CN115436907B - Incoherent scattering ionosphere parameter inversion method and system based on Bayesian filtering - Google Patents

Incoherent scattering ionosphere parameter inversion method and system based on Bayesian filtering Download PDF

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CN115436907B
CN115436907B CN202211390635.8A CN202211390635A CN115436907B CN 115436907 B CN115436907 B CN 115436907B CN 202211390635 A CN202211390635 A CN 202211390635A CN 115436907 B CN115436907 B CN 115436907B
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CN115436907A (en
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郝红连
赵必强
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Institute of Geology and Geophysics of CAS
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Abstract

The invention belongs to the field of signal and information processing, and particularly relates to an incoherent scattering ionospheric parameter inversion method, system and device based on Bayesian filtering, aiming at solving the problem of poor resolution of ionospheric parameters obtained by the existing incoherent scattering radar ionospheric parameter extraction method. The method comprises the following steps: obtainingkTheoretical initial values of basic parameters of the ionized layer on all range gates and corresponding prior variances of the basic parameters at all times; obtaining theoretical autocorrelation data; to obtainkThe ionospheric basic parameters and the corresponding error covariance matrix are fitted on each range gate at the moment; judging whether the fitting is finished or not, if not, obtaining the fitting through a Bayesian filtering methodkTheoretical initial values of basic parameters of the ionized layer on all range gates at +1 moment and corresponding prior variances of the basic parameters; if so, carrying out recursive smoothing processing through a Bayesian smoothing algorithm to obtain the finally inverted ionospheric base parameters. The invention improves the time and distance resolution of the incoherent scattering ionosphere parametric inversion.

Description

Incoherent scattering ionosphere parameter inversion method and system based on Bayesian filtering
Technical Field
The invention belongs to the field of signal and information processing, and particularly relates to a method, a system and a device for incoherent scattering ionospheric parameter inversion based on Bayesian filtering.
Background
For incoherent scattering detection of an ionized layer, the ionized layer can be regarded as a soft target which is continuously distributed in a large range, an echo signal received by a radar is a zero-mean backscatter random signal of an electromagnetic wave signal transmitted from the ground and modulated by the thermal fluctuation of electrons and ions in the ionized layer, the echo power is very weak relative to the transmission power, and the power spectral density of the echo signal is a function of parameters of the ionized layer such as electron density, electron temperature, ion temperature, plasma sight drift velocity and the like. In order to extract and obtain ionospheric basic parameters from weak incoherent scattering echo signals, a high-power phased array incoherent scattering radar is the most advanced and effective detection means at present and has the characteristics of wide detection range, more ionospheric parameter detection, higher time and space resolution and the like.
In incoherent scatter radar detection, long pulses and alternating codes are typically employed as radar transmission signals. The long pulse echo signal power is relatively high, but the range resolution is relatively poor, usually tens of kilometers, and the alternating code has relatively low echo signal power due to its phase encoding characteristic, but the range resolution is relatively high, usually hundreds of meters to several kilometers. The ionospheric parameter extraction is carried out aiming at echo signals of the two coding forms, the conventional inversion method is based on range gate analysis, namely, the autocorrelation of theoretical autocorrelation data and the autocorrelation of actually-measured incoherent scattering echo signals are subjected to nonlinear least square fitting one by one, the theoretical initial value used by each fitting height completely depends on an IRI theoretical model, the fitting between different range gates and different moments is mutually independent, and the ionospheric parameter with higher resolution, namely the incoherent scattering echo signals with high signal-to-noise ratio, can be obtained by the fitting method only through accurate measurement of incoherent scattering spectra. In order to improve the signal-to-noise ratio of the actually measured echo signal, it is necessary to perform multi-period accumulation at distance and time and then perform parametric inversion. Generally, in an incoherent scattering radar multi-beam scanning detection experiment of a phased array system, in order to obtain reliable ionospheric parameters, after a plurality of heights are accumulated for alternative code echo signals with higher distance resolution, range gate inversion is performed to obtain ionospheric parameters with time resolution of tens of minutes and distance resolution magnitude of tens of kilometers, and long pulse distance resolution becomes worse, which is far from sufficient for dynamics research of fast-changing ionospheric disturbance. Therefore, the invention combines Bayesian smoothing in time and the related prior knowledge in distance direction to obtain the ionospheric parameters with high time resolution and high distance resolution, which has important application value for the fine structure research of the ionospheric.
