• Inventors: Ogusu, Koji, Matsumoto, Naoki, Idogaki, Takaharu, Tamura, Shinichi
• Primary Examiner(s): Dombroske, George M.
• Assistant Examiner(s): AMROZOWICZ, PAUL DOUGLAS
• Application Number:
  US08/691,577
• Time in Patent Office: 655 Days
• Field of Search: 73/146, 73/146.2, 73/146.5, 73/146.8, 340/442, 364/558
• US Class Current: 73/146.2
• CPC Class Codes: B60C 23/061 by monitoring wheel speed measuring distance traversed on the ground by vehicles G01C22/00
• CPC Class Codes: B60C 23/062 Frequency spectrum analysis of wheel speed signals, e.g. using Fourier transformation

Abstract

To provide a tire pressure estimating system which is capable of estimating tire pressure based on a signal representing the rotational speed of a vehicle wheel via a small amount of processing by using low-capacity memory, a wheel speed sensor is provided for each wheel of a vehicle. A pulse signal output by the wheel speed sensor is supplied to a signal processor. In the signal processor, the rotational speed of each vehicle wheel is found from the pulse signal. The signal processor adopts a second-order linear prediction model for the rotational speed of the vehicle wheel and vibration of the tire using parameters identified from values of the rotational speed. A resonance frequency is then found from the identified parameters. Finally, the tire pressure is estimated from a linear relationship between the pressure and the resonance frequency.

Claims

1. A tire pressure estimating system comprising:

wheel speed detecting means for detecting a rotational speed of a vehicle wheel and for generating a signal representative thereof;

estimating means for estimating a linear estimation model of tire vibration of said vehicle wheel, said linear estimation model including a resonance component related to tire pressure, based on said wheel rotational speed signal; and

pressure determining means for determining at least one of said tire pressure and abnormality of said tire pressure based on said resonance frequency estimated by said linear estimation model.

2. A tire pressure estimating system according to claim 1, wherein:

said linear estimation model is expressed by

space="preserve" listing-type="equation">y(k)=-c1y(k-1)-c2y(k-2)-c3y(k-3) +d0m(k)+d1m(k-1)+d2m(k-2)

where k is a number of sampling operations, y(k) is said wheel rotational speed, m(k) is vibration input to said tire and c1, c2 . . . and d0, d1 . . . are parameters of said model; and

said pressure estimating means includes

parameter identifying means for identifying said parameters c1, c2 . . . and d0, d1 . . . ,

vibration component processing means for finding a vibration component of said wheel rotational speed from said parameters c1, c2 . . . and d0, d1 . . . identified by said parameter identifying means which is caused by said tire vibration, and

pressure processing means for finding a pressure of said tire from said vibration component found by said vibration component processing means.

3. A tire pressure estimating system according to claim 1, wherein:

said linear estimation model is expressed by

space="preserve" listing-type="equation">y(k)=-c1y(k-1)-c2y(k-2)-c3y(k-3) +d0(m(k)+d1m(k-1)+d2m(k-2)

where k is the number of sampling operations, y(k) is said wheel rotational speed, m(k) is vibration input to said tire and c1, c2 . . . and d0, d1 . . . are parameters of said model; and

said pressure estimating means includes

parameter identifying means for identifying said parameters c1, c2 . . . and d0, d1 . . . , and

pressure processing means for finding the pressure of said tire from said parameters c1, c2 . . . and d0, d1 . . . identified by said parameter identifying means.

4. A tire pressure estimating system according to claim 3, wherein said pressure processing means is for finding the pressure of said tire from one of said identified parameters c1, c2 . . . and d0, d1 . . . which does not change with a sampling attenuation coefficient.

5. A tire pressure estimating system according to claim 2, wherein said parameter identifying means is for identifying said parameters c1, c2 . . . and d0, d1 . . . using a batch least squares method.

6. A tire pressure estimating system according to claim 2, wherein said parameter identifying means is for identifying said parameters c1, c2 . . . and d0, d1 . . . by a recursive least squares method.

7. A tire pressure estimating system according to claim 2, wherein:

said linear prediction model for said tire vibration is a second-order discrete-time model approximated by

space="preserve" listing-type="equation">y(k)=-c1y(k-1)-c2y(k-2)+m(k) (3)

and

said parameter identifying means is for identifying parameters c1 and c2 in the above expression of said second-order discrete-time model.

