CN113835061A - Single-platform Doppler two-stage closed positioning method in presence of signal carrier frequency prior error - Google Patents

Single-platform Doppler two-stage closed positioning method in presence of signal carrier frequency prior error Download PDF

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CN113835061A
CN113835061A CN202110927203.5A CN202110927203A CN113835061A CN 113835061 A CN113835061 A CN 113835061A CN 202110927203 A CN202110927203 A CN 202110927203A CN 113835061 A CN113835061 A CN 113835061A
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stage
observation
matrix
error
radiation source
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CN113835061B (en
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王鼎
尹洁昕
唐涛
杨宾
郑娜娥
聂福全
张莉
王成
张龙
岳嘉颖
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Information Engineering University of PLA Strategic Support Force
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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
    • G01S1/00—Beacons or beacon systems transmitting signals having a characteristic or characteristics capable of being detected by non-directional receivers and defining directions, positions, or position lines fixed relatively to the beacon transmitters; Receivers co-operating therewith
    • G01S1/02—Beacons or beacon systems transmitting signals having a characteristic or characteristics capable of being detected by non-directional receivers and defining directions, positions, or position lines fixed relatively to the beacon transmitters; Receivers co-operating therewith using radio waves
    • G01S1/08—Systems for determining direction or position line
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

The invention discloses a single-platform Doppler two-stage closed positioning method in the presence of signal carrier frequency prior errors, which comprises the steps of firstly utilizing a single platform to perform linear motion to obtain FOA observed quantity of a radiation source, wherein the FOA observed quantity contains Doppler information; then, constructing a stage 1 linear observation equation by utilizing a triangular sine theorem; then, obtaining error statistical characteristics in the linear observation equation by using a first-order error analysis method, determining an optimal weighting matrix, and obtaining a radiation source position estimation value in the 1 st stage; substituting the estimated value into an original FOA observation equation, and obtaining a 2 nd stage linear observation equation through algebraic transformation; and then, obtaining the error statistical characteristics in the 2 nd-stage linear observation equation by using a first-order error analysis method, determining an optimal weighting matrix, and obtaining the 2 nd-stage radiation source position estimation value, namely a positioning result. Compared with the existing single-platform Doppler positioning method, the method can not only inhibit the influence of the prior error of the signal carrier frequency, but also obtain the positioning precision with the optimal asymptotic statistics.

Description

Single-platform Doppler two-stage closed positioning method in presence of signal carrier frequency prior error
Technical Field
The invention belongs to the technical field of radiation source positioning, and particularly relates to a single-platform Doppler two-stage closed positioning method in the presence of signal carrier frequency prior errors.
Background
As is well known, radiation source positioning technology plays an important role in many industrial and electronic information fields, such as target monitoring, navigation telemetry, seismic surveying, radio astronomy, emergency assistance, safety management, etc. The positioning (i.e. position parameter estimation) of the radiation source can be completed by using active equipment such as radar, laser, sonar and the like, which is called as an active positioning technology and has the advantages of all weather, high precision and the like. However, the active positioning system usually needs to be implemented by transmitting a high-power electromagnetic signal, so that the position of the active positioning system is easily exposed and easily found by the other party, and the active positioning system is affected by the electronic interference of the other party, so that the positioning performance is greatly deteriorated, and even the safety and reliability of the system are compromised.
Radiation source localization can also be achieved using target (active) radiated or (passive) scattered radio signals, a technique referred to as passive localization technique, which refers to estimating target location parameters by receiving target radiated or scattered radio signals without the observation platform actively transmitting electromagnetic signals. Compared with an active positioning system, the passive positioning system has the advantages of no active transmission of electromagnetic signals, strong viability, long reconnaissance action distance and the like, thereby being widely concerned and deeply researched by scholars at home and abroad. The passive positioning system can be divided into a single-platform passive positioning system and a multi-platform passive positioning system according to the number of observation platforms, wherein the single-platform passive positioning system has the advantages of high flexibility, strong maneuverability, simple system, no need of communication and synchronization between the platforms and the like, and the patent mainly relates to a single-platform passive positioning system.