Disclosure of Invention
In order to solve the above problems in the prior art, that is, to solve the problem of poor resolution of the ionospheric parameters obtained by the existing method for extracting the ionospheric parameters of the incoherent scattering radar, the first aspect of the present invention provides a method for inverting the incoherent scattering ionospheric parameters based on bayesian filtering, the method comprising:
step S100, acquiring an ionosphere model according to the IRIkTheoretical initial values of basic parameters of the ionized layer on all range gates and corresponding prior variances of the basic parameters at all times;kwhen the time is initialized, the time is the actual time corresponding to the actually measured autocorrelation data adopted in the first fitting; the ionospheric essential parameters include electron density, electron temperature, ion temperature and plasma line-of-sight drift velocity;
step S200 based onkCalculating a theoretical spectrum on each range gate through a scattering spectrum theoretical model according to a theoretical initial value of an ionosphere basic parameter on each range gate at any moment, and performing inverse Fourier transform on the theoretical spectrum on each range gate to obtain theoretical autocorrelation data;
step S300, for each range gate, carrying out nonlinear least square operation on the corresponding actual measurement autocorrelation data and theoretical autocorrelation data to obtainkThe ionospheric basic parameters and the corresponding error covariance matrix are fitted on each range gate at the moment;
step S400, judging whether the ionospheric basic parameters and the corresponding error covariance matrixes on all the range gates at all the moments in the set time period are fitted, if so, skipping to step S600; otherwise, skipping to the step S500;
step S500, obtaining through a Bayesian filtering methodkTheoretical initial values of ionospheric base parameters at +1 time points and corresponding prior variances, and orderk= k+1, skipping to step S200;
and step S600, performing recursive smoothing processing on the ionospheric basic parameters and the corresponding error covariance matrixes fitted on the range gates at all the moments in the set time period through a Bayes smoothing algorithm to obtain the final inverted ionospheric basic parameters.
In some preferred embodiments, the relationship between the measured autocorrelation data and the theoretical autocorrelation data is:
Figure 860712DEST_PATH_IMAGE001
wherein,
Figure 656630DEST_PATH_IMAGE002
、
Figure 675401DEST_PATH_IMAGE003
for the original complex signal echo sequence measured by the radar receiver,
Figure 291190DEST_PATH_IMAGE004
in order to be the value of the time delay,
Figure 53610DEST_PATH_IMAGE005
the autocorrelation of the incoherent scattered echo signal, i.e. the measured autocorrelation data,
Figure 704034DEST_PATH_IMAGE006
in order to be the impedance of the radar receiver,
Figure 362549DEST_PATH_IMAGE007
in order to transmit power for the radar,
Figure 996792DEST_PATH_IMAGE008
in order to transmit the pulse width of the pulse,
Figure 31744DEST_PATH_IMAGE009
as is the distance from the radar antenna to the scattering point,
Figure 551324DEST_PATH_IMAGE010
in order to be a function of the delay ambiguity,
Figure 911898DEST_PATH_IMAGE011
for a distance door
Figure 502279DEST_PATH_IMAGE012
Density of electrons in situ
Figure 340922DEST_PATH_IMAGE013
Electron temperature of
Figure 231518DEST_PATH_IMAGE014
Ion temperature
Figure 497414DEST_PATH_IMAGE015
Plasma line-of-sight drift velocity
Figure 575091DEST_PATH_IMAGE016
The theoretical autocorrelation data of the determined plasma,
Figure 951846DEST_PATH_IMAGE017
are system constants related to radar antenna gain, radar cross section, and the like.
In some preferred embodiments, for each range gate, performing nonlinear least squares operation on the corresponding measured autocorrelation data and theoretical autocorrelation data to obtain ionospheric base parameters fitted to each range gate, the method includes:
and according to the set range gate stepping interval, carrying out nonlinear least square operation on the measured autocorrelation data and the theoretical autocorrelation data corresponding to each range gate one by one to obtain the ionospheric basic parameters fitted on each range gate.
In some preferred embodiments, in the incoherent scattering radar detection, if an alternate code is used as a radar transmission signal, the minimum delay product at each detection distance of the delay profile matrix is removed, and the minimum delay product does not participate in the fitting of the range gate of the measured autocorrelation data.