15. A tire pressure estimating system according to claim 1, further comprising:

tire vibration input estimating means for estimating a magnitude of tire vibration inputs to be supplied to said wheel speed detecting means;

wherein said pressure estimating means is for evaluating reliability of an estimated pressure of said tire from said magnitude of said tire vibration inputs estimated by said tire vibration input estimating means and for discontinuing estimation of said pressure of said tire if a predetermined reliability is not obtained.

16. A tire pressure estimating system according to claim 15, wherein said pressure estimating means is for discontinuing estimation of the pressure of said tire if said magnitude of said tire vibration inputs estimated by said tire vibration input estimating means is greater than a predetermined value.

17. A tire pressure estimating system according to claim 15, wherein said pressure estimating means is for discontinuing estimation of the pressure of said tire if said magnitude of said tire vibration inputs estimated by said tire vibration input estimating means is smaller than a predetermined value.

18. A tire pressure estimating system according to claim 15, wherein said pressure estimating means is for discontinuing estimation of the pressure of said tire if said magnitude of said tire vibration inputs estimated by said tire vibration input estimating means is greater than a first predetermined value and is for discontinuing estimation of the pressure of said tire if said magnitude of said tire vibration inputs estimated by said tire vibration input estimating means is smaller than a second predetermined value.

19. A tire pressure estimating system according to claim 16, further comprising means for changing threshold values for said magnitude of said tire vibration inputs estimated by said tire vibration input estimating means in accordance with the rotational speed of said vehicle wheel detected by said wheel speed detecting means.

20. A tire pressure estimating system according to claim 15, wherein said tire vibration input estimating means is for estimating said magnitude of said tire vibration inputs by calculating a square root of a sum of squares of inputs supplied to said model adopted in said tire pressure estimating system.

21. A tire pressure estimating system according to claim 1, further comprising:

attenuation coefficient estimating means for estimating an attenuation coefficient of a vibration component to be supplied to said wheel speed detecting means;

wherein

said pressure estimating means is for evaluating reliability of an estimated pressure of said tire from said attenuation coefficient of said vibration component estimated by said attenuation coefficient estimating means and discontinues estimation of said pressure of said tire if a predetermined reliability is not obtained.

22. A tire pressure estimating system according to claim 21, wherein said pressure estimating means is for discontinuing estimation of the pressure of said tire if said attenuation coefficient of said vibration component estimated by said attenuation coefficient estimating means is greater than a predetermined value.

23. A tire pressure estimating system according to claim 21, wherein said pressure estimating means is for discontinuing estimation of the pressure of said tire if said attenuation coefficient of said vibration component estimated by said attenuation coefficient estimating means is smaller than a predetermined value.

24. A tire pressure estimating system according to claim 21, wherein said pressure estimating means is for discontinuing estimation of the pressure of said tire if said attenuation coefficient of said vibration component estimated by said attenuation coefficient estimating means is greater than a first predetermined value or if said attenuation coefficient and is for discontinuing estimation of the pressure of said tire if said vibration component estimated by said attenuation coefficient estimating means is smaller than a second predetermined value.

25. A tire pressure estimating system according to claim 22, further comprising means for changing threshold values for said attenuation coefficient of said vibration component estimated by said attenuation coefficient estimating means in accordance with the rotational speed of said vehicle wheel detected by said wheel speed detecting means.

26. A tire pressure estimating system according to claim 21, wherein said attenuation coefficient estimating means is for estimating said attenuation coefficient of said vibration component from parameters identified for said model adopted in said tire pressure estimating system.

8. A tire pressure estimating system comprising:

wheel speed detecting means for detecting a rotational speeds of vehicle wheels;

pressure estimating means for estimating a discrete-time model modeling distribution of vibration of said tires, including a resonance component related to tire pressure, said discrete-time model being expressed as one of a linear and a non-linear combination of a plurality of rotational speeds detected by said wheel speed detecting means; and

pressure determining means for determining one of said tire pressure and abnormality of said tire based on said resonance frequency estimated by said discrete-time model.

9. A tire pressure estimating system according to claim 8, wherein said pressure estimating means is for implementing said one of said linear and non-linear combination of two drive vehicle wheels on right and left sides.

