CN108507587A - A kind of three-dimensional vehicle mounted positioning navigation method based on coordinate transform - Google Patents
A kind of three-dimensional vehicle mounted positioning navigation method based on coordinate transform Download PDFInfo
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Abstract
The three-dimensional vehicle mounted positioning navigation method based on coordinate transform that the invention discloses a kind of, this method initially set up multiple nonlinear motion models；Then hybrid estimation is carried out to each motion model probability of vehicle, each motion model calculates separately the filtering initial value of oneself；Then Unscented kalman filtering is merged, GPS observations are added, the filtering output of each model of parallel computation updates the probability of each model after filtering, find best suit current vehicle movement model carry out output interaction, obtain total state estimation and total covariance estimation；Finally when vehicle is in slope surface state, two different coordinate systems of plane and slope surface are established using the method for coordinate transform, the front and back relationship of vehicle location three-dimensional coordinate variation is obtained, calculates its elevation information.The present invention is effectively improved the positioning accuracy of vehicle positioning accuracy in the height direction and entirety really, has stronger practical value.
Description
Technical field
The present invention relates to a kind of three-dimensional vehicle mounted positioning navigation method based on coordinate transform, the vehicle obtained using the method
Positioning height information can ensure the basic altitude location requirement of vehicle, in conjunction with GIS by vehicle location to specific a certain track,
It efficiently solves the problems, such as vehicle Wrong localization under the road conditions such as complicated viaduct, not only increases the positioning of vehicle-height direction
Precision also improves the whole positioning accuracy of automobile navigation, can be used in the road conditions of three dimensions complexity.
Background technology
Under real world conditions, actual systems most is nonlinear, the system equation of mobility model and observation
Equation is also all nonlinear.Unscented kalman filtering determines optimum gain according to the covariance matrix of the amount of being estimated and measurement
Battle array, does not have system equation and measurement equation extra additional requirement, algorithm not only to can be used for linear system but also can be used for non-
Linear system, but under conditions of nonlinear system, Unscented kalman filtering can more show its superiority, non-linear stronger,
Effect is more apparent.
In actual vehicular motion, it is impossible to be single motion model, the motion process of target vehicle is by a variety of
Maneuvering condition forms.Interacting multiple algorithm is a kind of Soft Handover Algorithm, has been obtained extensively in maneuvering target tracking field at present
Application.It can effectively overcome the problems, such as that the evaluated error that single model is brought is larger, by effective Weighted Fusion to system
Carry out state estimation.Interacting multiple algorithm be correspond to different motion state processes using different motion models, and by its
It is assumed to be a Markov process, that is, thinks that the mobile process of vehicle is multiple motion models under a markov coefficient
Fusion, when switching of each motion model controlled by transition probability, the output of each model is merged, as entire
The estimation of dbjective state.
Traditional Interactive Multiple-Model Unscented kalman filtering has a good filter effect for vehicle-mounted plane motion, but for
The positioning accuracy error of elevation information is larger, can not distinguish which layer that vehicle is located at complicated viaduct completely, be susceptible to
Navigation map matches the phenomenon that practical road conditions error.Due to GPS receiver signal and height above sea level and ground level conversion equal error
Factor, the height of car data error that GPS is provided is too big, is differed between several meters to tens meters, such altitude information is used
In filtering, hence it is evident that effect can not possibly be too accurate, and the too big problem of height of car position error still exists in actual life.
Coordinate transform is the location expression to spatial entities, is passed through from a kind of coordinate system transformation to another coordinate system
Correspondence between two coordinate systems is realized.The rotation of any dimension can be expressed as vector and multiply with the square formation of suitable dimension
Product.A final rotation is equivalent under another different coordinates to the restatement of position.In GIS-Geographic Information System,
Ambiguous coordinate transform, first, map projection transformation, i.e., be transformed into another map projection, ground from a kind of map projection
Each point coordinates changes on figure；Another is the conversion of measurement system coordinate, i.e., from earth coordinates to map coordinates system, number
Change the coordinate conversion between instrument coordinate system, plotter-unit coordinate or display coordinate.
Invention content
The three-dimensional vehicle mounted positioning navigation method based on coordinate transform that in view of the deficiencies of the prior art, the present invention proposes a kind of,
It first passes through Interactive Multiple-Model Unscented kalman filtering to estimate the vehicle-state of horizontal direction, when vehicle enters slope surface road conditions
The method for utilizing coordinate transform afterwards is established the governing equation between coordinate system variation fore-aft vehicle three-dimensional location coordinates, is utilized
The relationship of plane coordinates and height coordinate solves the height of car value of information, improves positioning accuracy of the vehicle in terms of height, then tie
GIS is closed by vehicle location to specific a certain track.