In some preferred embodiments, the error covariance matrix corresponding to each range gate is obtained by:
Figure 696948DEST_PATH_IMAGE018
wherein,
Figure 133746DEST_PATH_IMAGE019
in order to be the error covariance matrix,
Figure 964299DEST_PATH_IMAGE020
to fit the first order partial derivatives of the residuals,
Figure 144744DEST_PATH_IMAGE021
for the variance of the measured autocorrelation data,Tindicating transposition.
In some preferred embodiments, the obtaining is performed by a Bayesian filtering methodkThe method of the initial basic parameters on all the range gates at the +1 moment comprises the following steps:
if unknown ionospheric base parametersxA priori of
Figure 744353DEST_PATH_IMAGE022
True ionospheric base parametersxThe mapping relation of the theoretical initial value corresponding to the data is
Figure 352052DEST_PATH_IMAGE023
The prior variance is
Figure 404321DEST_PATH_IMAGE024
Then the linear relationship between them is:
Figure 388458DEST_PATH_IMAGE025
will be provided with
Figure 842573DEST_PATH_IMAGE023
、
Figure 621173DEST_PATH_IMAGE024
Expand in maximum second order difference form respectively:
Figure 160739DEST_PATH_IMAGE026
，
Figure 680057DEST_PATH_IMAGE027
wherein,
Figure 988679DEST_PATH_IMAGE028
、
Figure 938180DEST_PATH_IMAGE029
、
Figure 965042DEST_PATH_IMAGE030
respectively representing the prior variances of the zeroth order, the first order and the second order;
for each ionospheric base parameter, the difference matrix of the zeroth order is an identity matrix, i.e.
Figure 290981DEST_PATH_IMAGE031
First and second order difference matrices
Figure 985268DEST_PATH_IMAGE032
、
Figure 105671DEST_PATH_IMAGE033
Are respectively as
Figure 354249DEST_PATH_IMAGE034
And
Figure 218300DEST_PATH_IMAGE035
is expressed as:
Figure 767093DEST_PATH_IMAGE036
，
Figure 58397DEST_PATH_IMAGE037
wherein,
Figure 794272DEST_PATH_IMAGE038
representing the number of distance gates;
the error covariance matrixes on all range gates obtained by fitting at the previous moment can be used as a zeroth-order covariance matrix, so that first-order and second-order covariance matrixes can be further deduced, namely the first-order and second-order covariance matrixes are respectively
Figure 196434DEST_PATH_IMAGE039
Wherein,
Figure 599734DEST_PATH_IMAGE040
in order to take the diagonal line,
Figure 61939DEST_PATH_IMAGE041
in order to step the interval from the door,
Figure 550690DEST_PATH_IMAGE042
for the relevant length of each parameter, proportional to the plasma level
Figure 22122DEST_PATH_IMAGE043
，
Figure 14349DEST_PATH_IMAGE044
Is a constant value, and is characterized in that,
Figure 650385DEST_PATH_IMAGE045
representkAt the first moment
Figure 626432DEST_PATH_IMAGE046
A covariance matrix of range gates;
using least squares thought calculation
Figure 635976DEST_PATH_IMAGE047
To the minimum, then from the above equation for the linear relationship:
Figure 748288DEST_PATH_IMAGE048
wherein,
Figure 817876DEST_PATH_IMAGE049
is a parameter profile after the Bayesian filtering,
Figure 750059DEST_PATH_IMAGE050
is a covariance matrix after Bayesian filtering,Trepresenting a transpose; therefore, the method is based on the theoretical initial value of the basic parameters of the ionized layer at the next moment after Bayesian filtering
Figure 828874DEST_PATH_IMAGE051
And corresponding a priori variance
Figure 530114DEST_PATH_IMAGE052
Are respectively as
Figure 36181DEST_PATH_IMAGE053
Wherein,
Figure 455661DEST_PATH_IMAGE054
the time step interval, i.e. the integration time in the fitting process,
Figure 807008DEST_PATH_IMAGE055
is a constant value, and is characterized in that,
Figure 628334DEST_PATH_IMAGE056
is the process noise variance.
