CN107526073A - One kind motion passive TDOA-FDOA joint location method of multistation - Google Patents
One kind motion passive TDOA-FDOA joint location method of multistation Download PDFInfo
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- 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
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Abstract
The invention discloses one kind to move the passive TDOA-FDOA joint location method of multistation, belongs to passive location technical field.Comprise the following steps：Establish positioning using TDOA model；Establish frequency difference location model；Construct time difference frequency difference observing matrix ε1, design fitness function；Initialize population and every ginseng；Evaluate the fitness function value of each particle；All particles are ranked up；Current global optimum is exported when algorithm meets end condition：Reconstruct time difference frequency difference matrix ε2；It is θ to obtain weighted least-square solution2With its covariance matrix cov (θ2)；Obtain the Position And Velocity of radiation source.The fitness function that the present invention obtains to time difference frequency difference observing matrix carries out optimal value solution, and particle swarm optimization algorithm is combined with least-squares algorithm, the high accuracy positioning to target can be realized in the case of four base stations, while obtain the velocity information of target.The present invention can realize the high accuracy estimation to radiation source positions, do not limited by site layout, have higher location estimation precision.
Description
Technical field
The invention belongs to passive location technical field, and in particular to the passive TDOA-FDOA joint location side of one kind motion multistation
Method.
Background technology
Passive location technology has important application prospect in electronic countermeasure field, causes navigation, space flight, military affairs are detectd
Examine, the extensive concern of the every field such as global navigation satellite.Passive location technology has that positioning precision is high, operating distance is remote, war
The features such as survival ability is strong, can quickly realize to target be accurately positioned and track following.In the last few years, difference frequency when
Poor alignment by union technology has obtained rapid development and perfect, and the collaboration of more base stations is more suitable for other location methods compared with calmly
Position system is so as to completing to be accurately positioned target.For the radiation source of motion, wrapped in the information echo that base station is received
Containing reaching time-difference (time difference of arrival, TDOA) and how general difference on the frequency (frequency
Difference of arrival, FDOA) etc. information, can more accurately estimate target by using increased observed quantity
Position and speed, and have the advantages that real-time is good, scope of investigation is wide, positioning precision is high, wherein the Doppler frequency difference collected this
One information compensate for location ambiguity present in independent time difference positioning method and without solution problem just, when site is laid out necessarily
In the case of TDOA/FDOA joint positioning methods avoid the occlusion effect of earth curvature, while improve the positioning accurate of radiation source
Degree.At present, the Nonlinear System of Equations in TDOA/FDOA multistations co-located system easily makes positioning result deviation occur, and exists
The problems such as operand is big, and computation complexity is high, to prevent positioning result to be absorbed in local optimum and accelerating convergence of algorithm speed
Many scholars are proposed corresponding view.Such as Yang Jie etc. (Xian Electronics Science and Technology University's journal, 2015 volume 42 the 4th
Phase, iteration TDOA-FDOA joint location algorithm and its performance evaluation) institute's extracting method is that to utilize time difference frequency difference observing matrix to carry out safe
Series expansion is strangled, target position and speed are tried to achieve when algorithm meets the condition of convergence by alternative manner.This method can effectively drop
Low amount of calculation, but in data processing, measurement error needs Gaussian distributed, and otherwise positioning precision is decreased obviously.
The content of the invention
It is an object of the invention to provide solution to move Nonlinear Optimization Problem present in Multi-Station passive location system,
High accuracy positioning is realized to radiation source in the case where base station number is less, and the present speed of moving emitter can be obtained
A kind of motion passive TDOA-FDOA joint location method of multistation.
