CN103235297B - Space nutation target parameter estimation method based on broadband radar observation - Google Patents

Abstract

The invention discloses a space nutation target parameter estimation method based on broadband radar observation, which mainly solves the problem of nutation parameter estimation of an unknown target shape or an unknown scattering center position. The method is realized by the following steps that a broadband echo sequence of a space nutation target is obtained by a radar; after motion compensation is performed on the echo sequence, a high-resolution radial-distance sequence of a plurality of static scattering centers of the target is obtained, and spectral estimation is performed on the high-resolution radial-distance sequence, so as to obtain initial values of coning angular frequency, spin angular frequency and nutation angular frequency; a space motion model of the target is established in accordance with a geometric orientation diagram of the target and the line of sight of the radar; European three-dimensional reconstruction is performed on the high-resolution radial-distance sequence, so as to obtain a European motion reconstruction matrix; and according to the European motion reconstruction matrix, the space motion model and the initial values of the angular frequencies, an iterative optimization algorithm is adopted to estimate the coning angular frequency, the spin angular frequency, the nutation angular frequency, an amplitude of swing, an initial phase and a central angle of swing. The space nutation target parameter estimation method has the advantage of good estimation performance and can be used for space target recognition of the radar.

Description

Space chapter moving target parameter estimation method based on wideband radar observation

Technical field

The invention belongs to Radar Technology field, relate to method for parameter estimation, can be used for radar space target identification.

Background technology

Technology of Radar Target Identification has become an important research direction of current message area.Space Object Detection, identification and surveillance coverage have embodied national space strength and aerospace strategy, are the important component parts of national strategy strength.Basic theory and the technological approaches about extraterrestrial target, identified have: the identification based on motion feature, broadband ISAR imaging identification, the identification based on polarization characteristic, the statistics identification based on RCS sequence etc.In recent years, motion feature highlights its importance in target detection and identification day by day.

Complete description to a Target Motion Character comprises a plurality of parameters such as position, speed, attitude and angular velocity.Wherein the attitude information of target is an important parameter of target monitoring, as to the long-haul telemetry of satellite, aircraft and control.And using targeted attitude as supplementary, also in target following and interception field, be used widely.This is due to the rigid-object for artificial, especially the aerial target such as aircraft, guided missile, carry out the motions such as turning, conventionally to first carry out attitude adjustment, the reflection of target maneuver on target carriage change often will be prior to the reflection on changing at movement-state, and direction and the size of attitude adjustment also have close relationship with motor-driven direction and size simultaneously.

Attitude is estimated playing an important role aspect satellite stability analysis and the prediction of reentry stage pick-up point.Nowadays, except the aircraft of three-axis stabilization, many aircraft have all adopted the technology of spin stabilization or dual spin stabilization.Yet the variation of space environment can affect the motion morphology of spin aircraft, make the spin axis of aircraft around another axle crossing with it rotation, this motion is called coning.Spin is called precession with the hybrid motion of coning, and the angle of spin axis and coning axle is called angle of precession.When angle of precession is done periodic wobble with higher hunting frequency, less amplitude of fluctuation, this motion is called nutating.The variation of angle of precession is to affect the key factor that targeted attitude is analyzed.

Nowadays, radar tracking and imaging system have become the important tool of aircraft monitoring and remote sensing.And the ISAR imaging technique based on arrowband and broadband now all can obtain the orbit of aircraft from radar observation respectively.But because wideband radar can obtain about the more information of aircraft and estimation more accurately, therefore, wideband radar has been obtained very important status in aircraft monitoring with remote sensing field.MIT Lincoln laboratory in Study of Technology of Radar Target Identification field in first place in the world, Recent study radar target recognition and ULTRA-WIDEBAND RADAR fine motion pattern measurement, add again the upgrading of broadband In-Situ Observation Technique, make these observations can be used for real-time extraterrestrial target fine motion feature extraction and identification.Subsequently, a kind of rolling target attitude algorithm for estimating based on two-dimentional ISAR Image Acquisition three-dimensional feature is suggested.But this algorithm only considered that target is constant and rotatablely moved, and for real space target, precession is inevitably with together with the spin coupling of rolling target, and therefore how obtaining extraterrestrial target precession parameter estimation still needs further research.

Prior art to this solution is: model cone object space precession mathematical model, provide the relational expression of attitude angle and Spatial precession parameter, and the ratio of inertias of reflection aimed quality distribution character that utilized precession parameter acquiring, then by target RCS echo data is carried out to fitting of a polynomial, estimate precession parameter.Refer to list of references < < cone object space precession specificity analysis and parameter extraction > > thereof (inscription on ancient bronze objects is refined etc., aerospace journal, the 25th the 4th phase of volume in 2004)

Though above-mentioned solution can estimate the precession parameter of cone target effectively, but the method is only applicable to the cone target of precession, therefore,, in the situation for target shape the unknown or target scattering center Location-Unknown, the kinematic parameter of space nutating target cannot accurately be estimated.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, propose a kind of chapter moving target parameter estimation method based on wideband radar observation, to realize the accurate estimation of nutating target component.

