CN104157167B - A kind of vehicle collision avoidance method based on collaborative relative localization technology - Google Patents

A kind of vehicle collision avoidance method based on collaborative relative localization technology Download PDF

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CN104157167B
CN104157167B CN201410430510.2A CN201410430510A CN104157167B CN 104157167 B CN104157167 B CN 104157167B CN 201410430510 A CN201410430510 A CN 201410430510A CN 104157167 B CN104157167 B CN 104157167B
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vehicle
satellite
relative
pseudorange
orbit
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CN104157167A (en
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成华丽
温晓岳
章步镐
吴越
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银江股份有限公司
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Abstract

The present invention relates to intelligent transportation field, particularly relate to a kind of vehicle collision avoidance method based on collaborative relative localization technology, including: location based on V2V network information measurement and exchange;Enhancing relative positioning method based on pseudorange;Vehicle based on Kalman filtering is from predicting positioning navigation method;Vehicle collision avoidance judgment mechanism based on relative distance;By the information between vehicle V2V network transmission adjacent vehicle, calculate the relative distance between vehicle based on pseudorange or Kalman filtering, when relative distance is less than secure threshold time, trigger the alarm mechanism of vehicle.The beneficial effects of the present invention is: for the Multipath Transmission phenomenon in urban road, set up collaborative relative localization model and reject, according to dependency, the satellite-signal that spatial coherence is low, and use the method prediction vehicle location of Kalman filtering when gps signal interrupts.By collaborative relative positioning method, the probability of happening of vehicle accident in urban road can be reduced, improve predictablity rate.

Description

A kind of vehicle collision avoidance method based on collaborative relative localization technology

Technical field

The present invention relates to intelligent transportation field, particularly relate to a kind of vehicle collision avoidance side based on collaborative relative localization technology Method.

Background technology

GPS (Global Positioning System) global positioning system is that the Global Satellite that the U.S. sets up is led Boat alignment system, can realize high accuracy, round-the-clock, real-time navigation and test the speed.GPS technology is widely used to mapping in recent years Remote sensing, Aero-Space, communication, the every field such as traffic, and change the life of people deeply.

Location based on GPS system information analysis application the most progressively expands to intelligent transportation system ITS (Intelligent Transportation System).In modern ITS system, it is possible to use location information carry out vehicle automatic navigation and Safe driving.According to the principle of satellite navigation and location system, GPS location technology includes position estimation based on carrier phase and base In the position estimation of pseudorange, although the former location is very accurate, but there is the problem of integer ambiguity, although the latter is accurate Spend relatively low, but there is preferable real-time.But the factor affecting setting accuracy when vehicle GPS receives satellite-signal comprises The most several: gps satellite self error (including Satellite clock errors, satellite ephemeris error), transmission delay (include that ionosphere is prolonged Time and troposphere time delay), GPS receiver error (include receiver clock error, thermal noise and ground multidiameter delay Deng).It addition, in a ground strengthens system (GBAS, Ground-Based Augmentation System), one is positioned at The reference base station of known exact position can be to vehicle broadcasting satellite precise position information, and GPS receiver is according to himself Receive and revise again after comparing with broadcasts precise position information after satellite positioning signal calculates vehicle and intersatellite pseudorange Observation data, the method for this DGPS can effectively reduce identical propagation delay time error and satellite error.But, in road, city There is building in both sides, road, it means that the sight line path between gps satellite and vehicle may be blocked, i.e. vehicle GPS receives Machine can only receive the reflected signal of satellite.The different multipath tolerant signals deriving from different building constitute reception signal Multipath Transmission, its error caused may be up to tens of rice, and this reduces the precision of absolute fix undoubtedly.For DGPS system Speech, owing to GNSS reference base station is usually set up in free environments, and the reception signal between adjacent vehicle has spatial coherence Therefore the error of this Multipath Transmission can be reduced.

Summary of the invention

The present invention is to overcome above-mentioned weak point, it is therefore intended that provide a kind of relative position by road adjacent vehicle Detection and relatively position exceed the aposematic mechanism of threshold value it is thus possible to reduce the preventing collision of vehicles that city vehicle collision occurs with traffic accident Hit method.