10. A tire pressure estimating system according to claim 9, wherein:

said discrete-time model is expressed by

space="preserve" listing-type="equation">yR(k)-yL(k)=-cR1yR(k-1)-cR2yR(k-2)+mR(k) +cL1yL(k-1)+cL2yL(k-2)-mL(k)

where k is the number of sampling operations, yR(k) is a rotational speed of said drive vehicle wheel on a right side, yL(k) is a rotational speed of said drive vehicle wheel on a left side, mR(k) is vibration input to a tire on said drive vehicle wheel on the right side and mL(k) is vibration input to a tire on said drive vehicle wheel on the left side, cR1 and cR2 are parameters of said model associated with said drive vehicle wheel on the right side and cL1 and cL2 are parameters of said model associated with said drive vehicle wheel on the left side; and

said pressure estimating means includes

parameter identifying means for identifying said parameters cR1, cR2, cL1 and cL2,

vibration component processing means for finding a vibration component of said wheel rotational speed from said parameters cR1, cR2, cL1 and cL2 identified by said parameter identifying means which is caused by said tire vibration, and

pressure processing means for finding the pressure of said tire from said vibration component found by said vibration component processing means.

11. A tire pressure estimating system according to claim 9, wherein:

said discrete-time model is expressed by;

space="preserve" listing-type="equation">yR(k)-yL(k)=-cRF1yR(k-1)-cR2yR(k-2)+mR(k) +cL1yL(k-1)+cL2yL(k-2)-mL(k)

where k is the number of sampling operations, yR(k) is a rotational speed of said drive vehicle wheel on a right side, yL(k) is a rotational speed of said drive vehicle wheel on a left side, mR(k) is vibration input to a tire of said drive vehicle wheel on the right side and mL(k) is vibration input to a tire of said drive vehicle wheel on the left side, cR1 and cR2 are parameters of said model associated with said drive vehicle wheel on the right side and cL1 and cL2 are parameters of said model associated with said drive vehicle wheel on the left side; and

said pressure estimating means includes

parameter identifying means for identifying said parameters cR1, cR2, cL1 and cL2, and

pressure processing means for finding the pressure of said tire from said parameters cR1, cR2, cL1 and cL2 identified by said parameter identifying means.

12. A tire pressure estimating system according to claim 11, wherein said pressure processing means is for finding the pressure of said tire from one of said identified parameters cR1, cR2, cL1 and cL2 which does not change with a sampling attenuation coefficient.

13. A tire pressure estimating system according to claim 10, wherein said parameter identifying means is for identifying said parameters cR1, cR2, cL1 and cL2 . . . by a batch least squares method.

14. A tire pressure estimating system according to claim 10, wherein said parameter identifying means is for identifying said parameters cR1, cR2, cL1 and cL2 . . . by a recursive least squares method.

27. A tire pressure estimating system comprising:

wheel speed detecting means for detecting a rotational speed of a vehicle wheel and for generating a signal representative thereof, said signal including a component of vibration input to be received by the vehicle wheel;

estimating means for estimating a parameter of a predetermined linear estimation model modeling frequency distribution of tire vibration, including a resonant component, in relation to tire pressure, based on said signal; and

pressure determining means for determining at least one of tire pressure and abnormality of said tire based on the parameter.

28. A tire pressure estimating system according to claim 27, wherein:

said linear estimation model is expressed by

space="preserve" listing-type="equation">y(k)=-c1y(k-1)-c2y(k-2)-c3y(k-3) +d0m(k)+d1m(k-1)+d2m(k-2)

where k is a number of sampling operations, y(k) is said wheel rotational speed, m(k) is vibration input to said tire and c1, c2 . . . and d0, d1 . . . are said parameters; and

said pressure estimating means includes

parameter identifying means for identifying said parameters c1, c2 . . . and d0, d1 . . . ,

vibration component processing means for finding a vibration component of said wheel rotational speed from said parameters c1, c2 . . . and d0, d1 . . . identified by said parameter identifying means which is caused by said tire vibration, and

pressure processing means for finding a pressure of said tire from said vibration component found by said vibration component processing means.

29. A tire pressure estimating system according to claim 28, wherein said parameter identifying means is for identifying said parameters c1, c2 . . . and d0, d1 . . . using a batch least squares method.

30. A tire pressure estimating system according to claim 28, wherein said parameter identifying means is for identifying said parameters c1, c2 . . . and d0, d1 . . . by a sequential least squares method.

31. A tire pressure estimating system according to claim 28, wherein:

said linear estimation model for said tire vibration is a second-order discrete-time model approximated by

space="preserve" listing-type="equation">y(k)=-c1y(k-1)-c2y(k-2)+m(k)

and

said parameter identifying means is for identifying parameters c1 and c2 in the above expression of said second-order discrete-time model.

