CN108627667A - Based on luminosity sequence while estimation space unstability target precession and spin rate method - Google Patents
Based on luminosity sequence while estimation space unstability target precession and spin rate method Download PDFInfo
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Abstract
The invention discloses one kind based on luminosity sequence while estimation space unstability target precession and spin rate method, including：Obtain the luminosity sequence of Spatial Instability target；It is multiple intrinsic mode functions by luminosity sequence variation mode decomposition；Calculate the mutual information of each intrinsic mode function and luminosity sequence；Spin frequency and precession frequency of the corresponding intrinsic mode function frequency of maximum two association relationships as Spatial Instability target are extracted, converts the spin frequency of Spatial Instability target and precession frequency to precession and the spin rate of Spatial Instability target.The present invention carries out mode decomposition using VMD to luminosity sequence, based on Mutual Information Theory, precession and spin frequency to target are effectively extracted, can degree of precision estimate target precession and spin rate simultaneously, overcome Spectral Analysis Method, auto-correlation and the problem for intersecting the methods of estimation such as residual error method to extraterrestrial target rotary state estimated capacity deficiency.A kind of new reference thinking is provided for the estimation of extraterrestrial target rotary state.
Description
Technical field
The present invention relates to one kind being based on luminosity sequence estimation space unstability target precession and spin rate method simultaneously,
Belong to calculating field.
Background technology
With human development and using the quickening of outer space step, terrestrial space runs a large amount of culture.By
In reasons such as flakes hit, satellite catastrophic failure, in-orbit failures, ten hundreds of discarded space objects is produced, is pacified to space
Bring great threat entirely.Low orbit is discarded target and can be acted on by power such as aerodynamic moment, gravity gradient torque, geomagnetic torques,
Just understand re-entry burn-up after several years to decades；The high rail crowded in orbit space discards spacecraft, if do not taken master
Dynamic measure, will always exist.It is in-orbit based on spacecraft fuel adding, maintainable technology on-orbit and assembly, space junk removing
Service role (On-Orbit Serving, OOS) becomes more and more important, and it is to it to obtain unstability noncooperative target rotary state
The premise serviced.Out of control or unstability extraterrestrial target is generally in high speed rotation state, and the speed of rotation is to weigh space
The important parameter of dbjective state leads to since distance far can not carry out state detection by the methods of radar, laser acquisition to target
It crosses ground telescope to obtain the luminosity data of target and handled, its rotary state be estimated, and judge its work shape
State is a kind of effective Situation Awareness means.
The target of unstability rotation, due to by extraneous torque interference and the factors such as non-uniform mass influenced,
Target initial angular velocity vector and inertia axis are misaligned, and target rotational shows as spin axis and does coning precession around the axis of angular momentum, from
Spin axis precession rate is less than spin rate.In recent years, the Spectral Analysis Method, correlation method and intersection based on target light degree series are residual
The methods of poor method has carried out inverting to extraterrestrial target rotary state, wherein by carrying out Fourier transformation to luminosity sequence,
Frequency of the two high frequencies of energy as spin and precession, approximately estimates precession in long period and short cycle selection frequency spectrum
There is frequency multiplication in the estimated spectral of spin frequency in period, and evaluated error is larger；Intersect residual error method compared to correlation method advantage
It is the most apparent, but it is affected by sample frequency.From the result of inverting can be seen that the above method can only carry out precession or
The independent inverting of person's spin rate includes at a time luminosity ordered series of numbers the unstability extraterrestrial target of two kinds of frequencies, by ground
Obtained luminosity sequence is observed, can not determine in luminosity sequence the precession frequency and spin frequency for including simultaneously, the reason is as follows that：
1) Spectral Analysis Method, intersection residual error method and correlation method cannot carry out anti-while target spin and precession rate
It drills, can only individually estimate a rate in spin or precession.
2) empirical mode decomposition (EMD) is in decomposable process, and frequency alias is than more serious, and its mode number is adaptive
, it is uncontrollable；Spectral Analysis Method frequency multiplication is larger to the evaluated error of the target speed of rotation than more serious.
3) intersect residual error method and correlation method analysis：
For including the signal of cyclic dispersion data, autocorrelation calculation formula is：
In formula, N is the sum of measurement data, and auto-correlation coefficient L is (after Δ n) is expressed as former data x (n) and time delay Δ n
The mean value of data product.The periodicity of data, the interval numerical tabular between autocorrelogram peak value can be described with autocorrelogram
Show cycle T or the integral multiple of T.
Intersecting residual error method expression formula is：
In above formula, N is the sum of measurement data, and (Δ t) is expressed as the signal I (t after original signal I (t) and the Δ t that is delayed to R
The value range of the average value of the difference square of both+Δ t), time delay Δ t is [0, tmax/ 2], and the integer in sampling interval can only be taken
Times.Compared with correlation method, the form that numerically takes square so that the difference bigger between peak valley, it is contemplated that
Target light curve entirety envelope glitters with detail, and result is more accurate compared with autocorrelation method.