The present invention is to reach above-mentioned purpose by the following technical programs: one one kinds of vehicles based on collaborative relative localization technology Collision-proof method, location vehicle is provided with GPS transmission/receiver, and several satellite in orbit directly or indirectly position vehicle, bag Include following steps:

1) satellite information that analysis the first vehicle of relative localization, the second vehicle receiver arrive, determines the first vehicle, the second car Shared satellite in orbit, set up collaborative Relative positioning systems model;

2) V2V network set up by the first vehicle and the second vehicle, transmits packet, packet information by shared satellite in orbit Including: vehicle identification ID, vehicle destination absolute fix coordinate, three-dimensional vehicle speed, shared satellite signal to noise ratio and shared satellite Pseudorange;

3) gps signal use when stablizing enhancing relative positioning method based on pseudorange calculate the first vehicle, the second vehicle it Between relative distance;

4) gps signal uses vehicle based on Kalman filtering to predict the first car from prediction positioning navigation method when interrupting , relative distance between the second vehicle;

5) according to step 3) or step 4) relative distance that obtains carries out vehicle collision avoidance based on relative distance and judge, if When relative distance is less than or equal to safe distance, triggers car alarm and also trigger emergency brake of vehicle mechanism, described safety away from From:

D = | ( | v a | t + 1 2 s a t 2 ) - ( | v b | t + 1 2 s b t 2 ) | ( | v a | t + 1 2 s a t 2 ) + ( | v b | t + 1 2 s b t 2 ) M i n ( | v a | t + 1 2 s a t 2 , | v b | t + 1 2 s b t 2 )

Wherein, | va| the mapping on direction vector of the three-dimensional velocity of expression vehicle a, | vb| represent the three-dimensional velocity of vehicle b Mapping on direction vector, saRepresent the acceleration of vehicle a, sbRepresenting the acceleration of vehicle b, t represents that the burst of driver is handed over Interpreter thus reaction and process average executeaaafunction;

It is that two vehicle heading vector angles are less than 90 ° when vehicle a and vehicle b goes in the same direction, the most now occurs knocking into the back Accident,

When vehicle a and the vehicle b i.e. two cars travel direction vector angle that goes in the same direction is more than 90 °, hit before the most now occurring Accident,

When vehicle a and vehicle b is lateral, row i.e. two cars travel direction vector angle is equal to 90 °, side crash the most now occurs Accident,

As preferably, enhancing relative positioning method based on pseudorange comprises the following steps:

(11) location vehicle v is calculated together with the pseudorange between satellite s in-orbit according to formula (1):

p v s = ρ v s + c × ( Δt v - Δt s ) + d m , v s + d n , v s + ϵ v s - - - ( 1 )

Pseudorange carries out second order difference:

▿ Δ a , b k , j = ( p a k - p b k ) - ( p a j - p b j ) = ▿ Δρ a , b k , j + ( ϵ a k - ϵ b k ) - ( ϵ a j - ϵ b j ) - - - ( 2 ) ;

Wherein,Represent the propagation delay time that ionosphere is brought,Representing the propagation delay time that troposphere is brought, c represents light Speed, Δ tvRepresent location vehicle clocking error, Δ tsRepresent Satellite clock errors,Represent thermal noise and the impact of multi-path interference,Representing actual range, a represents the first vehicle, and b represents the second vehicle, and k, j represent all shared satellite in orbit;

(12) calculateValue and compare with predetermined threshold value, when value of calculation is less than pre- If during threshold value, then judge corresponding shared satellite in orbit and the location relevant property of vehicle, retain the shared satellite in orbit that relatedness is high.

As preferably, what location vehicle a, b received shared satellite in orbit j directly transmits signal, i.e.Then pseudo- Away from second order difference result it is

As preferably, vehicle based on Kalman filtering comprises the following steps from prediction positioning navigation method:

(21) initial value of state vector, error co-variance matrix is determined;

(22) the prediction state vector of subsequent time, error co-variance matrix value:

(23) state updates, and subsequent time arrives, and uses the location information prediction pseudorange receivedAnd try to achieve observation square Battle array;

(24) use error co-variance matrix, calculate the gain matrix of wave filter in conjunction with observing matrix;

(25) actual distance of vehicle and shared satellite is calculatedObservation and predictive value;

(26) state vector and the estimated value of error co-variance matrix are calculated.

