CN104375121A - Combined optimizing method of MIMO radar waveform and biased estimator based on prior information - Google Patents
Combined optimizing method of MIMO radar waveform and biased estimator based on prior information Download PDFInfo
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- CN104375121A CN104375121A CN201410039782.XA CN201410039782A CN104375121A CN 104375121 A CN104375121 A CN 104375121A CN 201410039782 A CN201410039782 A CN 201410039782A CN 104375121 A CN104375121 A CN 104375121A
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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
- 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
- G01S7/40—Means for monitoring or calibrating
-
- 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
- G01S7/42—Diversity systems specially adapted for radar
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- Radar, Positioning & Navigation (AREA)
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- Computer Networks & Wireless Communication (AREA)
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- General Physics & Mathematics (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
The invention discloses a combined optimizing method of an MIMO radar waveform and a biased estimator based on prior information in the clutter environment, wherein the parameter estimation performance of a point target is improved. The method includes the steps of firstly, establishing a combined optimizing model of the MIMO radar waveform and the biased estimator in the clutter scene; secondly, studying the combined optimizing problem of the MIMO radar waveform and the biased estimator under the weighted modulus constraint; thirdly, studying the combined optimizing problem of the MIMO radar waveform and the biased estimator under the spectral norm constraint; fourthly, solving the original optimizing problem through a convex optimization method. By means of the method, the MIMO radar parameter estimation performance is remarkably improved, the coordinate work capacity of an MIMO radar emitting end and an MIMO radar receiving end is enhanced, and the overall performance of an MIMO radar system is improved.
Description
Technical field
The invention belongs to signal transacting field, further relate under a kind of clutter environment based on the MIMO radar waveform of prior imformation and the combined optimization method of biased estimator, brightly significantly improve MIMO radar parameter estimation performance, enhance MIMO radar launching and receiving end harmoniously working capability, improve the overall performance of MIMO radar system.
Background technology
In the last few years, the optimization of MIMO radar waveform was subject to the attention of increasing scholar and slip-stick artist.According to the object module used in waveform optimization problem, current waveform optimization method can be divided into following two classes: (1) is based on the waveform optimization of point target (point target); (2) based on the waveform optimization of Extended target (extended target).Based on the Waveform Design of point target, the object of optimization is waveform Correlation Matrix (WCM, waveform covariance matrix) or radar ambiguity function (radar ambiguity function).Waveform optimization method based on WCM only designs the spatial domain of transmitted waveform instead of the overall feature of transmitted waveform.Specifically, the people such as D. R. Fuhrmann and G. S. Antonio designs to realize the distribution of specific energy spatial domain to WCM.And the people such as S. Peter have not only paid close attention to energy spatial domain and distribute, and have also contemplated that the spatial domain cross-correlation between different target, namely minimize spatial domain cross-correlation between different azimuth to improve the detection estimated performance of system.
Under the hypothesis that Received signal strength is not polluted by the clutter depending on transmitted waveform, the people such as J. Li propose the waveform optimization criterion of a few class based on CRB to optimize WCM thus the Parameter Estimation Precision of raising point target.But in many practical applications, the Received signal strength of radar system is inevitably subject to the impact of clutter.And what it is pointed out that CRB portrays is the lower bound of any minimum variance not utilizing the unbiased esti-mator device of prior imformation to reach.In fact, in Array Signal Processing field, usually have many prior imformations to utilize, these prior imformations can regard the constraint of parameter space to be estimated as.Some scholars are studied the Parameter Estimation Problem with prior imformation, and propose corresponding CRB, i.e. the so-called CRB(that is tied
constrainedcRB).Further, we know, biased estimator can obtain variance circle lower than unbiased esti-mator device usually.The CRB of biased estimator has been commonly called inclined CRB(
biasedcRB).In addition, biased estimator and prior imformation is utilized if combined, so variance circle of parameter estimation, compared to the CRB of unbiased esti-mator device, will the decline of highly significant.Ben-Haim Zvika and C. Eldar Yonina is studied variance circle under this scene, and obtaining so-called Constrained has inclined CRB(
constrained biasedcRB).In sum, from the angle of parameter estimation, comprehensive utilization prior imformation and biased estimator are studied the waveform optimization problem under clutter scene very has practical significance.