In order to solve the above technical problems, the present invention provides the three-dimensional vehicle mounted positioning navigation method based on coordinate transform, including
Following steps：
Step 1, m nonlinear motion model j is established, expression formulas of the model j at the k+1 moment is It is the white noise sequence that model j is zero in k moment hourly values,It is probability of the model j at the k moment, leads between motion model
Markov chain is crossed to control transfer；
Step 2, the non-linear observational equation Z of Unscented kalman filtering is establishedk=h (Xk,Vk), VkFor systematic observation noise
Sequence；
Step 3, the transition probability of model i to model j is pij, calculate the mixing probability in k-1 moment model i to model j
μij[(k-1)/(k-1)], admixtures of the computation model j at the k-1 moment are estimatedEstimate with mixing covariance
Count Pj[(k-1)/(k-1)], using the hybrid estimation obtained after calculating as the original state of cycle；
Step 4, model j is estimated in the admixture at k-1 momentGo out by U transformation calculations
Sigma point valuesAnd its corresponding single order weightsWith second order weightsWherein i indicates sigma points
Serial number；
Step 5, by sigma point valuesBy the state equation of model j, it is pre- to calculate the step to do well
Survey sigma point valuesWith the one-step prediction sigma point values of stateCalculate the step to do well
Predicted valueWith one-step prediction covariance matrixWherein, subscript x indicates that this matrix is shape
The covariance matrix of state value, one-step prediction valueEstimate the value at the k moment for admixture；
Step 6, by the one-step prediction sigma point values in step 5By systematic observation equation, sight is found out
The sigma point values of measured valueCalculating observation predicted value is Zj[(k)/(k-1)], observation covariance matrix areAnd state observation Cross-covariance isWherein subscript z indicates that this matrix is observation
The covariance matrix of value, subscript xz indicate that this matrix is state value and the Cross-covariance of observation；
Step 7, measurement updaue calculates gain battle array Kj, state estimations of the computation model j at the k momentAnd
Error co-variance matrix
Step 8, the likelihood function Λ of updated probabilistic model j is calculatedj(k), after new observation information Z (k) is added, more
New current model probability；
Step 9, output interaction, each model carry out above step, total shape are calculated after updating respective model probability parallel
State is estimatedEstimate P with total covarianceX[(k)/(k)]；
Step 10, judge whether vehicle is in slope surface, it is on the contrary then establish plane and sit if it is not, then return to step 3 continues to execute
Mark system S and slope surface coordinate system S1, according to the front and back relationship of two coordinate system variations, structure variation fore-aft vehicle three-dimensional location coordinates
Between equation, thus calculate vehicle in the elevation information of slope surface, return again to step 3 later and continue cycling through execution.
Further, in step 4, the circular of sigma point values is as follows：
In formula, n is state vector dimension, Pj[(k-1)/(k-1)] is mixing covariance estimation, and λ is scaling parameter,
Wherein i indicates the serial number of sigma points；
Further, in step 5, the one-step prediction value of state is calculatedWith one-step prediction covariance matrixThe specific method is as follows：
Wherein,One-step prediction sigma after the state equation for passing through model j for the sigma in step 4
Point value.
Further, in step 6, calculating observation predicted value is Zj[(k)/(k-1)], observation covariance matrix areAnd state observation Cross-covariance isThe specific method is as follows：
Wherein, Qk-1For observation noise covariance matrix,The sigma point values of observation.
Further, in step 9, total state estimation is calculatedEstimate P with total covarianceX[(k)/(k's)]
The specific method is as follows：
Wherein, μj(k) probability for being k moment motion models j.
Further, in step 10, the specific method is as follows for equation between calculating three-dimensional vehicle position coordinates：
Wherein,For the deflection of coordinate system S-transformation, θ is the elevation angle of coordinate system S-transformation, and ex1, ey1, ez1 are coordinate systems
The reference axis unit vector of S1, ex, ey, ez are the reference axis unit vectors of coordinate system S.
The advantageous effects that the present invention is reached：
1, it introduces Interactive Multiple-Model and corresponds to different motion state processes using different motion models, merge traditional nothing
Mark Kalman filtering solves the problems, such as that locating effect is bad when vehicular motion state suddenly change, can realize adaptive-filtering.