The beneficial effects of the present invention is: for the Multipath Transmission phenomenon in urban road, the collaborative relative localization of foundation Model can reject the low satellite-signal of spatial coherence according to dependency, and the use Kalman when occurring that gps signal interrupts The method prediction vehicle location of filtering.By the application of collaborative relative positioning method, vehicle accident in urban road can be reduced Probability of happening.Calculate the relative distance between vehicle, error can be cut down so that value of calculation be substantially equal to vehicle truly away from From, improve predictablity rate.

Accompanying drawing explanation

Fig. 1 is the flow chart of steps of the inventive method;

Fig. 2 is that the embodiment of the present invention works in coordination with Relative positioning systems model schematic;

Fig. 3 is the relative localization schematic diagram between neighbour's vehicle of the embodiment of the present invention.

Detailed description of the invention

Below in conjunction with specific embodiment, the present invention is described further, but protection scope of the present invention is not limited in This:

Embodiment 1: as it is shown in figure 1, a kind of vehicle collision avoidance method based on collaborative relative localization technology, including: based on The location information measurement of V2V network is with exchange, enhancing relative positioning method based on pseudorange, vehicle based on Kalman filtering certainly Prediction positioning navigation method, vehicle collision avoidance judgment mechanism based on relative distance, specifically include following steps:

1) satellite information that analysis the first vehicle of relative localization, the second vehicle receiver arrive, determines the first vehicle, the second car Shared satellite in orbit, set up collaborative Relative positioning systems model;

2) V2V network set up by the first vehicle and the second vehicle, transmits packet, packet information by shared satellite in orbit Including: vehicle identification ID, vehicle destination absolute fix coordinate, three-dimensional vehicle speed, shared satellite signal to noise ratio and shared satellite Pseudorange;

3) gps signal use when stablizing enhancing relative positioning method based on pseudorange calculate the first vehicle, the second vehicle it Between relative distance;

4) gps signal uses vehicle based on Kalman filtering to predict the first car from prediction positioning navigation method when interrupting , relative distance between the second vehicle;

5) according to step 3) or step 4) relative distance that obtains carries out vehicle collision avoidance based on relative distance and judge, if When relative distance is less than or equal to safe distance, triggers car alarm and trigger emergency brake of vehicle mechanism.

Assume as in figure 2 it is shown, satellite in orbit S1-S5To carry GPS transmission/receiver vehicle a, vehicle b transmit location Signal, and all right the sailing of vehicle a, vehicle b have in the urban traffic road of various building both sides, due to the resistance of building Gear, between vehicle and satellite, directly transmission path is blocked, so for vehicle a, vehicle b, receiving direct signal, Have and receive reflected signal, also do not receive satellite-signal.Wherein vehicle a can receive S1To S4Signal, and S1、S2And S4It is to directly receive signal, S3It it is reflected signal;Vehicle b can receive S1、S3、S4And S5Signal, and S4With S5It is the signal directly received, S1And S3Reflected signal.Obviously S2Can only be received and S by vehicle a5Can only be received by vehicle b Arrive, so when vehicle a and vehicle b positions the most respectively, the deviation of absolute fix coordinate is very big, the most directly passes through two cars Absolute coordinate location positioning calculate its relative position and can cause great measurement error at city complexity road environment, pass through Then absolute coordinate location carries out distance l being calculated between vehicle2Compare the two actual distance l1Increase error.The present invention Collaborative Relative positioning systems model in, first determine the shared satellite in orbit of vehicle a and vehicle b, i.e. S1、S3And S4.By docking The satellite-signal received is analyzed, it is known that S1Being direct signal for vehicle a but be reflected signal for vehicle b, this is right It it is low spatial dependency when vehicle carries out relative localization.Although vehicle a and b receives satellite S3Be all reflected signal, But their position error is substantially identical when the spacing of two cars is the shortest when.Therefore at collaborative relative localization mould In type, only use the shared satellite S with certain space dependency3And S4The framing signal of transmission, therefore at two cars absolute coordinate The when that position having roughly the same offset direction and deviation size relative to actual position, the relative position calculating the two is permissible Cut down same deviation value so that value of calculation is substantially equal to vehicle actual distance.

