CN103235297A - 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 nutating target component method of estimation based on wideband radar observation

Technical field

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

Background technology

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

Complete description to a target travel feature 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 long-haul telemetry and the control to satellite, aircraft.And, also be used widely in target following and interception field as supplementary with targeted attitude.This is because for artificial rigid body target, especially aerial target such as aircraft, guided missile, carry out motions such as turning, usually to carry out the attitude adjustment earlier, the reflection of target maneuver on targeted attitude changes 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 influence the motion morphology of spin aircraft, makes the spin axis of aircraft rotate around another and its crossing axle, and 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 with higher hunting frequency, when less amplitude of fluctuation is done periodic wobble, this motion is called nutating.The variation of angle of precession is to influence 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, now all can from radar observation, obtain the orbit of aircraft respectively based on the ISAR imaging technique in arrowband and broadband.But because wideband radar can obtain more information and more accurate estimation about aircraft, therefore, wideband radar has been obtained critical role in the aircraft monitoring with the remote sensing field.MIT Lincoln laboratory is in the first place in the world in the Study of Technology of Radar Target Identification field, Recent study radar target recognition and ULTRA-WIDEBAND RADAR fine motion pattern measurement, add the upgrading of broadband In-Situ Observation Technique again, 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 the real space target, and precession is coupled with the spin of rolling target inevitably, and therefore how obtaining extraterrestrial target precession parameter estimation still needs further research.

Prior art to this solution is: at first set up cone object space precession mathematical model, provide attitude angle and space precession parameter relationship, and the ratio of inertias of reflection aimed quality distribution character that utilized the precession parameter acquiring, by the target RCS echo data is carried out fitting of a polynomial, estimate the precession parameter then.See list of references " cone object space precession specificity analysis and parameter extraction thereof " (inscription on ancient bronze objects is refined etc., aerospace journal, 2004 the 25th the 4th phases of volume) for details

Though above-mentioned solution can estimate the precession parameter of cone target effectively, but this method is only applicable to the cone target of precession, therefore, under target shape the unknown or target scattering center condition of unknown, the kinematic parameter of space nutating target can't accurately be estimated.

Summary of the invention

The objective of the invention is to the deficiency at above-mentioned prior art, propose a kind of nutating target component method of estimation 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) obtain the wideband echoes sequence of space nutating target in observation process by radar, and this wideband echoes sequence is carried out the 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; Obtain the radial distance sequence matrix by the radial distance sequence and be designated as R, R=[r ₁r ₂R _mR _M], m=1 wherein, 2; , M, M are the pulse number in the observation process;

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

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, three-dimensional European reconstruct is carried out in motion to object space, 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 the quadrature rotation matrix;

5) according to the three-dimensional European restructuring matrix at radar visual angle Nutating object space motion model and coning angle frequencies omega _CWith the angle of nutation frequencies omega _NInitial value, with the following equation of optimizing 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 minimum of Model Matching, in the formula

It is European restructuring matrix

The m column element, T _PrBe the pulse repetition time, || || the computing of expression mould value;

6) according to the three-dimensional European restructuring matrix 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 equation of optimizing 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 minimum of Model Matching.

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 ₂Be second row element of quadrature rotation matrix O,

Expression o ₁Transposed matrix.

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

Description of drawings

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

Fig. 2 is the iteration optimization algorithms sub-process figure that finds the solution 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 among the present invention;

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

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

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

Fig. 6 is the spectrum estimated result figure that does not contain 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 point under Oxyz;

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

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

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

Embodiment

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

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

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

2a) the orbital motion information of target in the estimation 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 rail algorithm of surveying of radar sees list of references " The Trajectory Measuring of Ballistic Missile with Radar " (Wang Xiaohu etc. for details, the system emulation journal, 2004 the 16th the 1st phases of volume);

The range finding unit that 2b) obtains according to target orbit determination offsets the variation of this time 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 the observation process.

Step 3 is to the high-resolution radial distance sequence r of a plurality of static scattering centers _mCompose estimation, obtain the coning angle frequencies omega of space nutating target _C, the angle of nutation frequencies omega _NWith the spin angle frequencies omega _SInitial value.