Summary of the invention
The object of the invention is to the problem considering to improve MIMO radar parameter estimation performance under Received signal strength is polluted scene by the clutter depending on transmitted waveform, propose under a kind of clutter environment based on the MIMO radar waveform of prior imformation and the combined optimization method of biased estimator, improve MIMO radar parameter estimation performance, enhance MIMO radar launching and receiving end harmoniously working capability, improve the overall performance of MIMO radar system.
Basic ideas of the present invention are as follows: first set up clutter scene and issue ejected wave shape and biased estimator combined optimization model.Under the weighting modular constraint and spectral norm constraint of biased estimator Jacobian matrix, partially retrain CRB(based on having
constrained biasedcRB), consider that WCM and biased estimator combined optimization problem are to improve parameter estimation performance.Due to the nonlinear problem that WCM and biased estimator combined optimization are more complicated, be difficult to solve, therefore, this combined optimization problem relaxes as convex optimization problem by we, thus semi definite programming (SDP) can be utilized to solve efficiently.On this basis, by the approximate optimum solution obtaining initial joint optimization problem under relaxation problem optimum solution least square meaning.Concrete steps are as follows:
(1) MIMO radar waveform and the modeling of biased estimator combined optimization
1a) MIMO radar Received signal strength modeling under clutter scene
Consider following MIMO radar system: transmitting, reception array number are respectively
,
; The
the baseband sampling of individual transmitting array element transmitted waveform is
, wherein
for fast umber of beats.Then whole emission array waveform can be expressed as
.What suppose transmitting is narrow band signal, and transmitting procedure does not have dispersion, and so under clutter scene, the Received signal strength of MIMO radar can be expressed as:
In formula,
for the reception data of system;
for the complex magnitude proportional with target RCS;
for interested rang ring internal object number;
represent the parameter of target.It is pointed out that
and
need from data
middle estimation.Section 2 on the right of above formula represents the clutter data that system receives;
expression is positioned at
clutter refection coefficient; And
(
) be clutter Space domain sampling number.On the right of upper equation, Section 3 is interference and noise, independent of clutter.
each row can be assumed to be independent same distribution, and to submit to average be 0 unknown covariance matrix is
the multiple Gaussian distribution of Cyclic Symmetry.
with
represent respectively
the reception of individual target and transmitting steering vector.
1b) Fisher information matrix is derived
Fisher information matrix (FIM)
can be expressed as follows:
In formula,
1c)
constrained biasedcRB derives
constrained biasedthe derivation of CRB is based on following prior imformation: target amplitude to be estimated is known, namely
In formula,
, and
.Based on this, the target parameter to be estimated that the present invention considers can be expressed as
In formula,
;
;
;
;
.