For achieving the above object, the present invention includes following steps:

1) by radar, obtain the wideband echoes sequence of space nutating target in observation process, and this wideband echoes sequence is carried out to orbital motion compensation, the high-resolution radial distance sequence that obtains a plurality of static scattering centers of this target is designated as r _m, r _mbe the vector of N * 1, wherein N is the number of nutating target quiescent scattering center; By radial distance sequence, obtain radial distance sequence matrix and be designated as R, R=[r ₁r ₂r _mr _m], m=1 wherein, 2; , M, M is the pulse number in observation process;

2) the high-resolution radial distance sequence of a plurality of static scattering centers is composed to estimation, obtain containing spin information and containing two classes of spin information, do not compose estimated results, then according to spectrum estimated result, obtaining the initial value of coning angle frequency, angle of nutation frequency and the spin angle frequency of space nutating target;

3), according to the geometrical orientation figure of space nutating target and radar line of sight, set up the spatial movement model of nutating target;

4) utilize high-resolution radial distance sequence matrix R and the three-dimensional European restructing algorithm of a plurality of static scattering centers, to object space, three-dimensional European reconstruct is carried out in motion, obtains the European restructuring matrix of radar visual angle matrix or target rotation matrix C the relation table of these two matrixes is shown: wherein O is quadrature rotation matrix;

5) according to the European restructuring matrix of the three-dimensional at radar visual angle nutating object space motion model and coning angle frequencies omega _cwith angle of nutation frequencies omega _ninitial value, with the following optimization method of solution by iterative method:

$\begin{array}{cc}s.t.& o_3{o}_3^T=1\end{array}$

Obtain the estimated value of coning angle frequency the estimated value of angle of nutation frequency the estimated value of amplitude of fluctuation the estimated value of initial phase the estimated value at oscillation centre angle the azimuthal estimated value of radar line of sight the estimated value of the radar line of sight angle of pitch and the third line element o of quadrature rotation matrix O ₃, wherein,

This formula represents that m pulse constantly, do not exist the reconfiguration information of spin motion and the target movement model of foundation to mate, by adjusting the third line element o of coning angle frequency, angle of nutation frequency, amplitude of fluctuation, initial phase, oscillation centre angle, radar line of sight position angle, the radar line of sight angle of pitch and quadrature rotation matrix O ₃, make the error of Model Matching minimum, in formula it is European restructuring matrix m column element, T _prthe pulse repetition time, || || represent the computing of mould value;

6) according to the European restructuring matrix of the three-dimensional at radar visual angle nutating object space motion model, spin angle frequencies omega _sinitial value and the calculating parameter that obtains of step 5, with the following optimization method of solution by iterative method:

$\begin{array}{cc}s.t.& o_1{o}_1^T=1,o_3{o}_1^T=0\end{array}$

Obtain the estimated value of spin angle frequency and the first row element o of quadrature rotation matrix O ₁, wherein,

This formula represents that m pulse constantly, exists the reconfiguration information of spin motion and the target movement model of foundation to mate, by adjusting the first row element o of spin angle frequency and quadrature rotation matrix O ₁, make the error of Model Matching minimum.

7) according to the third line element o of quadrature rotation matrix O ₃with the first row element o ₁, through type o ₂=o ₁* o ₃with $O={\left[\begin{array}{ccc}{o}_1^T& o_2^T& o_3^T\end{array}\right]}^T,$ Obtain quadrature rotation matrix O, wherein o ₂for the second row element of quadrature rotation matrix O, represent o ₁transposed matrix.

The present invention is due to the space nutating target of or static scattering center Location-Unknown unknown to shape, according to radar observation, target travel is carried out to European three-dimensionalreconstruction, and reconstruction result is mated with the target nutation model of foundation, thereby can estimate accurately and effectively the nutation parameter of this target.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is the iteration optimization algorithms sub-process figure that solves coning angle frequency, angle of nutation frequency, amplitude of fluctuation, initial phase, oscillation centre angle, radar line of sight position angle and radar line of sight angle of pitch estimated value in the present invention;

Fig. 3 is the iteration optimization algorithms sub-process figure that solves spin angle frequency estimation in the present invention;

Fig. 4 is the model space geometric schematic diagram of radar line of sight and nutating target;

Fig. 5 is the high-resolution radial distance sequence chart in observation interval by 4 static scattering centers of emulation nutating target of the present invention;

Fig. 6 does not contain the spectrum estimated result figure of spin information with emulation of the present invention;

Fig. 7 is the spectrum estimated result figure that contains spin information with emulation of the present invention;

Fig. 8 is the three-dimensional actual path figure with emulation radar line of sight LOS of the present invention vector of unit length terminal under Oxyz;

Fig. 9 is the European reconstruct trajectory diagram of three-dimensional with emulation radar line of sight LOS of the present invention vector of unit length terminal under Oxyz;

Figure 10 is the 3 D motion trace figure through the postrotational radar line of sight LOS of quadrature vector of unit length terminal under Oxyz with emulation of the present invention;

Figure 11 is with the different signal to noise ratio (S/N ratio)s of emulation of the present invention and parameter estimation performance comparison diagram under a different scattering centers said conditions.