In a single-platform positioning system, the frequency of arrival (FOA) is a type of frequently used observation, which includes Doppler information, by which the radiation source can be positioned (Amar A, Weiss A J. localization of narrowband radio emission based on Doppler frequency shift [ J ]. IEEE Transactions on Signal Processing,2008,56(11): 5500.) (strict navigation, Yayayayakuan. Low-orbit single-satellite frequency measurement positioning technique and its accuracy analysis [ J ]. computer engineering, 2012,38(18):6-10.) (Yacaoxin. Single-satellite Doppler passive positioning algorithm and error analysis [ J ]. electronic measurement technique, 2017,40(2): 59-63.). Due to the non-linear nature of the FOA observations, iterations are typically required to obtain a localization result. However, the iterative method requires setting an initial value, and is prone to problems such as iterative divergence and local convergence. On the other hand, signal carrier frequency information is also needed for positioning by using FOA observation, but in a non-cooperative communication scene, the signal carrier frequency is also obtained through observation, wherein an a priori error exists, and the error can deteriorate the positioning performance.
Disclosure of Invention
The invention provides a single-platform Doppler two-stage closed positioning method in the presence of a priori error of a signal carrier frequency aiming at the problems of iterative divergence and local convergence in a single-platform positioning system and the problem of influence on positioning performance due to the prior error.
In order to achieve the purpose, the single-platform Doppler two-stage closed positioning method under the condition that the signal carrier frequency prior error exists comprises the steps of firstly utilizing a single motion observation platform to carry out linear motion, and utilizing a plurality of short time slots to obtain FOA observed quantity of a radiation source in the process of running each linear track, wherein the FOA observed quantity contains Doppler information. And then constructing a stage 1 linear observation equation by utilizing a triangular sine theorem. And then, based on the statistical characteristic of the FOA observation error and the statistical characteristic of the signal carrier frequency prior error, obtaining the error statistical characteristic in the linear observation equation by using a first-order error analysis method, and further determining an optimal weighting matrix, thereby obtaining the radiation source position estimation value in the 1 st stage. The theory proves that the estimated value of the 1 st stage does not have asymptotic statistical optimality, so the estimated value is substituted into the original FOA observation equation, and the linear observation equation of the 2 nd stage is obtained through certain algebraic transformation. And then, based on the statistical property of the estimated value in the 1 st stage, the statistical property of the FOA observation error and the statistical property of the signal carrier frequency prior error, obtaining the error statistical property in the linear observation equation in the 2 nd stage by using a first-order error analysis method, and further determining an optimal weighting matrix, thereby obtaining the estimated value of the radiation source position in the 2 nd stage, wherein the estimated value is the final positioning result. The invention specifically adopts the following technical scheme:
step 1: a single moving observation platform is used for positioning a static radiation source in space, the moving track of the platform consists of M straight line segments, and N is used together in the process of driving the mth straight line trackmObtaining FOA observations in a short time slot
Figure BDA0003209678170000021
The FOA observation quantity of the single motion observation platform in the nth short time slot of the mth straight track is represented;
step 2: using FOA observations
Figure BDA0003209678170000022
And carrier frequency prior value
Figure BDA0003209678170000023
Computing a set of vectors
Figure BDA0003209678170000031
And toMeasuring group
Figure BDA0003209678170000032
Angle therebetween
Figure BDA0003209678170000033
Wherein u ═ x(u) y(u)z(u)]TRepresenting a radiation source position vector;
Figure BDA0003209678170000034
a position vector representing the nth short time slot of the single motion observation platform in the mth straight track;
Figure BDA0003209678170000035
a velocity vector representing the nth short time slot of the single motion observation platform in the mth straight track;
and step 3: sequentially utilizing FOA observed quantity in each linear track
Figure BDA0003209678170000036
Observation matrix constructed based on triangular sine theorem
Figure BDA0003209678170000037
And observation vector
Figure BDA0003209678170000038
And 4, step 4: respectively will observe the matrix
Figure BDA0003209678170000039
And observation vector
Figure BDA00032096781700000310
Merging to form high-dimensional observation matrix
Figure BDA00032096781700000311
And high dimensional observation vector
Figure BDA00032096781700000312
And 5: calculating the initial value of the position of the radiation source
Figure BDA00032096781700000313
And use
Figure BDA00032096781700000314
Computing matrices
Figure BDA00032096781700000315
And
Figure BDA00032096781700000316
step 6: computing an error covariance matrix
Figure BDA00032096781700000317
Determining an optimal weighting matrix, and obtaining the estimated value of the position of the radiation source in the 1 st stage by using the optimal weighting matrix
Figure BDA00032096781700000318
And 7: aiming at each linear track in sequence, the estimated value of the position of the radiation source in the 1 st stage is utilized
Figure BDA00032096781700000319
Constructing an observation matrix
Figure BDA00032096781700000320
And observation vector
Figure BDA00032096781700000321
And 8: respectively will observe the matrix
Figure BDA00032096781700000322
And observation vector
Figure BDA00032096781700000323
Merging to form high-dimensional observation matrix
Figure BDA00032096781700000324
And high dimensional observation vector
Figure BDA00032096781700000325
And step 9: using estimation of radiation source position in stage 1
Figure BDA00032096781700000326
Computing matrices
Figure BDA00032096781700000327
And
Figure BDA00032096781700000328
step 10: computing an error covariance matrix
Figure BDA00032096781700000329
Determining an optimal weighting matrix, and obtaining the estimated value of the position of the radiation source in the 2 nd stage by using the optimal weighting matrix
Figure BDA00032096781700000330
And will be
Figure BDA00032096781700000331
As a final positioning result.