The purpose of the present invention is realized by following technical solution：
One kind motion passive TDOA-FDOA joint location method of multistation, comprises the following steps：
(1) positioning using TDOA model is established, determines the coordinate position of main website and extension station respectively, calculates target and each base station
Actual distance di, i=1,2 ..., M, draw the distance between target and main website d1And the distance between target and extension station di,
(i ≠ 1), M base station can form M-1 group range differences di1,(i≠1)；
(2) frequency difference location model is established, to target and the actual distance d of each base stationiCarry out derivation and obtain distance change
Rate, while ask for the time-derivative in moveout equation and obtain range difference rate of change, it is 0 that noise, which obeys average, variance σ2Height
This distribution；
(3) auxiliary variable d is introduced1WithConstruct time difference frequency difference observing matrix ε1, consider influence of the error to positioning precision,
And design fitness function；
(4) population and parameters are initialized, the scale of population, the dimension of problem, maximum iteration acceleration are set
Constant and region of search scope, the random speed for generating particle and position：
According to the above, the dimension D=6 of offering question, in the search space random initializtion particle of the potential solution of target
Position and speed, and set the number of particle as n=80, maximum iteration m=100, acceleration constant c1=c2=1,
Weight limit factor wmax=0.8, minimal weight factor wmin=0.2；
(5) fitness function value of each particle is evaluated, the parameter w of linear decrease weight is setmaxAnd wmin, while to grain
The speed of son is updated with position, and the fitness function value of all particles and the fitness function value of best particle are entered
Row compares, and is worth to individual extreme value and global extremum according to fitness function, and update global extremum；
(6) all particles are ranked up according to natural selection mechanism, with the speed of best half particle and position in body
Go to replace the speed of worst half particle and position in colony, while retain the individual memory of each particle：
Natural selection is the sequence according to the progress of the fitness function value of all particles from low to high, by colony preceding 1/2
The speed of 1/2 poor particle and position after replacing, while the history optimal value of each particle are gone in the speed of preferable particle and position
It will be retained；
(7) current global optimum is exported when algorithm meets end condition：
When algorithm reaches maximum iteration or meets the precision that pre-sets, then stop search, output result, otherwise
Return to step (5) continues search for target location；
(8) using the target location searched as initial target location θ, in covariance matrix QαTo be constructed during known conditions
Weighting matrix W1With covariance matrix cov (θ1), time difference frequency difference matrix ε is reconstructed according to obtained radiation source estimated values theta2；
(9) ε known to2It it is one on θ2System of linear equations, it is θ to obtain weighted least-square solution2With its covariance matrix
cov(θ2)；
(10) it is θ according to obtained weighted least-square solution2Obtain the Position And Velocity of radiation source.
The beneficial effects of the present invention are：
The fitness function that the present invention obtains to time difference frequency difference observing matrix carries out optimal value solution, when can effectively avoid
The problem of operand of difference frequency difference observing matrix is big, and computation complexity is high.
Least-squares algorithm can not accurately estimate the position of target in the case of four base stations, cannot get target location with
Particle swarm optimization algorithm is combined by the unique solution of speed, the present invention with least-squares algorithm, can in the case of four base stations
The high accuracy positioning to target is realized, while obtains the velocity information of target.
The present invention can realize the high accuracy estimation to radiation source positions, need not rely on the priori of initial target location
Condition just can quickly approach globally optimal solution, while accelerate convergence of algorithm speed, be less prone to location ambiguity and without solution
Situation.
The present invention is not limited by site layout, and also can carry out the overall situation to target area under being laid out in specific site searches
Rope, there is higher location estimation precision compared with conventional method.
Brief description of the drawings
Fig. 1 is the time difference/Doppler frequency difference positioning schematic；
Fig. 2 is the inventive method and the Position And Velocity root-mean-square error of particle swarm optimization algorithm and standard particle group's algorithm
Compare figure；
Fig. 3 be the inventive method with the Position And Velocity deviation ratio of particle swarm optimization algorithm and standard particle group's algorithm compared with
Figure；
Fig. 4 is that the inventive method puts the figure compared with velocity deviation in orientation under three kinds of different site layouts.
Embodiment
The embodiment of the present invention is described further below in conjunction with the accompanying drawings：
One kind motion passive TDOA-FDOA joint location method of multistation, comprises the following steps：
Step 1：Positioning using TDOA model is established, determines the coordinate position of main website and extension station respectively.Calculate target and each base
The actual distance d to standi, i=1,2 ..., M, draw the distance between target and main website d1And between target and extension station away from
From di, (i ≠ 1), M base station can form M-1 group range differences di1,(i≠1)。
Fig. 1 show the time difference/Doppler frequency difference location model, and M mobile receiver is placed in same three dimensions,
The coordinate position and speed of target wherein to be estimated are respectively u=[x, y, z]TWithThe coordinate position of receiver
For si=[xi,yi,zi]T, speed isT is the transposition of matrix, utilizes (*) ° to represent measurement
The actual value of variable (*).The situation of M=4 receiver is considered herein, but the position of 4 receivers can not be located at a plane
Or on same straight line so as to ensure solve target location uniqueness.
