CN109901171A - Automobile anti-rear end collision method for early warning - Google Patents

Automobile anti-rear end collision method for early warning Download PDF

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Publication number
CN109901171A
CN109901171A CN201910291349.8A CN201910291349A CN109901171A CN 109901171 A CN109901171 A CN 109901171A CN 201910291349 A CN201910291349 A CN 201910291349A CN 109901171 A CN109901171 A CN 109901171A
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sequence
speed
distance
suspicious object
trend
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CN109901171B (en
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苏玉娜
李赓
张延良
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Henan University of Technology
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Henan University of Technology
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    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02TCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00Road transport of goods or passengers
    • Y02T10/10Internal combustion engine [ICE] based vehicles
    • Y02T10/40Engine management systems

Abstract

This application provides a kind of automobile anti-rear end collision method for early warning, and the distance of suspicious object is monitored by microwave radar sensor, and suspicious object is located at automobile tail;When the distance for monitoring suspicious object is less than preset first threshold, executes following steps: obtaining the distance of suspicious object in real time by microwave radar sensor, obtain distance sequence;The speed for obtaining suspicious object in real time by microwave radar sensor obtains First Speed sequence;The speed for obtaining automobile in real time, obtains second speed sequence;The steering data for obtaining automobile in real time obtain turning to data sequence;According to distance sequence, First Speed sequence, second speed sequence turns to the probability that knocks into the back that data sequence determines suspicious object;If the probability that knocks into the back is greater than second threshold, alarm.Automobile anti-rear end collision method for early warning provided by the present application monitors suspicious object by microwave radar sensor, and carries out early warning according to the distance of suspicious object, the speed of suspicious object, the speed of automobile and the steering data of automobile.

Description

Automobile anti-rear end collision method for early warning
Technical field
This application involves radar data processing technology field more particularly to a kind of automobile anti-rear end collision method for early warning.
Background technique
China's traffic accident in recent years takes place frequently, and causes casualties and property loss, severe social situations get over people More to pay attention to automotive safety.
With computer technology, communication, the fast development of electronic technology, detection vehicle drive ring is carried out using electronic technology Border prevents traffic accident by early warning and has become possibility.
Most current vehicle measures barrier at a distance from automobile using ultrasonic wave, laser, infrared ray etc..
When ultrasonic echo mode measures, sound wave is emitted and is received by probe, and sound wave is run with the velocity of sound, because sound wave has instead Phenomena such as penetrating, reflecting exists, and therefore, ultrasonic radar is disturbed more, and early warning effect is poor.
Summary of the invention
To solve the above problems, the embodiment of the present application proposes a kind of automobile anti-rear end collision method for early warning.
101, the distance of suspicious object is monitored by microwave radar sensor, the suspicious object is located at automobile tail;
102, when the distance for monitoring suspicious object is less than preset first threshold, execute following steps:
102-1 is obtained the distance of the suspicious object in real time by microwave radar sensor, obtains distance sequence;
102-2 obtains the speed of the suspicious object by microwave radar sensor in real time, obtains First Speed sequence;
102-3 obtains the speed of automobile in real time, obtains second speed sequence;
102-4 obtains the steering data of automobile in real time, obtains turning to data sequence;
102-5, according to the distance sequence, the First Speed sequence, the second speed sequence, the steering data Sequence determines the probability that knocks into the back of the suspicious object;
102-6 alarms if the probability that knocks into the back is greater than preset second threshold.
Optionally, distance sequence is { d1,d2,…,dt,…,dT};
First Speed sequence { v1,v2,…,vt,…,vT};
Second speed sequence { v'1,v'2,…,v't,…,v'T};
Turn to data sequence { r1,r2,…,rt,…,rT};
Wherein, t is time identifier, dtFor the distance of suspicious object described in t moment, vtFor the speed of suspicious object described in t moment Degree, v'tFor the speed of automobile described in t moment, rtFor the steering data of automobile described in t moment;T is current time, described apart from sequence Column, the First Speed sequence, the second speed sequence, the element turned in data sequence are identical, are T;
The 102-5 includes:
102-5-1, if the element value ascending order of distance sequence arranges, it is determined that the probability that knocks into the back of the suspicious object is
Wherein, i is the component identification in distance sequence;
102-5-2, if the non-ascending order arrangement of the element value of distance sequence, calculates distance reference value D, according to D, described first Velocity series, the second speed sequence, the probability that knocks into the back for turning to data sequence and determining the suspicious object.