Since the minimum value of above-mentioned two methods time delay is only the sampling interval, which has limited the precision of the above method
In the sampling interval of limitation data.For example, for the data without any noise, the sampling interval is 1 second, and precision can only achieve
Second, to the data that the target speed of rotation is 4rves/min, between taking intersection residual error method that can accurately calculate between peak value very much
Away from being 15 seconds, precision is 1 second, and for the data of spin rate 6.5rves/min, it is divided between can only calculating 9 seconds, it is practical
It about 9.231 seconds, is influenced by data sampling interval, it is larger to calculate error.
4) selection of frequency.First, the frequency that Spectral Analysis Method obtains is divided into short cycle spectrum and long period spectrum, in short week
Rotational frequency of the highest frequency of energy as target is chosen respectively in phase and long period spectrum, and the differentiation of long and short cycle is not apparent
Boundary, and the high frequency of energy is not necessarily object representations target rotational frequency, since this method will appear frequency multiplication, frequency multiplication with
After frequency multiplication after frequency alias similar in frequency, energy will appear the situation higher than the speed energy of target.Second is that
By Spectral Analysis Method, correlation method and the signal for intersecting the different frequency that residual error method obtains, screened by 3 σ criterion of peak value,
The basic thought of 3 σ criterion is：Assuming that random error Normal Distribution, therefore accidentally absolute value of the difference is concentrated mainly near μ.3
The formula of σ criterion is：
P(|d|>3 σ+μ)=0.027
P(|d|>2 σ+μ)=0.046
P(|d|>σ+μ)=0.317
Therefore, when error is more than σ+μ, then 68.3% probability thinks that it is gross error；When error is more than 2 σ+μ
When, then there is 95.4% probability to think that it is gross error；When error is more than 3 σ+μ, then there is 97.3% probability to think that it is
Gross error.In practical application, if corresponding peak value σ+μ at a certain frequency, there is 68.2% probability to think that it is the primary period
Corresponding spike, the frequency are then the corresponding frequencies of swing circle.
Specifically choosing method is：
(1) mean square deviation and mean value are calculated：Mean square deviationMean value
(2) ask | di| the maximum value of (i=1,2,3 ...) | d |maxIf | d |max<σ+μ, then it is assumed that peak value is not present, otherwise
Into in next step.
(3) return | d |maxCorresponding frequency i, returns to step 1.
In above-mentioned steps, diIndicate that the amplitude of data, N are the number of data,For the root mean square of all amplitudes, μ is amplitude
Mean value.
Spectrum analysis, autocorrelation analysis are carried out to data and intersect residual analysis, according to the abscissa of acquired results peak value
And the distance between peak value carries out inverting to the rotation parameter of extraterrestrial target.For peak value unobvious, peak separation from differing
Handling result, according to 3 σ criterion carry out peak value screening.
Such method is for the complicated luminosity sequence of extraterrestrial target rolling, spectrum analysis, autocorrelation analysis and intersection residual error
Analysis obtains the equal unobvious of frequency spectral peaks difference, and peak Distribution is not concentrated, and this method applicability is not strong, while the choosing being spaced
It takes dependent on the distance between peak value, the speed of rotation that the case where frequency multiplication this method will be unable to select target occurs.
Invention content
In view of the foregoing drawbacks, the present invention provides one kind based on the estimation space unstability target precession simultaneously of luminosity sequence and oneself
Speed method is revolved, this method to luminosity sequence by carrying out variation mode decomposition (Variational Mode
Decomposition, VMD) algorithm, luminosity sequence is decomposed into intrinsic mode function (the Intrinsic Mode of different frequency
Function, IMF), by calculate each intrinsic mode function and luminosity sequence mutual information (Mutual Information,
MI), the extraction of target precession and spin frequency is carried out.The present invention carries out processing analysis to the luminosity data of target, can estimate simultaneously
Precession and the spin rate for counting out target, obtain more target status informations from the luminosity data of target.
In order to achieve the above objectives, the present invention implements by the following technical programs：
The present invention provides one kind based on luminosity sequence while estimation space unstability target precession and spin rate method, should
Method includes：
Step 1: obtaining the luminosity sequence of Spatial Instability target；
Step 2: being multiple intrinsic mode functions by luminosity sequence variation mode decomposition；
Step 3: calculating the mutual information of each intrinsic mode function and luminosity sequence；
Step 4: extracting the corresponding intrinsic mode function frequency of maximum two association relationships as Spatial Instability target
Spin frequency and precession frequency convert the spin frequency of Spatial Instability target and precession frequency to the precession of Spatial Instability target
And spin rate.
