CN103852750A - Robust MIMO radar waveform optimization method for improving worst estimated performance - Google Patents

Robust MIMO radar waveform optimization method for improving worst estimated performance Download PDF

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CN103852750A
CN103852750A CN201410039791.9A CN201410039791A CN103852750A CN 103852750 A CN103852750 A CN 103852750A CN 201410039791 A CN201410039791 A CN 201410039791A CN 103852750 A CN103852750 A CN 103852750A
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optimization
sane
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王洪雁
裴炳南
张玉霞
白云峰
裴腾达
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Dalian 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
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Abstract

The invention discloses a robust MIMO radar waveform optimization method for improving worst estimated performance. The method is used for improving the performance of an MIMO radar system. The method includes the steps that firstly, a robust MIMO radar waveform optimization model is built; secondly, robust waveform optimization is carried out based on the Det-opt principle and the Trace-opt principle. According to the method, parameter estimation errors are explicitly introduced into the waveform optimization problem, transmitted waveforms and the parameter estimation errors are jointly optimized, and therefore the robustness of the waveform optimization method is improved. The parameter estimation performance of the method in worst cases can be greatly improved, the sensitivity of the waveform optimization method to the parameter estimation errors can be significantly reduced, and therefore the method has strong practicality in engineering.

Description

Improve the method that the robust M IMO radar waveform of poor estimated performance is optimized
Technical field
The invention belongs to radar signal processing field, further relate to a kind of raising robust M IMO radar waveform optimization method of poor estimated performance.Institute's extracting method, by parameter estimating error explicitly is covered in waveform optimization problem, carries out combined optimization to transmitted waveform and parameter estimating error, thereby improves the sane performance of waveform optimization method.The method can significantly improve the parameter estimation performance under worst case, thereby can significantly reduce the susceptibility of waveform optimization method to parameter estimating error, thereby has good engineering practicability.
Background technology
In the last few years, the optimization of MIMO radar waveform was subject to increasing scholar and slip-stick artist's attention.According to the object module using in waveform optimization problem, current waveform optimization method can be divided into following two classes: (1) waveform optimization based on point target (point target); (2) waveform optimization based on expansion 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 the WCM only overall feature of the spatial domain to transmitted waveform rather than transmitted waveform designs.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 have distributed, and consider the spatial domain simple crosscorrelation between different target, minimize spatial domain simple crosscorrelation between different azimuth to improve the detection estimated performance of system.
From the above document about waveform optimization, optimization problem solve the explicit value that depends on target and scene parameter.And in actual applications, about the value of target and scene parameter can not be known in advance, if can know in advance, just there is no need to optimize waveform to improve Parameter Estimation Precision.Usually, about the value of target and scene parameter needs to estimate by certain method of estimation in actual applications, thereby inevitably there is evaluated error.In engineering application, waveform optimization is based upon on these estimated value bases.Therefore, waveform optimization method should be used for saying with regard to particular importance to engineering to whether parameter estimating error is responsive.If optimization method is more responsive to parameter estimating error, the waveform based on a certain group of estimates of parameters optimization may will make parameter estimation degradation under other one group of more rational estimated value condition, and this waveform optimization method does not just have practicality so.Thereby, from engineering application, must consider the waveform optimization method of the raising Parameter Estimation Precision based on estimates of parameters.
Summary of the invention
The present invention is directed to the problems referred to above, considered the waveform optimization method of the raising Parameter Estimation Precision based on estimates of parameters in actual conditions, in other words, consider to improve the sane waveform optimization method of Parameter Estimation Precision.
Realizing basic ideas of the present invention is, by parameter estimating error explicitly is covered in waveform optimization problem, transmitted waveform and parameter estimating error is carried out to combined optimization, thereby improves the sane performance of waveform optimization method.Due to the complicacy based on the sane waveform optimization of CRB, first utilize MATRIX INEQUALITIES that optimization problem is relaxed, then utilize the method for iteration alternately to optimize transmitted waveform and parameter estimating error.It is pointed out that iteration can be expressed as SDP problem each time, thereby can be solved efficiently.