Based on above-mentioned discussion,
constrained biasedcRB can be expressed as
In formula,
it is right to represent
deviation during estimation.Matrix
for:
(2) MIMO radar waveform and biased estimator combined optimization
2a) under weighting modular constraint, MIMO radar waveform and biased estimator combined optimization problem describe and solve
A. based on mark optimization (Trace-opt) criterion, this combined optimization problem is considered
Under total emission power constraint, this combined optimization problem can be expressed as
This nonlinear optimal problem can relax as following SDP problem:
B. feature based vector optimization (Eigen-opt) criterion, considers this combined optimization problem
Similar with the situation of Trace-opt criterion, optimization problem can be expressed as following SDP problem
2b) under spectral norm constraint, MIMO radar waveform and biased estimator combined optimization problem describe and solve
A. based on Trace-opt criterion, this combined optimization problem is considered
Similar with weighting modular constraint situation, the SDP that can obtain this problem is expressed as:
B. based on Eigen-opt criterion, this combined optimization problem is considered
Similar with weighting modular constraint situation, the SDP that can obtain this problem is expressed as:
(3) original optimization problem is solved under least square meaning
3a) under least square meaning, foundation solves original optimization problem model
Given
,
can by right
approaching under least square meaning obtains, namely
3b) based on the original optimization problem of convex Optimization Method
The present invention compared with prior art has the following advantages:
The first, under clutter scene, based on prior imformation, proposition transmitted waveform and biased estimator combined optimization method are to improve MIMO radar parameter estimation performance.The method based on weighting modular constraint and spectral norm constraint, with Trace-opt criterion and Eigen-opt criterion for Optimality Criteria, with
constrained biasedcRB is objective function, by combined optimization WCM and biased estimator, to obtaining the parameter estimation variance far below unbiased esti-mator device, thus improves Parameter Estimation Precision.
The second, because this combined optimization problem is nonlinearity function, thus compares and be difficult to solve.This problem relaxes as convex optimization problem by the present invention, thus convex optimization method can be utilized to carry out Efficient Solution to this problem.But, solve the solution that this convex problem directly can not obtain original optimization problem.Therefore, the present invention passes through the best approximation under SDP Optimum Solution least square meaning to obtain the optimum solution of primal problem.
Accompanying drawing explanation
Fig. 1 is the process flow diagram that the present invention realizes;
Fig. 2 and Fig. 3 be parameter estimation error free time CRB;
Fig. 4 and Fig. 5 is that biased estimator and prior imformation are respectively on the impact of CRB;
Fig. 6 is the impact of parameter estimating error on CRB.
Embodiment
Below in conjunction with accompanying drawing 1, performing step of the present invention is described in further detail.
step 1:mIMO radar waveform and biased estimator combined optimization model under establishment clutter environment
1a) MIMO radar Received signal strength modeling under clutter scene
1b) Fisher information matrix is derived
Fisher information matrix (FIM)
can be expressed as follows:
In formula,
1c)
constrained biasedcRB derives
constrained biasedthe derivation of CRB is based on following prior imformation: target amplitude to be estimated is known, namely
In formula,
, and
.Based on this, the target parameter to be estimated that the present invention considers can be expressed as
In formula,
;
;
;
;
.
Based on above-mentioned discussion,
constrained biasedcRB can be expressed as
In formula,
it is right to represent
deviation during estimation.Matrix
for:
step 2: the statement of MIMO radar waveform and biased estimator combined optimization problem with solve
2a) under weighting modular constraint, MIMO radar waveform and biased estimator combined optimization problem describe and solve
A. based on mark optimization (Trace-opt) criterion, this combined optimization problem is considered
Under total emission power constraint, this combined optimization problem can be expressed as
This nonlinear optimal problem can relax as following SDP problem:
B. feature based vector optimization (Eigen-opt) criterion, considers this combined optimization problem
Similar with the situation of Trace-opt criterion, optimization problem can be expressed as following SDP problem
2b) under spectral norm constraint, MIMO radar waveform and biased estimator combined optimization problem describe and solve
A. based on Trace-opt criterion, this combined optimization problem is considered
Similar with weighting modular constraint situation, the SDP that can obtain this problem is expressed as:
B. based on Eigen-opt criterion, this combined optimization problem is considered
Similar with weighting modular constraint situation, the SDP that can obtain this problem is expressed as:
step 3:original optimization problem is solved under least square meaning
3a) under least square meaning, foundation solves original optimization problem model
Given
,
can by right
approaching under least square meaning obtains, namely
3b) based on the original optimization problem of convex Optimization Method
Effect of the present invention further illustrates by following emulation:
Simulated conditions: launch array number
, receive array number
, hits
.In following experiment, we adopt the MIMO radar system of following two class difference configurations: MIMO radar (0.5,0.5) and MIMO radar (2.5,0.5) distance that two numerical value, in bracket represent each systems radiate respectively and receive between array element in units of half-wavelength.Under weighting modular constraint scene, make weighting matrix
and
; And in spectral norm situation, order
and
.Two targets with unit amplitude are had in the rang ring that this experiment is considered.Under MIMO radar (0.5,0.5) condition, two targets lay respectively at:
with
; And for MIMO radar (2.5,0.5),
with
.Array signal to noise ratio (S/N ratio) (ASNR) is defined as
, wherein
for the variance of additive white noise.In experiment below,
.Clutter in experiment can carry out modeling with discrete point.Discrete point can obtain by uniform sampling on rang ring, and hits is
.The RCS independent same distribution of discrete point, obeying average is 0, and variance is
gaussian distribution.And suppose that RCS is unchanged within the Coherent processing time (CPI).Miscellaneous noise ratio (CNR) is defined as
, span is in an experiment
.In position
have dry the making an uproar than (AINR) of array to be the strong jamming of 60 dB, AINR be defined as jamming power with
long-pending with
ratio.
