CN110940976A - Error correction-based multi-station multi-external radiation source radar moving target positioning method - Google Patents

Error correction-based multi-station multi-external radiation source radar moving target positioning method Download PDF

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CN110940976A
CN110940976A CN201911129934.4A CN201911129934A CN110940976A CN 110940976 A CN110940976 A CN 110940976A CN 201911129934 A CN201911129934 A CN 201911129934A CN 110940976 A CN110940976 A CN 110940976A
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左燕
蒋陶然
刘雪娇
郭宝峰
刘俊
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Hangzhou Electronic Science and Technology University
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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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
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Abstract

The invention discloses a method for positioning a moving target of a multi-station multi-external-radiation-source radar based on error correction. The method comprises the steps of firstly, pseudo-linearizing the double-base-distance and double-base-distance change rate nonlinear measurement equation of the multi-station multi-external-radiation-source radar to obtain the joint estimation of the position and the speed of a moving target and the system deviation. And (4) considering the association of the auxiliary variable with the target position and speed, constructing a multi-step association least square estimation model and optimally solving to reduce the estimation error of the target position and speed. And finally, correcting by using the system deviation estimated value, and performing posterior iteration to further improve the estimation performance of the target position and speed. The method considers the influence of the system deviation on the positioning precision, jointly estimates the target state and the system deviation, and improves the positioning precision of the moving target through error correction. And meanwhile, a multi-step associated least square estimation and posterior iterative algorithm is adopted, so that the estimation error of the target state is further reduced.

Description

Error correction-based multi-station multi-external radiation source radar moving target positioning method
Technical Field
The invention belongs to the field of radar data processing, and particularly relates to a multi-station multi-external-radiation-source radar moving target positioning method based on error correction.
Background
The multi-station multi-external radiation source radar detects a target by utilizing a plurality of third-party non-cooperative signal sources (broadcasting, television, satellites, base stations and the like), receives signals and direct wave signals emitted by the target scattered by the third-party external radiation sources through a plurality of receiving stations (also called observation stations), and obtains the arrival time difference and the arrival frequency difference measurement of the signals by adopting coherent processing. Under the multi-base structure, the time difference and frequency difference parameters are converted into double-base-distance and double-base-distance change rate parameters, and a plurality of groups of double-base-distance/double-base-distance change rates are fused to position the moving target.
At present, the problem of positioning the external radiation source based on the double base distances and the double base distance change rates is widely concerned, and the method mainly focuses on some special simplified scenes, including single-station multiple-external-radiation-source scenes and multi-station single-external-radiation-source scenes. And the multi-station multi-external radiation source positioning scene is more challenging and difficult. Noroozi et al propose a two-step weighted least square algorithm based on grouping for the multi-station multi-external radiation source positioning problem; on this basis, Zhao Yongsheng et al propose a three-step weighted least squares algorithm without grouping, and the above estimation methods all assume that all metrology values from the same target are unbiased. In the actual problem, clocks between the third-party external radiation source and the receiving station are not synchronous; the difference of the reference path and the actual path generates a multipath phenomenon when the signal propagates, and the inherent system deviation of the external radiation source radar causes the fixed deviation of the measured value. Neglecting the effects of bias can cause the target location estimation performance to degrade significantly, even producing false targets. Therefore, the joint error correction and target positioning are a key technology for data processing of the external radiation source radar system. The patent (201811601502.4) researches target positioning and error correction in a single-station multi-external radiation source scene, the method cannot be directly applied to a multi-station multi-external radiation source scene, and a multi-station multi-external radiation source radar moving target positioning method based on error correction is designed.
Disclosure of Invention
The invention provides a multi-step weighted least square estimation algorithm based on error correction by considering the influence of deviation and utilizing double base distances and double base distance change rate measurement values aiming at a multi-station multi-external radiation source radar network. By jointly estimating the target state (position and velocity) and correcting the deviation, more accurate moving target positioning is obtained.
The method comprises the following specific steps:
step 1, in a multi-station multi-external radiation source radar system, selecting the distance between a target and a receiving station
Figure BDA0002278013410000021
Pseudo-linearizing a double-base-distance nonlinear measurement equation for an auxiliary variable to establish a pseudo-linear equation of double-base-distance measurement and a target state (position and speed);
step 2, the above-mentioned double-base distance pseudo-linear equation is derived to time to obtain the relation between double-base distance change rate measurement and target state, and the distance between target and receiving station is selected
Figure BDA0002278013410000022
And rate of change of distance
Figure BDA0002278013410000023
And establishing a pseudo-linear equation of the double-base-distance change rate for the auxiliary variable.