Further, in step 1, the FOA observation amount
Figure BDA00032096781700000332
The expression of (a) is:
Figure BDA00032096781700000333
in the formula ofmnRepresenting a gaussian observation error; c represents the propagation speed of the radiation source signal; f. of0Representing the carrier frequency of the radiation source signal, a priori of which
Figure BDA00032096781700000417
The error of the prior is contained, and the corresponding expression is as follows:
Figure BDA0003209678170000041
where ξ represents the gaussian prior error.
Further, in the step 2, the vector group is calculated as follows
Figure BDA00032096781700000418
And vector set
Figure BDA0003209678170000042
Angle therebetween
Figure BDA0003209678170000043
Figure BDA0003209678170000044
Further, in the step 3, the matrix is observed
Figure BDA0003209678170000045
And observation vector
Figure BDA0003209678170000046
The corresponding calculation formula is:
Figure BDA0003209678170000047
Figure BDA0003209678170000048
further, in step 4, a high-dimensional observation matrix
Figure BDA0003209678170000049
And high dimensional observation vector
Figure BDA00032096781700000410
The corresponding expression is:
Figure BDA00032096781700000411
further, in the step 5, the initial value of the position of the radiation source is calculated as follows
Figure BDA00032096781700000412
Figure BDA00032096781700000413
Then use
Figure BDA00032096781700000414
Computing matrices
Figure BDA00032096781700000415
And
Figure BDA00032096781700000416
the corresponding calculation formula is:
Figure BDA0003209678170000051
in the formula
Figure BDA0003209678170000052
Wherein
Figure BDA0003209678170000059
Figure BDA0003209678170000053
Figure BDA0003209678170000054
Figure BDA0003209678170000055
Wherein
Figure BDA0003209678170000056
Figure BDA0003209678170000057
Figure BDA0003209678170000058
Figure BDA0003209678170000061
Figure BDA0003209678170000062
Figure BDA0003209678170000063
Wherein
Figure BDA0003209678170000064
Represents Nm×NmOrder unit matrix
Figure BDA0003209678170000065
Column 1 in (1);
Figure BDA0003209678170000066
represents Nm×NmOrder unit matrix
Figure BDA0003209678170000067
The nth column of (1);
Figure BDA0003209678170000068
represents (N)m-1)×(Nm-1) order identity matrix
Figure BDA0003209678170000069
Column n-1 of (1);
Figure BDA00032096781700000610
to represent
Figure BDA00032096781700000611
An order all-zero matrix;
Figure BDA00032096781700000612
to represent
Figure BDA00032096781700000613
An all zero matrix of order.
Further, in step 6, the error covariance matrix is calculated according to the following formula
Figure BDA00032096781700000614
Figure BDA00032096781700000615
Wherein E represents an FOA observation error covariance matrix;
Figure BDA00032096781700000616
variance, σ, representing the prior error of the carrier frequencyfStandard deviation representing the prior error of the carrier frequency;
the stage 1 radiation source position estimate is then calculated as follows
Figure BDA00032096781700000617
Figure BDA00032096781700000618
Further, in step 7, an observation matrix is constructed as follows
Figure BDA00032096781700000619
And observation vector
Figure BDA0003209678170000071
Figure BDA0003209678170000072
Further, in step 8, a high-dimensional observation matrix
Figure BDA0003209678170000073
And high dimensional observation vector
Figure BDA0003209678170000074
The corresponding expression is:
Figure BDA0003209678170000075
further, in step 9, the matrix is calculated according to the following formula
Figure BDA0003209678170000076
And
Figure BDA0003209678170000077
Figure BDA0003209678170000078
in the formula
Figure BDA0003209678170000079
Wherein
Figure BDA00032096781700000710
Figure BDA00032096781700000711
Figure BDA00032096781700000712
Further, in the step 10, the error covariance matrix is calculated according to the following formula
Figure BDA00032096781700000713
Figure BDA00032096781700000714
Then, the estimated position of the radiation source in the 2 nd stage is obtained according to the following formula
Figure BDA0003209678170000081
Figure BDA0003209678170000082
(Vector)
Figure BDA0003209678170000083
Namely the final positioning result.
