System and method for detecting a collision using a continuous mode hidden Markov model

• US 20050096817A1
• Filed: 10/04/2004
• Published: 05/05/2005
• Est. Priority Date: 10/28/2003
• Status: Active Grant

• Current Assignee: Oakland University
• Original Assignee: Oakland University
• Inventors: Song, Haiping, Singh, Gautam B.
• Granted Patent: US 7,113,079 B2
• Time in Patent Office: Days
• US Class Current: 701/45
• CPC Class Codes: B60R 21/0132 responsive to vehicle motion parameters , e.g. to vehicle longitudinal or transversal deceleration or speed value
• CPC Class Codes: B60R 21/01332 by frequency or waveform analysis
• CPC Class Codes: B60R 21/01338 using vector analysis

Abstract

A system and method detects a crash of a motor vehicle. A parameter of the motor vehicle is sensed and a continuous signal is responsively generated. A crash is detected as a function of the continuous signal and a hidden Markov model operating in a continuous mode.

Claims

1. A system for detecting a crash of a motor vehicle, comprising:

at least one sensor for sensing a parameter of the motor vehicle and generating a continuous signal as a function of the sensed parameter;

a controller for implementing a hidden Markov model operating in a continuous mode, for receiving the continuous signal and detecting a crash of the motor as a function of the continuous signal and the hidden Markov model.

2. A system, as set forth in claim 1, wherein the hidden Markov model is an N-state fully-connected model.

3. A system, as set forth in claim 2, wherein the hidden Markov model is a N-state left-right model.

4. A system, as set forth in claim 1, wherein the parameter is acceleration.

5. A system, as set forth in claim 1, wherein the hidden Markov model is of the form:

λ

={A, π

, Cov, μ

}, where A is a matrix representing transition probabilities between each state, π

is a matrix representing the probability of each state for the first observation, Cov is a covariance matrix representing the variance and covariance of each variable, and μ

is a mean vector representing the mean value of each state.

6. A system, as set forth in claim 5, wherein the continuous signal is represented by an observation sequence, O=O₁O₂ . . . O_T, the hidden Markov model has N states, and a state sequence is represented by Q=q₁ q₂ . . . q_T.

7. A system, as set forth in claim 6, wherein QT, in the state sequence, Q, represents a crash, and a probability associated with the observation sequence, O, is determined as a sum of a probability associated with each possible state sequences which lead to Q.

8. A system, as set forth in claim 7, wherein the probability associated with the observation, O, is determined using the equation:

$P<br><br>\left(O❘<br><br>\mathrm{\lambda <br><br>}\right)=\underset{\mathrm{all}<br><br>\text{\hspace{1em}<br><br>}<br><br>Q}{\sum <br><br>}<br><br>P<br><br>\left(O❘<br><br>Q,\mathrm{\lambda <br><br>}\right)<br><br>P<br><br>\left(Q❘<br><br>\mathrm{\lambda <br><br>}\right),$

where P(O|Q,λ

) is the probability of the observation sequence, O, for the state sequence, Q, and P(Q|λ

) is the probability of the state sequence.

9. A system, as set forth in claim 8, wherein P(O|Q,λ

) is determined by the equation;

$\begin{array}{c}P<br><br>\left(O❘<br><br>Q,\mathrm{\lambda <br><br>}\right)=<br><br>\underset{t=1}{\overset{T}{\prod <br><br>}}<br><br>P<br><br>\left(O_t❘<br><br>q_t,\mathrm{\lambda <br><br>}\right)\\ =<br><br>b_{q_1}<br><br>\left(O_1\right)<br><br>b_{q_2}<br><br>\left(O_2\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>b_{q_T}<br><br>\left(O_T\right),\mathrm{where}<br><br>\text{\hspace{1em}<br><br>}<br><br>b_{q_i}<br><br>\left(o_i\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{is}\\ <br><br>\mathrm{conditional}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{probability}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{of}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{the}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{observation},O_i,\\ <br><br>\mathrm{given}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{the}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{hidden}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{state},q_i.\end{array}$

10. A system, as set forth in claim 9, where P(Q|λ

) is determined by the equations;

P(Q|λ

)=π

_q1a_q1q2a_q2q3 . . . a_qT-1qT, where a_qiqj is transition probability from state, q_i to state, q_j.

11. A system, as set forth in claim 10, wherein P(O|λ

) is determined by the equation;

P(O|λ

)=Σ

π

_q1b_q1(O₁)a_q1q2b_q2(O₂) . . . a_qT-1qTb_qT(O_T)

12. A system, as set forth in claim 7, wherein the probability associated with the observation sequence, O, is determined as a function of a forward variable (α

_t(i)), the forward variable (α

_t(i)) is determined using the equation;

α

_t(i)=P(O₁O₂ . . . O_t,q_t=S_i|λ

).