Step 3, establishing a pseudo linear equation of the double-base distance and the double-base distance change rate, establishing a joint estimation model of the state (position and speed) and the deviation of the moving target, and converting the joint estimation model into a matrix form h of A ξ + Be;
step 4, obtaining a joint estimation value of the state and the deviation of the moving target by adopting an iterative weighted least square estimation algorithm
Figure BDA0002278013410000024
Wherein the weight W ═ E [ ee [ ]T]＝(BQB)-1。
And 5, further correcting the estimation error in the step 4 according to the relevance of the auxiliary variable and the target state (position and speed). Introducing new intermediate variables
Figure BDA0002278013410000025
Establishing an association estimation model h1＝A1ξ1+B1Δ ξ, and solving by using a weighted least square algorithm to obtain the operationJoint estimation of moving target states and biases
Figure BDA0002278013410000026
Wherein W1＝E[ΔξΔξT]＝(ATWA)-1。
Step 6, according to the intermediate variable rhop,
Figure BDA0002278013410000027
The correlation with the target state (position and speed) further corrects the estimation error in the step 5, and a new correlation estimation model h is established2＝A2ξ2+B2Δξ1And solving by adopting a weighted least square algorithm to obtain a joint estimation value of the state and the deviation of the moving target
Figure BDA0002278013410000028
Wherein W2＝E[Δξ1Δξ1 T]＝(A1 TW1A1)-1。
And 7, substituting the deviation estimation value into a measurement equation, and correcting the double-base distance and the double-base distance change rate measurement value. And (4) based on the corrected double-base-distance and double-base-distance change rate parameters, carrying out target positioning and deviation calibration again, and turning to the step 3. The above process is iterated until the system deviation estimated value tends to a certain smaller threshold epsilon, and the iteration is stopped.
The invention has the beneficial effects that:
1. and considering the influence of the system deviation on the positioning precision, jointly estimating the target state and the system deviation, and improving the positioning precision of the moving target through error correction.
2. In a multi-station multi-external radiation source radar system, a double-base-distance/double-base-distance change rate nonlinear measurement equation is subjected to pseudo-linearization by selecting a proper auxiliary variable, a combined estimation algebraic equation of a target state and a target deviation is established, and the complexity of nonlinear estimation is reduced on the premise of ensuring the estimation performance.
3. And (4) considering the association of the auxiliary variable with the target position state and the deviation, designing a multi-step association least square algorithm, and gradually improving the target positioning estimation precision.
4. And correcting the deviation by adopting posterior iteration to further reduce the estimation error of the target state.
The specific implementation mode is as follows:
a multi-station multi-external radiation source radar moving target positioning method based on error correction specifically comprises the following steps:
step 1: in the multi-station multi-external-radiation-source radar network, the multi-station multi-external-radiation-source radar network comprises M external radiation sources, N receiving stations and P targets, and the positioning dimension is D-3. The m < th > external radiation source is positioned
Figure BDA0002278013410000031
The location of the nth receiving station is
Figure BDA0002278013410000032
Position of the target p
Figure BDA0002278013410000033
Speed of rotation
Figure BDA0002278013410000034
The receiving station n receives the signal emitted by the external radiation source m scattered by the target p to obtain the following dual-base-distance measurement
Figure BDA0002278013410000035
Wherein u ism,n,pThe sum of the distances of the target p from the external radiation source m and the receiving station n;
Figure BDA0002278013410000036
the distance of the external radiation source m from the target p,
Figure BDA0002278013410000037
is the distance of the receiving station n from the target p; deltam,nMeasuring the fixed deviation for the double base distances; e.g. of the typem,n,pIs a dual-baseline measurement noise, and is an independent white gaussian zero mean noise.