Compared with the prior art, the invention has the following beneficial effects:
the invention discloses a single-platform Doppler two-stage closed positioning method under the condition of a single-motion observation platform passive positioning scene, aiming at an FOA observation equation, two groups of linear observation equations are sequentially constructed, corresponding closed solutions are respectively obtained, and high-precision positioning of a radiation source is realized through two-stage calculation. Compared with the existing single-platform Doppler positioning method, the method provided by the invention can inhibit the influence of the prior error of the signal carrier frequency, and can obtain the positioning precision with the optimal asymptotic statistics.
Drawings
FIG. 1 is a basic flowchart of a single-platform Doppler two-stage closed positioning method in the presence of a signal carrier frequency prior error according to an embodiment of the present invention;
FIG. 2 is a scatter plot of radiation source positioning results and an elliptical curve of positioning error (X-Y plane coordinates);
FIG. 3 is a scatter plot of radiation source positioning results and an elliptical curve of positioning error (Y-Z plane coordinates);
FIG. 4 shows the RMS error of an estimated source position as a function of the standard deviation σeThe variation curve of (d);
FIG. 5 shows the RMS error of an estimated source position as a function of the standard deviation σfThe change curve of (2).
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
as shown in fig. 1, a single-platform doppler two-stage closed positioning method in the presence of a signal carrier frequency prior error includes:
step 1: a single moving observation platform is used for positioning a static radiation source in space, the moving track of the platform consists of M straight line segments, and N is used together in the process of driving the mth straight line trackmObtaining FOA observations in a short time slot
Figure BDA0003209678170000084
The FOA observation quantity of the single motion observation platform in the nth short time slot of the mth straight track is represented;
step 2: using FOA observations
Figure BDA0003209678170000085
And carrier frequency prior value
Figure BDA0003209678170000086
Computing a set of vectors
Figure BDA0003209678170000091
And vector set
Figure BDA0003209678170000092
Angle therebetween
Figure BDA0003209678170000093
And step 3: sequentially utilizing FOA observed quantity in each linear track
Figure BDA0003209678170000094
Observation matrix constructed based on triangular sine theorem
Figure BDA0003209678170000095
And observation vector
Figure BDA0003209678170000096
And 4, step 4: respectively will observe the matrix
Figure BDA0003209678170000097
And observation vector
Figure BDA0003209678170000098
Merging to form high-dimensional observation matrix
Figure BDA0003209678170000099
And high dimensional observation vector
Figure BDA00032096781700000910
And 5: calculating the initial value of the position of the radiation source
Figure BDA00032096781700000911
And use
Figure BDA00032096781700000912
Computing matrices
Figure BDA00032096781700000913
And
Figure BDA00032096781700000914
step 6: computing an error covariance matrix
Figure BDA00032096781700000915
Determining an optimal weighting matrix, and obtaining the estimated value of the position of the radiation source in the 1 st stage by using the optimal weighting matrix
Figure BDA00032096781700000916
And 7: aiming at each linear track in sequence, the estimated value of the position of the radiation source in the 1 st stage is utilized
Figure BDA00032096781700000917
Constructing an observation matrix
Figure BDA00032096781700000918
And observation vector
Figure BDA00032096781700000919
And 8: respectively will observe the matrix
Figure BDA00032096781700000920
And observation vector
Figure BDA00032096781700000921
Merging to form high-dimensional observation matrix
Figure BDA00032096781700000922
And high dimensional observation vector
Figure BDA00032096781700000923
And step 9: using estimation of radiation source position in stage 1
Figure BDA00032096781700000924
Computing matrices
Figure BDA00032096781700000925
And
Figure BDA00032096781700000926
step 10: computing an error covariance matrix
Figure BDA00032096781700000927
Determining an optimal weighting matrix, and obtaining the estimated value of the position of the radiation source in the 2 nd stage by using the optimal weighting matrix
Figure BDA00032096781700000928
And will be
Figure BDA00032096781700000929
As a final positioning result.