First receiver is selected as reference receiver, radiation source u and receiver siThe distance between be
In formula, | | | | it is 2 norms, M receiver can form M-1 group range differences, then target and receiver siAnd mesh
Mark and reference receiver s1The distance between difference be
di1=c τi1=di-d1 (2)
Wherein c be light spread speed, τi1Represent reaching time-difference.After formula (2) is transplanted, obtain
di1+d1=di (3)
Formula (1) is substituted into formula (3), while one group of new moveout equation is obtained after carrying out square transposition to both sides
di1 2+2di1d1=si Tsi-s1 Ts1-2(si-s1)Tu (4)
Step 2：Frequency difference location model is established, to target and the actual distance d of each base stationiCarry out derivation and obtain distance change
Rate, while ask for the time-derivative in moveout equation and obtain range difference rate of change, it is 0 that noise, which obeys average, variance σ2's
Gaussian Profile.
Derivation is carried out to formula (1) and show that the expression formula of range rate is
Then target is to receiver siWith receiver s1The distance between poor rate of change be expressed as
Therefore, the time-derivative in formula (4) is asked for
Remember d=[d21,d31,...,dM1,]TFor containing noisy range difference,To contain noise
Range difference rate of change, do=[d21 o,d31 o,...,dM1 o]TFor the actual value of range difference.For
The actual value of range difference rate of change, then it can be expressed as about TDOA and FDOA measurement models
D=c τ=do+n (8)
Wherein, n=[n21,n31,...,nM1]TWithRespectively corresponding measurement noise.
τ=[τ21,τ31,...,τM1]TFor reaching time-difference, Fd=[fd21,fd31,...,fdM1,]TDoppler frequency is poor, f0
To radiate source frequency.Two groups of noise variances are independently distributed and average is zero, noteIts covariance matrix is
E[ααT]=Qα (10)
Step 3：Introduce auxiliary variable d1WithConstruct time difference frequency difference observing matrix ε1, consider shadow of the error to positioning precision
Ring, and design fitness function.
D is understood by time difference frequency difference positioning equationi1°=di1-ni1, therefore can be obtained according to formula (4)
εt,i=di1 2+2di1d1-si Tsi+s1 Ts1+2(si-s1)Tu (11)
Remember εt=[εt,1,εt,2,...,εt,M]T, moveout equation matrix is constructed using formula (11)
εt=ht-Gtθ1 (12)
Wherein
Wherein, 0 null matrix arranged for 3 rows 1, θ1In include the position u and speed of target to be estimatedDetermined by time difference frequency difference
Azimuth equation is understoodTherefore can be obtained according to formula (7)
Remember εf=[εf,1,εf,2,...,εf,M]T, the matrix about frequency difference equation is constructed using formula (16)
εf=hf-Gfθ1 (17)
Wherein
H is obtained according to formula (12) and (17)1=[ht,hf]T, G1=[Gt,Gf]T, time difference frequency difference Combined estimator observing matrix
It can be expressed as
ε in formula (20)1For 6 rows 1 row matrix, in order to estimated using particle swarm optimization algorithm the initial position of target with
Speed is, it is necessary to ask for the numerical value of fitness function in particle cluster algorithm, therefore obtain fitness function and be
Fit=| | h1-G1θ1|| (21)
Step 4：Population and parameters are initialized, set the scale of population, the dimension of problem, maximum iteration to accelerate
Spend constant and region of search scope, the random speed for generating particle and position.
According to the above, the dimension D=6 of offering question, in the search space random initializtion particle of the potential solution of target
Position and speed, and set the number of particle as n=80, maximum iteration m=100, acceleration constant c1=c2=1,
Weight limit factor wmax=0.8, minimal weight factor wmin=0.2.
Step 5：The fitness function value of each particle is evaluated, the parameter w of linear decrease weight is setmaxAnd wmin, simultaneously
The speed and position of particle are updated, by the fitness function value of all particles and the fitness function of best particle
Value is compared, and is worth to individual extreme value and global extremum according to fitness function, and update global extremum.
The position of each particle after initialization is updated in fitness function fit, corresponding each particle is right
A fitness function value is answered, the fitness value of each particle and current location are stored in individual extreme value pbestIn, by all
Optimal individual body position and fitness value deposit global extremum g in body extreme valuebestIn.One defined in all individual extreme values
Individual global extremum, then by the fitness function value of each particle and global extremum gbestIt is compared, if i-th of particle
Fitness function fit (i) be better than gbest, then global extremum gbestReplace with fit (i).
Position and the speed of each particle are updated using formula (22).