The present invention considers based on constraint CRB( constrainedcramer-Rao Bound) improve the sane waveform optimization problem of Parameter Estimation Precision.Due to based on constrainedthe nonlinear problem that the sane waveform optimization problem of CRB is more complicated, is very difficult to apply protruding Optimization Method, and therefore the present invention utilizes the famous inequalities in matrix theory to relax to this problem.For this relaxation problem, the present invention proposes a kind of iterative algorithm with the CRB under optimization worst case under the convex set scene being uncertain of parameter formation.This algorithm can be converted into positive semidefinite planning (SDP) problem in iteration each time, thereby can utilize ripe Optimization Toolbox to carry out Efficient Solution.Compared with uncorrelated waveform, emulation experiment shows, institute's extracting method can significantly improve the parameter estimation performance under worst case, thereby can significantly reduce the susceptibility of waveform optimization method to parameter estimating error, thereby has good engineering practicability.Concrete steps are as follows:
(1) robust M IMO radar waveform Optimization Modeling
1a) statement MIMO radar return signal
Consider following MIMO radar system: transmitting, reception array number are respectively
Figure 148911DEST_PATH_IMAGE001
,
Figure 905514DEST_PATH_IMAGE002
; The
Figure 632774DEST_PATH_IMAGE003
the baseband sampling of individual transmitting array element transmitted waveform is
Figure 474828DEST_PATH_IMAGE004
, wherein
Figure 683087DEST_PATH_IMAGE005
for fast umber of beats.The waveform of whole emission array can be expressed as
Figure 497459DEST_PATH_IMAGE006
.What suppose transmitting is narrow band signal, and transmitting procedure do not have dispersion, and the reception signal of MIMO radar can be expressed as so:
Figure 382238DEST_PATH_IMAGE007
In formula,
Figure 462321DEST_PATH_IMAGE008
for system receives data;
Figure 723538DEST_PATH_IMAGE009
for complex magnitude proportional to target RCS;
Figure 205466DEST_PATH_IMAGE010
for the target numbers in rang ring interested;
Figure 198830DEST_PATH_IMAGE011
represent the parameter of target.It is pointed out that
Figure 15476DEST_PATH_IMAGE009
and
Figure 562608DEST_PATH_IMAGE011
need to be from data middle estimation.The Section 2 on above formula the right is for disturbing and noise.
Figure 391203DEST_PATH_IMAGE013
each row can be assumed to be independent same distribution, and to submit to average be that 0 unknown covariance matrix is
Figure 695146DEST_PATH_IMAGE014
the multiple Gaussian distribution of Cyclic Symmetry.
Figure 970269DEST_PATH_IMAGE015
with
Figure 426789DEST_PATH_IMAGE016
represent respectively
Figure 824273DEST_PATH_IMAGE017
the reception of individual target and transmitting steering vector.
1b) constrainedcRB derives
In formula,
Figure 507375DEST_PATH_IMAGE019
Figure 815472DEST_PATH_IMAGE020
Wherein,
Figure 587119DEST_PATH_IMAGE021
,
Figure 600074DEST_PATH_IMAGE022
and
Figure 357946DEST_PATH_IMAGE023
.
1c)
Figure 523479DEST_PATH_IMAGE017
the matrix modeling of individual target physical channel
Figure 528344DEST_PATH_IMAGE024
In formula,
Figure 779328DEST_PATH_IMAGE025
with
Figure 199945DEST_PATH_IMAGE026
be respectively
Figure 734832DEST_PATH_IMAGE017
the Jacobian matrix of the true and hypothesis access matrix of individual target, and
Figure 658401DEST_PATH_IMAGE027
for the difference between the two, can suppose that it belongs to the following convex set that knows
Figure 645948DEST_PATH_IMAGE028
For preventing that singularity from occurring, order
Figure 683306DEST_PATH_IMAGE029
1d) sane waveform optimization problem statement
The sane waveform optimization problem of improving parameter estimation performance can be expressed as follows: by optimizing WCM with in convex set
Figure 807120DEST_PATH_IMAGE030
and under total transmit power constraint, minimize the CRB under worst case (worst-case),
In formula,
Figure 379363DEST_PATH_IMAGE032
for total emissive power.Section 3 constraint be due to each transmitting array element in practice emissive power can not be less than 0.In formula,
Figure 220412DEST_PATH_IMAGE033
be about constrainedthe function of CRB.
