CN109991572A - A kind of two-shipper passive location method based on azimuth and pitch angle information - Google Patents
A kind of two-shipper passive location method based on azimuth and pitch angle information Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/04—Position of source determined by a plurality of spaced direction-finders
Abstract
A kind of two-shipper passive location method based on azimuth and pitch angle information, belongs to target positioning field.Existing tradition Single passive location is unable to complete instantaneous positioning, and weighted least-squares (WLS) expression-form of multistation location is complicated, the bad problem of accumulated time characteristic.A kind of two-shipper passive location method based on azimuth and pitch angle information, in order to which the position coordinates to positioning target solve, first according to actual location scene, building utilizes the dual station observation model of angle of arrival determination/composition, again by the azimuth of arriving signal proposed by the present invention and pitch angle seat mode input, while considering that observation error carries out the high accuracy positioning of target.The present invention can be realized instantaneous positioning, simplify passive location process, accumulated time good convergence.
Description
Technical field
The two-shipper passive location method based on azimuth and pitch angle information that the present invention relates to a kind of.
Background technique
DF and location method (Angles Of Arrival, AOA) is the angle information that observation station is only reached using signal,
To estimate the location information of target.Either single passive localization algorithm, or in various united location algorithms
In, AOA is that research and application are all very wide, and the method for various classics is all developing always.No matter in what location algorithm,
Angle information is all most basic metrical information, and often in some environments, other sensors cannot be surveyed effectively
Amount, can only obtain angle information, so DF and location has very important research significance.
After observation station obtains the observation information of target, how using angle information observational equation is established, and complete to sight
The solution for surveying equation, can just obtain the estimation of target position information.Least-squares estimation is used as to linear (and pseudo- linear) equation
Group solve classical way, have the advantages that objective function easily find, solution form it is clear, be widely used in various positioning
In the coordinate of problem solves.Traditional Single passive location is unable to complete instantaneous positioning, and the weighted least-squares of multistation location
(WLS) expression-form is complicated, and accumulated time characteristic is bad.
Summary of the invention
The purpose of the present invention is to solve existing traditional Single passive locations to be unable to complete instantaneous positioning, and multistation is fixed
Weighted least-squares (WLS) expression-form of position is complicated, the bad problem of accumulated time characteristic, and proposes a kind of based on azimuth
With the two-shipper passive location method of pitch angle information.
A kind of two-shipper passive location method based on azimuth and pitch angle information, the described method comprises the following steps:
Step 1: space angle observation model and target source signal between two observation stations of building and target to be positioned
Incoming wave azimuth and pitch angle；
Step 2: establishing the matrix observation equation containing unknown object coordinate using the equilibrium relationships containing angle information；
Step 3: using weighted least square method and pseudoinverse technique, to the matrix observation equation established in step 2 into
Row solves, and obtains the Spatial outlier position coordinates of target to be positioned.
The invention has the benefit that
The present invention carries out model foundation from actual angle, to dual station passive location, utilizes the azimuth of arriving signal
Input with pitch angle as model is released in conjunction with the orthogonality relation and geometry site of space vector with succinct right
The observational equation of the expression-form of title.It is completed in the presence of having measurement error in conjunction with WLS solution by the amendment of weighting matrix
Target source location estimation improves accumulated time constringency performance.
By the method for the invention, it can be achieved with Instantaneous Passive positioning merely with the observation of two stations, and angular observation be used only and believes
Breath completes the resolving to target position, and the passive location problem of senior general's complexity is simplified.It, can be small under this model
The reconnaissance UAV of type carries measuring device (such as phase-interferometer), there is higher practicability, has accomplished miniaturization well
The scouting of flexibility detects.Furthermore the cloth station location of two observation stations can carry out mobile observation without special consideration, very clever
It is living.
AOA observation model proposed by the present invention, there is original advantage using weighted least-square solution method.In location model
In only need the angle information of input measurement, reduce error introducing to a certain extent；And it is in target source apart from farther out
When far field condition, model is insensitive to observation station self-position error, can be ignored, i.e. containing of the model to various errors
Property is stronger.Weighted least-squares method utilizes the calculating to weighting matrix to update, and completes to there are certain correctings of error, and
And with the measurement of time integral, WLS has good time Convergence.