In a second aspect of the present invention, a system for inverting incoherent scattering ionospheric parameters based on bayesian filtering is provided, the system comprising: the system comprises a parameter initial value acquisition module, a theoretical autocorrelation calculation module, a parameter output module, a circulation judgment module, a Bayesian filtering module and a Bayesian smoothing module;
the parameter initial value acquisition module is configured to acquire the parameter initial value according to the IRI ionosphere modelkTheoretical initial values of basic parameters of the ionized layer on all range gates and corresponding prior variances of the basic parameters at all times;kwhen the time is initialized, the actual time is corresponding to the actually measured autocorrelation data adopted during the first fitting; the ionospheric base parameters including electron densityDegree, electron temperature, ion temperature, and plasma line-of-sight drift velocity;
the theoretical autocorrelation calculating module is configured to be based onkCalculating a theoretical spectrum on each range gate through a scattering spectrum theoretical model according to a theoretical initial value of an ionosphere basic parameter on each range gate at any moment, and performing inverse Fourier transform on the theoretical spectrum on each range gate to obtain theoretical autocorrelation data;
the parameter output module is configured to perform nonlinear least square operation on the corresponding measured autocorrelation data and theoretical autocorrelation data of each range gate to obtainkThe ionospheric basic parameters and the corresponding error covariance matrix are fitted on each range gate at the moment;
the loop judgment module is configured to judge whether the ionospheric basic parameters and the corresponding error covariance matrixes on the distance gates at all moments in a set time period are fitted or not, and if yes, the Bayesian smoothing module is skipped; otherwise, skipping the Bayesian filtering module;
the Bayesian filtering module is configured to obtain the signal by a Bayesian filtering methodkTheoretical initial values of ionospheric base parameters at +1 time points and corresponding prior variances, and orderk= k+1, skipping the theoretical autocorrelation calculation;
and the Bayesian smoothing module is configured to perform recursive smoothing on the ionospheric basis parameters and the corresponding error covariance matrix fitted on each range gate at all moments in a set time period through a Bayesian smoothing algorithm to obtain final inverted ionospheric basis parameters.
In a third aspect of the present invention, a storage device is provided, in which a plurality of programs are stored, and the programs are loaded and executed by a processor to implement the above-mentioned non-coherent scatter ionospheric parametric inversion method based on bayesian filtering.
In a fourth aspect of the present invention, a processing apparatus is provided, which includes a processor, a storage device; a processor adapted to execute programs; a storage device adapted to store a plurality of programs; the program is suitable for being loaded and executed by a processor to realize the incoherent scattering ionospheric parameter inversion method based on Bayesian filtering.
The invention has the beneficial effects that:
the invention improves the time and distance resolution of incoherent scattering ionospheric parameter inversion.
The method combines parameters obtained by fitting at the previous moment in ionosphere parameter inversion and error covariance thereof, predicts a theoretical initial value and prior variance of distance gate fitting at the next moment based on a Bayesian filtering method, and controls the gradients of plasma parameters in time and space by utilizing the correlation of prior information between different heights, thereby obtaining the ionosphere parameters with high resolution.
Drawings
Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings.
FIG. 1 is a schematic flow chart of a method for inverting incoherent scattering ionospheric parameters based on Bayesian filtering according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of range gate formation of autocorrelation data of a measured incoherent scattered echo signal according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a framework of a Bayesian filtering-based incoherent scattering ionospheric parametric inversion system according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of ionospheric parametric inversion results of alternative code echo signals according to an embodiment of the invention;
FIG. 5 is a schematic illustration of the ionospheric parametric inversion results of long pulse echo signals, in accordance with an embodiment of the invention;
fig. 6 is a schematic structural diagram of a computer system of an electronic device suitable for implementing the embodiments of the present application according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The present application will be described in further detail with reference to the following drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be noted that, for convenience of description, only the portions related to the related invention are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict.