(2) the sane waveform optimization based on two class criterions
2a) based on trace-optthe sane waveform optimization of criterion
A. based on trace-optthe sane waveform optimization problem statement of criterion
Figure 464311DEST_PATH_IMAGE034
B. the internal layer optimization problem based on relaxation method
Based on relaxation method, this sane waveform optimization problem can be expressed equivalently as following SDP problem:
Figure 464104DEST_PATH_IMAGE035
In formula,
Figure 426243DEST_PATH_IMAGE036
,
Figure 992354DEST_PATH_IMAGE037
,
Figure 107072DEST_PATH_IMAGE038
Figure 529963DEST_PATH_IMAGE039
,
Figure 730131DEST_PATH_IMAGE040
C. outer optimization problem
By what obtain
Figure 99932DEST_PATH_IMAGE041
the sane optimization problem of substitution,
Figure 52845DEST_PATH_IMAGE042
can obtain by solving following SDP,
Figure 662949DEST_PATH_IMAGE043
D. the sane optimization problem based on iteration optimization
Based on above-mentioned analysis, can be by fixing solve , also can
Figure 414149DEST_PATH_IMAGE041
solve
Figure 382105DEST_PATH_IMAGE042
.Thus, we can propose a kind of iterative algorithm with right
Figure 291287DEST_PATH_IMAGE041
with
Figure 65208DEST_PATH_IMAGE042
replace optimization, thereby can improve the parameter estimation performance under worst condition.Arthmetic statement is as follows:
algorithm:given initial WCM, based on trace-optcriterion,
Figure 743445DEST_PATH_IMAGE041
and
Figure 944619DEST_PATH_IMAGE042
can replace optimization by following steps:
1. solve internal layer SDP problem and obtain optimum
Figure 341096DEST_PATH_IMAGE041
.
2. will obtain the sane optimization problem of substitution, solves outer SDP problem to obtain
Figure 638403DEST_PATH_IMAGE042
.
Repeating step 1,2 until CRB no longer obviously reduce.
2b) based on det-optthe sane waveform optimization of criterion
A. based on det-optthe sane waveform optimization problem statement of criterion
Figure 758281DEST_PATH_IMAGE044
B. the internal layer optimization problem based on relaxation method
Based on relaxation method, this sane waveform optimization problem can be expressed equivalently as be similar to based on trace-optthe internal layer SDP optimization problem of criterion.
C. outer optimization problem
By what obtain
Figure 704371DEST_PATH_IMAGE041
the sane optimization problem of substitution,
Figure 820095DEST_PATH_IMAGE042
can obtain by solving following SDP,
D. the sane optimization problem based on iteration optimization
Be similar to trace-optcriterion, for det-optcriterion, we can replace optimization by alternative manner
Figure 15901DEST_PATH_IMAGE041
with
Figure 308342DEST_PATH_IMAGE042
to improve the Parameter Estimation Precision under worst condition, step with based on trace-optcriterion is identical, repeats no more.
 
The present invention compared with prior art has the following advantages:
The first, the present invention, from engineering application reality, to relatively sensitive issue of parameter estimating error, has considered to improve based on CRB the sane waveform optimization problem of Parameter Estimation Precision for existing waveform optimization method.By parameter estimating error explicitly is covered in waveform optimization problem, transmitted waveform and parameter estimating error are carried out to combined optimization, thereby improve the sane performance of waveform optimization method.
The second, due to the nonlinear problem that this sane waveform optimization problem is more complicated, be very difficult to apply protruding Optimization Method, therefore we utilize the famous inequalities in matrix theory to relax to this problem.For this relaxation problem, the present invention proposes a kind of iterative algorithm with the CRB under optimization worst case under the convex set scene being uncertain of parameter formation.This algorithm can be converted into SDP problem in iteration each time, thereby can utilize ripe Optimization Toolbox to carry out Efficient Solution.
Accompanying drawing explanation
Fig. 1 is the process flow diagram that the present invention realizes;
Fig. 2 is that angle estimation exists the optimum transmitting pattern obtaining under ASNR=10 dB condition under error scene;
There is CRB under the worst condition that institute's extracting method of the present invention under error scene and uncorrelated waveform the obtain change curve with ASNR for angle estimation in Fig. 3;
Fig. 4 is that transmitting receiving array exists the optimum transmitting pattern obtaining under ASNR=10 dB condition under correction error scene;
There is CRB under the worst condition that institute's extracting method of the present invention under correction error scene and uncorrelated waveform the obtain change curve with ASNR for transmitting receiving array in Fig. 5.
Embodiment
Below in conjunction with accompanying drawing 1, performing step of the present invention is described in further detail.