Embodiment

With reference to Fig. 1, the specific implementation step of the present embodiment is as follows:

Step 1, observes space nutating target, by radar, obtains space nutating target wideband echoes sequence in observation process.

Step 2, carries out orbital motion compensation to wideband echoes sequence, obtains the high-resolution radial distance sequence of a plurality of static scattering centers of nutating target.

2a) estimate the orbital motion information of target in echo sequence:

According to echo sequence, calculate the initial value of target travel track, adopt the optimum survey of radar rail algorithm to obtain the range finding unit of target orbit determination, the optimum survey of radar rail algorithm refers to the radar survey rail algorithm > > (Wang little Hu etc. of list of references < < ballistic missile, Journal of System Simulation, the 16th the 1st phase of volume in 2004);

Range finding unit 2b) obtaining according to target orbit determination offsets the variation of this observation echo sequence radial distance that target causes because of orbital motion, is about to the difference of the radial distance that each scattering center obtains to the radial distance of radar and survey rail algorithm as the high-resolution radial distance sequence r of a plurality of static scattering centers of nutating target _m, and obtain its radial distance sequence matrix and be: R-[r ₁r ₂r _mr _m], r wherein _mbe the vector of N * 1, N is the number of nutating target quiescent scattering center, and M is the pulse number in observation process.

Step 3, the high-resolution radial distance sequence r to a plurality of static scattering centers _mcompose estimation, obtain the coning angle frequencies omega of space nutating target _c, angle of nutation frequencies omega _nwith spin angle frequencies omega _sinitial value.

3a) high-resolution radial distance sequence is composed to estimation, the method that spectrum is estimated has: period map method, is divided into direct method and indirect method; The parameter model spectrum estimation technique, comprises AR model, MA model, arma modeling etc.; The nonparametric model spectrum estimation technique, comprises least variance method and MUSIC method, and this example adopts but is not limited to MUSIC algorithm composes estimation, obtains containing spin information and containing two classes of spin information, does not compose estimated results;

3b), for not containing the spectrum estimated result of the radial distance sequence of spin information on spin axis, the first order component has 4 frequency spike, and wherein minimum frequency component is as coning angle frequencies omega _cinitial value, the difference of maximum frequency component and minimum frequency component is as angle of nutation frequencies omega _ninitial value;

3c), for the spectrum estimated result of the radial distance sequence that contains spin information on non-spin axis, the first order component has 13 frequency spike, will be wherein maximum frequency component and 3b) in the difference of maximum frequency component as spin angle frequencies omega _sinitial value.

Step 4, according to the geometrical orientation figure of space nutating target and radar line of sight, sets up space nutating target movement model.

4a) according to the model space geometric of the radar shown in Fig. 3 and nutating target, obtain the vector of unit length of spin axis z axle under OXYZ and be $\stackrel{\&CenterDot;}{z}\left(t\right)={\left[\cos \mathrm{\&alpha;}\left(t\right)\sin \mathrm{\&beta;}\left(t\right)\sin \mathrm{\&alpha;}\left(t\right)\sin \mathrm{\&beta;}\left(t\right)\cos \mathrm{\&beta;}\left(t\right)\right]}^T,$ α (t)=ω wherein _ct+ α ₀for the position angle of t moment spin axis under OXYZ, α ₀the position angle of initial time spin axis under OXYZ, ω _cfor coning angle frequency, β (t) is the t angle of pitch of spin axis under OXYZ constantly, initial phase, oscillation centre angle, ω _nfor angle of nutation frequency, A _nfor amplitude of fluctuation, [] ^texpression is to Matrix Calculating transposition;

4b) the vector of unit length l=[cos η sin γ sin η sin γ cos γ under OXYZ according to radar line of sight LOS] ^t, obtain the cosine value of the pitching angle theta (t) of radar line of sight under Oxyz,

$\cos \left(\mathrm{\&theta;}\left(t\right)\right)=\frac{1^T\stackrel{\&CenterDot;}{z}\left(t\right)}{\left|\right|1\left|\right|\left|\right|\stackrel{\&CenterDot;}{z}\left(t\right)\left|\right|}$

$=\cos \mathrm{\&beta;}\left(t\right)\cos \mathrm{\&gamma;}+\sin \mathrm{\&gamma;}\sin \mathrm{\&beta;}\left(t\right)(\cos \mathrm{\&alpha;}\left(t\right)\cos \mathrm{\&eta;}+\sin \mathrm{\&alpha;}\left(t\right)\sin \mathrm{\&eta;})$