Optionally, if the element value descending of distance sequence arranges, the calculating distance reference value D, comprising:
The average distance of the suspicious object is calculated by following formula
Compensated distance value w is calculated by following formula:
Wherein, α is the range error of the microwave radar sensor.
Optionally, if the non-descending of the element value of distance sequence arranges, and the element value of distance sequence nor ascending order arrangement, then The calculating distance reference value D, comprising:
The average distance of the suspicious object is calculated by following formula
Compensated distance value w is calculated by following formula:
Wherein, α is the range error of the microwave radar sensor;
β is penalty coefficient, if (dT-dT-1)-(dT-2-dT-3) > 0, β=- 1, if (dT-dT-1)-(dT-2-dT-3)=0, then β=0, if (dT-dT-1)-(dT-2-dT-3) < 0, then β=1;
Optionally, described according to D, the First Speed sequence, the second speed sequence, the steering data sequence is true The probability that knocks into the back of the fixed suspicious object, comprising:
If the element value of the First Speed sequence is descending arrangement, and the element value of the second speed sequence is ascending order Arrangement, it is determined that the probability that knocks into the back of the suspicious object is
If the element value of the First Speed sequence is ascending order arrangement, and the element value of the second speed sequence is descending Arrangement, it is determined that the probability that knocks into the back of the suspicious object is
If the element value of the First Speed sequence is descending arrangement, and the non-ascending order of element value of the second speed sequence Arrangement, alternatively, if the element value of the First Speed sequence is that ascending order arranges, and the non-drop of element value of the second speed sequence Sequence arrangement, alternatively, if the non-descending of the element value of the First Speed sequence arranges, and the element value of the First Speed sequence is non- Ascending order arrangement, it is determined that temporal reference value B, according to D, B, the data sequence that turns to determines that knocking into the back for the suspicious object is general Rate.
Optionally, the determining temporal reference value B, comprising:
Speed trend is determined according to the First Speed sequence and the second speed sequence;
B is determined according to the speed trend.
It is optionally, described that speed trend is determined according to the First Speed sequence and the second speed sequence, comprising:
According to the First Speed sequence and the second speed sequence, deterministic trend sequence { v1-v'1,v2-v'2,…, vt-v't,…,vT-v'T};
If the mean value of all elements is greater than 0 in trend sequence, it is determined that speed trend is ascendant trend;
If the mean value of all elements is less than 0 in trend sequence, it is determined that speed trend is downward trend;
If the mean value of all elements is equal to 0 in trend sequence, it is determined that speed trend is moderate tone.
It is optionally, described that B is determined according to the speed trend, comprising:
If speed trend is ascendant trend,
Wherein, j is the component identification in velocity series;
If speed trend is moderate tone, B=1;
If speed trend is downward trend,
Wherein,Max { } is maximizing function, and min { } is function of minimizing.
It is optionally, described according to D, B, the probability that knocks into the back for turning to data sequence and determining the suspicious object, comprising:
It is determined according to the steering data sequence and turns to reference value R;
Optionally, described determined according to the steering data sequence turns to reference value R, comprising:
Calculating and turning to difference sequence is { r2-r1,r3-r2,…,rt-rt-1,…,rT-rT-1};
Determine non-zero number of elements M in the steering difference sequence;
It has the beneficial effect that:
Suspicious object is monitored by microwave radar sensor, and according to the distance of suspicious object, the speed of suspicious object, vapour The speed of vehicle and the steering data of automobile carry out early warning, improve early warning effect.
Detailed description of the invention
The specific embodiment of the application is described below with reference to accompanying drawings, in which:
Fig. 1 shows a kind of flow diagram of automobile anti-rear end collision method for early warning of one embodiment of the application offer.
Specific embodiment
In order to which technical solution and the advantage of the application is more clearly understood, below in conjunction with attached drawing to the exemplary of the application Embodiment is described in more detail, it is clear that and described embodiment is only a part of the embodiment of the application, rather than The exhaustion of all embodiments.And in the absence of conflict, the feature in the embodiment and embodiment in this explanation can be mutual It combines.