P in formulabestFor individual optimal value, gbestFor global optimum, vi,jRepresent the flying speed of population, xi,jRepresent
The current position of particle.The expression formula of Linear recurring series is
W=wmax-(t)×(wmax-wmin)/m (23)
Step 6：All particles are ranked up according to natural selection mechanism, with the speed of best half particle and position in body
Put and replace the speed of worst half particle and position in colony.Retain the individual memory of each particle simultaneously.
Natural selection is the sequence according to the progress of the fitness function value of all particles from low to high, by colony preceding 1/2
The speed of 1/2 poor particle and position after replacing, while the history optimal value of each particle are gone in the speed of preferable particle and position
It will be retained.
Step 7：Current global optimum is exported when algorithm meets end condition.
When algorithm reaches maximum iteration or meets the precision that pre-sets, then stop search, output result.Otherwise
Return to step 5 continues search for target location.
Step 8：Using the target location searched as initial target location θ, in covariance matrix QαFor known conditions when
Construct weighting matrix W1With covariance matrix cov (θ1), time difference frequency difference matrix ε is reconstructed according to obtained radiation source estimated values theta2。
Work as QαFor known conditions when weighting matrix W1Expression formula be
Wherein
In formula (26)P is appropriate dimension
Null matrix.
Therefore, according to G1And W1It can obtain θ1Covariance matrix be
cov(θ1)=(G1 TW1G1)-1 (26)
Time difference frequency difference matrix is reconstructed according to obtained radiation source estimated values theta, obtained
ε2=h2-G2θ2 (27)
In formula (29), I is the unit matrix of 3 rows 3 row, the full null matrix that O arranges for 3 rows 3,1 all 1's matrix arranged for 3 rows 1, and 0
For the full null matrix of 3 rows 1 row, ⊙ represents dot product.
Step 9：Known ε2It it is one on θ2System of linear equations, it is θ to obtain weighted least-square solution2With its covariance
Matrix cov (θ2)。
Known formula (27) to formula (30) is one on θ2System of linear equations, its weighted least-square solution is
Therefore on θ2Covariance matrix be
Wherein weighting matrix W2Expression formula be
B2Matrix expression be
Step 10：It is θ according to obtained weighted least-square solution2Obtain the Position And Velocity of radiation source.
According to formula (31), target location and the speed of radiation source are respectively defined as
Wherein, Π=diag { sgn (θ1(1:3)-s1) it is in order to avoid symbol ambiguity caused by square root calculation ,/table
Show and a little remove.
Embodiment：
Fig. 2 is the inventive method and the Position And Velocity root-mean-square error of particle swarm optimization algorithm and standard particle group's algorithm
Compare figure, wherein time error Gaussian distributed.As seen from the figure, with the increase of measurement error, this method positioning precision compared with
It is high, it is not necessary to the estimation of target initial position can avoid being absorbed in local optimum with regard to that can reach higher positioning precision, with compared with
Fast convergence rate approaches globally optimal solution.
Fig. 3 be the inventive method with the Position And Velocity deviation ratio of particle swarm optimization algorithm and standard particle group's algorithm compared with
Figure, wherein time error Gaussian distributed.The Position And Velocity of this method target in the case of high s/n ratio as seen from the figure
Deviation still has higher positioning precision compared with other two methods.
Fig. 4 is that the inventive method root-mean-square error of square Position And Velocity under three kinds of different site layouts compares
Figure.As seen from the figure as the increase star of measurement noise and the position positioning precision of del are consistent substantially, parallel four
The position positioning precision of side shape is optimal.The positioning precision of radiation source positions can be effectively improved by changing site layout, and to spoke
The speed for penetrating source does not have considerable influence.
The preferred embodiments of the present invention are the foregoing is only, are not intended to limit the invention, for the skill of this area
For art personnel, the present invention can have various modifications and variations.Within the spirit and principles of the invention, that is made is any
Modification, equivalent substitution, improvement etc., should be included in the scope of the protection.