Further, in the step 1, a single moving observation platform is used for positioning the stationary radiation source in space, the moving track of the platform is composed of M straight line segments, and a total of N straight line segments are used in the process of driving the mth straight line trackmObtaining FOA observations in a short time slot
Figure BDA00032096781700000930
The corresponding expression is:
Figure BDA00032096781700000931
wherein u ═ x(u) y(u) z(u)]TRepresenting a radiation source position vector;
Figure BDA0003209678170000101
presentation sheetThe position vector (known quantity) of the nth short time slot of the platform in the mth straight track;
Figure BDA0003209678170000102
a velocity vector (known quantity) representing the nth short time slot of the single platform in the mth straight track; epsilonmnRepresenting a gaussian observation error; c represents the propagation velocity (known quantity) of the radiation source signal; f. of0Representing the carrier frequency of the radiation source signal, a priori of which
Figure BDA0003209678170000103
The error of the prior is contained, and the corresponding expression is as follows:
Figure BDA0003209678170000104
where ξ represents the gaussian prior error.
Further, in the step 2, the FOA observation quantity is used
Figure BDA0003209678170000105
And carrier frequency prior value
Figure BDA0003209678170000106
Computing a set of vectors
Figure BDA0003209678170000107
And vector set
Figure BDA0003209678170000108
Angle therebetween
Figure BDA0003209678170000109
The corresponding calculation formula is:
Figure BDA00032096781700001010
further, in step 3, the FOA observation in each linear track is sequentially utilizedMeasurement of
Figure BDA00032096781700001011
Observation matrix constructed based on triangular sine theorem
Figure BDA00032096781700001012
And observation vector
Figure BDA00032096781700001013
The corresponding calculation formula is:
Figure BDA00032096781700001014
Figure BDA00032096781700001015
further, in the step 4, the observation matrixes are respectively used
Figure BDA00032096781700001016
And observation vector
Figure BDA00032096781700001017
Merging to form high-dimensional observation matrix
Figure BDA0003209678170000111
And high dimensional observation vector
Figure BDA0003209678170000112
The corresponding expression is:
Figure BDA0003209678170000113
further, in the step 5, an initial value of the radiation source position is calculated
Figure BDA0003209678170000114
The corresponding calculation formula is:
Figure BDA0003209678170000115
then using the value to calculate a matrix
Figure BDA0003209678170000116
And
Figure BDA0003209678170000117
the corresponding calculation formula is:
Figure BDA0003209678170000118
in the formula
Figure BDA0003209678170000119
Wherein
Figure BDA00032096781700001115
Figure BDA00032096781700001110
Figure BDA00032096781700001111
Figure BDA00032096781700001112
Wherein
Figure BDA00032096781700001113
Figure BDA00032096781700001114
Figure BDA0003209678170000121
Figure BDA0003209678170000122
Figure BDA0003209678170000123
Figure BDA0003209678170000124
Wherein
Figure BDA0003209678170000125
Represents Nm×NmOrder unit matrix
Figure BDA0003209678170000126
Column 1 in (1);
Figure BDA0003209678170000127
represents Nm×NmOrder unit matrix
Figure BDA0003209678170000128
The nth column of (1);
Figure BDA0003209678170000129
represents (N)m-1)×(Nm-1) order identity matrix
Figure BDA00032096781700001210
Column n-1 of (1);
Figure BDA00032096781700001211
to represent
Figure BDA00032096781700001212
An order all-zero matrix;
Figure BDA00032096781700001213
to represent
Figure BDA00032096781700001214
An all zero matrix of order.