2, since GPS altitude location errors are too big, cause vehicle that can not carry out accurate altitude location.Traditional barometer
Vehicle can be assisted to carry out the positioning of height to a certain extent, but the factor for influencing air pressure includes more：Temperature, humidity, sea
Degree of lifting, atmospheric density etc., barometrical service condition are easy to be influenced by weather condition, highly unstable, altitude location
Precision can not reach overpass floor height rank.The altitude location navigation problem of vehicle is solved by the method for coordinate transform,
There can not only be good precision improvement in terms of height, also have corresponding promotion for the three-dimensional localization precision of vehicle entirety, and
It is free from the influence of the external environment.
Description of the drawings
Fig. 1 is the implementation flow chart of the present invention；
Fig. 2 is the schematic diagram of coordinate S and coordinate S1 transformation
Fig. 3 is three-dimensional vehicle movement locus estimation figure of the present invention；
Fig. 4 is vehicle of the present invention in X-direction velocity estimation figure；
Fig. 5 is vehicle of the present invention velocity estimation figure in the Y direction；
Fig. 6 is vehicle of the present invention in Z-direction position error figure；
Fig. 7 is the vehicle using IMMUKF-3D algorithms in Z-direction position error figure；
Fig. 8 is comparison diagram of the present invention with the vehicle using IMMUKF-3D algorithms in Z-direction position error；
Fig. 9 is comparison diagram of the present invention with the vehicle using IMMUKF-3D algorithms in whole position error.
Specific implementation mode
With reference to specific embodiment, the invention will be further described.Following embodiment is only used for clearly illustrating
Technical scheme of the present invention, and not intended to limit the protection scope of the present invention.
Patent of the present invention is further illustrated with reference to the accompanying drawings and examples.
A kind of three-dimensional vehicle mounted positioning navigation method based on coordinate transform, as shown in Figure 1, specifically comprising the following steps：
Step 1, m nonlinear motion model j is established, expression formulas of the model j at the k+1 moment isXkIt is the state vector of system, f () is nonlinear procedure function,It is
The white noise sequence that model j is zero in k moment hourly values,It is probability of the model j at the k moment, passes through horse between motion model
Markov's chain shifts to control；
Step 2, the non-linear observational equation Z of Unscented kalman filtering is establishedk=h (Xk,Vk), ZkIt is observation vector, h
() is the nonlinear function of observation, VkFor systematic observation noise sequence, observation vector dimension be necessarily less than or equal to state to
The dimension of amount.
Step 3, the transition probability of model i to model j is pij, prediction probability, that is, normaliztion constant of model j isMeter
Calculate the mixing probability μ in k-1 moment model i to model jij[(k-1)/(k-1)], admixtures of the computation model j at the k-1 moment
EstimationEstimate P with mixing covariancej[(k-1)/(k-1)], using the hybrid estimation obtained after calculating as
The original state of cycle；
Step 4, model j is estimated in the admixture at k-1 momentGo out by U transformation calculations
Sigma point valuesAnd its corresponding single order weightsWith second order weightsWherein i indicates sigma points
Serial number；The circular of sigma point values is as follows：
In formula, n is state vector dimension, Pj[(k-1)/(k-1)] is mixing covariance estimation, and λ is scaling parameter,
Wherein i indicates the serial number of sigma points；
Step 5, by sigma point valuesBy the state equation of model j, it is pre- to calculate the step to do well
Survey sigma point valuesWith the one-step prediction sigma point values of stateCalculate the step to do well
Predicted valueWith one-step prediction covariance matrixWherein, subscript x indicates that this matrix is shape
The covariance matrix of state value, one-step prediction valueEstimate the value at the k moment for admixture；
The one-step prediction value of calculating stateWith one-step prediction covariance matrixTool
Body method is as follows：
Wherein,One-step prediction sigma after the state equation for passing through model j for the sigma in step 4
Point value.
Step 6, by the one-step prediction sigma point values in step 5By systematic observation equation, sight is found out
The sigma point values of measured valueCalculating observation predicted value is Zj[(k)/(k-1)], observation covariance matrix areAnd state observation Cross-covariance isWherein subscript z indicates that this matrix is observation
The covariance matrix of value, subscript xz indicate that this matrix is state value and the Cross-covariance of observation；
Calculating observation predicted value is Zj[(k)/(k-1)], observation covariance matrix areAnd state observation
Cross-covariance isThe specific method is as follows：
Wherein, Qk-1For observation noise covariance matrix,The sigma point values of observation.