In the step 1, the method for obtaining the luminosity sequence of Spatial Instability target includes：
One or more modes in being measured based on numerical computations, actual observation and/or laboratory simulation are obtained space and lost
The luminosity sequence of steady target.
It is multiple intrinsic mode functions by luminosity sequence variation mode decomposition in the step 2, including：
Luminosity sequence is passed through variational problem by the mode based on classical Wiener filtering, Hilbert transform and frequency compounding
Construction and two process variation mode decompositions of solution of variational problem are multiple intrinsic mode functions.
The construction of the variational problem includes：
Assuming that each mode is the finite bandwidth for having centre frequency, variational problem is described as seeking K intrinsic mode letters
Number uk(t) so that the sum of estimation bandwidth of each mode minimum, constraints are that the sum of each mode is equal to input light degree series f,
Steps are as follows for specific configuration：
1. by Hilbert transform, each intrinsic mode function u is obtainedk(t) analytic signal, and it is unilateral to obtain its
Spectrum：
2. each mode analytic signal is mixed, centre frequency is estimatedBy the spectrum modulation of each mode to accordingly
Base Band：
3. calculating square L of demodulated signal gradient2Norm estimates each mode signals bandwidth, controlled variational problem
It is as follows：
Wherein, { uk}={ u1,...,uk}、{ωk}={ ω1,...,ωkIt is variation mode decomposition to a intrinsic mode of K
The set of function component and intrinsic mode function centre frequency, the rotational frequency of Spatial Instability target are included in the collection of centre frequency
In conjunction, f is the luminosity sequence of input, and δ (t) is impulse function, and * indicates that convolution, j are imaginary unit, and luminosity sequence f length is T,
Then [0, T] t ∈, s.t. indicate restrictive condition, symbolIndicate that variable seeks partial derivative to t.
The solution of the variational problem includes：
1. introducing secondary penalty factor α (also becoming Constraints of Equilibrium coefficient) and Lagrangian λ (t), binding character is become
Point problem becomes non-binding variational problem, and the Lagrangian formulation of extension is as follows：
2. the above variational problem is solved using multiplication operator alternating direction method, by alternately updatingWithIt seeks
The saddle point of extension Lagrangian formulation is sought, whereinProblems of value can be expressed as：
Wherein, * indicates that convolution, n indicate that iterations, j are imaginary unit, and luminosity sequence f length is T, then [0, T] t ∈,
ωkIt is equal to It is equal touiIndicate i-th of mode function, X is indicated until second order is led can accumulate and
Square-integrable space, symbolIndicate that variable seeks partial derivative to t；Equidistantly become using Parseval/Plancherel Fourier
It changes, it willProblems of value be converted to frequency domain：
By angular frequency ω-ωkInstead of then：
Be converted to the integrated form of non-negative frequency separation：
At this point, the solution of double optimization problem is：
According to same process, the problems of value of centre frequency is transformed into frequency domain first：
Solve the update method of centre frequency：
Wherein,It is equivalent to current surplusWiener filtering；For current mode function work(
Rate composes center；It is rightInverse Fourier transform is carried out, real part is then { uk(t)}；
The modal components of variation mode are multiple intrinsic in frequency domain continuous renewal, then by being fourier transformed into Time Domain Decomposition
Mode function；Detailed process is as follows：
1. initializingIt is 0 with iterations n；
2. updating u according to the update method of the integrated form formula of non-negative frequency separation and centre frequencykAnd ωk；
3. updating λ, wherein τ is that step-length updates coefficient：
4. for giving discrimination precision e ＞ 0, ifThen stop iteration, otherwise return to step 2.~4..
In the step 3, calculates each intrinsic mode function and the mutual information of luminosity sequence includes：
Each modal components { u that input light degree series f and decomposition obtaink}={ u1,...,uk}；
Calculate the mutual information MI values I of each modal components and luminosity sequencek(uk,f)：
Wherein, P (uk), P (f) be respectively ukWith the marginal probability distribution of f, P (uk, f) and it is ukWith the joint probability distribution of f,
H (f) is the entropy of f, is defined as H (f)=- ∫fP (f) logP (f), f distribution are more discrete, and the value of H (f) is higher, and H (f | uk) indicate
Known ukIn the case of, the uncertainty of f, Ik(uk, f) then indicate by ukIntroduce and make the amount of f uncertainty reductions.