Emulation 1: suppose that the estimates of parameters that calculating constrained biased CRB uses does not have error.Under ASNR=50 dB and CNR=10 dB condition, the optimum transmitting pattern obtained based on Trace-opt criterion as shown in Figures 2 and 3.In fig. 2, a dark depression has been there is in the position of closely disturbing.And it is comparatively large that two targets obtain power difference, this is overall CRB owing to minimizing target in institute's extracting method, instead of the CRB of single parameter.Therefore for some parameters, compared to irrelevant waveform, the CRB that institute's extracting method obtains may be larger.But for overall CRB, the CRB of institute's extracting method is then much smaller than irrelevant waveform.The curve that the overall CRB that Fig. 3 obtains for institute's extracting method and irrelevant waveform changes with ASNR or CNR.Can find out that the CRB that two kinds of methods obtain reduces along with the increase of ASNR, and increase along with the increase of CNR.Further, no matter why ASNR and CNR is worth, and the CRB that institute's extracting method obtains is significantly less than irrelevant waveform.Can also see, under identical modular constraint condition, Trace-opt criterion, compared to Eigen-opt criterion, can obtain lower CRB.In addition, by comparison diagram 3 (a) and (c) or Fig. 3 (b) and (d), the CRB obtained under known MIMO radar (2.5,0.5) scene will much smaller than MIMO radar (0.5,0.5).This is that the virtual aperture formed due to MIMO radar (2.5,0.5) is greater than MIMO radar (0.5,0.5)
Emulation 2, in this test, we by research biased estimator and prior imformation respectively on the impact of CRB, to verify that herein institute's extracting method utilizes the validity of biased estimator and prior imformation.
In Fig. 4, suppose only to use biased estimator in institute's extracting method.So, in this scene, matrix can be made
equal unit matrix, other parameter remains unchanged.As previously mentioned, the CRB under this situation and so-calledly have inclined CRB.Fig. 5 is the change curve of CRB with ASNR or CNR.Can find out, generally, optimum biased estimator can obtain the CRB less than uncorrelated waveform, and also can obtain the CRB larger than uncorrelated waveform under partial picture.This is not mainly because the CRB of target amplitude takes at this.If consider that target amplitude CRB is interior, so optimum biased estimator can obtain the CRB less than uncorrelated waveform in any case.In Fig. 5, we consider that institute's extracting method only utilizes the situation of prior imformation.In such a scenario, can make
for null matrix, and other parameter remains unchanged.Corresponding to the CRB of this scene, i.e. so-called constraint CRB.The CRB that Fig. 4 obtains for institute's extracting method under this kind of scene is with the change curve of ASNR or CNR.Can find out, the contribution of prior imformation to two design criterias is about the same, and compared with uncorrelated waveform, can significantly improve Parameter Estimation Precision.