Further, in the step 6, an error covariance matrix is calculated
Figure BDA00032096781700001215
The corresponding calculation formula is:
Figure BDA00032096781700001216
wherein E represents an FOA observation error covariance matrix;
Figure BDA00032096781700001217
variance, σ, representing the prior error of the carrier frequencyfRepresenting the standard deviation of the prior error of the carrier frequency. Then using the matrix
Figure BDA00032096781700001218
Determining an optimal weighting matrix as
Figure BDA00032096781700001221
And obtaining the estimated value of the position of the radiation source in the 1 st stage by using the optimal weighting matrix
Figure BDA00032096781700001219
The corresponding calculation formula is:
Figure BDA00032096781700001220
further, in step 7, the estimated value of the radiation source position in the 1 st stage is used for each linear track in turn
Figure BDA0003209678170000131
Constructing an observation matrix
Figure BDA0003209678170000132
And observation vector
Figure BDA0003209678170000133
The corresponding calculation formula is:
Figure BDA0003209678170000134
further, in the step 8, the observation matrixes are respectively set
Figure BDA0003209678170000135
And observation vector
Figure BDA0003209678170000136
Merging to form high-dimensional observation matrix
Figure BDA0003209678170000137
And high dimensional observation vector
Figure BDA0003209678170000138
The corresponding expression is:
Figure BDA0003209678170000139
further, in the step 9, the estimated value of the position of the radiation source in the stage 1 is used
Figure BDA00032096781700001310
Computing matrices
Figure BDA00032096781700001311
And
Figure BDA00032096781700001312
corresponding calculation is disclosedThe formula is as follows:
Figure BDA00032096781700001313
in the formula
Figure BDA00032096781700001314
Wherein
Figure BDA00032096781700001315
Figure BDA00032096781700001316
Figure BDA00032096781700001317
Further, in the step 10, an error covariance matrix is calculated
Figure BDA0003209678170000141
The corresponding calculation formula is:
Figure BDA0003209678170000142
then using the matrix
Figure BDA0003209678170000143
Determining an optimal weighting matrix as
Figure BDA0003209678170000144
And obtaining the estimated value of the position of the radiation source in the 2 nd stage by using the optimal weighting matrix
Figure BDA0003209678170000145
Corresponding toThe calculation formula is as follows:
Figure BDA0003209678170000146
(Vector)
Figure BDA0003209678170000147
namely the final positioning result.
To verify the effect of the present invention, the following experiment was performed:
let the radiation source position vector be u [ -223 ]]T(kilometer), the carrier frequency of the radiation signal is 500MHz, a single observation platform runs 4 straight tracks in total, 6 short time slots are utilized in each track to obtain FOA observed quantity, the position coordinates of the short time slots of the single observation platform in each straight track are shown in tables 1 to 4, and the speed of the single observation platform in each straight track is shown in table 5. The FOA observation error obeys zero mean value and variance
Figure BDA0003209678170000148
(ii) a gaussian distribution of; the prior error of the signal carrier frequency is subjected to the mean value of zero and the variance of
Figure BDA0003209678170000149
Of a Gaussian distribution of where σeAnd σfAre all standard deviations.
TABLE 1 position coordinates (unit: kilometer) of 6 short time slots of a single observation platform in the 1 st straight-line track of travel
Figure BDA00032096781700001410
TABLE 2 position coordinates (units: kilometers) of 6 short time slots of a single observation platform in the 2 nd straight-line track of travel
Figure BDA00032096781700001411
Figure BDA0003209678170000151
TABLE 3 position coordinates (unit: kilometer) of 6 short time slots of single observation platform in the 3 rd straight-line track
Figure BDA0003209678170000152
TABLE 4 position coordinates (unit: kilometer) of 6 short time slots of single observation platform in the 4 th straight-line track
Figure BDA0003209678170000153
TABLE 5 speed of a single observation platform (units: kilometers per second) while traveling each straight track
Figure BDA0003209678170000154
First, the standard deviation σ is calculatedeAnd σfAre respectively set to sigma e3 and σfFig. 2 shows a scatter diagram of the positioning result of the radiation source and an elliptic curve of the positioning error (X-Y plane coordinates); figure 3 shows a scatter plot of the radiation source positioning results versus an elliptical plot of the positioning error (Y-Z plane coordinates). As can be seen from fig. 2 and 3, the shape of the localization result scattergram of the localization method disclosed by the present invention is consistent with the positioning error ellipse shape, and the large probability corresponds to the large area ellipse, and the small probability corresponds to the small area ellipse, thereby verifying the validity of the method of the present invention.
The standard deviation σ is then calculatedfIs set to sigma f5, and varying the standard deviation σeFigure 4 gives the root mean square error of the radiation source position estimate as a function of the standard deviation sigmaeThe variation curve of (d); the standard deviation sigmaeIs set to sigma e3, and varying the standard deviation σfFigure 5 shows the root mean square error of the radiation source position estimate as a function of the standard deviation sigmafThe change curve of (2). As can be seen from fig. 4 and 5: (1) the Doppler two-stage closed positioning method disclosed by the patent can achieve the Cramer-Rao bound for the root mean square error of the radiation source position estimation, thereby verifying the asymptotic statistical optimality of the new method; (2) the estimation accuracy of the Doppler two-stage closed positioning method disclosed by the patent is higher than that of the existing closed positioning method, and the advantages of the Doppler two-stage closed positioning method are more obvious along with the increase of FOA observation errors and carrier frequency prior errors, because the new method obtains the positioning accuracy which is asymptotically statistically optimal through two-stage processing.