Before adjacent vehicle exchanging orientation information, each vehicle needs the observation satellite received location data to include: defend The star transmission signal to noise ratio snr of signal, the elevation angle of observation satellite, satellite ephemeris data and the observation satellite obtained by ephemeris Orbit coordinate.Obviously can accordingly calculating observation satellite to the pseudorange of GPS receiver, meanwhile each car also will survey Measure himself three-dimensional velocity and travel direction.To sum up, after vehicle establishes V2V network, collaborative Relative positioning systems mould The packet information that type is transmitted comprises: vehicle identification ID, vehicle destination absolute fix coordinate, three-dimensional vehicle speed, shares Satellite signal to noise ratio and shared satellite pseudorange.

Each car can be able to be sentenced by the packet of the packet content of himself transmission and the adjacent vehicle received Do not go out the shared satellite in orbit of two cars.Herein relative localization is measured consideration based on spatial coherence, only selects and share The location information of satellite is used for relative localization.Table 1 is packet content.

Table 1

Enhancing relative positioning method based on pseudorange is i.e. according to known N number of observation satellite and N vehicle coordinate meter to be measured Calculate vehicle to be measured relative distance between any two, according to observation satellite Calculation for Ephemerides pseudorange, with accurate distance and the difference of pseudorange Value updates observation data and improves positioning precision.Determine satellite s 3, satellite s 4 for calculating vehicle a, the relative pseudorange of vehicle b, as Shown in Fig. 3, s3 is designated as k, s4 and is designated as j,Represent the actual range between satellite k and vehicle a,Represent satellite k and vehicle Actual distance between b,Represent the actual distance between satellite j and vehicle a,Represent between satellite j and vehicle b is true Actual distance is from, θkRepresent the satellite k elevation angle degree relative to vehicle a, θjRepresent the satellite j elevation angle degree relative to vehicle a.

Pseudorange between vehicle v and satellite s can calculate according to following formula:

p v s = ρ v s + c × ( Δt v - Δt s ) + d m , v s + d n , v s + ϵ v s - - - ( 1 )

The when of between two cars enough closely, we are it is reasonable that the method being referred to traditional difference DGPS disappears Remove the propagation delay time brought due to ionosphere and troposphereWithAnd Satellite clock errors Δ ts, Δ tvRepresent location Vehicle clock error,Represent thermal noise and the impact of multi-path interference,Represent actual range.Then for a shared satellite Speech, two cars (v=a, pseudo range difference b) can be calculated by following formula:

Δp a , b s = Δρ a , b s + c × Δt a , b + Δϵ a , b s - - - ( 2 )

Can disappear the different GPS clocking error of two cars by pseudorange being carried out second order difference according to formula (2) Δtv:

▿ Δp a , b k , j = ( p a k - p b k ) - ( p a j - p b j ) = ▿ Δρ a , b k , j + ( ϵ a k - ϵ b k ) - ( ϵ a j - ϵ b j ) - - - ( 3 )

In its computation of pseudoranges, compare other factor thermal noises and be generally small enough to such an extent as to be negligible, therefore pass through formula The calculating of relative distance can be converted into the calculating to multiple shared satellite multi-path interference factors by the second order difference of three.Due to city The transmission environment that zones of different is complicated, for a shared satellite likely car receive its directly transmission signal and another What car received is reflected signal.In other words, same satellite positioning signal is existed the error that Multipath Transmission causes, thereforeError be typically due to the Multipath Transmission error that different building reflected signal causes, need a shared satellite The dependency of pseudorange detect.Then when two cars all receives the directly transmission signal of shared satellite j, The most now only existing the impact of reflected signal, namely we can obtain such as lower approximate value:

▿ Δp a , b k , j - ▿ Δρ a , b k , j ≈ ϵ a k - ϵ b k - - - ( 4 )

Using shared satellite j as basis of reference, whenValue than a default experience threshold Value hour, we are it is reasonable that the framing signal that two cars receives from satellite k has dependency.Basis reference is defended Star choose the elevation angle being often based on vehicle relative to satellite.The satellite that in the shared satellite of vehicle, the elevation angle is maximum will be chosen for Basis reference satellite, because the probability that can receive its direct signal for this satellite vehicle is maximum.