Step 7, measurement updaue calculates gain battle array Kj, state estimations of the computation model j at the k momentWith
And error co-variance matrix
Step 8, the likelihood function Λ of updated probabilistic model j is calculatedj(k), after new observation information Z (k) is added, more
New current model probability；
Step 9, output interaction, each model carry out above step, total shape are calculated after updating respective model probability parallel
State is estimatedEstimate P with total covarianceX[(k)/(k)]；Calculate total state estimationWith total association
Variance evaluation PX[(k)/(k)] the specific method is as follows：
Wherein, μj(k) probability for being k moment motion models j.
Step 10, judge whether vehicle is in slope surface, it is on the contrary then establish plane and sit if it is not, then return to step 3 continues to execute
Mark system S and slope surface coordinate system S1, it is Z1 axis that slope surface normal vector is taken in slope surface coordinate system S1, takes coordinate system S horizontal rotatio directions
For X1 axis, slope surface elevation direction is Y1 axis, according to the front and back relationship of two coordinate system variations, structure variation fore-aft vehicle three-dimensional position
Set the equation between coordinate, thus calculate vehicle slope surface elevation information.Step 3 is returned again to later continue cycling through hold
Row.The specific method is as follows for equation between calculating three-dimensional vehicle position coordinates：
Wherein,For the deflection of coordinate system S-transformation, θ is the elevation angle of coordinate system S-transformation.Ex1, ey1, ez1 are coordinate systems
The reference axis unit vector of S1, ex, ey, ez are the reference axis unit vectors of coordinate system S.
Embodiment
The method performance and positioning accuracy improvement effect of this method are further illustrated by being implemented as follows：
The state vector that the present invention is arranged includes displacement, speed and the acceleration information of vehicle, and dimension is 6 dimensions, observe to
Amount includes mileage and displacement, and dimension is 3 dimensions.Vehicle does the movement of S types, 45 degree of deflection, the gradient 45 in three dimensions in emulation 1
Degree, initial position are located at (100,500,0) coordinate, and initial velocity is (0,10,0), by 250 filter point of straight line uniform motion
Later, start to go up a slope and carry out the movement of speed change S types.Sampling period is 0.1 second.Method such as Fig. 2 institutes of coordinate S and coordinate S1 transformation
Show.Three-dimensional vehicle movement locus estimation figure is as shown in Figure 3.Velocity tracking scenario when state of motion of vehicle suddenly change is tested,
Experimental result is as shown in Figure 4 and Figure 5, as seen from the figure, proposed by the present invention at the time of suddenly change occurs for state of motion of vehicle
Filtering algorithm can also make estimating speed track standard speed well.Vehicle is measured in the position error of Z-direction, experimental result
As shown in fig. 6, also on level land when due to preceding 250 filter point, coordinate is also non-transformed, so without height error, height later is missed
Difference is average at 2 meters or so, and position error is obviously reduced compared with Fig. 7.Vehicle is measured using IMMUKF-3D algorithms in Z-direction
Position error, experimental result is as shown in fig. 7, height error is average at 4 meters or so, and in this error range, vehicle is overhead etc.
The inaccurate phenomenon of positioning is susceptible at complex road condition.It is fixed in Z-direction with the vehicle using IMMUKF-3D algorithms to measure the present invention
Comparison in the error of position, experimental data unit are rice (m), and experimental result such as Fig. 8 institutes show, compared with IMMUKF-3D methods, this
Inventive method smaller in Z-direction position error.The present invention is measured to miss in integrally positioning with the vehicle using IMMUKF-3D algorithms
Comparison in difference, experimental data unit are rice (m), and experimental result is as shown in figure 9, compared with IMMUKF-3D methods, side of the present invention
Method smaller in whole position error.Experimental comparison's performance of this method and IMMUKF-3D methods.The method performance boost
It is larger.
Present invention introduces Interactive Multiple-Models, and different motion state processes, fusion tradition are corresponded to using different motion models
Unscented kalman filtering, solve the problems, such as that locating effect is bad when vehicular motion state suddenly change, can realize adaptive
Filtering.The altitude location navigation problem of vehicle is solved by the method for coordinate transform, can not only be had in terms of height very well
Precision improvement, also have corresponding promotion for the three-dimensional localization precision of vehicle entirety, and free from the influence of the external environment.
The present invention is disclosed with preferred embodiment above, so it is not intended to limiting the invention, all to take equivalent replacement
Or the technical solution that the scheme of equivalent transformation is obtained, it all falls in protection scope of the present invention.