In the step 4, the corresponding intrinsic mode function frequency of maximum two association relationships is extracted as Spatial Instability
The spin frequency and precession frequency of target convert the spin frequency of Spatial Instability target and precession frequency to Spatial Instability target
Precession and spin rate, including：
The spin frequency and precession frequency of the corresponding Spatial Instability target of maximum mutual information value in intrinsic mode function are extracted,
It is translated into precession and the spin rate V (rves/min) of Spatial Instability target；
Conversion formula is Vs=Fs× 60, Vp=Fp×60；
Wherein, Fs、FpThe spin respectively estimated and precession frequency, unit Hz, Vs、VpFor the spin that estimates and
Precession rate.When conversion, for native to this world stationary orbit Spatial Instability target, since the variation of the distance between survey station and target is led
When causing target luminosity curve whole dull, the mode that frequency is 0 is rejected.
As variable ukWith f it is completely irrelevant or mutual indepedent when, MI values are minimum, result 0, it means that two variable uk
There is no the information of overlapping between f；Conversely, the degree that interdepends of the two is higher, the value of MI is bigger, including identical letter
Breath is also more.It is target spin and precession frequency to choose corresponding two frequencies of maximum two IMF of MI.It should be noted that
Forbid track target for native to this world, since the variation of the distance between survey station and target causes target luminosity curve whole dull
When, luminosity curve will appear the situation of whole dullness, cause without any periodic mode IMF1 (its frequency is 0) with it is original
The MI values of luminosity sequence are larger, and such situation must reject IMF1.
The beneficial effects of the invention are as follows：
Technical solution provided by the invention, by carrying out variation mode decomposition (Variational Mode to luminosity sequence
Decomposition, VMD) algorithm, luminosity sequence is decomposed into intrinsic mode function (the intrinsic mode of different frequency
Function, IMF), by calculate each intrinsic mode function and luminosity sequence mutual information (Mutual Information,
MI), the extraction of target precession and spin frequency is carried out.The present invention can estimate target precession and spin rate simultaneously, more
The inverting of extraterrestrial target state provides reference frame from now on, makes it possible to excavate target more information based on luminosity curve.
Description of the drawings
Fig. 1 show it is provided by the invention based on luminosity sequence simultaneously estimation space unstability target precession and spin rate side
The simulating scenes of the low rail target of method are illustrated.
Fig. 2 show it is provided by the invention based on luminosity sequence simultaneously estimation space unstability target precession and spin rate side
The sun, survey station polar plot under the satellite body of method.
Fig. 3 show it is provided by the invention based on luminosity sequence simultaneously estimation space unstability target precession and spin rate side
The 8 luminosity sequence of scene and VMD decomposition results of method.
Fig. 4 show it is provided by the invention based on luminosity sequence simultaneously estimation space unstability target precession and spin rate side
The 9 luminosity sequence of scene and VMD decomposition results of method.
Fig. 5 show it is provided by the invention based on luminosity sequence simultaneously estimation space unstability target precession and spin rate side
The spectrogram of 3 preceding 5 mode of scene of method.
Fig. 6 show it is provided by the invention based on luminosity sequence simultaneously estimation space unstability target precession and spin rate side
The mutual information degree of the scene 8 each mode and initial data of method.
Fig. 7 show it is provided by the invention based on luminosity sequence simultaneously estimation space unstability target precession and spin rate side
The high rail scene analysis resultant error of method.
Fig. 8 show it is provided by the invention based on luminosity sequence simultaneously estimation space unstability target precession and spin rate side
The low rail scene analysis resultant error of method.
Fig. 9 show it is provided by the invention based on luminosity sequence simultaneously estimation space unstability target precession and spin rate side
One flow chart of embodiment of method.
Specific implementation mode
Technical scheme of the present invention is specifically addressed below, it should be pointed out that technical scheme of the present invention is unlimited
Embodiment described in embodiment, those skilled in the art's reference and the content for using for reference technical solution of the present invention, in this hair
The improvement and design carried out on the basis of bright, should belong to the scope of protection of the present invention.
Embodiment one
As shown in figure 9, the embodiment of the present invention one provide it is a kind of based on luminosity sequence simultaneously estimation space unstability target into
Dynamic and spin rate method, the method comprising the steps of one to step 4：
Step 1: obtaining the luminosity sequence of Spatial Instability target；
Step 2: being multiple intrinsic mode functions by luminosity sequence variation mode decomposition；
Step 3: calculating the mutual information of each intrinsic mode function and luminosity sequence；
Step 4: extracting the corresponding intrinsic mode function frequency of maximum two association relationships as Spatial Instability target
Spin frequency and precession frequency convert the spin frequency of Spatial Instability target and precession frequency to the precession of Spatial Instability target
And spin rate.
In the step 1, the method for obtaining the luminosity sequence of Spatial Instability target includes：
One or more modes in being measured based on numerical computations, actual observation and/or laboratory simulation are obtained space and lost
The luminosity sequence of steady target.
In the step 2 by luminosity sequence variation mode decomposition be multiple intrinsic mode functions, including：
Luminosity sequence is passed through variational problem by the mode based on classical Wiener filtering, Hilbert transform and frequency compounding
Construction and two process variation mode decompositions of solution of variational problem are multiple intrinsic mode functions.