Detailed description of the invention
Fig. 1 is the method for the present invention overview flow chart；
Fig. 2 is the method for the present invention specific steps flow chart；
Fig. 3 is two observation stations of the invention simultaneously to the observation model of radiant source target；
Fig. 4 is that the present invention in angle error is 1 °, and instantaneous positioning carries out the simulation experiment result figures of 1000 estimations；
Fig. 5 is that the present invention in angle error is 0.5 °, and instantaneous positioning carries out the simulation experiment result figures of 1000 estimations；
Fig. 6 is that the present invention in angle error is 0.5 °, and observation 20s carries out the simulation experiment result figures of 20 estimations；
Fig. 7 is that the present invention in angle error is 0.5 °, and observation 30s carries out the simulation experiment result figures of 20 estimations；
Fig. 8 is the positioning accuracy the simulation experiment result figure that WLS changes under different accumulated times with error angle respectively；
Fig. 9 is that WLS accumulates 60s, and wherein blue dot is the estimation point of preceding 30s, the emulation for the estimation point that green point is rear 30s
Experimental result picture；
Specific embodiment
Specific embodiment 1:
A kind of two-shipper passive location method based on azimuth and pitch angle information of present embodiment, in order to positioning mesh
Target position coordinates are solved, and first according to actual location scene, building is observed using the dual station of angle of arrival determination/composition
Model, then azimuth and pitch angle seat mode input by arriving signal proposed by the present invention, at the same consider observation error into
The high accuracy positioning of row target；It the described method comprises the following steps:
Step 1: space angle observation model and target source signal between two observation stations of building and target to be positioned
Incoming wave azimuth and pitch angle；
Step 2: establishing the matrix observation equation containing unknown object coordinate using the equilibrium relationships containing angle information；
Step 3: using weighted least square method and pseudoinverse technique, to the matrix observation equation established in step 2 into
Row solves, and obtains the Spatial outlier position coordinates of target to be positioned.
Specific embodiment 2:
Unlike specific embodiment one, a kind of two-shipper based on azimuth and pitch angle information of present embodiment
Passive location method in the step one, constructs the space angle observation model between two observation stations and target to be positioned
And the incoming wave azimuth of target source signal and the process of pitch angle are,
In a space rectangular coordinate system, angular observation is carried out to the radiation source of target to be positioned simultaneously by two observation stations, obtained
Meet the space angle observation model under actual scene out, as shown in Figure 1, the angle information (θ of measurementi,φi), observation station (xi,
yi) and target (x to be positionedT,yT) position three between geometry calculated relationship, pass through formula (1) express:
The position coordinates of target are u=(xT,yT,zT)T, the position coordinates of two observation stations are Si=(xi,yi,zi)T, i=1,
2, the symbol and meaning of measurement parameter are as follows: θiThe azimuth of observation station, φ are reached for target emanation signal to be positionediIt is to be positioned
Target emanation signal reaches the pitch angle of observation station, and θiAnd φiIt is measured value, all brings into actually calculating and missed containing measurement
The angle information of difference.
Specific embodiment 3:
Unlike specific embodiment two, a kind of two-shipper based on azimuth and pitch angle information of present embodiment
Passive location method in the step two, contains unknown object coordinate using the equilibrium relationships foundation containing angle information
The process of matrix observation equation is,
The observational equation of single observer is obtained according to angle and mutual alignment relation, then the observational equation of observation station 1 is such as public
Formula (2) indicates:
In formula, G1Indicate the observing matrix in the observational equation of observation station 1；P1Indicate the ginseng in the observational equation of observation station 1
Matrix number；For each position element of the observing matrix of observation station 1；
Step 2 one, the observation equilibrium relationships in conjunction with represented by the observational equation of single observer, by the information of two observation stations
It is placed in same observing matrix and establishes matrix equation, i.e., all observational equations of two observation stations are organized in an equation,
Unified observational equation is established, is obtained:
→ indicate the form after expansion；
Step 2 two, the citation form obtained in formula (1)~(3) observational equation on the basis of, then obtain its time
Accumulating form:
1), it is located at the particular content of matrix in observational equation are as follows: by HtThe observing matrix for indicating moment t, by PtIndicate the moment
The parameter matrix of t:
2) observational equation of accumulated time form, such as formula, are obtained after observation t seconds with the increase of cumulative observations time
