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 PDFInfo
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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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- 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
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
,
; The
the baseband sampling of individual transmitting array element transmitted waveform is
, wherein
for fast umber of beats.The waveform of whole emission array can be expressed as
.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:
In formula,
for system receives data;
for complex magnitude proportional to target RCS;
for the target numbers in rang ring interested;
represent the parameter of target.It is pointed out that
and
need to be from data
middle estimation.The Section 2 on above formula the right is for disturbing and noise.
each row can be assumed to be independent same distribution, and to submit to average be that 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)
constrainedcRB derives
In formula,
In formula,
with
be respectively
the Jacobian matrix of the true and hypothesis access matrix of individual target, and
for the difference between the two, can suppose that it belongs to the following convex set that knows
For preventing that singularity from occurring, order
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),
In formula,
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,
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
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:
C. outer optimization problem
D. the sane optimization problem based on iteration optimization
Based on above-mentioned analysis, can be by fixing
solve
, also can
solve
.Thus, we can propose a kind of iterative algorithm with right
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,
and
can replace optimization by following steps:
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
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
D. the sane optimization problem based on iteration optimization
Be similar to
trace-optcriterion, for
det-optcriterion, we can replace optimization by alternative manner
with
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:
1b)
constrainedcRB derives
In formula,
1c)
the matrix modeling of individual target physical channel
In formula,
with
be respectively
the Jacobian matrix of the true and hypothesis access matrix of individual target, and
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
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:
C. outer optimization problem
D. the sane optimization problem based on iteration optimization
Based on above-mentioned analysis, can be by fixing
solve
, also can
solve
.Thus, we can propose a kind of iterative algorithm with right
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,
and
can replace optimization by following steps:
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
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
D. the sane optimization problem based on iteration optimization
Be similar to
trace-optcriterion, for
det-optcriterion, we can replace optimization by alternative manner
with
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:
.Array signal to noise ratio (S/N ratio) (ASNR, array signal-to-noise ratio) is defined as
, wherein
for the variance of additive white noise.In experiment below,
.In experiment scene in position
having dry making an uproar than (AINR) of array is the strong jamming of 60 dB, AINR be defined as jamming power with
long-pending with
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
, can obtain
.Through can be calculated for MIMO radar (0.5,0.5), can obtain
, and for MIMO radar (1.5,0.5),
.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
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),
.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:
1b)
constrainedcRB derives
In formula,
In formula,
with
be respectively
the Jacobian matrix of the true and hypothesis access matrix of individual target, and
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),
(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
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:
C. outer optimization problem
D. the sane optimization problem based on iteration optimization
Based on above-mentioned analysis, can be by fixing
solve
, also can
solve
, thus, a kind of iterative algorithm can be proposed with right
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,
and
can replace optimization by following steps:
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:
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
D. the sane optimization problem based on iteration optimization
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