32. A tire pressure estimating system according to claim 27, wherein:

said linear estimation model is expressed by

space="preserve" listing-type="equation">y(k)=-c1y(k-1)-c2y(k-2)-c3y(k-3) +d0(m(k)+d1m(k-1)+d2m(k-2)

where k is the number of sampling operations, y(k) is said wheel rotational speed, m(k) is vibration input to said tire and c1, c2 . . . and d0, d1 . . . are said parameters; and

said pressure estimating means includes

parameter identifying means for identifying said parameters c1, c2 . . . and d0, d1 . . . , and

pressure processing means for finding the pressure of said tire from said parameters c1, c2 . . . and d0, d1 . . . identified by said parameter identifying means.

33. A tire pressure estimating system according to claim 32, wherein said pressure processing means is for finding the pressure of said tire from one of said identified parameters c1, c2 . . . and d0, d1 . . . which does not change with a sampling attenuation coefficient.

34. A tire pressure estimating system according to claim 27, further comprising:

tire vibration input estimating means for estimating a magnitude of tire vibration inputs to be supplied to said wheel speed detecting means;

wherein said pressure estimating means is for evaluating reliability of an estimated pressure of said tire from said magnitude of said tire vibration inputs estimated by said tire vibration input estimating means and for discontinuing estimation of said pressure of said tire if a predetermined reliability is not obtained.

35. A tire pressure estimating system according to claim 34, wherein said pressure estimating means is for discontinuing estimation of the pressure of said tire if said magnitude of said tire vibration inputs estimated by said tire vibration input estimating means is greater than a predetermined value.

36. A tire pressure estimating system according to claim 35, further comprising means for changing threshold values for said magnitude of said tire vibration inputs estimated by said tire vibration input estimating means in accordance with the rotational speed of said vehicle wheel detected by said wheel speed detecting means.

37. A tire pressure estimating system according to claim 34, wherein said pressure estimating means is for discontinuing estimation of the pressure of said tire if said magnitude of said tire vibration inputs estimated by said tire vibration input estimating means is smaller than a predetermined value.

38. A tire pressure estimating system according to claim 34, wherein said pressure estimating means is for discontinuing estimation of the pressure of said tire if said magnitude of said tire vibration inputs estimated by said tire vibration input estimating means is greater than a first predetermined value and is for discontinuing estimation of the pressure of said tire if said magnitude of said tire vibration inputs estimated by said tire vibration input estimating means is smaller than a second predetermined value.

39. A tire pressure estimating system according to claim 34, wherein said tire vibration input estimating means is for estimating said magnitude of said tire vibration inputs by calculating a square root of a sum of squares of inputs supplied to said model adopted in said tire pressure estimating system.

40. A tire pressure estimating system according to claim 27, further comprising:

attenuation coefficient estimating means for estimating an attenuation coefficient of a vibration component to be supplied to said wheel speed detecting means;

wherein

said pressure estimating means is for evaluating reliability of an estimated pressure of said tire from said attenuation coefficient of said vibration component estimated by said attenuation coefficient estimating means and discontinues estimation of said pressure of said tire if a predetermined reliability is not obtained.

41. A tire pressure estimating system according to claim 40, wherein said pressure estimating means is for discontinuing estimation of the pressure of said tire if said attenuation coefficient of said vibration component estimated by said attenuation coefficient estimating means is greater than a predetermined value.

42. A tire pressure estimating system according to claim 41, further comprising means for changing threshold values for said attenuation coefficient of said vibration component estimated by said attenuation coefficient estimating means in accordance with the rotational speed of said vehicle wheel detected by said wheel speed detecting means.

43. A tire pressure estimating system according to claim 40, wherein said pressure estimating means is for discontinuing estimation of the pressure of said tire if said attenuation coefficient of said vibration component estimated by said attenuation coefficient estimating means is smaller than a predetermined value.

44. A tire pressure estimating system according to claim 40, wherein said pressure estimating means is for discontinuing estimation of the pressure of said tire if said attenuation coefficient of said vibration component estimated by said attenuation coefficient estimating means is greater than a first predetermined value or if said attenuation coefficient and is for discontinuing estimation of the pressure of said tire if said vibration component estimated by said attenuation coefficient estimating means is smaller than a second predetermined value.

45. A tire pressure estimating system according to claim 40, wherein said attenuation coefficient estimating means is for estimating said attenuation coefficient of said vibration component from parameters identified for said model adopted in said tire pressure estimating system.