$=\cos \mathrm{\&beta;}\left(t\right)\cos \mathrm{\&gamma;}+\sin \mathrm{\&gamma;}\sin \mathrm{\&beta;}\left(t\right)\cos (\mathrm{\&eta;}-\mathrm{\&alpha;}\left(t\right))$

Wherein η and γ are respectively position angle and the angle of pitch of radar line of sight LOS under OXYZ;

4c) by t moment x axle and the vector of unit length of y axle under OXYZ with be expressed as:

$\stackrel{\&CenterDot;}{x}\left(t\right)={\left[\begin{array}{ccc}-{\cos \mathrm{\&omega;}}_{s}t\sin \mathrm{\&alpha;}\left(t\right)-{\sin \mathrm{\&omega;}}_{s}t\cos \mathrm{\&alpha;}\left(t\right)\cos \mathrm{\&beta;}\left(t\right)& {\cos \mathrm{\&omega;}}_{s}t\cos \mathrm{\&alpha;}\left(t\right)-{\sin \mathrm{\&omega;}}_{s}t\sin \mathrm{\&alpha;}\left(t\right)\cos \mathrm{\&beta;}\left(t\right)& {\sin \mathrm{\&omega;}}_{s}t\sin \mathrm{\&beta;}\left(t\right)\end{array}\right]}^T$

$\stackrel{\&CenterDot;}{y}\left(t\right)={\left[\begin{array}{cc}{\cos \mathrm{\&omega;}}_{s}t\cos \mathrm{\&alpha;}\left(t\right)\cos \mathrm{\&beta;}\left(t\right)-{\sin \mathrm{\&omega;}}_{s}t\sin \mathrm{\&alpha;}\left(t\right)& \cos {\mathrm{\&omega;}}_{s}t\sin \mathrm{\&alpha;}\left(t\right)\cos \mathrm{\&beta;}\left(t\right)+{\sin \mathrm{\&omega;}}_{s}t\cos \mathrm{\&alpha;}\left(t\right)-{\cos \mathrm{\&omega;}}_{s}t\sin \mathrm{\&beta;}\left(t\right)\end{array}\right]}^T;$

4d) by the cosine value h of the angle of t moment radar line of sight LOS and x axle ₁and radar line of sight LOS and y axle clamp cosine of an angle value h (t) ₂(t) be expressed as:

$h_1\left(t\right)=\cos \mathrm{\&phi;}\left(t\right)\sin \mathrm{\&theta;}\left(t\right)=1^T\stackrel{\&CenterDot;}{x}\left(t\right)={\cos \mathrm{\&omega;}}_{S}t\sin \mathrm{\&gamma;}\left[\sin (\mathrm{\&eta;}-\mathrm{\&alpha;}\left(t\right))\right]+{\sin \mathrm{\&omega;}}_{S}t[\sin \mathrm{\&beta;}\left(t\right)\cos \mathrm{\&gamma;}-\cos \mathrm{\&beta;}\left(t\right)\sin \mathrm{\&gamma;}\cos (\mathrm{\&eta;}-\mathrm{\&alpha;}\left(t\right))]$

$h_2\left(t\right)=\sin \mathrm{\&phi;}\left(t\right)\sin \mathrm{\&theta;}\left(t\right)=1^T\stackrel{\&CenterDot;}{y}\left(t\right)={\sin \mathrm{\&omega;}}_{S}t\sin \mathrm{\&gamma;}\left[\sin (\mathrm{\&eta;}-\mathrm{\&alpha;}\left(t\right))\right]-{\cos \mathrm{\&omega;}}_{S}t[\sin \mathrm{\&beta;}\left(t\right)\cos \mathrm{\&gamma;}-\cos \mathrm{\&beta;}\left(t\right)\sin \mathrm{\&gamma;}\cos (\mathrm{\&eta;}-\mathrm{\&alpha;}\left(t\right))].$

Step 5, according to the three-dimensional motion of the European restructing algorithm reconstruct of three-dimensional nutating target.

5a), according to high-resolution radial distance sequence matrix R=SC, matrix R is carried out to svd, obtain the Affine Reconstruction matrix S of target location matrix S _aaffine Reconstruction Matrix C with radar visual angle Matrix C _a, the relation table of these four matrixes is shown: S _a=SM, C _a=M ^-1c, wherein M is affine transformation matrix, M ^-1the inverse matrix of representing matrix M;

5b) according to Affine Reconstruction Matrix C _aand relational expression C _a=M ^-1c, through type diag (C ^tc)=1, obtains affine transformation matrix M, wherein diag (C ^tc) representing matrix C ^tthe vector that C the elements in a main diagonal forms, C ^tthe transposed matrix of representing matrix C;

5c) according to affine transformation matrix M, obtain the European restructuring matrix of target location matrix S european restructuring matrix with radar visual angle Matrix C

${\hat{S}}_E=S_A{M}^{-1},$

${\hat{C}}_E={\mathrm{MC}}_A.$

Step 6, according to three-dimensionalreconstruction matrix, nutating target movement model, coning angle frequency initial value and angle of nutation frequency initial value, obtains the estimated value of coning angle frequency the estimated value of angle of nutation frequency the estimated value of amplitude of fluctuation the estimated value of initial phase the estimated value at oscillation centre angle the azimuthal estimated value of radar line of sight the estimated value of the radar line of sight angle of pitch and quadrature rotation matrix O the third line element o ₃.