The construction of the variational problem includes：
Assuming that each mode is the finite bandwidth for having centre frequency, variational problem is described as seeking K intrinsic mode letters
Number uk(t) so that the sum of estimation bandwidth of each mode minimum, constraints are that the sum of each mode is equal to input light degree series f,
Steps are as follows for specific configuration：
1. by Hilbert transform, each intrinsic mode function u is obtainedk(t) analytic signal, and it is unilateral to obtain its
Spectrum：
2. each mode analytic signal is mixed, centre frequency is estimatedBy the spectrum modulation of each mode to accordingly
Base Band：
3. calculating square L of demodulated signal gradient2Norm estimates each mode signals bandwidth, controlled variational problem
It is as follows：
Wherein, { uk}={ u1,...,uk}、{ωk}={ ω1,...,ωkIt is variation mode decomposition to a intrinsic mode of K
The set of function component and intrinsic mode function centre frequency, the rotational frequency of Spatial Instability target are included in the collection of centre frequency
In conjunction, f is the luminosity sequence of input, and δ (t) is impulse function, and * indicates that convolution, j are imaginary unit, and luminosity sequence f length is T,
Then [0, T] t ∈, s.t. indicate restrictive condition, symbolIndicate that variable seeks partial derivative to t.
The solution of the variational problem includes：
1. introducing secondary penalty factor α (also becoming Constraints of Equilibrium coefficient) and Lagrangian λ (t), binding character is become
Point problem becomes non-binding variational problem, and the Lagrangian formulation of extension is as follows：
2. the above variational problem is solved using multiplication operator alternating direction method, by alternately updatingWithIt seeks
The saddle point of extension Lagrangian formulation is sought, whereinProblems of value can be expressed as：
Wherein, * indicates that convolution, n indicate that iterations, j are imaginary unit, and luminosity sequence f length is T, then [0, T] t ∈,
ωkIt is equal to It is equal touiIndicate i-th of mode function, X is indicated until second order is led can accumulate and
Square-integrable space, symbolIndicate that variable seeks partial derivative to t；Equidistantly become using Parseval/Plancherel Fourier
It changes, it willProblems of value be converted to frequency domain：
By the ω-ω of the angular frequency in frequency domainkInstead of then：
Be converted to the integrated form of non-negative frequency separation：
At this point, the solution of double optimization problem is：
According to same process, the problems of value of centre frequency is transformed into frequency domain first：
Solve the update method of centre frequency：
Wherein,It is equivalent to current surplusWiener filtering；For current mode function work(
Rate composes center；It is rightInverse Fourier transform is carried out, real part is then { uk(t)}；
The modal components of variation mode are multiple intrinsic in frequency domain continuous renewal, then by being fourier transformed into Time Domain Decomposition
Mode function；Detailed process is as follows：
1. initializingIt is 0 with iterations n；
2. updating u according to the update method of the integrated form formula of non-negative frequency separation and centre frequencykAnd ωk；
3. updating λ, wherein τ is that step-length updates coefficient：
4. for giving discrimination precision e ＞ 0, ifThen stop iteration, otherwise return to step 2.~4..
In terms of the algorithm final from VMD, first, each mode is directly constantly updated in frequency domain, finally by being fourier transformed into
Time domain；Second, as the power spectrum center of each mode, centre frequency is estimated, and is cyclically updated with this again；Third, together
When consider time domain and frequency domain so that the signal of synchronization, frequency domain has physical significance, is influenced by the sampling interval smaller.
In the step 3, calculates each intrinsic mode function and the mutual information of luminosity sequence includes：
Each modal components { u that input light degree series f and decomposition obtaink}={ u1,...,uk}；
Calculate the mutual information MI values I of each modal components and luminosity sequencek(uk,f)：
Wherein, P (uk), P (f) be respectively ukWith the marginal probability distribution of f, P (uk, f) and it is ukWith the joint probability distribution of f,
H (f) is the entropy of f, is defined as H (f)=- ∫fP (f) logP (f), f distribution are more discrete, and the value of H (f) is higher, and H (f | uk) indicate
Known ukIn the case of, the uncertainty of f, Ik(uk, f) then indicate by ukIntroduce and make the amount of f uncertainty reductions.
Related or related coefficient can only reflect the linear correlation between two variables, can not weigh non-between two variables
Linear relationship.Mutual information (Mutual Information, MI) is from the angle of information theory, for indicating two variable Xs and Y
Complementary degree is indicated to co-own the content of information and the power of relationship between two variables, and is not limited to linear
Relationship, it can be estimated that between variable share information content number.
Mutual information degree is a kind of useful measure information in information theory, can regard the pass for including in a stochastic variable as
In the information content of another stochastic variable, or perhaps stochastic variable due to a known stochastic variable and reduction
It is uncertain.