46. A tire pressure estimating system comprising:

wheel speed detecting means for detecting a rotational speeds of vehicle wheels;

estimating means for estimating a parameter of a discrete-time model modeling a frequency distribution of vibration of said tires, including a resonance component related to tire pressure, said discrete-time model being expressed as one of a linear and a non-linear combination of a plurality of rotational speeds detected by said wheel speed detecting means; and

pressure determining means for determining at least one of said tire pressure and abnormality of said tire based on said estimated parameter.

47. A tire pressure estimating system according to claim 46, wherein said pressure estimating means is for implementing said one of said linear and non-linear combination of two drive vehicle wheels on right and left sides.

48. A tire pressure estimating system according to claim 47, wherein:

said discrete-time model is expressed by

space="preserve" listing-type="equation">yR(k)-yL(k)=-cR1yR(k-1)-cR2yR(k-2)+mR(k) +cL1yL(k-1)+cL2yL(k-2)-mL(k)

where k is the number of sampling operations, yR(k) is a rotational speed of said drive vehicle wheel on a right side, yL(k) is a rotational speed of said drive vehicle wheel on a left side, mR(k) is vibration input to a tire on said drive vehicle wheel on the right side and mL(k) is vibration input to a tire on said drive vehicle wheel on the left side, cR1 and cR2 are said parameters associated with said drive vehicle wheel on the right side and cL1 and cL2 are said parameters associated with said drive vehicle wheel on the left side; and

said pressure estimating means includes

parameter identifying means for identifying said parameters cR1, cR2, cL1 and cL2,

vibration component processing means for finding a vibration component of said wheel rotational speed from said parameters cR1, cR2, cL1 and cL2 identified by said parameter identifying means which is caused by said tire vibration, and

pressure processing means for finding the pressure of said tire from said vibration component found by said vibration component processing means.

49. A tire pressure estimating system according to claim 48, wherein said parameter identifying means is for identifying said parameters cR1, cR2, cL2 and cL2 . . . by a batch least squares method.

50. A tire pressure estimating system according to claim 48, wherein said parameter identifying means is for identifying said parameters cR1, cR2, cL1 and cL2 . . . by a sequential least squares method.

51. A tire pressure estimating system according to claim 47, wherein:

said discrete-time model is expressed by;

space="preserve" listing-type="equation">yR(k)-yL(k)=-cRF1yR(k-1)-cR2yR(k-2)+mR(k) +cL1yL(k-1)+cL2yL(k-2)-mL(k)

where k is the number of sampling operations, yR(k) is a rotational speed of said drive vehicle wheel on a right side, yL(k) is a rotational speed of said drive vehicle wheel on a left side, mR(k) is vibration input to a tire of said drive vehicle wheel on the right side and mL(k) is vibration input to a tire of said drive vehicle wheel on the left side, cR1 and cR2 are said parameters associated with said drive vehicle wheel on the right side and cL1 and cL2 are said parameters associated with said drive vehicle wheel on the left side; and

said pressure estimating means includes

parameter identifying means for identifying said parameters cR1, cR2, cL1 and cL2, and

pressure processing means for finding the pressure of said tire from said parameters cR1, cR2, cL1 and cL2 identified by said parameter identifying means.

52. A tire pressure estimating system according to claim 51, wherein said pressure processing means is for finding the pressure of said tire from one of said identified parameters cR1, cR2, cL1 and cL2 which does not change with a sampling attenuation coefficient.

53. A tire pressure estimating system comprising:

wheel speed detecting means for detecting a rotational speed of a vehicle wheel including a component of vibration provided to a tire of said wheel and for generating a signal representative thereof;

calculating means for calculating a linear estimation model representative of a frequency distribution of tire vibration of said tire, said distribution including a resonance component related to tire pressure of said tire, based on said rotational speed signal; and

pressure determining means for at least one of determining abnormality of said tire pressure and estimating said tire pressure based on the resonance frequency which is decided by said linear estimation model.

61. A tire pressure estimating system according to claim 53, wherein:

said linear estimation model is expressed by a mathematical expression model which has factors including a number of sampling operations, wheel rotational speed, vibration input to said tire;

said linear estimation model uses, for each of said factors, a plurality of sampled values of said factor; and

each of said sampled values has a parameter of said model associated therewith.