With reference to Fig. 2, the idiographic flow of this step is as follows:

6a) make iterations k=1, set the initial value of amplitude of fluctuation the initial value of initial phase the initial value at oscillation centre angle the azimuthal initial value η of radar line of sight ⁽⁰⁾, the radar line of sight angle of pitch initial value γ ⁽⁰⁾initial value with quadrature rotation matrix O the third line element and maximum iteration time L, and the initial value of the coning angle frequency that step 3 is obtained is designated as angle of nutation frequency initial value is designated as

6b) according to amplitude of fluctuation initial phase oscillation centre angle radar line of sight position angle the radar line of sight angle of pitch coning angle frequency angle of nutation frequency quadrature rotation matrix O the third line element and European restructuring matrix with Levenberg-Marquardt nonlinear optimization algorithm, solve following the first optimization method:

Obtain coning angle frequency amplitude of fluctuation angle of nutation frequency initial phase oscillation centre angle radar line of sight position angle η ^(k)and radar line of sight angle of pitch γ ^(k),

Wherein:

In formula it is European restructuring matrix m column element, T _prthe pulse repetition time, || || represent the computing of mould value;

6c) according to quadrature rotation matrix O the third line element european restructuring matrix and step 6b) calculating parameter obtaining in, use following the second optimization method of seqential quadratic programming Algorithm for Solving:

$\begin{array}{cc}s.t.& o_3{o}_3^T\&le;1\end{array}$

Obtain the third line element of quadrature rotation matrix O

6d) through type right normalization, wherein || || ₂two norm calculation;

6e) make iterations k=k+1;

6f) by current iteration number of times k and maximum iteration time L comparison, when k ≠ L, repeat 6b) to 6f), when k=L, iteration finishes, and obtains the estimated value of coning angle frequency the estimated value of angle of nutation frequency the estimated value of amplitude of fluctuation the estimated value of initial phase the estimated value at oscillation centre angle the azimuthal estimated value of radar line of sight the estimated value of the radar line of sight angle of pitch and quadrature rotation matrix O the third line element o ₃.

Step 7, according to the calculating parameter obtaining in three-dimensionalreconstruction matrix, nutating target movement model, spin angle frequency initial value and step 6, obtains the estimated value of spin angle frequency and the first row element o of quadrature rotation matrix O ₁.

With reference to Fig. 3, the idiographic flow of this step is as follows:

7a) make iterations k=1, set the initial value of quadrature rotation matrix O the first row element and maximum iteration time L, the spin angle frequency initial value obtaining in step 3 is designated as ;

7b) according to European restructuring matrix quadrature rotation matrix O the first row element and spin angle frequency utilize the coning angle frequency estimation obtaining in step 6 angle of nutation frequency estimation amplitude of fluctuation estimated value initial phase estimated value oscillation centre angle estimated value radar line of sight position angle estimated value radar line of sight angle of pitch estimated value with Levenberg-Marquardt nonlinear optimization algorithm, solve following the 3rd optimization method:

Obtain spin angle frequency

Wherein:

7c) according to European restructuring matrix with quadrature rotation matrix O the first row element utilize the coning angle frequency estimation obtaining in step 6 angle of nutation frequency estimation amplitude of fluctuation estimated value initial phase estimated value oscillation centre angle estimated value radar line of sight position angle estimated value radar line of sight angle of pitch estimated value and step 7b) the spin angle frequency obtaining in with following the 4th optimization method of seqential quadratic programming Algorithm for Solving:

$\begin{array}{cc}s.t.& o_1{o}_1^T\&le;1,o_3{o}_1^T=0\end{array}$

Obtain the first row element of quadrature rotation matrix O

7d) through type $o_1^{\left(k\right)}=o_1^{\left(k\right)}/{\left|\right|o_1^{\left(k\right)}\left|\right|}_2,$ Right normalization;

7e) make iterations k=k+1;

7f) by current iteration number of times k and maximum iteration time L comparison, when k ≠ L, repeat 7b) to 7f), when k=L, iteration finishes, and obtains the estimated value of spin angle frequency and the first row element o of quadrature rotation matrix O ₁.

Step 8, according to the third line element o of quadrature rotation matrix O ₃with the first row element o ₁, obtain quadrature rotation matrix O.

Through type o ₂=o ₁* o ₃with $O={\left[\begin{array}{ccc}{o}_1^T& o_2^T& o_3^T\end{array}\right]}^T,$ Obtain quadrature rotation matrix O, wherein o ₂the second row element for quadrature rotation matrix O.

Step 9, assessment extraterrestrial target nutation parameter estimated performance.