Step 2: introduction of adjuvantsVariable of help
Figure BDA0002278013410000038
The nonlinear equation (1) is converted into a pseudo-linear equation. The concrete form is as follows
Figure BDA0002278013410000039
Wherein,
Figure BDA00022780134100000310
step 3, obtaining the time derivative by simultaneously obtaining the equation of the formula (2)
Figure BDA00022780134100000311
Wherein the rate of change of the double base distance
Figure BDA0002278013410000041
Figure BDA0002278013410000042
Is the deviation of the rate of change of the double base distance;
Figure BDA0002278013410000043
the measurement error of the double-base-distance change rate is independent Gaussian zero-mean white noise; the auxiliary variable being the rate of change of the target-to-receiving station distance
Figure BDA0002278013410000044
And step 3: simultaneous equations (2) and (3) are used for establishing a joint estimation pseudo-linear model of target states (positions and speeds) and deviations, and the matrix form of the joint estimation pseudo-linear model is as follows
h＝Aξ+Be (4)
Wherein,
Figure BDA0002278013410000045
Figure BDA0002278013410000046
Figure BDA0002278013410000047
Figure BDA0002278013410000048
Figure BDA0002278013410000049
Figure BDA00022780134100000410
Figure BDA00022780134100000411
Figure BDA00022780134100000412
Figure BDA00022780134100000413
Figure BDA00022780134100000414
Figure BDA00022780134100000415
Figure BDA00022780134100000416
Figure BDA0002278013410000051
Figure BDA0002278013410000052
Figure BDA0002278013410000053
and 4, step 4: and obtaining a joint estimation value of the target state and the system deviation by adopting an iterative weighted least square algorithm.
Step 4.1: and roughly estimating the target state and the system deviation by adopting a least square method, substituting the target state and the system deviation into a matrix B, and calculating the weight W ═ BQB-1；
Step 4.2: obtaining a joint estimation value of a target state and a system deviation by adopting a weighted least square estimation algorithm
Figure BDA0002278013410000054
Step 4.3, calculate estimate error covariance cov (Δ ξ) ═ aTWA)-1。
Step 5. consider the auxiliary variable
Figure BDA0002278013410000055
Correlation with target position and velocity, and error of estimated value of step 4
Figure BDA0002278013410000056
Designing the estimation value of the associated least square algorithm to the step 4
Figure BDA0002278013410000057
The improvement is as follows:
step 5.1. order
Figure BDA0002278013410000058
Establishing auxiliary variables
Figure BDA0002278013410000059
And target position
Figure BDA00022780134100000510
And target speed
Figure BDA00022780134100000511
The relationship between
Figure BDA00022780134100000512
The associated least squares estimation model is constructed as follows
h1＝A1ξ1+B1Δξ (6)
Wherein,
Figure BDA00022780134100000513
Figure BDA00022780134100000514
Figure BDA00022780134100000515
Figure BDA00022780134100000516
Figure BDA00022780134100000517
Figure BDA0002278013410000061
Figure BDA0002278013410000062
Figure BDA0002278013410000063
Figure BDA0002278013410000064
Figure BDA0002278013410000065
step 5.2: obtaining a joint estimation value of a target state and a system deviation by adopting a weighted least square estimation algorithm
Figure BDA0002278013410000066
Wherein W1＝cov(Δξ)＝(ATWA)-1。
Step 5.3 calculation of estimation error covariance cov (Δ ξ)1)＝(A1 TW1A1)-1。
Step 6, considering the intermediate variable rhopAnd
Figure BDA0002278013410000067
and (5) constructing a correlation least square estimation model on the estimation result of the step (5) by using correlation constraint with the target position state, and further improving the estimation performance of the target state and the system deviation.
Step 6.1: taking into account the intermediate variable pp,
Figure BDA0002278013410000068
Constraint relationship with target state
Figure BDA0002278013410000069
Figure BDA00022780134100000610
And step 5. estimation error
Figure BDA00022780134100000611
Selecting a target position square term, a product of a target position and a speed and a system error as variables, and constructing a correlation estimation model as follows
h2＝A2ξ2+B2Δξ1(7)
Wherein,
Figure BDA00022780134100000612
Figure BDA00022780134100000613
Figure BDA00022780134100000614
Figure BDA00022780134100000615
Figure BDA00022780134100000616
Figure BDA0002278013410000071
Figure BDA0002278013410000072
Figure BDA0002278013410000073
step 6.2: obtaining an estimate using a weighted least squares estimation algorithm
Figure BDA0002278013410000074
Wherein W2＝cov(Δξ1)＝(A1 TW1A1)-1。
Step 6.3: the square of the position of the target p is obtained according to step 6.2
Figure BDA0002278013410000075
And
Figure BDA0002278013410000076
the square root operation is carried out on the obtained product to obtain the product
Figure BDA0002278013410000077
Wherein,
Figure BDA0002278013410000078
sgn (·) is a sign function. The method aims to eliminate the condition of plus-minus sign ambiguity in the process of square operation.