Claims (8)
1. one kind motion passive TDOA-FDOA joint location method of multistation, it is characterised in that comprise the following steps：
(1) positioning using TDOA model is established, respectively the coordinate position of determination main website and extension station, calculating target is true with each base station
Distance di, i=1,2 ..., M, draw the distance between target and main website d1And the distance between target and extension station di,(i≠
1), M base station can form M-1 group range differences di1,(i≠1)；
(2) frequency difference location model is established, to target and the actual distance d of each base stationiCarry out derivation and obtain range rate, together
When the time-derivative asked in moveout equation obtain range difference rate of change, it is 0 that noise, which obeys average, variance σ2Gauss point
Cloth；
(3) auxiliary variable d is introduced1WithConstruct time difference frequency difference observing matrix ε1, consider influence of the error to positioning precision, and set
Count fitness function；
(4) population and parameters are initialized, the scale of population, the dimension of problem, maximum iteration acceleration constant are set
With region of search scope, the random speed for generating particle and position：
According to the above, the dimension D=6 of offering question, in the position of the search space random initializtion particle of the potential solution of target
Put and speed, and set the number of particle as n=80, maximum iteration m=100, acceleration constant c1=c2=1, most authority
Repeated factor wmax=0.8, minimal weight factor wmin=0.2；
(5) fitness function value of each particle is evaluated, the parameter w of linear decrease weight is setmaxAnd wmin, while to particle
Speed is updated with position, and the fitness function value of all particles and the fitness function value of best particle are compared
Compared with being worth to individual extreme value and global extremum according to fitness function, and update global extremum；
(6) all particles are ranked up according to natural selection mechanism, go to replace with the speed of best half particle and position in body
The speed of worst half particle and position in colony are changed, while retains the individual memory of each particle：
Natural selection is the sequence according to the progress of the fitness function value of all particles from low to high, preferable by colony preceding 1/2
The speed of 1/2 poor particle and position after replacing are gone in the speed of particle and position, while the history optimal value of each particle will be by
Retain；
(7) current global optimum is exported when algorithm meets end condition：
When algorithm reaches maximum iteration or meets the precision that pre-sets, then stop search, output result, otherwise return
Step (5) continues search for target location；
(8) using the target location searched as initial target location θ, in covariance matrix QαTo construct weighting during known conditions
Matrix W1With covariance matrix cov (θ1), time difference frequency difference matrix ε is reconstructed according to obtained radiation source estimated values theta2；
(9) ε known to2It it is one on θ2System of linear equations, it is θ to obtain weighted least-square solution2With its covariance matrix cov
(θ2)；
(10) it is θ according to obtained weighted least-square solution2Obtain the Position And Velocity of radiation source.
2. a kind of motion passive TDOA-FDOA joint location method of multistation according to claim 1, it is characterised in that described
The step of (1) specifically include：
M mobile receiver is placed in same three dimensions, wherein the coordinate position of target to be estimated and speed are respectively u
=[x, y, z]TWithThe coordinate position of receiver is si=[xi,yi,zi]T, speed is
T is the transposition of matrix, is utilized (*)oRepresent measurand (*) actual value；
The situation of M=4 receiver is considered herein, but the position of 4 receivers can not be located at a plane or same is straight
On line；
First receiver is selected as reference receiver, radiation source u and receiver siThe distance between be
In formula, | | | | it is 2 norms, M receiver can form M-1 group range differences, then target and receiver siWith target and ginseng
Examine receiver s1The distance between difference be
di1=c τi1=di-d1 (2)
Wherein c be light spread speed, τi1Reaching time-difference is represented, after formula (2) is transplanted, is obtained
di1+d1=di (3)
Formula (1) is substituted into formula (3), while one group of new moveout equation is obtained after carrying out square transposition to both sides
di1 2+2di1d1=si Tsi-s1 Ts1-2(si-s1)Tu。
3. according to claim 1, a kind of motion passive TDOA-FDOA joint location method of multistation described in 2, it is characterised in that institute
The step of stating (2) specifically includes：
Derivation is carried out to formula (1) and show that the expression formula of range rate is
Then target is to receiver siWith receiver s1The distance between poor rate of change be expressed as
Therefore, the time-derivative in formula (4) is asked for
Remember d=[d21,d31,...,dM1,]TFor containing noisy range difference,For containing it is noisy away from
Deviation rate of change, do=[d21 o,d31 o,...,dM1 o]TFor the actual value of range difference,For range difference