The above shows only the preferred embodiments of the present invention, and it should be noted that it is obvious to those skilled in the art that various modifications and improvements can be made without departing from the principle of the present invention, and these modifications and improvements should also be considered as the protection scope of the present invention.

Claims (10)

1. A single-platform Doppler two-stage closed positioning method under the condition of signal carrier frequency prior error is characterized by comprising the following steps:
step 1: a single moving observation platform is used for positioning a static radiation source in space, the moving track of the platform consists of M straight line segments, and N is used together in the process of driving the mth straight line trackmObtaining FOA observations in a short time slot
Figure FDA0003209678160000011
Figure FDA0003209678160000012
The FOA observation quantity of the single motion observation platform in the nth short time slot of the mth straight track is represented;
step 2: using FOA observations
Figure FDA0003209678160000013
And carrier frequency prior value
Figure FDA0003209678160000014
Computing a set of vectors
Figure FDA0003209678160000015
And vector set
Figure FDA0003209678160000016
Angle therebetween
Figure FDA0003209678160000017
Wherein u ═ x(u)y(u)z(u)]TRepresenting a radiation source position vector;
Figure FDA0003209678160000018
a position vector representing the nth short time slot of the single motion observation platform in the mth straight track;
Figure FDA0003209678160000019
a velocity vector representing the nth short time slot of the single motion observation platform in the mth straight track;
and step 3: sequentially utilizing FOA observed quantity in each linear track
Figure FDA00032096781600000110
Observation matrix constructed based on triangular sine theorem
Figure FDA00032096781600000111
And observation vector
Figure FDA00032096781600000112
And 4, step 4: respectively will observe the matrix
Figure FDA00032096781600000113
And observation vector
Figure FDA00032096781600000114
Merging to form high-dimensional observation matrix
Figure FDA00032096781600000115
And high dimensional observation vector
Figure FDA00032096781600000116
And 5: calculating the initial value of the position of the radiation source
Figure FDA00032096781600000117
And use
Figure FDA00032096781600000118
Computing matrices
Figure FDA00032096781600000119
And
Figure FDA00032096781600000120
step 6: computing an error covariance matrix
Figure FDA00032096781600000121
Determining an optimal weighting matrix, and obtaining the estimated value of the position of the radiation source in the 1 st stage by using the optimal weighting matrix
Figure FDA00032096781600000122
And 7: aiming at each linear track in sequence, the estimated value of the position of the radiation source in the 1 st stage is utilized
Figure FDA00032096781600000123
Constructing an observation matrix
Figure FDA00032096781600000124
And observation vector
Figure FDA00032096781600000125
And 8: respectively will observe the matrix
Figure FDA00032096781600000126
And observation vector
Figure FDA00032096781600000127
Merging to form high-dimensional observation matrix
Figure FDA00032096781600000128
And high dimensional observation vector
Figure FDA00032096781600000129
And step 9: using estimation of radiation source position in stage 1
Figure FDA0003209678160000021
Computing matrices
Figure FDA0003209678160000022
And
Figure FDA0003209678160000023
step 10: computing an error covariance matrix
Figure FDA0003209678160000024
Determining an optimal weighting matrix, and obtaining the estimated value of the position of the radiation source in the 2 nd stage by using the optimal weighting matrix
Figure FDA0003209678160000025
And will be
Figure FDA0003209678160000026
As a final positioning result.
2. The method of claim 1The single-platform Doppler two-stage closed positioning method under the condition of signal carrier frequency prior error is characterized in that in the step 1, FOA observed quantity
Figure FDA0003209678160000027
The expression of (a) is:
Figure FDA0003209678160000028
in the formula ofmnRepresenting a gaussian observation error; c represents the propagation speed of the radiation source signal; f. of0Representing the carrier frequency of the radiation source signal, a priori of which
Figure FDA0003209678160000029
The error of the prior is contained, and the corresponding expression is as follows:
Figure FDA00032096781600000210
where ξ represents the gaussian prior error.