According to the target position
Figure BDA0002278013410000079
Calculating a target velocity estimate
Figure BDA00022780134100000710
And 7, substituting the system deviation estimated value into a double-base-distance and double-base-distance change rate measurement equation to correct the double-base-distance and double-base-distance change rate measurement.
Step 7.1 the i +1 st iteration measurement information is
Figure BDA00022780134100000711
In the formula,
Figure BDA00022780134100000712
for the double base distance measurement after the ith correction,
Figure BDA00022780134100000713
is a measured value of the double-base distance change rate after the ith correction,
Figure BDA00022780134100000714
and
Figure BDA00022780134100000715
is the ith system deviation estimation result.
And 7.2, positioning the target based on the corrected double-base-distance measurement and the double-base-distance change rate measurement, and turning to the step 2. The above process is iterated until the system deviation estimate is satisfied
Figure BDA00022780134100000716
And is
Figure BDA00022780134100000717
(ε1And ε2To allow for error) the algorithm iteration stops.

Claims (1)

1. The method for positioning the moving target of the multi-station multi-external radiation source radar based on error correction specifically comprises the following steps:
step 1: the multi-station multi-external radiation source radar network comprises M external radiation sources, N receiving stations and P targets, wherein the positioning dimension is D-3; the m < th > external radiation source is positioned
Figure FDA0002278013400000011
The location of the nth receiving station is
Figure FDA0002278013400000012
Position of the target p
Figure FDA0002278013400000013
Speed of rotation
Figure FDA0002278013400000014
The receiving station n receives the signal emitted by the external radiation source m scattered by the target p to obtain the following dual-base-distance measurement
Figure FDA0002278013400000015
Wherein u ism,n,pThe sum of the distances of the target p from the external radiation source m and the receiving station n;
Figure FDA0002278013400000016
the distance of the external radiation source m from the target p,
Figure FDA0002278013400000017
is the distance of the receiving station n from the target p; deltam,nMeasuring the fixed deviation for the double base distances; e.g. of the typem,n,pThe noise is double-base-distance measurement noise and is independent Gaussian zero-mean white noise;
step 2: introducing auxiliary variables
Figure FDA0002278013400000018
Converting the nonlinear equation (1) into a pseudo linear equation; the concrete form is as follows
Figure FDA0002278013400000019
Wherein,
Figure FDA00022780134000000110
step 3, obtaining the time derivative by simultaneously obtaining the equation of the formula (2)
Figure FDA00022780134000000111
Wherein the rate of change of the double base distance
Figure FDA00022780134000000112
Figure FDA00022780134000000113
Is the deviation of the rate of change of the double base distance;
Figure FDA00022780134000000114
the measurement error of the double-base-distance change rate is independent Gaussian zero-mean white noise; the auxiliary variable being the rate of change of the target-to-receiving station distance
Figure FDA00022780134000000115
And step 3: simultaneous equations (2) and (3) are used for establishing a joint estimation pseudo-linear model of the target state and the deviation, and the matrix form of the joint estimation pseudo-linear model is as follows
h＝Aξ+Be (4)
Wherein,
Figure FDA0002278013400000021
Figure FDA0002278013400000022
Figure FDA0002278013400000023
Figure FDA0002278013400000024
Figure FDA0002278013400000025
Figure FDA0002278013400000026
Figure FDA0002278013400000027
Figure FDA0002278013400000028
Figure FDA0002278013400000029
Figure FDA00022780134000000210
Figure FDA00022780134000000211
Figure FDA00022780134000000212
Figure FDA00022780134000000213
Figure FDA00022780134000000214
Figure FDA00022780134000000215
and 4, step 4: obtaining a joint estimation value of a target state and a system deviation by adopting an iterative weighted least square algorithm;
step 4.1: and roughly estimating the target state and the system deviation by adopting a least square method, substituting the target state and the system deviation into a matrix B, and calculating the weight W ═ BQB-1；
Step 4.2: obtaining a joint estimation value of a target state and a system deviation by adopting a weighted least square estimation algorithm