Nutating estimated parameter and actual nutation parameter according to obtaining in step 6 and step 7, utilize step 4c) h of middle radar line of sight and x axle clamp angle cosine value ₁(t) expression formula, obtains the normalization root-mean-square error RNMSE of parameter estimation by following formula,

Wherein:

This formula is the h to radar line of sight and x axle clamp angle cosine value ₁(t) time discretization expression formula, has comprised all nutation parameter information, thereby utilizes this formula to estimate to carry out estimated performance assessment to nutation parameter.

Effect of the present invention is by further illustrating the experiment of emulated data below:

1. experiment scene:

Test nutating target in space used and radar line of sight geometrical orientation figure as shown in Figure 4, target nutation parameter arranges as follows: spin angle frequencies omega _s=3 π rad/s, coning angle frequencies omega _c=π rad/s, angle of nutation frequencies omega _n=18 π rad/s, amplitude of fluctuation A _n=1 °, initial phase , oscillation centre angle , target has 4 static scattering centers; Position angle η=120 ° of radar line of sight under OXYZ, angle of pitch γ=30 °; Radar emission signal parameter arranges as follows: signal bandwidth is 2GHz, and range resolution is 0.075m, the pulse repetition time the radar observation time is 4s, signal to noise ratio snr=12dB.

2. experimental procedure and result:

2.1) radar observation space nutating target, obtains the high-resolution radial distance sequence of 4 static scattering centers of target in observation interval, and result as shown in Figure 5.

2.2) to step 2.1) in the high-resolution radial distance sequence that provides compose estimation, as shown in Figure 6 and Figure 7, wherein, Fig. 6 (a) is not containing the spectrum estimated result figure of spin information to result; Fig. 6 (b) amplifies for Fig. 6 (a) being carried out to part, obtains the spectrum estimated result figure of first order frequency component 0～10Hz; The spectrum estimated result figure of 7 (a) for containing spin information; 7 (b) amplify for Fig. 7 (a) being carried out to part, obtain the spectrum estimated result figure of first order frequency component 0～15Hz; According to this two classes spectrum estimated result, determine coning angle frequencies omega _c, angle of nutation frequencies omega _nwith spin angle frequencies omega _sinitial value, these three values all in the drawings sign out.

2.3) the three-dimensional actual path of emulation radar line of sight LOS vector of unit length terminal under Oxyz, result as shown in Figure 8.

2.4) in signal to noise ratio (S/N ratio), be under 12dB, to step 2.1) in the high-resolution radial distance sequence that provides adopt three-dimensional European restructing algorithm to obtain the three-dimensional motion reconstruct trajectory diagram of radar line of sight LOS vector of unit length terminal under Oxyz, as shown in Figure 9.

2.5) according to 2.2) in the coning angle frequencies omega that obtains _c, angle of nutation frequencies omega _nand spin angle frequencies omega _sinitial value, adopt iteration optimization algorithms, obtain spin angle frequencies omega _s, coning angle frequencies omega _c, angle of nutation frequencies omega _n, amplitude of fluctuation A _n, initial phase oscillation centre angle with the estimated value of three-dimensional rotation matrix O, and the 3 D motion trace figure of the process postrotational radar line of sight LOS of quadrature vector of unit length terminal under Oxyz, as shown in figure 10.

2.6) according to 2.5) in the nutating estimated parameter and the actual nutation parameter that obtain, calculating parameter estimated performance, different signal to noise ratio (S/N ratio)s and parameter estimation performance comparison diagram under a different scattering centers said conditions, as shown in figure 11.

3. interpretation:

As can be seen from Figure 5, the static scattering center in target with different spatial presents the distance movement locus of different rules in one-dimensional distance sequence, wherein the characteristics of motion of the one dimension radial distance sequence of scattering center 1 and the scattering center of other positions has larger difference, by analysis, can tell scattering center 1 is positioned on spin axis, and other scattering points are positioned at other positions on non-spin axis, this is not have spin motion owing to being positioned at the scattering center 1 of spin axis, and other scattering centers all exist spin motion.

From Fig. 6 and Fig. 7, can find out, the spectrum that the radial distance sequence of a plurality of scattering centers is done is estimated, can obtain containing spin information and not containing two class spectrum estimated results of spin information, according to this two classes spectrum estimated result, obtain coning angle frequencies omega _c, angle of nutation frequencies omega _nand spin angle frequencies omega _sinitial value, and these frequency values all in the drawings mark out.

From Fig. 8 and Fig. 9, can find out, there is a three-dimensional rotation arbitrarily in the three-dimensional motion reconstruction result of radar line of sight LOS vector of unit length terminal under Oxyz and its real trace.

From Fig. 8 and Figure 10, can find out that the method three-dimensional motion of reconstruction attractor nutating target more exactly that the present invention is used estimates the nutation parameter of space nutating target effectively.

As can be seen from Figure 11, the estimated performance of the present invention's method used improves along with the increase of the increase of signal to noise ratio (S/N ratio) or the scattering center number of observation.