When variable X and Y it is completely irrelevant or mutual indepedent when, mutual information is minimum, result 0, it means that two variables
Between there is no overlapping information；Conversely, the degree that interdepends of the two is higher, the value of mutual information is bigger, including it is identical
Information is also more.This method of mutual information relationship need not be done any it is assumed that being frequently used for text point between feature and classification
The correlation degree of characteristic item and classification is extracted in the registration work of the feature and classification of class.In invention, by VMD by primary light
Degree series are decomposed into the modal components of all multi-frequencies comprising precession and spin frequency, calculate each modal components and original luminosity
The mutual information degree of data carries out the extraction of precession and spin frequency.
In the step 4, the corresponding intrinsic mode function frequency of maximum two association relationships is extracted as Spatial Instability
The spin frequency and precession frequency of target convert the spin frequency of Spatial Instability target and precession frequency to Spatial Instability target
Precession and spin rate, including：
Extract in intrinsic mode function the spin frequency of the corresponding Spatial Instability target of maximum two association relationships and into
Dynamic frequency is translated into precession and the spin rate V (rves/min) of Spatial Instability target；
Conversion formula is Vs=Fs× 60, Vp=Fp×60；
Wherein, Fs、FpThe spin respectively estimated and precession frequency, unit Hz, Vs、VpFor the spin that estimates and
Precession rate.When conversion, for native to this world stationary orbit Spatial Instability target, since the variation of the distance between survey station and target is led
When causing target luminosity curve whole dull, the mode that frequency is 0 is rejected.
One preferred embodiment verifies the present invention, as Figure 1-Figure 8,
There is the extraterrestrial target of a large amount of unstability in space, due to its time of day be difficult to it is previously known, for verification this
The effect of invention takes the mode of numerical computations to obtain the luminosity sequence of target.To illustrate the applicability on classification of track, grind
It is that the low rail that the geostationary orbit target and orbit inclination angle positioned at China overhead are 56 ° of orbit altitude 1000Km justifies rail to study carefully object
Road target, it is surface-based observing station that Chinese Yaoan station (25.6 ° of N, 101.1 ° of E, 2.465Km), which is arranged, and observation condition is target by too
Positive direct projection, survey station is in umbra or penumbra region, target to be seen by survey station, and simulation step length is 1 second.High rail simulation time section is：
21 days 14 January in 2011 when simulation time section is UTCG:12:24.358~14:32:24.358,1200 groups of luminosity datas are obtained,
Phase angle(angle between the sun-target-survey station) is changed by 47 ° to 43 °；2015 when low rail simulation time section is UTCG
On June 2 12:17:23.230~12:24:19.230,416 groups of luminosity datas are obtained, phase angle is changed by 83 ° to 50 °.Fig. 1 shows
The simulating scenes for low rail target of having anticipated, object module and observation geometrical relationship are as shown in Figure 2.Wherein, Body X, Body Y,
Body Z are the body shaft of satellite, and FacInSat, SunInSat are respectively the survey station vector sum sun under satellite body coordinate system
Vector.Satellite spins around body shaft X-axis, spin rate Vs, precession axis is X-axis, and precession rate is Vp, nutational angle size is θ.
Applicability to illustrate the invention and effect simulate the luminosity sequence of target difference rotary state, and satellite rotary state is arranged
Such as table 2.Wherein, scene 1~8 is high rail scene, 9~14 be low rail scene.
The rotary state of 2 target of table is arranged
By the report capability of STK, generate in simulation time section, the coordinate sequence of survey station and the sun under ontology coordinate,
The calculating of luminosity data for target.The present invention is by 3 dimension module of 3DS MAX software buildings satellite, to improve computer sim- ulation
Precision does creped to body surface, and fold relief height is 1cm, and fold fluctuating number is 3, and in satellite body table
Bread, which covers extraterrestrial target, often uses golden film material, windsurfing to coat GaAs, and antenna coats white paint, 3ds files is generated, using for sky
Between the improved Phong models of target common material Fresnel reflection phenomenon, based on improved OpenGL pickup technologies carry out sight
Scattering section (Optical Cross Section, OCS) calculates, and passes through OCS and apparent magnitude conversion formula：OCS sequences are converted into the distance of magnitude sequence M, R between survey station-target.
First, VMD decomposition is carried out to the luminosity sequence that experiment obtains, sets mode number K as 10；α uses the default value of VMD
2000；Update step-length τ is selected as 0.001, discrimination precision e=10-7, to ensure the fidelity of actual signal decomposition.Decomposition result Fig. 2
The initial data and first four mode of scene 8 and 9 are shown with Fig. 4.