Vehicle based on Kalman filtering is from predicting positioning navigation method:

Vehicle in urban area travels is frequently encountered the situation that gps signal interrupts, and shares satellite owing to using This situation is caused to occur more.Kalman filtering can, observation sequence to object space limited, that comprise noise from a group Row (may have deviation) dope coordinate and the speed of object space.Therefore can predict and GPS by combining vehicle coordinate Location information uses Kalman filtering to predict the position coordinates of vehicle when gps signal interrupts.Kalman filtering is a kind of linear Minimum variance estimate algorithm, uses the thought of Recursive Filtering to introduce the concept of state space, such that it is able to according to the state of system Equation of transfer estimates the state value of subsequent time according to the state value of previous moment and the observation of current time.Use puppet herein Away from the observation as Kalman filtering, then the fundamental equation of Kalman filtering is shown below:

Xkk,k-1Xk-1+Wk (5)

Zk=HkXk+Vk (6)

Formula (5) is state equation, and formula (6) is observational equation, wherein XkFor state vector, Φk,k-1Shape for system State transfer matrix, WkFor system noise sequence and assume its meet average be zero, covariance matrix be QkMultivariate normal distributions, I.e. Wk~N (0, Qk), ZkFor to time of day XkA measurement, HkFor observing matrix, it is mapped to observation time of day space Space, VkFor its average of observation noise sequence be zero, covariance matrix be RkAnd Normal Distribution, i.e. Vk~N (0, Rk).Root According to formula (1) formula observation model to pseudorange, it is known thatIt is about state vector XkNonlinear equation, useTo state To measuring local derviation.

At forecast period, wave filter uses the estimation of laststate, makes the estimation to current state.In the more new stage, Wave filter utilizes the predictive value obtained the observation optimization of current state at forecast period, newly estimates more accurately obtaining one Evaluation.So error co-variance matrix P of Kalman filteringkCan represent with following formula:

P k , k - 1 = X k P k - 1 , k - 1 X k T + Q k - - - ( 7 )

To sum up, the vehicle using Kalman filtering includes following process from prediction location navigation:

1) initial value of state vector, error co-variance matrix is determined;

2) the prediction state vector of subsequent time, error co-variance matrix value;

3) state updates, and subsequent time arrives, and uses the location information prediction pseudorange receivedAnd try to achieve observation square Battle array;

4) use error co-variance matrix, calculate the gain matrix of wave filter in conjunction with observing matrix;

5) actual distance of vehicle and shared satellite is calculatedObservation and predictive value;

6) state vector and the estimated value of error co-variance matrix are calculated.

The second step of said process, to the next state renewal process that the 6th step is Kalman filter, is providing first In the case of the initial value of step, the predictive value obtaining subsequent time in an iterative manner can be constantly updated, it is not necessary to record is seen The historical information surveyed or estimate.

Vehicle collision avoidance judgment mechanism based on relative distance:

Vehicle a, the b position when moment t can by it in the position of moment t-1, speed and acceleration predicted estimate Obtain, thenCan according to moment t time share satellite (s=k, j) (v=a, three-dimensional coordinate position b) calculate with vehicle Know, i.e. for vehicle (v=a, other shared satellites b), the second order difference of surveyed pseudorange and the second order difference of estimation range findingResult of calculation and empirical value compare thus choose the shared satellite with high spatial dependency.

Thus, eliminate the shared satellite that dependency is low, according to the packet of the V2V network transmission that step 1 provides, it is known that The speed of vehicleAcceleration maWith enforcement directionWe assume that the burst vehicle accident of driver is anti- Should be t with the average executeaaafunction processed.For the packet received, first determine whether the travel direction of vehicle, if vehicle a With vehicle b in the same direction and row i.e. two vehicle heading vector angles less than 90 °, be the most now likely to occur for rear-end collision;As Really vehicle a and the vehicle b i.e. two cars travel direction vector angle that goes in the same direction is more than 90 °, be the most now likely to occur be before hit Accident;If if vehicle a and vehicle b is lateral, row i.e. two cars travel direction vector angle is equal to 90 °, the most now may go out Existing is side crash accident.Assume | va| and | vb| it is the mapping on direction vector of the three-dimensional velocity of vehicle a and vehicle b respectively, then The safe distance of three of the above classification respective anticollision mechanism can be simplified shown as:

D = | ( | v a | t + 1 2 s a t 2 ) - ( | v b | t + 1 2 s b t 2 ) | ( | v a | t + 1 2 s a t 2 ) + ( | v b | t + 1 2 s b t 2 ) M i n ( | v a | t + 1 2 s a t 2 , | v b | t + 1 2 s b t 2 ) - - - ( 8 )

When relative distance is less than or equal to safe distance, triggers car alarm and automatically trigger emergency brake of vehicle machine Make thus ensure the safety of occupant.