3a) high-resolution radial distance sequence is composed estimation, the spectrum estimation approach 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 the MUSIC algorithm composes estimation, obtains the two classes spectrum estimated result that contains spin information and do not contain spin information;

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

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

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

4a) according to the model space geometric of radar shown in Figure 3 and nutating target, obtain the vector of unit length of spin axis z axle under OXYZ and be $\stackrel{\·}{z}\left(t\right)={\left[\cos \mathrm{\α}\left(t\right)\sin \mathrm{\β}\left(t\right)\sin \mathrm{\α}\left(t\right)\sin \mathrm{\β}\left(t\right)\cos \mathrm{\β}\left(t\right)\right]}^T,$ α (t)=ω wherein _CT+ α ₀Be the position angle of t moment spin axis under OXYZ, α ₀Be the position angle of initial time spin axis under OXYZ, ω _CBe the coning angle frequency, β (t) is the t angle of pitch of spin axis under OXYZ constantly,

Be initial phase, Be the oscillation centre angle, ω _NBe angle of nutation frequency, A _NBe amplitude of fluctuation, [] ^TExpression is asked transposition to matrix;

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

$\cos \left(\mathrm{\θ}\left(t\right)\right)=\frac{1^T\stackrel{\·}{z}\left(t\right)}{\left|\right|1\left|\right|\left|\right|\stackrel{\·}{z}\left(t\right)\left|\right|}$

$=\cos \mathrm{\β}\left(t\right)\cos \mathrm{\γ}+\sin \mathrm{\γ}\sin \mathrm{\β}\left(t\right)(\cos \mathrm{\α}\left(t\right)\cos \mathrm{\η}+\sin \mathrm{\α}\left(t\right)\sin \mathrm{\η})$

$=\cos \mathrm{\β}\left(t\right)\cos \mathrm{\γ}+\sin \mathrm{\γ}\sin \mathrm{\β}\left(t\right)\cos (\mathrm{\η}-\mathrm{\α}\left(t\right))$

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

4c) with t moment x axle and the vector of unit length of y axle under OXYZ

With

Be expressed as:

$\stackrel{\·}{x}\left(t\right)={\left[\begin{array}{ccc}-{\cos \mathrm{\ω}}_{s}t\sin \mathrm{\α}\left(t\right)-{\sin \mathrm{\ω}}_{s}t\cos \mathrm{\α}\left(t\right)\cos \mathrm{\β}\left(t\right)& {\cos \mathrm{\ω}}_{s}t\cos \mathrm{\α}\left(t\right)-{\sin \mathrm{\ω}}_{s}t\sin \mathrm{\α}\left(t\right)\cos \mathrm{\β}\left(t\right)& {\sin \mathrm{\ω}}_{s}t\sin \mathrm{\β}\left(t\right)\end{array}\right]}^T$

$\stackrel{\·}{y}\left(t\right)={\left[\begin{array}{cc}{\cos \mathrm{\ω}}_{s}t\cos \mathrm{\α}\left(t\right)\cos \mathrm{\β}\left(t\right)-{\sin \mathrm{\ω}}_{s}t\sin \mathrm{\α}\left(t\right)& \cos {\mathrm{\ω}}_{s}t\sin \mathrm{\α}\left(t\right)\cos \mathrm{\β}\left(t\right)+{\sin \mathrm{\ω}}_{s}t\cos \mathrm{\α}\left(t\right)-{\cos \mathrm{\ω}}_{s}t\sin \mathrm{\β}\left(t\right)\end{array}\right]}^T;$

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

$h_1\left(t\right)=\cos \mathrm{\φ}\left(t\right)\sin \mathrm{\θ}\left(t\right)=1^T\stackrel{\·}{x}\left(t\right)={\cos \mathrm{\ω}}_{S}t\sin \mathrm{\γ}\left[\sin (\mathrm{\η}-\mathrm{\α}\left(t\right))\right]+{\sin \mathrm{\ω}}_{S}t[\sin \mathrm{\β}\left(t\right)\cos \mathrm{\γ}-\cos \mathrm{\β}\left(t\right)\sin \mathrm{\γ}\cos (\mathrm{\η}-\mathrm{\α}\left(t\right))]$

$h_2\left(t\right)=\sin \mathrm{\φ}\left(t\right)\sin \mathrm{\θ}\left(t\right)=1^T\stackrel{\·}{y}\left(t\right)={\sin \mathrm{\ω}}_{S}t\sin \mathrm{\γ}\left[\sin (\mathrm{\η}-\mathrm{\α}\left(t\right))\right]-{\cos \mathrm{\ω}}_{S}t[\sin \mathrm{\β}\left(t\right)\cos \mathrm{\γ}-\cos \mathrm{\β}\left(t\right)\sin \mathrm{\γ}\cos (\mathrm{\η}-\mathrm{\α}\left(t\right))].$