(6) shown in:
Specific embodiment 4:
Unlike specific embodiment three, a kind of two-shipper based on azimuth and pitch angle information of present embodiment
Passive location method, in the step three, using weighted least square method and pseudoinverse technique, to the square established in step 2
Battle array observational equation is solved, and the process for obtaining the Spatial outlier position coordinates of target to be positioned is,
Step 3 one sets observation vector k=[θ1,φ1,θ2,φ2]TThe physical parameter measured is needed for entire method, by it
The input parameter of model；When the azimuth and pitch angle inputted in space angle observation model is there are when observation error, exist
On the basis of observation error, the input angle containing error and its mathematical approach are indicated are as follows:
In formula,For real angle θ1Observation with error；^ is the band error estimate of ideal matrix, and △ is practical
With ideal difference；
Step 3 two, then observational equation of basis under the conditions of first-order error, bring every matrix element of error into, obtain
The expression formula of error vector:
In formula, B indicates error vector；ε expression parameter error；^ is the band error estimate of ideal matrix, △ be it is practical with
Ideal difference；
Step 3 three obtains the weighting matrix in weighted least square method by error vector and observation vector error,
It indicates are as follows:
In formula, m1Indicate the azimuth angle error of observation station 1, n1Indicate the pitching angle error of observation station 1；m2Indicate observation station 2
Azimuth angle error, n2Indicate the pitching angle error of observation station 2；Q is the covariance matrix of error vector, and E is to take mathematic expectaion
Value；
Step 3 four, when considering that target to be positioned there are when observation error, solves expression formula according to the standard of WLS, solve
The coordinate of target radiation source to be positioned, abbreviation go out final expression formula, are as follows:
It is the calculated result estimated value to target position；T is transposition.
Specific embodiment 5:
Unlike specific embodiment three, a kind of two-shipper based on azimuth and pitch angle information of present embodiment
Passive location method, in the step three, using weighted least square method and pseudoinverse technique, to the square established in step 2
Battle array observational equation is solved, and the process of the Spatial outlier position coordinates of target to be positioned is obtained are as follows:
Step 3 one sets observation vector k=[θ1,φ1,θ2,φ2]TThe physical parameter measured is needed for entire method, by it
The input parameter of model；When the azimuth and pitch angle inputted in space angle observation model is there are when observation error, exist
On the basis of observation error, the input angle containing error and its mathematical approach are indicated are as follows:
In formula,For real angle θ1Observation with error；
Step 3 two, then observational equation of basis under the conditions of first-order error, bring every matrix element of error into, obtain
The expression formula of error vector:
In formula, B indicates error vector；ε expression parameter error；^ is the band error estimate of ideal matrix, △ be it is practical with
Ideal difference；
Step 3 three obtains the weighting matrix in weighted least square method by error vector and observation vector error,
It indicates are as follows:
In formula, m1Indicate the azimuth angle error of observation station 1, n1Indicate the pitching angle error of observation station 1；m2Indicate observation station 2
Azimuth angle error, n2Indicate the pitching angle error of observation station 2；Q is the covariance matrix of error vector, and E is to take mathematic expectaion
Value；
Step 3 four, when target to be positioned is in far field condition, ignore observation station location error, utilize the method for pseudoinverse
Instead of matrix inversion, simplifies complicated solution form, obtains the coordinate of target radiation source to be positioned:
In formula, symbolIndicate pseudo-inverse operation.
Wherein,
The weighted least square algorithm (Weighted Least Square estimation, WLS), is general
A kind of popularization of logical least square, it is Generalized Least Square that wherein allowable error covariance matrix, which is different from a unit matrix,
A kind of special case (error matrix is diagonal matrix).It is then WLS when all off-diagonal items of the correlation matrix of residual error are sky
The case where, the value on the case where there is also Singular variances, that is, covariance matrix diagonal line is unequal.The hypotheses of this method are
Error between each independent variable is uncorrelated.In the AOA observation model proposed in the present invention and the matrix equation of building, often
One instantaneous moment effective information is 4 equation equations, and wherein metrical information includes certain observation error.Instantaneously to target
Solution at least needs three equations, is then converted into the high-precision Solve problems for determining equation group.WLS is by considering observation error
Influence, calculating update is carried out to weighting matrix, the influence of error can be reduced to a certain extent, to improve positioning accurate
Degree.