54. A tire pressure estimating system comprising:

wheel speed estimating means for detecting a rotational speed of a vehicle wheel including a component of vibration provided to a tire of said wheel and for generating a signal representative thereof;

calculating means for calculating a discrete-time model representative of a frequency distribution of tire vibration of said tire, said distribution including a resonance component related to tire pressure, said discrete-time model being expressed as one of a linear combination and a non-linear combination of a plurality of rotational speed signals detected by said wheel speed detecting means; and

pressure determining means for determining abnormality of said tire pressure or estimating said tire pressure based on the resonance frequency which is decided by said linear estimation model.

62. A tire pressure estimating system according to claim 54, wherein:

said discrete-time model is expressed by a second-order approximation mathematical model which has a number of sampling operations factor, wheel rotational speed factor, vibration input to said tire factor;

said linear estimation model uses, for each of said factors, a plurality of sampled values of said factor; and

each of said sampled values has a parameter of said model associated therewith.

55. A tire pressure estimating system comprising:

wheel speed estimating means for detecting a rotational speed of a vehicle wheel including a component of vibration provided to a tire of said wheel and for generating a signal representative thereof;

calculating means for calculating a parameter of a linear estimation model representative of a frequency distribution of tire vibration of said tire, said distribution including a resonance component related to tire pressure of said tire, based on said rotational speed signal; and

pressure determining means for at least one of determining abnormality of said tire pressure and estimating said tire pressure based on the parameter calculated by said calculating means.

63. A tire pressure estimating system according to claim 55, wherein said parameter is a parameter of said model associated with one of a number of sampling operations, wheel rotational speed, and vibration input to said tire.

56. A tire pressure estimating system comprising:

wheel speed estimating means for detecting a rotational speed of a vehicle wheel including a component of vibration provided to a tire of said wheel and for generating a signal representative thereof;

calculating means for calculating a parameter of a discrete-time model representative of a frequency distribution of tire vibration of said tire, said distribution including a resonance component related to tire pressure of said tire, said discrete-time model being expressed as one of a linear and a non-linear combination of a plurality of rotational speed signals detected by said wheel speed detecting means; and

pressure determining means for at least one of determining abnormality of said tire pressure and estimating said tire pressure based on the parameter calculated by said calculating means.

64. A tire pressure estimating system according to claim 56, wherein said parameter is a parameter of said model associated with one of a number of sampling operations, wheel rotational speed, and vibration input to said tire.

57. A tire pressure estimating system comprising:

wheel speed estimating means for detecting a rotational speed of a vehicle wheel including a component of vibration provided to a tire of said wheel and for generating a signal representative thereof;

calculating means for calculating a predetermined mathematical expression model representative of tire vibration of said tire using a linear estimation method and said signal of said wheel speed detecting means;

estimating means for estimating a resonance frequency of said tire based on the calculated mathematical expression model; and

pressure determining means for determining abnormality of said tire pressure or estimating said tire pressure based on the resonance frequency which is estimated by estimating means.

58. A tire pressure estimating system comprising:

wheel speed estimating means for detecting a rotational speed of a vehicle wheel including a component of vibration provided to a tire of said wheel and for generating a signal representative thereof;

calculating means for calculating a predetermined mathematical expression model representative of tire vibration of said tire using a discrete-time method and one of a linear and non-linear combination of a plurality of rotational speed signal detected by said wheel speed detecting means;

estimating means for estimating a resonance frequency of said tire based on the calculated mathematical expression model; and

pressure determining means for determining abnormality of said tire pressure or estimating said tire pressure based on the resonance frequency which is estimated by estimating means.

59. A tire pressure estimating system comprising:

wheel speed estimating means for detecting a rotational speed of a vehicle wheel including a component of vibration provided to a tire of said wheel and for generating a signal representative thereof;

calculating means for calculating a parameter of a predetermined mathematical expression model representative of tire vibration of said tire using a linear estimation method and the output signal of said wheel speed detecting means;

estimating means for estimating a resonance frequency of said tire based on the calculated parameter; and

pressure determining means for determining abnormality of said tire pressure or estimating said tire pressure based on the parameter which is estimated by estimating means.

60. A tire pressure estimating system comprising:

wheel speed estimating means for detecting a rotational speed of a vehicle wheel including a component of vibration provided to a tire of said wheel and for generating a signal representative thereof;

calculating means for calculating a parameter of a predetermined mathematical expression model representative of tire vibration of said tire using a discrete-time method and one of a linear and non-linear combination of plurality of rotational speed signal detected by said wheel speed detecting means;

estimating means for estimating a resonance frequency of said tire based on the calculated parameter; and

pressure determining means for determining abnormality of said tire pressure or estimating said tire pressure based on the parameter which is estimated by estimating means.