It is the specific embodiment of the present invention and the know-why used described in Yi Shang, if conception under this invention institute Make change, function produced by it still without departing from description and accompanying drawing contained spiritual time, must belong to the present invention's Protection domain.

Claims (4)

1. a vehicle collision avoidance method based on collaborative relative localization technology, location vehicle is provided with GPS and sends/receive Machine, several satellite in orbit directly or indirectly position vehicle, it is characterised in that comprise the following steps:
1) analyze the satellite information that the first vehicle of relative localization, the second vehicle receiver arrive, determine the first vehicle, the second vehicle Share satellite in orbit, set up collaborative Relative positioning systems model;
2) V2V network set up by the first vehicle and the second vehicle, transmits packet, packet information bag by shared satellite in orbit Include: vehicle identification ID, vehicle destination absolute fix coordinate, three-dimensional vehicle speed, shared satellite signal to noise ratio and shared satellite are pseudo- Away from;
3) gps signal uses enhancing relative positioning method based on pseudorange to calculate phase between the first vehicle, the second vehicle when stablizing Adjust the distance;
4) gps signal use when interrupting vehicle based on Kalman filtering from prediction positioning navigation method predict the first vehicle, the Relative distance between two vehicles;
5) according to step 3) or step 4) relative distance that obtains carries out vehicle collision avoidance based on relative distance and judge, if relatively When distance is less than or equal to safe distance, triggers car alarm and trigger emergency brake of vehicle mechanism, described safe distance:
Wherein, | va| the mapping on direction vector of the three-dimensional velocity of expression vehicle a, | vb| represent that the three-dimensional velocity of vehicle b is in side Mapping on vector, saRepresent the acceleration of vehicle a, sbRepresenting the acceleration of vehicle b, t represents the burst traffic thing of driver Therefore reaction and the average executeaaafunction of process;
It is that two vehicle heading vector angles are less than 90 ° when vehicle a and vehicle b goes in the same direction, rear-end collision the most now occurs,
When vehicle a and the vehicle b i.e. two cars travel direction vector angle that goes in the same direction is more than 90 °, before the most now occurring, hit accident,
When vehicle a and vehicle b is lateral, row i.e. two cars travel direction vector angle is equal to 90 °, side crash accident the most now occurs,
A kind of vehicle collision avoidance method based on collaborative relative localization technology the most according to claim 1, it is characterised in that Enhancing relative positioning method based on pseudorange comprises the following steps:
(11) location vehicle v is calculated together with the pseudorange between satellite s in-orbit according to formula (1):
Pseudorange carries out second order difference:
Wherein,Represent the propagation delay time that ionosphere is brought,Representing the propagation delay time that troposphere is brought, c represents the light velocity, Δ tvRepresent location vehicle clocking error, Δ tsRepresent Satellite clock errors,Represent thermal noise and the impact of multi-path interference,Table Showing that actual range, a represent the first vehicle, b represents the second vehicle, and k, j represent all shared satellite in orbit;
(12) calculateValue and compare with predetermined threshold value, when value of calculation less than preset threshold During value, then judge corresponding shared satellite in orbit and the location relevant property of vehicle, retain the shared satellite in orbit that relatedness is high.
A kind of vehicle collision avoidance method based on collaborative relative localization technology the most according to claim 2, it is characterised in that What location vehicle a, b received shared satellite in orbit j directly transmits signal, i.e.Then pseudorange second order difference result is
A kind of vehicle collision avoidance method based on collaborative relative localization technology the most according to claim 1, it is characterised in that Vehicle based on Kalman filtering comprises the following steps from prediction positioning navigation method:
(21) initial value of state vector, error co-variance matrix is determined;
(22) the prediction state vector of subsequent time, error co-variance matrix value;
(23) state updates, and subsequent time arrives, and uses the location information prediction pseudorange receivedAnd try to achieve observing matrix;
(24) use error co-variance matrix, calculate the gain matrix of wave filter in conjunction with observing matrix;
(25) actual distance of vehicle and shared satellite is calculatedObservation and predictive value;
(26) state vector and the estimated value of error co-variance matrix are calculated.
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