China's traffic accident in recent years takes place frequently, and causes casualties and property loss, severe social situations get over people More to pay attention to automotive safety.
With computer technology, communication, the fast development of electronic technology, detection vehicle drive ring is carried out using electronic technology Border prevents traffic accident by early warning and has become possibility.Most current vehicle is using ultrasonic wave, laser, infrared ray etc. Barrier is measured at a distance from automobile.When ultrasonic echo mode measures, sound wave is emitted and is received by probe, and sound wave is transported with the velocity of sound Row, because of phenomena such as sound wave is with the presence of reflection, refraction, ultrasonic radar is disturbed more, and early warning effect is poor.
Based on this, the application provides a kind of automobile anti-rear end collision method for early warning, monitors suspicious item by microwave radar sensor Body, and early warning is carried out according to the distance of suspicious object, the speed of suspicious object, the speed of automobile and the steering data of automobile, it mentions Early warning effect is risen.
Referring to Fig. 1, automobile anti-rear end collision method for early warning implementation process provided in this embodiment is as follows:
101, the distance of suspicious object is monitored by microwave radar sensor.
Wherein, suspicious object is located at automobile tail.
When the prior art is measured using ultrasonic echo mode, sound wave is emitted and is received by probe, and sound wave is run with the velocity of sound, Because of phenomena such as sound wave is with the presence of reflection, refraction, ultrasonic radar is disturbed more, and early warning effect is poor.
The application monitors suspicious object using microwave radar sensor, and microwave radar sensor orientation is good, and speed is equal to The light velocity, the interference received are less.The radar wave of microwave radar sensor is run with the light velocity, and microwave encounters vehicle and is reflected back toward immediately Come, then level signal be converted by electronic component, ensure that in very short time and stablize and precise measurement, has measuring speed fast, The advantages that precision is high.Therefore, the real-time sexual intercourse of the distance for the suspicious object that the application is got is high, and accuracy is also higher.
102, it, can according to the distance of suspicious object when the distance for monitoring suspicious object is less than preset first threshold The speed of object is doubted, the speed of automobile and the steering data of automobile carry out early warning.
First threshold can be 1.2 meters or 1.5 meters etc., and the present embodiment is not defined the occurrence of first threshold.
By execute step 101 may be implemented to (such as 3 meters, alternatively, 4 meters) in pre-determined distance with the presence or absence of suspicious object into Row monitoring, but not monitor that suspicious object is just alarmed, but determine the need for alarming by step 102.
In addition, the suspicious object monitored in step 101 at a distance from automobile may farther out may also be relatively close, for farther out The suspicious object suspicious object of preset first threshold (distance be more than or equal to), there is no the risks that knocks into the back, and can continue Monitoring, does not need to do any processing.For suspicious object (suspicious item of the distance less than preset first threshold being closer Body), a possibility that being knocked into the back according to it dynamic early-warning.Specifically, according to the distance of suspicious object, the speed of suspicious object, automobile Speed and automobile steering data carry out early warning process it is as follows:
102-1 is obtained the distance of suspicious object in real time by microwave radar sensor, obtains distance sequence.
102-2 obtains the speed of suspicious object by microwave radar sensor in real time, obtains First Speed sequence.
102-3 obtains the speed of automobile in real time, obtains second speed sequence.
102-4 obtains the steering data of automobile in real time, obtains turning to data sequence.
Wherein, the number of total coils that data can turn for steering wheel is turned to, distinguishes or turn right, for example, left-hand rotation number of total coils, or Person, steering wheel right-hand rotation number of total coils, it is specific turn left for+value, turn right as-value, alternatively, turn left for-be worth, turn right as+value etc..It turns to Data can also be turning radius, distinguish or turn right, for example, turning radius to the left, alternatively, turning radius to the right, specifically Left-hand rotation be+value, turn right as-value, alternatively, turn left for-be worth, turn right as+value etc..The present embodiment is not to the specific interior of steering data Appearance is defined, as long as can describe motor turning direction and turn to the data of size.