The actual value of rate of change, then it can be expressed as about TDOA and FDOA measurement models
D=c τ=do+n (8)
Wherein, n=[n21,n31,...,nM1]TWithRespectively corresponding measurement noise, τ=[τ21,
τ31,...,τM1]TFor reaching time-difference, Fd=[fd21,fd31,...,fdM1,]TDoppler frequency is poor, f0To radiate source frequency；Two
Group noise variance is independently distributed and average is zero, noteIts covariance matrix is
E[ααT]=Qα (10)。
4. according to claim 1, a kind of motion passive TDOA-FDOA joint location method of multistation described in 3, it is characterised in that institute
The step of stating (3) specifically includes：
D is understood by time difference frequency difference positioning equationi1 o=di1-ni1, therefore can be obtained according to formula (4)
εt,i=di1 2+2di1d1-si Tsi+s1 Ts1+2(si-s1)Tu (11)
Remember εt=[εt,1,εt,2,...,εt,M]T, moveout equation matrix is constructed using formula (11)
εt=ht-Gtθ1 (12)
Wherein
Wherein, 0 null matrix arranged for 3 rows 1, θ1In include the position u and speed of target to be estimatedBy time difference frequency difference positioning side
Cheng KezhiTherefore can be obtained according to formula (7)
Remember εf=[εf,1,εf,2,...,εf,M]T, the matrix about frequency difference equation is constructed using formula (16)
εf=hf-Gfθ1 (17)
Wherein
H is obtained according to formula (12) and (17)1=[ht,hf]T, G1=[Gt,Gf]T, time difference frequency difference Combined estimator observing matrix can be with
It is expressed as
ε in formula (20)1The matrix arranged for 6 rows 1, in order to estimate the initial position and speed of target using particle swarm optimization algorithm,
Need to ask for the numerical value of fitness function in particle cluster algorithm, therefore obtain fitness function and be
Fit=| | h1-G1θ1|| (21)。
A kind of 5. motion passive TDOA-FDOA joint location method of multistation according to claim Isosorbide-5-Nitrae, it is characterised in that institute
The step of stating (5) specifically includes：
The position of each particle after initialization is updated in fitness function fit, corresponding each particle corresponding one
Individual fitness function value, the fitness value of each particle and current location are stored in individual extreme value pbestIn, by all individual poles
Optimal individual body position and fitness value deposit global extremum g in valuebestIn；
A global extremum defined in all individual extreme values, then by the fitness function value and global extremum of each particle
gbestIt is compared, if the fitness function fit (i) of i-th of particle is better than gbest, then global extremum gbestReplace with fit
(i)；
Position and the speed of each particle are updated using formula (22)：
The expression formula of Linear recurring series is
W=wmax-(t)×(wmax-wmin)/m (23)
P in formulabestFor individual optimal value, gbestFor global optimum, vi,jRepresent the flying speed of population, xi,jRepresent particle
Current position.
6. according to claim 1, a kind of motion passive TDOA-FDOA joint location method of multistation described in 5, it is characterised in that institute
The step of stating (8) specifically includes：
Work as QαFor known conditions when weighting matrix W1Expression formula be
Wherein
B=2diag (d in formula (26)2 o,d3 o,...,dM o),P is the zero moment of appropriate dimension
Battle array；
Therefore, according to G1And W1It can obtain θ1Covariance matrix be
cov(θ1)=(G1 TW1G1)-1 (26)
Time difference frequency difference matrix is reconstructed according to obtained radiation source estimated values theta, obtained
ε2=h2-G2θ2 (27)
In formula (29), I is the unit matrix of 3 rows 3 row, and O is the full null matrix of 3 rows 3 row, and 1 is all 1's matrix of 3 rows 1 row, and 0 is 3 rows 1
The full null matrix of row, ⊙ represent dot product.
7. according to claim 1, a kind of motion passive TDOA-FDOA joint location method of multistation described in 6, it is characterised in that institute
The step of stating (9) specifically includes：
Known formula (27) to formula (30) is one on θ2System of linear equations, its weighted least-square solution is
Therefore on θ2Covariance matrix be
Wherein weighting matrix W2Expression formula be
B2Matrix expression be
8. according to claim 1, a kind of motion passive TDOA-FDOA joint location method of multistation described in 7, it is characterised in that institute
The step of stating (10) specifically includes：
According to formula (31), target location and the speed of radiation source are respectively defined as
Wherein, Π=diag { sgn (θ1(1:3)-s1) it is in order to avoid symbol ambiguity caused by square root calculation ,/expression point
Remove.
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Cited By (27)
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| CN112285645A (en) * | 2020-12-25 | 2021-01-29 | 中国人民解放军国防科技大学 | Positioning method, storage medium and system based on high-orbit satellite observation platform |
| CN112327248A (en) * | 2020-11-05 | 2021-02-05 | 中国人民解放军32802部队 | Multi-station positioning and tracking method for narrow-band continuous wave signals |
| CN112346010A (en) * | 2020-09-28 | 2021-02-09 | 中国人民解放军海军航空大学 | Dual-machine passive positioning method based on scale difference and time difference |
| CN112444776A (en) * | 2020-10-21 | 2021-03-05 | 山东大学 | High-precision positioning method for unmanned aerial vehicle based on TDOA and FDOA |
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