Step 1: robust M IMO radar waveform Optimization Modeling
1a) statement MIMO radar return signal
The reception signal of MIMO radar can be expressed as:
Figure 978489DEST_PATH_IMAGE007
1b) constrainedcRB derives
Figure 735092DEST_PATH_IMAGE018
In formula,
Figure 196773DEST_PATH_IMAGE019
Figure 242090DEST_PATH_IMAGE020
Wherein,
Figure 699616DEST_PATH_IMAGE021
,
Figure 123775DEST_PATH_IMAGE022
and
Figure 24866DEST_PATH_IMAGE023
.
1c) the matrix modeling of individual target physical channel
In formula,
Figure 769465DEST_PATH_IMAGE025
with
Figure 90725DEST_PATH_IMAGE026
be respectively
Figure 655174DEST_PATH_IMAGE017
the Jacobian matrix of the true and hypothesis access matrix of individual target, and
Figure 392186DEST_PATH_IMAGE027
for the difference between the two, can suppose that it belongs to the following convex set that knows
1d) sane waveform optimization problem statement
The sane waveform optimization problem of improving parameter estimation performance can be expressed as follows: by optimizing WCM with in convex set and under total transmit power constraint, minimize the CRB under worst case (worst-case),
Step 2: based on the sane waveform optimization of two class criterions
2a) based on trace-optthe sane waveform optimization of criterion
A. based on trace-optthe sane waveform optimization problem statement of criterion
Figure 612897DEST_PATH_IMAGE034
B. the internal layer optimization problem based on relaxation method
Based on relaxation method, this sane waveform optimization problem can be expressed equivalently as following SDP problem:
In formula,
Figure 529217DEST_PATH_IMAGE036
,
Figure 258139DEST_PATH_IMAGE037
,
Figure 147073DEST_PATH_IMAGE038
Figure 707367DEST_PATH_IMAGE039
,
Figure 26484DEST_PATH_IMAGE040
C. outer optimization problem
By what obtain
Figure 305019DEST_PATH_IMAGE041
the sane optimization problem of substitution,
Figure 574DEST_PATH_IMAGE042
can obtain by solving following SDP,
D. the sane optimization problem based on iteration optimization
Based on above-mentioned analysis, can be by fixing
Figure 170972DEST_PATH_IMAGE042
solve , also can
Figure 901960DEST_PATH_IMAGE041
solve .Thus, we can propose a kind of iterative algorithm with right
Figure 284717DEST_PATH_IMAGE041
with
Figure 22997DEST_PATH_IMAGE042
replace optimization, thereby can improve the parameter estimation performance under worst condition.Arthmetic statement is as follows:
algorithm:given initial WCM, based on trace-optcriterion,
Figure 122671DEST_PATH_IMAGE041
and
Figure 512064DEST_PATH_IMAGE042
can replace optimization by following steps:
1. solve internal layer SDP problem and obtain optimum
Figure 796415DEST_PATH_IMAGE041
.
2. will obtain
Figure 84308DEST_PATH_IMAGE041
the sane optimization problem of substitution, solves outer SDP problem to obtain .
Repeating step 1,2 until CRB no longer obviously reduce.
2b) based on det-optthe sane waveform optimization of criterion
A. based on det-optthe sane waveform optimization problem statement of criterion
Figure 900747DEST_PATH_IMAGE044
B. the internal layer optimization problem based on relaxation method
Based on relaxation method, this sane waveform optimization problem can be expressed equivalently as be similar to based on trace-optthe internal layer SDP optimization problem of criterion.
C. outer optimization problem
By what obtain
Figure 355999DEST_PATH_IMAGE041
the sane optimization problem of substitution,
Figure 68871DEST_PATH_IMAGE042
can obtain by solving following SDP,
D. the sane optimization problem based on iteration optimization
Be similar to trace-optcriterion, for det-optcriterion, we can replace optimization by alternative manner
Figure 733388DEST_PATH_IMAGE041
with
Figure 172590DEST_PATH_IMAGE042
to improve the Parameter Estimation Precision under worst condition, step with based on trace-optcriterion is identical, repeats no more.