Each moment can obtain the distance of suspicious object, the speed of suspicious object, the speed of automobile, the steering number of automobile According to.Therefore, distance sequence, First Speed sequence, second speed sequence, turn to data sequence in element there are temporal right It should be related to, and the element total quantity in distance sequence, First Speed sequence, second speed sequence, steering data sequence is identical.
For example, distance sequence is { d1,d2,…,dt,…,dT}。
First Speed sequence { v1,v2,…,vt,…,vT}。
Second speed sequence { v'1,v'2,…,v't,…,v'T}。
Turn to data sequence { r1,r2,…,rt,…,rT}。
Wherein, t is time identifier, dtFor the distance of t moment suspicious object, vtFor the speed of t moment suspicious object, v'tFor The speed of t moment automobile, rtFor the steering data of t moment automobile.T is current time, distance sequence, First Speed sequence, Two velocity series, the element turned in data sequence are identical, are T.
102-5, according to distance sequence, First Speed sequence, second speed sequence turns to data sequence and determines suspicious object The probability that knocks into the back.
The implementation of step 102-5 is as follows:
102-5-1, if the element value ascending order of distance sequence arranges, it is determined that the probability that knocks into the back of suspicious object is
Wherein, i is the component identification in distance sequence.
That is, illustrating suspicious object far from vapour if suspicious object is increasingly remoter over time at a distance from automobile Vehicle determines that the probability that knocks into the back of suspicious object is at this time
102-5-2, if the non-ascending order arrangement of the element value of distance sequence,
The case where element value of distance sequence non-ascending order arrangement, there is 2 kinds, and a kind of element value descending for distance sequence arranges, Another kind is that the element value of distance sequence is disorderly arranged, i.e. the non-ascending order arrangement of the element value of distance sequence nor descending arrangement.
No matter which kind of situation, according to distance sequence, First Speed sequence, second speed sequence turns to data sequence and determines The implementation of the probability that knocks into the back of suspicious object includes but is not limited to:
102-5-2-1 calculates distance reference value D.
The implementation of this step includes but is not limited to:
If 1, the element value descending arrangement of distance sequence,
1.1 calculate the average distance of suspicious object by following formula
1.2 calculate compensated distance value w by following formula:
Wherein, α is the range error of microwave radar sensor.Range error and microwave radar sensor itself are related, out When factory it can be learnt that.
1.3 distance reference values
If 2, the non-descending arrangement of the element value of distance sequence, and the element value of distance sequence nor ascending order arrangement, then
2.1 calculate the average distance of suspicious object by following formula
2.2 calculate compensated distance value w by following formula:
Wherein, α is the range error of microwave radar sensor.
β is penalty coefficient, if (dT-dT-1)-(dT-2-dT-3) > 0, β=- 1, if (dT-dT-1)-(dT-2-dT-3)=0, then β=0, if (dT-dT-1)-(dT-2-dT-3) < 0, then β=1.
102-5-2-2, according to D, First Speed sequence, second speed sequence turns to data sequence and determines suspicious object Knock into the back probability.
The implementation of 102-5-2-2 is as follows:
1) if the element value of First Speed sequence is descending arrangement, and the element value of second speed sequence is ascending order arrangement, Then the probability that knocks into the back of determining suspicious object is
2) if the element value of First Speed sequence is ascending order arrangement, and the element value of second speed sequence is descending arrangement, Then the probability that knocks into the back of determining suspicious object is
3) if the element value of First Speed sequence is descending arrangement, and the non-ascending order of element value of second speed sequence arranges, Alternatively, if the element value of First Speed sequence is ascending order arrangement, and the non-descending of element value of second speed sequence arranges, alternatively, If the non-descending arrangement of the element value of First Speed sequence, and the non-ascending order arrangement of element value of First Speed sequence, then
3.1) temporal reference value B is determined.
Wherein it is determined that the implementation of temporal reference value B are as follows:
(1) speed trend is determined according to First Speed sequence and second speed sequence.
For example, according to First Speed sequence and second speed sequence, deterministic trend sequence { v1-v'1,v2-v'2,…,vt- v't,…,vT-v'T}。
If the mean value of all elements is greater than 0 in trend sequence, it is determined that speed trend is ascendant trend.