By carrying out spectrum analysis to scene 8, frequency spectrum is near 0, can not be obtained and be existed simultaneously precession and spin
In any period, Fig. 5, which is shown, to be passed through after VMD, and initial data is broken down into 10 mode functions comprising rotational frequency component,
The frequency component of 2.5rves/min precession rate and 8rves/min spin rates that middle IMF2 and IMF4 is arranged with scene 8 is very
It is close, and smaller bandwidth, avoid aliasing.When carrying out precession and spin rate extraction to other scenes, target
The speed of rotation is in which mode is different, in order to obtain the mode of target precession and spin rate, using calculating each mode
It with primary light degree series mutual information MI, and is normalized, chooses effective mode of VMD, extract precession and spin rate.
For scene 8, extraction result such as Fig. 6.It is 0 and itself and original pass luminosity sequence to mode IMF1 centre frequencies for low rail scene
The larger situation of row mutual information is rejected.Fig. 3 shows that 8 luminosity sequence of scene and VMD decomposition results, Fig. 7, Fig. 8 are shown respectively
The relative error of high rail and the estimated result of low rail scene is shown.
Fig. 7, Fig. 8 show, for high rail and low rail target, small nutating angular region (20 ° of θ ＜) present invention method into
Dynamic rate and spin rate realize while estimating that relative error is below 3%.Fig. 7 shows that small nutational angle estimates precession rate
Meter influences less, and with the increase of nutational angle, when θ is in 25 ° nearby, target is in tumbling state in great disorder, right
The rate estimation error of precession and spin is larger, when θ continues to increase, causes target ontology ± X-direction by the sun by precession
Survey station receives the face element number of target reflection and increases simultaneously for irradiation, while the parallel ontology of X-axis receives sunlight to other directions
Scattering, what survey station more captured is the brightness change caused by precession, and the influence of spin is smaller, and then to the estimated accuracy of precession
It is higher.
The beneficial effects of the invention are as follows：
The technical solution provided through the invention, by carrying out variation mode decomposition (Variational to luminosity sequence
Mode Decomposition, VMD) algorithm, luminosity sequence is decomposed into the intrinsic mode function (Intrinsic of different frequency
Mode Function, IMF), by the mutual information (Mutual for calculating each intrinsic mode function and luminosity sequence
Information, MI), carry out the extraction of target precession and spin frequency.The present invention can estimate target precession and oneself simultaneously
Rate is revolved, more the inverting of extraterrestrial target state provides reference frame from now on, makes more to believe based on luminosity curve excavation target
Breath is possibly realized.
The present invention is used by different orbit space target difference rotary states, carrying out the numerical computations of luminosity sequence
VMD carries out mode decomposition to luminosity sequence, is based on Mutual Information Theory, precession and spin frequency to target are effectively carried
Take, can degree of precision simultaneously estimate target precession and spin rate, overcome Spectral Analysis Method, auto-correlation and intersect residual error method
Etc. methods of estimation to the problem of extraterrestrial target rotary state estimated capacity deficiency.The present invention simulates Design Laboratory detecting strategy
Actual observation obtains and handles optical diffusion characteristic data of the contracting than extraterrestrial target, further verified to the method for the present invention.This
The method of invention provides a kind of new reference thinking for the estimation of extraterrestrial target rotary state.
Disclosed above is only several specific embodiments of the present invention, and still, the present invention is not limited to above-described embodiment,
The changes that any person skilled in the art can think of should all fall into protection scope of the present invention.
Claims (7)
1. one kind is based on luminosity sequence while estimation space unstability target precession and spin rate method, which is characterized in that the party
Method includes：
Step 1: obtaining the luminosity sequence of Spatial Instability target；
Step 2: being multiple intrinsic mode functions by luminosity sequence variation mode decomposition；
Step 3: calculating the mutual information of each intrinsic mode function and luminosity sequence；
Step 4: extracting spin of the corresponding intrinsic mode function frequency of maximum two association relationships as Spatial Instability target
Frequency and precession frequency, by the spin frequency of Spatial Instability target and precession frequency be converted into Spatial Instability target precession and from
Revolve rate.
2. the method as described in claim 1, which is characterized in that in the step 1, obtain the luminosity sequence of Spatial Instability target
The method of row includes：
One or more modes in being measured based on numerical computations, actual observation and/or laboratory simulation obtain Spatial Instability mesh
Target luminosity sequence.
3. method as claimed in claim 1 or 2, which is characterized in that in the step 2, by luminosity sequence variation mode decomposition
For multiple intrinsic mode functions, including：
The construction that luminosity sequence is passed through variational problem by the mode based on classical Wiener filtering, Hilbert transform and frequency compounding
Two process variation mode decompositions of solution with variational problem are multiple intrinsic mode functions.