Figure FDA0002278013400000031
Step 4.3, calculate estimate error covariance cov (Δ ξ) ═ aTWA)-1；
Step 5. consider the auxiliary variable
Figure FDA0002278013400000032
Figure FDA0002278013400000033
Correlation with target position and velocity, and joint estimation of step 4Value of
Figure FDA0002278013400000034
Wherein Δ ξ represents the estimation error of ξ, and the joint estimation value of the associated least squares algorithm to the step 4 is designed
Figure FDA0002278013400000035
The improvement is as follows:
step 5.1. order
Figure FDA0002278013400000036
Establishing auxiliary variables
Figure FDA0002278013400000037
Figure FDA0002278013400000038
And target position
Figure FDA0002278013400000039
And target speed
Figure FDA00022780134000000310
The relationship between
Figure FDA00022780134000000311
The associated least squares estimation model is constructed as follows
h1＝A1ξ1+B1Δξ (6)
Wherein,
Figure FDA00022780134000000312
Figure FDA00022780134000000313
Figure FDA00022780134000000314
Figure FDA00022780134000000315
Figure FDA00022780134000000316
Figure FDA00022780134000000317
Figure FDA00022780134000000318
Figure FDA0002278013400000041
Figure FDA0002278013400000042
Figure FDA0002278013400000043
step 5.2: obtaining a joint estimation value of a target state and a system deviation by adopting a weighted least square estimation algorithm
Figure FDA0002278013400000044
Wherein W1＝cov(Δξ)＝(ATWA)-1；
Step 5.3 calculation of estimation error covariance cov (Δ ξ)1)＝(A1 TW1A1)-1；
Step 6, considering the intermediate variable rhopAnd
Figure FDA0002278013400000045
and (5) constructing a correlation least square estimation model on the estimation result of the step (5) by using correlation constraint with the target position state, and further improving the estimation performance of the target state and the system deviation;
step 6.1: taking into account the intermediate variable pp,
Figure FDA0002278013400000046
Constraint relationship with target state
Figure FDA0002278013400000047
Figure FDA0002278013400000048
And step 5. estimation error
Figure FDA0002278013400000049
Selecting a target position square term, a product of a target position and a speed and a system error as variables, and constructing a correlation estimation model as follows
h2＝A2ξ2+B2Δξ1(7)
Wherein,
Figure FDA00022780134000000410
Figure FDA00022780134000000411
Figure FDA00022780134000000412
Figure FDA00022780134000000413
Figure FDA00022780134000000414
Figure FDA00022780134000000415
Figure FDA00022780134000000416
Figure FDA0002278013400000051
step 6.2: obtaining an estimate using a weighted least squares estimation algorithm
Figure FDA0002278013400000052
Wherein W2＝cov(Δξ1)＝(A1 TW1A1)-1；
Step 6.3: obtaining the position of the target p according to step 6.2
Figure FDA0002278013400000053
Square of
Figure FDA0002278013400000054
And
Figure FDA0002278013400000055
the square root operation is carried out on the obtained product to obtain the product
Figure FDA0002278013400000056
Wherein,
Figure FDA0002278013400000057
sgn (·) is a sign function;
according to the target position
Figure FDA0002278013400000058
Calculating a target velocity estimate
Figure FDA0002278013400000059
Step 7, substituting the system deviation estimated value into a double-base-distance and double-base-distance change rate measurement equation to correct the double-base-distance and double-base-distance change rate measurement;
step 7.1 the i +1 st iteration measurement information is
Figure FDA00022780134000000510
In the formula,
Figure FDA00022780134000000511
for the double base distance measurement after the ith correction,
Figure FDA00022780134000000512
is a measured value of the double-base distance change rate after the ith correction,
Figure FDA00022780134000000513
and
Figure FDA00022780134000000514
the system deviation estimation result of the ith time is obtained;
7.2, positioning the target based on the corrected double-base-distance measurement and the double-base-distance change rate measurement, and turning to the step 2; the above process is iterated until the system deviation estimate is satisfied
Figure FDA00022780134000000515
And is
Figure FDA00022780134000000516
ε1And ε2To allow for error, the algorithm iteration stops.
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CN111983572A (en) * 2020-06-30 2020-11-24 江西锐迪航空科技发展有限公司 Receiver error correction method based on position known radiation source
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