Step 5 is 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 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, obtain affine transformation matrix M, wherein diag (C ^TC) representing matrix C ^TThe vector that C principal diagonal element is formed, 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

The oscillation centre angle

The radar line of sight position angle The radar line of sight angle of pitch

The coning angle frequency

The angle of nutation frequency

Quadrature rotation matrix O the third line element

And European restructuring matrix

Find the solution following first with the Levenberg-Marquardt nonlinear optimization algorithm and optimize equation:

Obtain the coning angle frequency

Amplitude of fluctuation

The angle of nutation frequency

Initial phase

The oscillation centre angle Radar line of sight position angle η ^(k)And radar line of sight angle of pitch γ ^(k),

Wherein:

In the formula

It is European restructuring matrix The m column element, T _PrBe the pulse repetition time, || || the computing of expression mould value;

6c) according to quadrature rotation matrix O the third line element

European restructuring matrix

And step 6b) calculating parameter that obtains in, find the solution following second with the seqential quadratic programming algorithm and optimize equation:

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

Obtain the third line element of quadrature rotation matrix O

6d) through type

Right

Normalization, wherein || || ₂Be two norm calculation;

6e) make iterations k=k+1;

6f) with current iteration number of times k and maximum iteration time L relatively, 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 that obtains in three-dimensionalreconstruction matrix, nutating target movement model, spin angle frequency initial value and the 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 first row element

And maximum iteration time L, the spin angle frequency initial value that obtains in the step 3 is designated as

7b) according to European restructuring matrix

Quadrature rotation matrix O first row element

And spin angle frequency

Utilize the coning angle frequency estimation that obtains in the step 6 The angle of nutation frequency estimation The amplitude of fluctuation estimated value

The 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

Find the solution the following the 3rd with the Levenberg-Marquardt nonlinear optimization algorithm and optimize equation:

Obtain the spin angle frequency

Wherein:

7c) according to European restructuring matrix

With quadrature rotation matrix O first row element

Utilize the coning angle frequency estimation that obtains in the step 6

The angle of nutation frequency estimation

The amplitude of fluctuation estimated value

The 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 that obtains in

Find the solution the following the 4th with the seqential quadratic programming algorithm and optimize equation:

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

Obtain 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) with current iteration number of times k and maximum iteration time L relatively, 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 is 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 ₂Second row element for quadrature rotation matrix O.

Step 9, assessment extraterrestrial target nutating parameter estimation performance.

According to the nutating estimated parameter and the actual nutating parameter that obtain in step 6 and the 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 nutating parameter informations, thereby utilizes this formula that the nutating parameter estimation is carried out the estimated performance assessment.

Effect of the present invention further specifies by following experiment to emulated data:

1. experiment scene:

Test used space nutating target and radar line of sight geometrical orientation figure as shown in Figure 4, target nutating parameter arranges as follows: the spin angle frequencies omega _S=3 π rad/s, the coning angle frequencies omega _C=π rad/s, the angle of nutation frequencies omega _N=18 π rad/s, amplitude of fluctuation A _N=1 °, initial phase

, the 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 °; The 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, obtaining the high-resolution radial distance sequence of 4 static scattering centers of target in the observation time interval, the result is as shown in Figure 5.

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

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

2.4) be under the 12dB, to step 2.1 in signal to noise ratio (S/N ratio)) and 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 point under Oxyz, as shown in Figure 9.

2.5) according to 2.2) and in the coning angle frequencies omega that obtains _C, the angle of nutation frequencies omega _NAnd spin angle frequencies omega _SInitial value, adopt iteration optimization algorithms, obtain the spin angle frequencies omega _S, the coning angle frequencies omega _C, the angle of nutation frequencies omega _N, amplitude of fluctuation A _N, initial phase

The 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 point under Oxyz, as shown in figure 10.

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

3. interpretation:

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

As can be seen, the spectrum that the radial distance sequence of a plurality of scattering centers is done is estimated that from Fig. 6 and Fig. 7 two classes that can obtain containing spin information and not containing spin information are composed estimated result, obtained the coning angle frequencies omega according to this two classes spectrum estimated result _C, the angle of nutation frequencies omega _NAnd spin angle frequencies omega _SInitial value, and these frequency values all in the drawings mark come out.

As can be seen, there are a three-dimensional rotation arbitrarily in the three-dimensional motion reconstruction result of radar line of sight LOS vector of unit length terminal point under Oxyz and its real trace from Fig. 8 and Fig. 9.