3. The single-stage Doppler two-stage closed positioning method in the presence of signal carrier frequency prior error as claimed in claim 2, wherein in the step 2, the vector group is calculated as follows
Figure FDA00032096781600000211
And vector set
Figure FDA00032096781600000212
Angle therebetween
Figure FDA00032096781600000213
Figure FDA00032096781600000214
4. The single-platform Doppler two-stage closed positioning method according to claim 1, wherein in step 3, the observation matrix is used for estimating the Doppler spread spectrum in the presence of the prior error of the signal carrier frequency
Figure FDA00032096781600000215
And observation vector
Figure FDA00032096781600000216
The corresponding calculation formula is:
Figure FDA00032096781600000217
Figure FDA0003209678160000031
5. the single-platform Doppler two-stage closed positioning method in the presence of signal carrier frequency prior error according to claim 1 or 4, characterized in that in the step 4, the high-dimensional observation matrix
Figure FDA0003209678160000032
And high dimensional observation vector
Figure FDA0003209678160000033
The corresponding expression is:
Figure FDA0003209678160000034
6. the single-stage Doppler two-stage closed positioning method according to claim 5, wherein the single-stage Doppler two-stage closed positioning method is performed in the presence of signal carrier frequency prior error, and is characterized in thatIn step 5, the initial value of the radiation source position is calculated as follows
Figure FDA0003209678160000035
Figure FDA0003209678160000036
Then use
Figure FDA0003209678160000037
Computing matrices
Figure FDA0003209678160000038
And
Figure FDA0003209678160000039
the corresponding calculation formula is:
Figure FDA00032096781600000310
in the formula
Figure FDA00032096781600000311
Wherein
Figure FDA00032096781600000312
Figure FDA00032096781600000313
Figure FDA00032096781600000314
Figure FDA00032096781600000315
Wherein
Figure FDA0003209678160000041
Figure FDA0003209678160000042
Figure FDA0003209678160000043
Figure FDA0003209678160000044
Figure FDA0003209678160000045
Figure FDA0003209678160000046
Wherein
Figure FDA0003209678160000047
Represents Nm×NmOrder unit matrix
Figure FDA0003209678160000048
Column 1 in (1);
Figure FDA0003209678160000049
represents Nm×NmOrder unit matrix
Figure FDA00032096781600000410
The nth column of (1);
Figure FDA00032096781600000411
represents (N)m-1)×(Nm-1) order identity matrix
Figure FDA00032096781600000412
Column n-1 of (1);
Figure FDA00032096781600000413
to represent
Figure FDA00032096781600000414
An order all-zero matrix;
Figure FDA00032096781600000415
to represent
Figure FDA00032096781600000416
An all zero matrix of order.
7. The single-stage Doppler two-stage closed positioning method in the presence of signal carrier frequency prior errors as claimed in claim 1, wherein in step 6, the error covariance matrix is calculated according to the following formula
Figure FDA0003209678160000051
Figure FDA0003209678160000052
Wherein E represents an FOA observation error covariance matrix;
Figure FDA0003209678160000053
variance, σ, representing the prior error of the carrier frequencyfIndicating a priori error of carrier frequencyStandard deviation;
the stage 1 radiation source position estimate is then calculated as follows
Figure FDA0003209678160000054
Figure FDA0003209678160000055
8. The single-platform Doppler two-stage closed positioning method in the presence of signal carrier frequency prior error according to claim 1, wherein in the step 7, the observation matrix is constructed as follows
Figure FDA0003209678160000056
And observation vector
Figure FDA0003209678160000057
Figure FDA0003209678160000058
9. The single-platform Doppler two-stage closed positioning method in the presence of signal carrier frequency prior error according to claim 1, wherein in the step 9, the matrix is calculated according to the following formula
Figure FDA0003209678160000059
And
Figure FDA00032096781600000510
Figure FDA00032096781600000511
in the formula
Figure FDA00032096781600000512
Wherein
Figure FDA0003209678160000061
Figure FDA0003209678160000062
Figure FDA0003209678160000063
10. The single-stage doppler two-stage closed positioning method according to claim 9, wherein in step 10, the error covariance matrix is calculated according to the following formula
Figure FDA0003209678160000064
Figure FDA0003209678160000065
Then, the estimated position of the radiation source in the 2 nd stage is obtained according to the following formula
Figure FDA0003209678160000066
Figure FDA0003209678160000067
(Vector)
Figure FDA0003209678160000068
Namely the final positioning result.
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