, can be by formula theoretical proof when being solved using weighted least square method to observational equation, precision is full
The required precision of sufficient Cramér-Rao lower bound.When only considering first-order error, missed using Fei Sheer information matrix and the root mean square of positioning
Difference is completed to prove.
Beneficial effects of the present invention are verified using following embodiment:
Embodiment one:
Spatial scene simulation is carried out to the position measurement of target to two observation stations, while passing through matlab simulation calculation
Process condition.The starting point coordinate for enabling observation station 1 is (90,60,10) km, and the starting point coordinate of observation station 2 is (50,20,8) km, mesh
Cursor position (20,100,0) km.The every 1s in two observation stations completes the primary observation to target, observes 20s, 30s and 60s, angle measurement respectively
The case where error is 0.5 ° and 1 ° carries out 1000 independent emulation experiments, is all made of weighted least square method and carries out equation
It solves, show that 1000 estimation points of target surround the distribution situation of locations of real targets.
The angle measurement error of the present embodiment is configured according to existing measuring device precision level, and two observation stations can be with
In fixed position or mobile observation, actual conditions are reasonably simulated, carry out target positioning using method of the invention.Specifically
It follows the steps below:
Step 1: two observation stations of building and the space angle observation model for positioning target obtain the incoming wave of target source signal
Deflection and pitch angle；
Step 2: the matrix equation containing unknown object coordinate is established using the equilibrium relationships containing angle information；
Step 3: the solution for completing equation in step 2 is solved using weighted least square method and pseudoinverse；
Step 4: the estimated location that step 3 is obtained calculates the root-mean-square value of range difference compared with true location coordinate,
Shown in calculation such as formula (14).
The simulation experiment result is as shown in Fig. 4-Fig. 8.Fig. 4, the result is that the instantaneous positioning that angle error is 1 ° and 0.5 ° in 5
In the case of, distribution situation of 1000 estimation points near real goal, MSE is respectively 3.0256km and 1.4879km；Fig. 6,7
In the result is that angle error is 0.5 °, the positioning scene of cumulative observations 20s and 30s respectively, 20 estimation points are attached in real goal
Close distribution situation, MSE are respectively 0.5906km and 0.5115km；In Fig. 8 the result is that WLS respectively under different accumulated times with
The positioning accuracy the simulation experiment result figure of error angle variation, it can be seen that have certain error convergence；Fig. 9 is tired for WLS
Product 60s, wherein blue dot is the estimation point of preceding 30s, and the estimation point that green point is rear 30s is distributed, from its spatial position
Find out, WLS has good time Convergence, space better astringency.
Above the results showed that only measuring the angle information of incoming wave signal, observation model and equation are constructed, to radiation source
Carrying out positioning calculation has preferable effect.Model and method meet actual scene, input using measurement as few as possible, knot
Suitable calculation method is closed, the positioning of degree of precision can be completed.
The present invention can also have other various embodiments, without deviating from the spirit and substance of the present invention, this field
Technical staff makes various corresponding changes and modifications in accordance with the present invention, but these corresponding changes and modifications all should belong to
The protection scope of the appended claims of the present invention.
Claims (5)
1. a kind of two-shipper passive location method based on azimuth and pitch angle information, it is characterised in that: the method includes with
Lower step:
Step 1: constructing coming for the space angle observation model and target source signal between two observation stations and target to be positioned
Wave azimuth and pitch angle；
Step 2: establishing the matrix observation equation containing unknown object coordinate using the equilibrium relationships containing angle information；
Step 3: being asked using weighted least square method and pseudoinverse technique the matrix observation equation established in step 2
Solution, obtains the Spatial outlier position coordinates of target to be positioned.
2. a kind of two-shipper passive location method based on azimuth and pitch angle information according to claim 1, feature
It is: in the step one, constructs the space angle observation model and target between two observation stations and target to be positioned
The incoming wave azimuth of source signal and the process of pitch angle be,
In a space rectangular coordinate system, angular observation is carried out to the radiation source of target to be positioned simultaneously by two observation stations, obtains symbol
Close the space angle observation model under actual scene, the position three of the angle information of measurement, observation station and target to be positioned it
Between geometry calculated relationship, pass through formula (1) express:
The position coordinates of target are u=(xT,yT,zT)T, the position coordinates of two observation stations are Si=(xi,yi,zi)T, i=1,2, θi
The azimuth of observation station, φ are reached for target emanation signal to be positionediIt is that target emanation signal to be positioned reaches bowing for observation station
The elevation angle, and θiAnd φiIt is measured value.