Effect of the present invention can further illustrate by following emulation:
Simulated conditions: transmitting array number is set , receive array number , hits .In following experiment, we adopt the MIMO radar system of the different configurations of following two classes: MIMO radar (0.5,0.5) and MIMO radar (1.5,0.5), two numerical value in bracket represent that respectively each system transmits and receives the distance take wavelength as unit between array element.The target with unit amplitude is positioned at:
Figure 364964DEST_PATH_IMAGE049
.Array signal to noise ratio (S/N ratio) (ASNR, array signal-to-noise ratio) is defined as
Figure 36117DEST_PATH_IMAGE050
, wherein
Figure 209609DEST_PATH_IMAGE051
for the variance of additive white noise.In experiment below,
Figure 95657DEST_PATH_IMAGE052
.In experiment scene in position
Figure 876662DEST_PATH_IMAGE053
having dry making an uproar than (AINR) of array is the strong jamming of 60 dB, AINR be defined as jamming power with
Figure 35111DEST_PATH_IMAGE002
long-pending with
Figure 294185DEST_PATH_IMAGE051
ratio.Interference can be modeled as point source, transmitting and the incoherent white Gaussian signal of MIMO radar waveform.
For than the validity of more comprehensive inspection institute extracting method, in experiment below, we consider two scenes:
Only have the scene of angle estimation error, and there is the scene of correction error in transmitting receiving array.Due to trace-optwith det-optcriterion is of equal value under the condition of only having a target, and therefore, at this, we only consider trace-optcriterion.
Emulation 1: suppose that angle estimation error is
Figure 487269DEST_PATH_IMAGE054
, can obtain
Figure 459683DEST_PATH_IMAGE055
.Through can be calculated for MIMO radar (0.5,0.5), can obtain
Figure 43111DEST_PATH_IMAGE056
, and for MIMO radar (1.5,0.5),
Figure 355144DEST_PATH_IMAGE057
.Fig. 2 be based on trace-optthe optimum transmitting pattern that criterion obtains under ASNR=10 dB condition.Can see that institute's extracting method placed a spike at target proximity, this means that the parameter estimation performance under worst case can improve.Meanwhile, for MIMO radar (1.5,0.5), occur in the drawings graing lobe, this is the transmitting array element configuration sparse due to this radar.CRB under the worst condition that Fig. 3 obtains for institute's extracting method and uncorrelated waveform is with the change curve of ASNR.Can see, the CRB obtaining reduces with the increase of ASNR.And with respect to uncorrelated waveform, the CRB that institute's extracting method obtains is significantly little.In addition along with the increase of ASNR, the CRB that institute's extracting method obtains with uncorrelated waveform is consistent gradually.
Emulation 2: suppose that transmitting and receiving array exist correction error (such as array element phase place, amplitude and site error).This correction error can be portrayed in the following manner: each element of transmitting receiving array steering vector is obeyed zero-mean, and variance is
Figure 153467DEST_PATH_IMAGE058
the noise pollution of multiple Gaussian distribution.Through emulation, can obtain, for MIMO radar (0.5,0.5), ; And for MIMO radar (1.5,0.5),
Figure 409316DEST_PATH_IMAGE060
.By Fig. 4,5 conclusions and Fig. 2,3 is similar, repeats no more.