Claims (6)
1. a kind of three-dimensional vehicle mounted positioning navigation method based on coordinate transform, it is characterised in that include the following steps：
Step 1, m nonlinear motion model j is established, expression formulas of the model j at the k+1 moment is It is the white noise sequence that model j is zero in k moment hourly values,It is probability of the model j at the k moment, leads between motion model
Markov chain is crossed to control transfer；
Step 2, the non-linear observational equation Z of Unscented kalman filtering is establishedk=h (Xk,Vk), VkFor systematic observation noise sequence；
Step 3, the transition probability of model i to model j is pij, calculate the mixing probability μ in k-1 moment model i to model jij
[(k-1)/(k-1)], admixtures of the computation model j at the k-1 moment are estimatedWith mixing covariance estimation
Pj[(k-1)/(k-1)], using the hybrid estimation obtained after calculating as the original state of cycle；
Step 4, model j is estimated in the admixture at k-1 momentGo out sigma points by U transformation calculations
ValueAnd its corresponding single order weightsWith second order weightsWherein i indicates the serial number of sigma points；
Step 5, by sigma point valuesBy the state equation of model j, the one-step prediction to do well is calculated
Sigma point valuesWith the one-step prediction sigma point values of stateIt is pre- to calculate the step to do well
Measured valueWith one-step prediction covariance matrixWherein, subscript x indicates that this matrix is state
The covariance matrix of value, one-step prediction valueEstimate the value at the k moment for admixture；
Step 6, by the one-step prediction sigma point values in step 5By systematic observation equation, observation is found out
Sigma point valuesCalculating observation predicted value is Zj[(k)/(k-1)], observation covariance matrix areAnd state observation Cross-covariance isWherein subscript z indicates that this matrix is observation
The covariance matrix of value, subscript xz indicate that this matrix is state value and the Cross-covariance of observation；
Step 7, measurement updaue calculates gain battle array Kj, state estimations of the computation model j at the k momentAnd error
Covariance matrix
Step 8, the likelihood function Λ of updated probabilistic model j is calculatedj(k), after new observation information Z (k) is added, update is worked as
Preceding model probability；
Step 9, output interaction, each model carries out above step parallel, updates and calculates total state after respective model probability and estimate
MeterEstimate P with total covarianceX[(k)/(k)]；
Step 10, judge whether vehicle is in slope surface, it is on the contrary then establish plane coordinate system if it is not, then return to step 3 continues to execute
S and slope surface coordinate system S1, according to the front and back relationship of two coordinate system variations, structure changes between fore-aft vehicle three-dimensional location coordinates
Equation, thus calculate vehicle in the elevation information of slope surface, return again to step 3 later and continue cycling through execution.
2. the three-dimensional vehicle mounted positioning navigation method according to claim 1 based on coordinate transform, it is characterised in that：Step 4
In, the circular of sigma point values is as follows：
In formula, n is state vector dimension, Pj[(k-1)/(k-1)] is mixing covariance estimation, and λ is scaling parameter, wherein i
Indicate the serial number of sigma points.
3. the three-dimensional vehicle mounted positioning navigation method according to claim 1 based on coordinate transform, it is characterised in that：Step 5
In, calculate the one-step prediction value of stateWith one-step prediction covariance matrixSpecific side
Method is as follows：
Wherein,One-step prediction sigma point values after the state equation for passing through model j for the sigma in step 4.
4. the three-dimensional vehicle mounted positioning navigation method according to claim 1 based on coordinate transform, it is characterised in that：Step 6
In, calculating observation predicted value is Zj[(k)/(k-1)], observation covariance matrix areAnd the mutual side of association of state observation
Poor matrix isThe specific method is as follows：
Wherein, Qk-1For observation noise covariance matrix,The sigma point values of observation.
5. the three-dimensional vehicle mounted positioning navigation method according to claim 1 based on coordinate transform, it is characterised in that：Step 9
In, calculate total state estimationEstimate P with total covarianceX[(k)/(k)] the specific method is as follows：
Wherein, μj(k) probability for being k moment motion models j.
6. the three-dimensional vehicle mounted positioning navigation method according to claim 1 based on coordinate transform, it is characterised in that：Step 10
In, the specific method is as follows for equation between calculating three-dimensional vehicle position coordinates：
Wherein,For the deflection of coordinate system S-transformation, θ is the elevation angle of coordinate system S-transformation, and ex1, ey1, ez1 are coordinate system S1
Reference axis unit vector, ex, ey, ez are the reference axis unit vectors of coordinate system S.
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