The incoherent scattering ionosphere parametric inversion method based on Bayesian filtering, as shown in FIG. 1, comprises the following steps:
step S100, obtaining an IRI ionosphere modelkTheoretical initial values of basic parameters of the ionized layer on all range gates and corresponding prior variances of the basic parameters at all times;kwhen the time is initialized, the actual time is corresponding to the actually measured autocorrelation data adopted during the first fitting; the ionospheric basic parameters comprise electron density, electron temperature, ion temperature and plasma line-of-sight drift velocity;
step S200 based onkCalculating a theoretical spectrum on each range gate through a scattering spectrum theoretical model according to a theoretical initial value of an ionospheric basic parameter on each range gate at any moment, and performing inverse Fourier transform on the theoretical spectrum on each range gate to obtain theoretical autocorrelation data;
step S300, for each range gate, carrying out nonlinear least square operation on the corresponding actual measurement autocorrelation data and theoretical autocorrelation data to obtainkThe ionospheric basic parameters and the corresponding error covariance matrix are fitted on each range gate at the moment;
step S400, judging whether the ionospheric basic parameters and the corresponding error covariance matrixes on all the range gates at all the moments in the set time period are fitted, if so, skipping to step S600; otherwise, skipping to the step S500;
step S500, obtaining through a Bayesian filtering methodkTheoretical initial values of ionospheric base parameters at +1 moment and their corresponding prior variances, and orderk= k+1, skipping to step S200;
and step S600, performing recursive smoothing processing on the ionospheric basic parameters and the corresponding error covariance matrixes fitted on the range gates at all the moments in the set time period through a Bayes smoothing algorithm to obtain the final inverted ionospheric basic parameters.
In order to more clearly explain the incoherent scattering ionospheric parameter inversion method based on bayesian filtering, the following describes each step in an embodiment of the method in detail with reference to the accompanying drawings.
Step S100, obtaining an IRI ionosphere modelkTheoretical initial values of ionospheric basic parameters at all range gates and corresponding prior variances at all times;kwhen the time is initialized, the time is the actual time corresponding to the actually measured autocorrelation data adopted in the first fitting; the ionospheric basic parameters comprise electron density, electron temperature, ion temperature and plasma line-of-sight drift velocity;
in this embodiment, the electron density, which is the basic parameters of the four ionosphere to be measured at all range gates at the first time, is obtained from the IRI ionosphere model
Figure 305303DEST_PATH_IMAGE057
Electron temperature, electron temperature
Figure 212079DEST_PATH_IMAGE014
Ion temperature of
Figure 367117DEST_PATH_IMAGE058
Plasma line-of-sight drift velocity
Figure 42949DEST_PATH_IMAGE016
And the variance is used as the initial value of the parameter for calculating the theoretical spectrum, and the corresponding prior variance is also obtained and used for the weighting coefficient in the fitting process. Wherein the first moment iskThe time is an actual time corresponding to the measured autocorrelation data used in the first fitting at the time of initialization.
Step S200 based onkCalculating a theoretical spectrum on each range gate through a scattering spectrum theoretical model according to a theoretical initial value of an ionosphere basic parameter on each range gate at any moment, and performing inverse Fourier transform on the theoretical spectrum on each range gate to obtain theoretical autocorrelation data;
in the embodiment, the theoretical initial value of the ionospheric essential parameter is used as the initial input of the scattering spectrum theoretical model, and the theoretical spectrum at each range gate is calculated. The power spectrum and the autocorrelation are a Fourier transform pair, and the theoretical spectrum further obtains theoretical autocorrelation data through inverse Fourier transform.
Step S300, for each range gate, carrying out nonlinear least square operation on the corresponding actual measurement autocorrelation data and theoretical autocorrelation data to obtainkThe ionospheric basic parameters and the corresponding error covariance matrix are fitted on each range gate at the moment;
in this embodiment, the range gate of the measured autocorrelation data is formed as shown in fig. 2, and taking the present invention as an example, it is assumed that the delay profile matrix includes eight detection ranges, and each detection range has four delay products such as
Figure 890819DEST_PATH_IMAGE059
、
Figure 284891DEST_PATH_IMAGE060
、
Figure 243620DEST_PATH_IMAGE061
、
Figure 36608DEST_PATH_IMAGE062
And performing data recombination at each time delay product according to a set range gate summation rule, for example, forming autocorrelation data on a range gate by time delay products at every three detection ranges, namely for
Figure 524221DEST_PATH_IMAGE059
Will delay profileIn a planar matrix
Figure 671169DEST_PATH_IMAGE063
、
Figure 168009DEST_PATH_IMAGE064
、
Figure 818433DEST_PATH_IMAGE065
Of
Figure 8106DEST_PATH_IMAGE059
With data rearrangement to form range gate 0
Figure 111191DEST_PATH_IMAGE059
The data of the data is transmitted to the data receiver,
Figure 146143DEST_PATH_IMAGE066
、
Figure 916653DEST_PATH_IMAGE067
、
Figure 277228DEST_PATH_IMAGE068
of
Figure 867609DEST_PATH_IMAGE059
With data rearrangement to form range gates 1
Figure 706252DEST_PATH_IMAGE059
And D, repeating the steps to complete the time delay product recombination of all the preset distance gates. Especially for alternate codes, because
Figure 596847DEST_PATH_IMAGE059
Has a large distance ambiguity, so it is necessary to make the position of the object to be measured
Figure 862744DEST_PATH_IMAGE059
The time delay product is removed and does not participate in the fitting of the range gate.