3. a kind of two-shipper passive location method based on azimuth and pitch angle information according to claim 2, feature
It is: in the step two, establishes the matrix observation containing unknown object coordinate using the equilibrium relationships containing angle information
The process of equation are as follows:
The observational equation of single observer is obtained according to angle and mutual alignment relation, then the observational equation of observation station 1 are as follows:
In formula, G1Indicate the observing matrix in the observational equation of observation station 1；P1Indicate the parameter square in the observational equation of observation station 1
Battle array；For each position element of the observing matrix of observation station 1；
Step 2 one, the observation equilibrium relationships in conjunction with represented by the observational equation of single observer, the information of two observation stations is placed on
Matrix equation is established in same observing matrix, is obtained:
→ indicate the form after expansion；
Step 2 two, the citation form obtained in formula (1)~(3) observational equation on the basis of, then obtain its accumulated time
Form:
1) it, sets: in observational equation, by HtThe observing matrix for indicating moment t, by PtIndicate the parameter matrix of moment t:
2), the observational equation of accumulated time form is obtained, such as formula (6) after observation t seconds with the increase of cumulative observations time
It is shown:
4. a kind of two-shipper passive location method based on azimuth and pitch angle information according to claim 3, feature
It is: in the step three, using weighted least square method and pseudoinverse technique, to the matrix observation side established in step 2
Cheng Jinhang is solved, and obtains the process of the Spatial outlier position coordinates of target to be positioned are as follows:
Step 3 one, when the azimuth and pitch angle inputted in space angle observation model is there are when observation error, seen existing
It surveys on the basis of error, the input angle containing error and its mathematical approach indicate are as follows:
In formula,For real angle θ1Observation with error；
Step 3 two, then observational equation of basis under the conditions of first-order error, bring every matrix element of error into, obtain error
The expression formula of vector:
In formula, B indicates error vector；ε expression parameter error；^ is the band error estimate of ideal matrix, and △ is practical and ideal
Difference；
Step 3 three obtains the weighting matrix in weighted least square method by error vector and observation vector error, indicates
Are as follows:
In formula, m1Indicate the azimuth angle error of observation station 1, n1Indicate the pitching angle error of observation station 1；m2Indicate the side of observation station 2
Parallactic angle error, n2Indicate the pitching angle error of observation station 2；Q is the covariance matrix of error vector, and E is to take mathematical expectation；
Step 3 four, when target to be positioned is there are when observation error, expression formula is solved according to the standard of WLS, solves mesh to be positioned
The coordinate of radiation source is marked, abbreviation goes out final expression formula, are as follows:
It is the calculated result estimated value to target position；T is transposition.
5. a kind of two-shipper passive location method based on azimuth and pitch angle information according to claim 3, feature
It is: in the step three, using weighted least square method and pseudoinverse technique, to the matrix observation side established in step 2
Cheng Jinhang is solved, and the process for obtaining the Spatial outlier position coordinates of target to be positioned is,
Step 3 one, when the azimuth and pitch angle inputted in space angle observation model is there are when observation error, seen existing
It surveys on the basis of error, the input angle containing error and its mathematical approach indicate are as follows:
In formula,For real angle θ1Observation with error；
Step 3 two, then observational equation of basis under the conditions of first-order error, bring every matrix element of error into, obtain error
The expression formula of vector:
In formula, B indicates error vector；ε expression parameter error；^ is the band error estimate of ideal matrix, and △ is practical and ideal
Difference；
Step 3 three obtains the weighting matrix in weighted least square method by error vector and observation vector error, are as follows:
In formula, m1Indicate the azimuth angle error of observation station 1, n1Indicate the pitching angle error of observation station 1；m2Indicate the side of observation station 2
Parallactic angle error, n2Indicate the pitching angle error of observation station 2；Q is the covariance matrix of error vector, and E is to take mathematical expectation；
Step 3 four, when target to be positioned is in far field condition, ignore observation station location error, utilize pseudoinverse method replace
Matrix inversion simplifies complicated solution form, obtains the coordinate of target radiation source to be positioned:
In formula, symbolIndicate pseudo-inverse operation.
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Application publication date: 20190709 |