EvenThen determine that speed trend is upper The trend of liter, illustrates that suspicious object speed is faster than automobile, and the possibility that knocks into the back is promoted.
If the mean value of all elements is less than 0 in trend sequence, it is determined that speed trend is downward trend.
EvenUnder then determining that speed trend is Drop trend illustrates that suspicious object speed is faster than automobile, and the possibility that knocks into the back reduces.
If the mean value of all elements is equal to 0 in trend sequence, it is determined that speed trend is moderate tone.
EvenThen determine that speed trend is upper The trend of liter, illustrates that suspicious object speed is identical as car speed, the possibility that knocks into the back is constant.
(2) B is determined according to speed trend.
Specifically,
If speed trend is ascendant trend,
Wherein, j is the component identification in velocity series, and velocity series herein are First Speed sequence and second speed sequence Column.
If speed trend is moderate tone, B=1.
If speed trend is downward trend,
Wherein,Max { } is maximizing function, and min { } is function of minimizing, i.e. φ is to become The quotient of greatest member value and least member value in gesture sequence.
3.2) according to D, B, the probability that knocks into the back that data sequence determines suspicious object is turned to.
Specifically,
(1) according to turning to, data sequence is determining to turn to reference value R.
Wherein,
M is to turn to difference sequence as { r2-r1,r3-r2,…,rt-rt-1,…,rT-rT-1In non-zero number of elements.
If automobile keeps executing, turn to that data are constant, the steering data at current time and the steering of previous moment at this time Data difference is 0.
(2)
102-6 alarms if the probability that knocks into the back is greater than preset second threshold.
Automobile anti-rear end collision method for early warning provided in this embodiment, not microwave radar sensor discovery suspicious object at once into Row alarm, but in suspicious object away from just determining its probability that knocks into the back in automobile first threshold, when probability be greater than second threshold again into Row early warning, it is therefore prevented that unnecessary early warning ensure that the accuracy of early warning.
In addition, fully considering the distance of suspicious object, the speed of suspicious object, the speed of automobile when probability is knocked into the back in calculating The steering data of degree and automobile.The distance of suspicious object describes the relative distance between suspicious object and automobile, suspicious object Speed and the speed of automobile describe the relative velocity between suspicious object and automobile, the steering data of automobile describe automobile Whether turn to.By relative distance, relative velocity and a possibility that comprehensive assessment suspicious object knocks into the back whether is turned to, ensure that and comment The accuracy estimated improves early warning effect.
It should be noted that " first " in the present embodiment and subsequent embodiment, " second " is only used for distinguishing suspicious object Velocity series and automobile velocity series, distinguish different threshold values etc., do not have any particular meaning.
The utility model has the advantages that
Suspicious item is monitored by microwave radar sensor, and according to the distance of suspicious object, the speed of suspicious object, automobile Speed and automobile steering data carry out early warning, improve early warning effect.

Claims (10)

1. a kind of automobile anti-rear end collision method for early warning, which is characterized in that the described method includes:
101, the distance of suspicious object is monitored by microwave radar sensor, the suspicious object is located at automobile tail;
102, when the distance for monitoring suspicious object is less than preset first threshold, execute following steps:
102-1 is obtained the distance of the suspicious object in real time by microwave radar sensor, obtains distance sequence;
102-2 obtains the speed of the suspicious object by microwave radar sensor in real time, obtains First Speed sequence;
102-3 obtains the speed of automobile in real time, obtains second speed sequence;
102-4 obtains the steering data of automobile in real time, obtains turning to data sequence;
102-5, according to the distance sequence, the First Speed sequence, the second speed sequence, the steering data sequence Determine the probability that knocks into the back of the suspicious object;
102-6 alarms if the probability that knocks into the back is greater than preset second threshold.