4. method as claimed in claim 3, which is characterized in that the construction of the variational problem includes：
Assuming that each mode is the finite bandwidth for having centre frequency, variational problem is described as seeking K intrinsic mode function uk
(t) so that the sum of estimation bandwidth of each mode minimum, constraints are that the sum of each mode is equal to input light degree series f, specifically
Constitution step is as follows：
1. by Hilbert transform, each intrinsic mode function u is obtainedk(t) analytic signal, and obtain its unilateral spectrum：
2. each mode analytic signal is mixed, centre frequency is estimatedBy the spectrum modulation of each mode to corresponding fundamental frequency
Band：
3. calculating square L of demodulated signal gradient2Norm, estimates each mode signals bandwidth, and controlled variational problem is as follows：
Wherein, { uk}={ u1,...,uk}、{ωk}={ ω1,...,ωkIt is variation mode decomposition to K intrinsic mode function
The set of component and intrinsic mode function centre frequency, the rotational frequency of Spatial Instability target are included in the set of centre frequency
In, f is the luminosity sequence of input, and δ (t) is impulse function, and * indicates that convolution, j are imaginary unit, and luminosity sequence f length is T, then
T ∈ [0, T], s.t. indicate restrictive condition, symbolIndicate that variable seeks partial derivative to t.
5. method as claimed in claim 3, which is characterized in that the solution of the variational problem includes：
1. introducing secondary penalty factor α (also becoming Constraints of Equilibrium coefficient) and Lagrangian λ (t), restrictive variation is asked
Topic becomes non-binding variational problem, and the Lagrangian formulation of extension is as follows：
2. the above variational problem is solved using multiplication operator alternating direction method, by alternately updatingWithSeek to expand
The saddle point of Lagrangian formulation is opened up, whereinProblems of value can be expressed as：
Wherein, * indicates that convolution, n indicate that iterations, j are imaginary unit, and luminosity sequence f length is T, then [0, T] t ∈, ωkDeng
It is same as It is equal touiIndicate i-th of mode function, X is indicated until second order is led can accumulate and square
The space that can be accumulated, symbolIndicate that variable seeks partial derivative to t；It, will using Parseval/Plancherel Fourier's equilong transformationsProblems of value be converted to frequency domain：
By angular frequency ω-ωkInstead of then：
Be converted to the integrated form of non-negative frequency separation：
At this point, the solution of double optimization problem is：
According to same process, the problems of value of centre frequency is transformed into frequency domain first：
Solve the update method of centre frequency：
Wherein,It is equivalent to current surplusWiener filtering；For current mode function power spectrum
Center；It is rightInverse Fourier transform is carried out, real part is then { uk(t)}；
The modal components of variation mode are constantly updated in frequency domain, then by being fourier transformed into time domain, are decomposed into multiple eigen modes
State function；Detailed process is as follows：
1. initializingIt is 0 with iterations n；
2. updating u according to the update method of the integrated form formula of non-negative frequency separation and centre frequencykAnd ωk；
3. updating λ, wherein τ is that step-length updates coefficient：
4. for giving discrimination precision e ＞ 0, ifThen stop iteration, otherwise return to step 2.~4..
6. the method as described in claim 1, which is characterized in that in the step 3, calculate each intrinsic mode function and light
The mutual information of degree series includes：
Each modal components { u that input light degree series f and decomposition obtaink}={ u1,...,uk}；
Calculate the mutual information MI values I of each modal components and luminosity sequencek(uk,f)：
Wherein, P (uk), P (f) be respectively ukWith the marginal probability distribution of f, P (uk, f) and it is ukWith the joint probability distribution of f, H (f)
It is the entropy of f, is defined as H (f)=- ∫fP (f) logP (f), f distribution are more discrete, and the value of H (f) is higher, and H (f | uk) indicate known
ukIn the case of, the uncertainty of f, Ik(uk, f) then indicate by ukIntroduce and make the amount of f uncertainty reductions.
7. the method as described in one of claim 1-6, which is characterized in that in the step 4, extract maximum two mutual trusts
Spin frequency and precession frequency of the corresponding intrinsic mode function frequency of breath value as Spatial Instability target, by Spatial Instability target
Spin frequency and precession frequency be converted into precession and the spin rate of Spatial Instability target, including：
The spin frequency and precession frequency for extracting the corresponding Spatial Instability target of maximum mutual information value in intrinsic mode function, by it
It is converted into precession and the spin rate V (rves/min) of Spatial Instability target；
Conversion formula is Vs=Fs× 60, Vp=Fp×60；
Wherein, Fs、FpThe spin respectively estimated and precession frequency, unit Hz, Vs、VpFor spin and the precession speed estimated
Rate.When conversion, for native to this world stationary orbit Spatial Instability target, since the variation of the distance between survey station and target leads to target
When luminosity curve is whole dull, the mode that frequency is 0 is rejected.
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