Claims (6)

1. the space chapter moving target parameter estimation method based on wideband radar observation, comprises the steps:

1) by radar, obtain the wideband echoes sequence of space nutating target in observation process, and this wideband echoes sequence is carried out to orbital motion compensation, the high-resolution radial distance sequence that obtains a plurality of static scattering centers of this target is designated as r _m, r _mbe the vector of N * 1, wherein N is the number of nutating target quiescent scattering center; By radial distance sequence, obtain radial distance sequence matrix and be designated as R, R=[r ₁r ₂r _mr _m], m=1 wherein, 2 ..., M, M is the pulse number in observation process;

2) the high-resolution radial distance sequence of a plurality of static scattering centers is composed to estimation, obtain containing spin information and containing two classes of spin information, do not compose estimated results, then according to spectrum estimated result, obtaining the initial value of coning angle frequency, angle of nutation frequency and the spin angle frequency of space nutating target;

3), according to the geometrical orientation figure of space nutating target and radar line of sight, set up the spatial movement model of nutating target;

4) utilize high-resolution radial distance sequence matrix R and the three-dimensional European restructing algorithm of a plurality of static scattering centers, to object space, three-dimensional European reconstruct is carried out in motion, obtains the European restructuring matrix of radar visual angle matrix or target rotation matrix C the relation table of these two matrixes is shown: wherein O is quadrature rotation matrix;

5) according to the European restructuring matrix of the three-dimensional at radar visual angle nutating object space motion model and coning angle frequencies omega _cwith angle of nutation frequencies omega _ninitial value, with the following optimization method of solution by iterative method:

$s.t.o_3{o}_3^T=1$

Obtain the estimated value of coning angle frequency the estimated value of angle of nutation frequency the estimated value of amplitude of fluctuation the estimated value of initial phase the estimated value at oscillation centre angle the azimuthal estimated value of radar line of sight the estimated value of the radar line of sight angle of pitch and the third line element o of quadrature rotation matrix O ₃, wherein,

This formula represents that m pulse constantly, do not exist the reconfiguration information of spin motion and the target movement model of foundation to mate, by adjusting the third line element o of coning angle frequency, angle of nutation frequency, amplitude of fluctuation, initial phase, oscillation centre angle, radar line of sight position angle, the radar line of sight angle of pitch and quadrature rotation matrix O ₃, make the error of Model Matching minimum, in formula it is European restructuring matrix m column element, T _prthe pulse repetition time, ‖. ‖ represents the computing of mould value, ω _cfor coning angle frequency, A _nfor amplitude of fluctuation, ω _nfor angle of nutation frequency, initial phase, be oscillation centre angle, η and γ are respectively position angle and the angle of pitch of radar line of sight LOS under OXYZ;

6) according to the European restructuring matrix of the three-dimensional at radar visual angle nutating object space motion model, spin angle frequencies omega _sinitial value and the calculating parameter that obtains of step 5, with the following optimization method of solution by iterative method:

$s.t.o_1{o}_1^T=1,o_3{o}_1^T=0$

Obtain the estimated value of spin angle frequency and the first row element o of quadrature rotation matrix O ₁, wherein,

This formula represents that m pulse constantly, exists the reconfiguration information of spin motion and the target movement model of foundation to mate, by adjusting the first row element o of spin angle frequency and quadrature rotation matrix O ₁, make the error of Model Matching minimum;

7) according to the third line element o of quadrature rotation matrix O ₃with the first row element o ₁, through type o ₂=o ₁* o ₃with $O={\left[\begin{array}{ccc}{o}_1^T& o_2^T& o_3^T\end{array}\right]}^T,$ Obtain quadrature rotation matrix O, wherein o ₂for the second row element of quadrature rotation matrix O, represent o ₁transposed matrix.

2. the space chapter moving target parameter estimation method based on wideband radar observation according to claim 1, step 1 wherein) described in, wideband echoes sequence is carried out to orbital motion compensation, be the range finding unit orbital motion information that first estimates target in each echo of current observation, then change according to the radial distance that the range finding unit of orbit determination offsets this observation echo causing because of orbital motion.

3. the space chapter moving target parameter estimation method based on wideband radar observation according to claim 1, step 2 wherein) described in, according to spectrum estimated result, obtain the initial value of coning angle frequency, angle of nutation frequency and the spin angle frequency of space nutating target, carry out as follows:

2a) for not containing the spectrum estimated result of the radial distance sequence of spin information on spin axis, the first order component has 4 frequency spike, using minimum frequency component wherein as the initial value of coning angle frequency, the initial value using the difference of maximum frequency component and minimum frequency component as angle of nutation frequency;

2b), for the spectrum estimated result of the radial distance sequence that contains spin information on non-spin axis, the first order component has 13 frequency spike, will be wherein maximum frequency component and step 2a) difference of middle maximum frequency component is as the initial value of spin angle frequency.