Claims (1)

1. improve the method that the robust M IMO radar waveform of poor estimated performance is optimized, it is characterized in that, comprise the steps:
(1) robust M IMO radar waveform Optimization Modeling
1a) statement MIMO radar return signal
The reception signal of MIMO radar can be expressed as:
Figure 2014100397919100001DEST_PATH_IMAGE001
1b) constrainedcRB derives
Figure DEST_PATH_IMAGE002
In formula,
Figure 2014100397919100001DEST_PATH_IMAGE003
Wherein,
Figure 2014100397919100001DEST_PATH_IMAGE005
,
Figure 2014100397919100001DEST_PATH_IMAGE006
and
Figure 2014100397919100001DEST_PATH_IMAGE007
;
1c)
Figure DEST_PATH_IMAGE008
the matrix modeling of individual target physical channel
Figure 2014100397919100001DEST_PATH_IMAGE009
In formula,
Figure DEST_PATH_IMAGE010
with be respectively
Figure 402310DEST_PATH_IMAGE008
the Jacobian matrix of the true and hypothesis access matrix of individual target, and
Figure DEST_PATH_IMAGE012
for the difference between the two, can suppose that it belongs to the following convex set that knows
Figure 2014100397919100001DEST_PATH_IMAGE013
1d) sane waveform optimization problem statement
The sane waveform optimization problem of improving parameter estimation performance can be expressed as follows: by optimizing WCM with in convex set
Figure DEST_PATH_IMAGE014
and under total transmit power constraint, minimize the CRB under worst case (worst-case),
Figure 2014100397919100001DEST_PATH_IMAGE015
(2) the sane waveform optimization based on two class criterions
2a) based on trace-optthe sane waveform optimization of criterion
A. based on trace-optthe sane waveform optimization problem statement of criterion
Figure DEST_PATH_IMAGE016
B. the internal layer optimization problem based on relaxation method
Based on relaxation method, this sane waveform optimization problem can be expressed equivalently as following SDP problem:
Figure 2014100397919100001DEST_PATH_IMAGE017
In formula,
Figure DEST_PATH_IMAGE018
,
Figure 2014100397919100001DEST_PATH_IMAGE019
,
Figure DEST_PATH_IMAGE020
Figure 2014100397919100001DEST_PATH_IMAGE021
,
Figure DEST_PATH_IMAGE022
C. outer optimization problem
By what obtain the sane optimization problem of substitution,
Figure DEST_PATH_IMAGE024
can obtain by solving following SDP,
D. the sane optimization problem based on iteration optimization
Based on above-mentioned analysis, can be by fixing
Figure 254203DEST_PATH_IMAGE024
solve
Figure 971624DEST_PATH_IMAGE023
, also can
Figure 803051DEST_PATH_IMAGE023
solve
Figure 555107DEST_PATH_IMAGE024
, thus, a kind of iterative algorithm can be proposed with right
Figure 315252DEST_PATH_IMAGE023
with replace optimization, thereby can improve the parameter estimation performance under worst condition;
Arthmetic statement is as follows:
algorithm:given initial WCM, based on trace-optcriterion,
Figure 175595DEST_PATH_IMAGE023
and
Figure 782157DEST_PATH_IMAGE024
can replace optimization by following steps:
Solve internal layer SDP problem and obtain optimum
Figure 713204DEST_PATH_IMAGE023
;
By what obtain
Figure 405216DEST_PATH_IMAGE023
the sane optimization problem of substitution, solves outer SDP problem to obtain
Figure 578446DEST_PATH_IMAGE024
;
Repeating step 1,2 until CRB no longer obviously reduce;
2b) based on det-optthe sane waveform optimization of criterion
A. based on det-optthe sane waveform optimization problem statement of criterion:
Figure DEST_PATH_IMAGE026
B. the internal layer optimization problem based on relaxation method
Based on relaxation method, this sane waveform optimization problem can be expressed equivalently as be similar to based on trace-optthe internal layer SDP optimization problem of criterion
C. outer optimization problem
By what obtain
Figure 39514DEST_PATH_IMAGE023
the sane optimization problem of substitution,
Figure 407042DEST_PATH_IMAGE024
can obtain by solving following SDP,
Figure 2014100397919100001DEST_PATH_IMAGE027
D. the sane optimization problem based on iteration optimization
Be similar to trace-optcriterion, for det-optcriterion, replaces optimization by alternative manner with
Figure 175988DEST_PATH_IMAGE024
to improve the Parameter Estimation Precision under worst condition, step with based on trace-optcriterion is identical.
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CN105319545A (en) * 2015-11-09 2016-02-10 大连大学 MIMO radar waveform design method for improving STAP detection performance
CN105319545B (en) * 2015-11-09 2018-05-04 大连大学 Improve the MIMO-OFDM radar waveform design methods of STAP detection performances
CN105974391A (en) * 2016-04-28 2016-09-28 大连大学 MIMO (multiple-input multiple-output) radar robust waveform design method with target prior knowledge unknown
CN105807275A (en) * 2016-04-28 2016-07-27 大连大学 MIMO-OFDM-STAP steady waveform design method based on partial clutter priori knowledge
CN105974391B (en) * 2016-04-28 2018-09-25 大连大学 The non-steady waveform design method of MIMO radar under the conditions of knowing target priori
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CN108681622B (en) * 2018-04-09 2022-05-31 中国科学院电子学研究所 Method for optimizing ground penetrating radar waveform
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CN113189574B (en) * 2021-04-02 2022-10-11 电子科技大学 Cloud MIMO radar target positioning Clarithrome bound calculation method based on quantization time delay
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Application publication date: 20140611