As can be seen, the method three-dimensional motion of reconstruction attractor nutating target more exactly that the present invention is used estimates the nutating parameter of space nutating target effectively from Fig. 8 and Figure 10.

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

Claims (6)

1. the space nutating target component method of estimation based on wideband radar observation comprises the steps:

1) obtain the wideband echoes sequence of space nutating target in observation process by radar, and this wideband echoes sequence is carried out the 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; Obtain the radial distance sequence matrix by the radial distance sequence and be designated as R, R=[r ₁r ₂R _mR _M], m=1 wherein, 2 ..., M, M are the pulse number in the observation process;

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

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, three-dimensional European reconstruct is carried out in motion to object space, 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 the quadrature rotation matrix;

5) according to the three-dimensional European restructuring matrix at radar visual angle Nutating object space motion model and coning angle frequencies omega _CWith the angle of nutation frequencies omega _NInitial value, with the following equation of optimizing 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 minimum of Model Matching, in the formula

It is European restructuring matrix

The m column element, T _PrBe the pulse repetition time, || || the computing of expression mould value;

6) according to the three-dimensional European restructuring matrix 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 equation of optimizing 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 minimum of Model Matching.

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 ₂Be second row element of quadrature rotation matrix O, Expression o ₁Transposed matrix.

2. the space nutating target component method of estimation based on wideband radar observation according to claim 1, wherein described in the step 1) wideband echoes sequence is carried out orbital motion compensation, be the range finding unit orbital motion information that estimates target in each time echo of current observation earlier, the radial distance of offsetting this time observation echo that causes because of orbital motion according to the range finding unit of orbit determination changes again.

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

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

2b) for the spectrum estimated result of the radial distance sequence that contains spin information on the non-spin axis, 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 nutating target component method of estimation based on wideband radar observation according to claim 1, utilize high-resolution radial distance sequence matrix R and the European three-dimensionalreconstruction algorithm of a plurality of static scattering centers in the wherein said step 4), three-dimensional European reconstruct is carried out in motion to object space, carries out as follows:

4a) according to high-resolution radial distance sequence matrix R=SC, matrix R is carried out 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, obtain affine transformation matrix M, wherein diag (C ^TC) representing matrix C ^TThe vector that C principal diagonal element is formed, 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 nutating target component method of estimation based on wideband radar observation according to claim 1 is optimized equation with solution by iterative method in the wherein said step 5), carries 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 of radar line of sight The initial value γ of the radar line of sight angle of pitch ⁽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

The oscillation centre angle

Radar line of sight position angle η ^(k-1), radar line of sight angle of pitch γ ^(k-1), the coning angle frequency

The angle of nutation frequency

Quadrature rotation matrix O the third line element

And European restructuring matrix

Find the solution first and optimize equation:

Obtain the coning angle frequency

Amplitude of fluctuation

The angle of nutation frequency Initial phase

The 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 that obtains in, find the solution second and optimize equation:

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

Obtain the third line element of quadrature rotation matrix O

5d) through type Right

Normalization, wherein || || ₂Be two norm calculation;

5e) make iterations k=k+1;

5f) with current iteration number of times k and maximum iteration time L relatively, 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 nutating target component method of estimation based on wideband radar observation according to claim 1 is optimized equation with solution by iterative method in the wherein said step 6), carries out as follows:

6a) make iterations k=1, set the initial value of quadrature rotation matrix O first row element

And maximum iteration time L, the spin angle frequency initial value that obtains in the step 2 is designated as

6b) according to European restructuring matrix

Quadrature rotation matrix O first row element

And spin angle frequency

Utilize the coning angle frequency estimation that obtains in the step 5

The angle of nutation frequency estimation

The amplitude of fluctuation estimated value

The 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

Find the solution the 3rd and optimize equation:

Obtain the spin angle frequency

6c) according to European restructuring matrix

With quadrature rotation matrix O first row element

Utilize the estimated value of the coning angle frequency that obtains in the step 5

The angle of nutation frequency estimation

The amplitude of fluctuation estimated value

The 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 that obtains in

Find the solution the 4th and optimize equation:

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

Obtain 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) with current iteration number of times k and maximum iteration time L relatively, when k ≠ L, repeat 6b) to 6f) when k=L, iteration finishes, and obtains the estimated value of spin angle frequency

And the quadrature rotation matrix O first row element o ₁

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