Emulation 3: in this test, we study angle or clutter evaluated error to the impact of overall CRB.It is pointed out that this experiment is defined as follows the relative error that clutter is estimated: the ratio of clutter power evaluated error and accurate clutter power.
Fig. 6 be under ASNR=-10 dB and CNR=50 dB condition CRB with the change curve of angle or clutter evaluated error.As can be seen from the figure, with two class error changes clearly, this illustrates that institute's extracting method is more responsive to parameter estimating error to CRB.And in practical engineering application, parameter estimating error is inevitable.Therefore, in research process afterwards, for making the method for proposition more press close to use, sane waveform optimization method is highly paid close attention to.
Claims (1)
1., based on the MIMO radar waveform of prior imformation and the combined optimization method of biased estimator, it is characterized in that, comprise the steps:
(1) MIMO radar waveform and the modeling of biased estimator combined optimization
1a) MIMO radar Received signal strength modeling under clutter scene
Consider following MIMO radar system: transmitting, reception array number are respectively
,
; The
the baseband sampling of individual transmitting array element transmitted waveform is
, wherein
for fast umber of beats, then whole emission array waveform can be expressed as
,
What suppose transmitting is narrow band signal, and transmitting procedure does not have dispersion, and so under clutter scene, the Received signal strength of MIMO radar can be expressed as:
In formula,
for the reception data of system;
for the complex magnitude proportional with target RCS;
for interested rang ring internal object number;
represent the parameter of target,
and
need from data
middle estimation, the Section 2 on the right of above formula represents the clutter data that system receives,
expression is positioned at
clutter refection coefficient; And
(
) be clutter Space domain sampling number, on the right of upper equation, Section 3 is interference and noise, independent of clutter,
each row can be assumed to be independent same distribution, and to submit to average be 0 unknown covariance matrix is
the multiple Gaussian distribution of Cyclic Symmetry,
with
represent respectively
the reception of individual target and transmitting steering vector;
1b) Fisher information matrix is derived
Fisher information matrix (FIM)
can be expressed as follows:
In formula,
1c)
constrained biasedcRB derives
constrained biasedthe derivation of CRB is based on following prior imformation: target amplitude to be estimated is known, namely
In formula,
, and
,
Based on this, target parameter to be estimated can be expressed as:
In formula,
;
;
;
;
;
Based on above-mentioned discussion,
constrained biasedcRB can be expressed as:
In formula,
it is right to represent
deviation during estimation, matrix
for:
(2) MIMO radar waveform and biased estimator combined optimization
2a) under weighting modular constraint, MIMO radar waveform and biased estimator combined optimization problem describe and solve
A. based on mark optimization (Trace-opt) criterion, this combined optimization problem is considered
Under total emission power constraint, this combined optimization problem can be expressed as:
This nonlinear optimal problem can relax as following SDP problem:
B. feature based vector optimization (Eigen-opt) criterion, considers this combined optimization problem
Similar with the situation of Trace-opt criterion, optimization problem can be expressed as following SDP problem
2b) under spectral norm constraint, MIMO radar waveform and biased estimator combined optimization problem describe and solve
A. based on Trace-opt criterion, consider this combined optimization problem and weighting modular constraint situation similar, the SDP that can obtain this problem is expressed as:
B. based on Eigen-opt criterion, consider this combined optimization problem and weighting modular constraint situation similar, the SDP that can obtain this problem is expressed as:
(3) original optimization problem is solved under least square meaning
3a) under least square meaning, foundation solves original optimization problem model
Given
,
can by right
approaching under least square meaning obtains, namely
3b) based on the original optimization problem of convex Optimization Method
。
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| CN104808180A (en) * | 2015-04-09 | 2015-07-29 | 大连大学 | Steady waveform optimizing method for MIMO radar in clutter background |
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| CN109459727A (en) * | 2018-12-12 | 2019-03-12 | 南京航空航天大学 | Based on the stealthy radar of radio frequency-communication association system optimum waveform design method |
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Application publication date: 20150225 |