13. A system, as set forth in claim 12, wherein the probability associated with the observation, O, is determined using the equation:

$P<br><br>\left(O❘<br><br>\mathrm{\lambda <br><br>}\right)=\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>{\mathrm{\alpha <br><br>}}_T<br><br>\left(i\right),$

where P(O|Q,λ

) is the probability of the observation sequence, O, for the state sequence, Q, and P(Q|λ

) is the probability of the state sequence.

14. A system, as set forth in claim 7, wherein the crash is detected if the probability associated with the observation sequence is greater than a predetermined value.

15. A system, as set forth in claim 7, wherein the probability associated with the observation sequence is expressed in terms of a logarithm.

16. A method for detecting a crash of a motor vehicle, comprising:

sensing a parameter of the motor vehicle and generating a continuous signal as a function of the sensed parameter; and

,

receiving the continuous signal and detecting a crash of the motor as a function of the continuous signal and a hidden Markov model operating in a continuous mode.

17. A method, as set forth in claim 16, wherein the hidden Markov model is an N-state fully-connected model.

18. A method, as set forth in claim 17, wherein the hidden Markov model is a N-state left-right model.

19. A method, as set forth in claim 16, wherein the parameter is acceleration.

20. A method, as set forth in claim 16, wherein the hidden Markov model is of the form:

λ

={A, π

, Cov, μ

}, where A is a matrix representing transition probabilities between each state, π

is a matrix representing the probability of each state for the first observation, Cov is a covariance matrix representing the variance and covariance of each variable, and μ

is a mean vector representing the mean value of each state.

21. A method, as set forth in claim 20, wherein the continuous signal is represented by an observation sequence, O=O₁O₂ . . . O_T, the hidden Markov model has N states, and a state sequence is represented by Q=q₁ q₂ . . . q_T.

22. A method, as set forth in claim 21, wherein Q_T, in the state sequence, Q, represents a crash, and a probability associated with the observation sequence, O, is determined as a sum of a probability associated with each possible state sequences which lead to Q.

23. A method, as set forth in claim 22, wherein the probability associated with the observation, O, is determined using the equation:

$P<br><br>\left(O❘<br><br>\mathrm{\lambda <br><br>}\right)=\underset{\mathrm{all}<br><br>\text{\hspace{1em}<br><br>}<br><br>Q}{\sum <br><br>}<br><br>P<br><br>\left(O❘<br><br>Q,\mathrm{\lambda <br><br>}\right)<br><br>P<br><br>\left(Q❘<br><br>\mathrm{\lambda <br><br>}\right),$

where P(O|Q,λ

) is the probability of the observation sequence, O, for the state sequence, Q, and P(Q|λ

) is the probability of the state sequence.

24. A method, as set forth in claim 23, wherein P(O|Q,λ

) is determined by the equation;

$\begin{array}{c}P<br><br>\left(O❘<br><br>Q,\mathrm{\lambda <br><br>}\right)=<br><br>\underset{t=1}{\overset{T}{\prod <br><br>}}<br><br>P<br><br>\left(O_t❘<br><br>q_t,\mathrm{\lambda <br><br>}\right)\\ =<br><br>b_{q_1}<br><br>\left(O_1\right)<br><br>b_{q_2}<br><br>\left(O_2\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>b_{q_T}<br><br>\left(O_T\right),\mathrm{where}<br><br>\text{\hspace{1em}<br><br>}<br><br>b_{q_i}<br><br>\left(o_i\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{is}\\ <br><br>\mathrm{conditional}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{probability}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{of}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{the}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{observation},O_i,\\ <br><br>\mathrm{given}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{the}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{hidden}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{state},q_i.\end{array}$

25. A method, as set forth in claim 24, where P(Q|λ

), is determined by the equations;

P(Q|λ

)=π

_q1a_q1q2a_q2q3 . . . a_qT-1qT, where a_qiqj is transition probability from state, q_i to state, q_j.

26. A method, as set forth in claim 25, wherein P(O|λ

), is determined by the equation;

P(O|λ

)=Σ

π

_q1b_q1(O₁)a_q1q2b_q2(O₂) . . . a_qT-1qTb_qT(O_T)

27. A method, as set forth in claim 22, wherein the probability associated with the observation sequence, O, is determined as a function of a forward variable (α

_t(i)), the forward variable (α

_t(i)) is determined using the equation;

α

_t(i)=P(O₁O₂ . . . O_t,q_t=S_i|λ

).

28. A method, as set forth in claim 27, wherein the probability associated with the observation, O, is determined using the equation:

$P<br><br>\left(O❘<br><br>\mathrm{\lambda <br><br>}\right)=\underset{i=1}{\overset{N}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}_T<br><br>\left(i\right),$

where P(O|Q,λ

) is the probability of the observation sequence, O, for the state sequence, Q, and P(Q|λ

) is the probability of the state sequence.

29. A method, as set forth in claim 22, wherein the crash is detected if the probability associated with the observation sequence is greater than a predetermined value.

30. A method, as set forth in claim 22, wherein the probability associated with the observation sequence is expressed in terms of a logarithm.