4. the space chapter moving target parameter estimation method based on wideband radar observation according to claim 1, wherein said step 4) in, utilize high-resolution radial distance sequence matrix R and the European three-dimensionalreconstruction algorithm of a plurality of static scattering centers, to object space, three-dimensional European reconstruct is carried out in motion, carries out as follows:

4a), according to high-resolution radial distance sequence matrix R=SC, matrix R is carried out to svd, obtain the Affine Reconstruction matrix S of target location matrix S _aaffine Reconstruction Matrix C with radar visual angle Matrix C _a, the relation table of these four matrixes is shown: S _a=SM, C _a=M ^-1c, wherein M is affine transformation matrix, M ^-1the inverse matrix of representing matrix M;

4b) according to Affine Reconstruction Matrix C _aand relational expression C _a=M ^-1c, through type diag (C ^tc)=1, obtains affine transformation matrix M, wherein diag (C ^tc) representing matrix C ^tthe vector that C the elements in a main diagonal forms, C ^tthe transposed matrix of representing matrix C;

4c) according to affine transformation matrix M, obtain the European restructuring matrix of target location matrix S european restructuring matrix with radar visual angle Matrix C

${\hat{S}}_E=S_A{M}^{-1},$

${\hat{C}}_E={\mathrm{MC}}_A.$

5. the space chapter moving target parameter estimation method based on wideband radar observation according to claim 1, wherein said step 5), use solution by iterative method optimization method, carry out as follows:

5a) make iterations k=1, set the initial value of amplitude of fluctuation the initial value of initial phase the initial value at oscillation centre angle the azimuthal initial value η of radar line of sight ⁽⁰⁾, the radar line of sight angle of pitch initial value γ ⁽⁰⁾initial value with quadrature rotation matrix O the third line element and maximum iteration time L, and the initial value of the coning angle frequency that step 2 is obtained is designated as angle of nutation frequency initial value is designated as

5b) according to amplitude of fluctuation initial phase oscillation centre angle radar line of sight position angle η ^(k-1), radar line of sight angle of pitch γ ^(k-1), coning angle frequency angle of nutation frequency quadrature rotation matrix O the third line element and European restructuring matrix solve the first optimization method:

Obtain coning angle frequency amplitude of fluctuation angle of nutation frequency initial phase oscillation centre angle radar line of sight position angle η ^(k)and radar line of sight angle of pitch γ ^(k);

5c) according to quadrature rotation matrix O the third line element european restructuring matrix and step 5b) calculating parameter obtaining in, solves the second optimization method:

$s.t.o_3{o}_3^T\&le;1$

Obtain the third line element of quadrature rotation matrix O

5d) through type right normalization, wherein ‖. ‖ ₂two norm calculation;

5e) make iterations k=k+1;

5f) by current iteration number of times k and maximum iteration time L comparison, when k ≠ L, repeat 5b) to 5f), when k=L, iteration finishes, and obtains the estimated value of coning angle frequency the estimated value of angle of nutation frequency the estimated value of amplitude of fluctuation the estimated value of initial phase the estimated value at oscillation centre angle the azimuthal estimated value of radar line of sight the estimated value of the radar line of sight angle of pitch and quadrature rotation matrix O the third line element o ₃.

6. the space chapter moving target parameter estimation method based on wideband radar observation according to claim 1, wherein said step 6), use solution by iterative method optimization method, carry out as follows:

6a) make iterations k=1, set the initial value of quadrature rotation matrix O the first row element and maximum iteration time L, the spin angle frequency initial value obtaining in step 2 is designated as

6b) according to European restructuring matrix quadrature rotation matrix O the first row element and spin angle frequency utilize the coning angle frequency estimation obtaining in step 5 angle of nutation frequency estimation amplitude of fluctuation estimated value initial phase estimated value oscillation centre angle estimated value radar line of sight position angle estimated value radar line of sight angle of pitch estimated value solve the 3rd optimization method:

Obtain spin angle frequency

6c) according to European restructuring matrix with quadrature rotation matrix O the first row element utilize the estimated value of the coning angle frequency obtaining in step 5 angle of nutation frequency estimation amplitude of fluctuation estimated value initial phase estimated value oscillation centre angle estimated value radar line of sight position angle estimated value radar line of sight angle of pitch estimated value and step 6b) the spin angle frequency obtaining in solve the 4th optimization method:

s.t.o ₁o ₁ ^T≤1,o ₃o ₁ ^T＝0

Obtain the first row element of quadrature rotation matrix O

6d) through type $o_1^{\left(k\right)}=o_1^{\left(k\right)}/{\left|\right|o_1^{\left(k\right)}\left|\right|}_2,$ Right normalization;

6e) make iterations k=k+1;

6f) by current iteration number of times k and maximum iteration time L comparison, when k ≠ L, repeat 6b) to 6f), when k=L, iteration finishes, and obtains the estimated value of spin angle frequency and quadrature rotation matrix O the first row element o ₁.