2. the method according to claim 1, wherein
Distance sequence is { d1,d2,…,dt,…,dT};
First Speed sequence { v1,v2,…,vt,…,vT};
Second speed sequence { v'1,v'2,…,v't,…,v'T};
Turn to data sequence { r1,r2,…,rt,…,rT};
Wherein, t is time identifier, dtFor the distance of suspicious object described in t moment, vtFor the speed of suspicious object described in t moment, v'tFor the speed of automobile described in t moment, rtFor the steering data of automobile described in t moment;T is current time, the distance sequence, The First Speed sequence, the second speed sequence, the element turned in data sequence are identical, are T;
The 102-5 includes:
102-5-1, if the element value ascending order of distance sequence arranges, it is determined that the probability that knocks into the back of the suspicious object is
Wherein, i is the component identification in distance sequence;
102-5-2, if the non-ascending order arrangement of the element value of distance sequence, calculates distance reference value D, according to D, the First Speed Sequence, the second speed sequence, the probability that knocks into the back for turning to data sequence and determining the suspicious object.
3. according to the method described in claim 2, it is characterized in that, if the element value descending of distance sequence arranges, the meter Calculate distance reference value D, comprising:
The average distance of the suspicious object is calculated by following formula
Compensated distance value w is calculated by following formula:
Wherein, α is the range error of the microwave radar sensor.
4. according to the method described in claim 2, it is characterized in that, if the non-descending arrangement of the element value of distance sequence, and distance The element value nor ascending order of sequence arrange, then the calculating distance reference value D, comprising:
The average distance of the suspicious object is calculated by following formula
Compensated distance value w is calculated by following formula:
Wherein, α is the range error of the microwave radar sensor;
β is penalty coefficient, if (dT-dT-1)-(dT-2-dT-3) > 0, β=- 1, if (dT-dT-1)-(dT-2-dT-3)=0, then β= 0, if (dT-dT-1)-(dT-2-dT-3) < 0, then β=1;
5. the method according to claim 3 or 4, which is characterized in that described according to D, the First Speed sequence, described Two velocity series, the probability that knocks into the back for turning to data sequence and determining the suspicious object, comprising:
If the element value of the First Speed sequence is descending arrangement, and the element value of the second speed sequence is ascending order row Column, it is determined that the probability that knocks into the back of the suspicious object is
If the element value of the First Speed sequence is ascending order arrangement, and the element value of the second speed sequence is descending row Column, it is determined that the probability that knocks into the back of the suspicious object is
If the element value of the First Speed sequence is descending arrangement, and the non-ascending order of element value of the second speed sequence is arranged Column, alternatively, if the element value of the First Speed sequence is that ascending order arranges, and the non-descending of element value of the second speed sequence Arrangement, alternatively, if the non-descending arrangement of the element value of the First Speed sequence, and the non-liter of element value of the First Speed sequence Sequence arrangement, it is determined that temporal reference value B, according to D, B, the probability that knocks into the back for turning to data sequence and determining the suspicious object.
6. according to the method described in claim 5, it is characterized in that, the determining temporal reference value B, comprising:
Speed trend is determined according to the First Speed sequence and the second speed sequence;
B is determined according to the speed trend.
7. according to the method described in claim 6, it is characterized in that, it is described according to the First Speed sequence and it is described second speed Degree series determine speed trend, comprising:
According to the First Speed sequence and the second speed sequence, deterministic trend sequence { v1-v'1,v2-v'2,…,vt-v 't,…,vT-v'T};
If the mean value of all elements is greater than 0 in trend sequence, it is determined that speed trend is ascendant trend;
If the mean value of all elements is less than 0 in trend sequence, it is determined that speed trend is downward trend;
If the mean value of all elements is equal to 0 in trend sequence, it is determined that speed trend is moderate tone.
8. the method according to the description of claim 7 is characterized in that described determine B according to the speed trend, comprising:
If speed trend is ascendant trend,
Wherein, j is the component identification in velocity series;
If speed trend is moderate tone, B=1;
If speed trend is downward trend,
Wherein,Max { } is maximizing function, and min { } is function of minimizing.
9. according to the method described in claim 8, it is characterized in that, described according to D, B, described in the steering data sequence determines The probability that knocks into the back of suspicious object, comprising:
It is determined according to the steering data sequence and turns to reference value R;
It is described
10. according to the method described in claim 9, it is characterized in that, described determined according to the steering data sequence turns to ginseng Examine value R, comprising:
Calculating and turning to difference sequence is { r2-r1,r3-r2,…,rt-rt-1,…,rT-rT-1};
Determine non-zero number of elements M in the steering difference sequence;
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