The relationship between the theoretical autocorrelation and the autocorrelation of the measured incoherent scattered echo signal is expressed as:
Figure 206000DEST_PATH_IMAGE069
（1）
wherein,
Figure 582755DEST_PATH_IMAGE070
、
Figure 327857DEST_PATH_IMAGE003
for the original complex signal echo sequence measured by the radar receiver,
Figure 764655DEST_PATH_IMAGE004
is a time delay value, is an integer multiple of the sampling interval,
Figure 595208DEST_PATH_IMAGE071
the autocorrelation of the incoherent scattered echo signal, i.e. the measured autocorrelation data,
Figure 775653DEST_PATH_IMAGE072
in order to be the impedance of the radar receiver,
Figure 366473DEST_PATH_IMAGE007
for the radar transmission power (W),
Figure 974172DEST_PATH_IMAGE008
in order to transmit the pulse width(s),
Figure 26441DEST_PATH_IMAGE009
is the distance (m) from the radar antenna to the scattering point,
Figure 10578DEST_PATH_IMAGE073
in order to be a function of the delay ambiguity,
Figure 464693DEST_PATH_IMAGE074
for a distance door
Figure 243293DEST_PATH_IMAGE075
Density of electrons in situ
Figure 48438DEST_PATH_IMAGE013
Electron temperature of
Figure 305107DEST_PATH_IMAGE014
Ion temperature
Figure 879308DEST_PATH_IMAGE015
Plasma line-of-sight drift velocity
Figure 828809DEST_PATH_IMAGE016
The determined theoretical autocorrelation data of the plasma,
Figure 121250DEST_PATH_IMAGE017
is a system constant related to the radar antenna gain and radar scattering cross section (
Figure 181610DEST_PATH_IMAGE076
）。
And then continuously adjusting the input value of a theoretical spectrum by a Levenberg-Marquardt nonlinear least square algorithm, and stopping iterative computation when the sum of squares of residual errors of theoretical autocorrelation and actual autocorrelation reaches the minimum value, thereby obtaining four finally credible ionized layer basic parameters including electron density, electron temperature, ion temperature and plasma sight drift velocity. Meanwhile, a matrix with 4 multiplied by 4 of error covariance matrix corresponding to each range gate can be obtained:
Figure 344738DEST_PATH_IMAGE018
（2）
wherein,
Figure 730720DEST_PATH_IMAGE077
in order to be the error covariance matrix,
Figure 244878DEST_PATH_IMAGE020
to fit the residual to first orderThe partial derivatives of the light beams are deflected,
Figure 108929DEST_PATH_IMAGE078
for the variance of the measured autocorrelation data,Tindicating transposition.
According to the set range gate stepping interval, the nonlinear least square operation is carried out on the actually measured autocorrelation data and the theoretical autocorrelation data corresponding to each range gate one by one, and then the ionospheric basic parameters fitted on each range gate are obtained.
The four ionospheric basis parameter matrices on all range gates are in the form:
Figure 657722DEST_PATH_IMAGE079
（3）
wherein,
Figure 949026DEST_PATH_IMAGE038
the distance between the door and the door is the number,
Figure 950480DEST_PATH_IMAGE080
、
Figure 615292DEST_PATH_IMAGE081
、
Figure 18592DEST_PATH_IMAGE082
、
Figure 480797DEST_PATH_IMAGE083
respectively obtained by inversionkTime of day
Figure 438389DEST_PATH_IMAGE046
The electron density, electron temperature, ion temperature, and plasma line-of-sight drift velocity matrices for each range gate, and the error covariance matrix are also defined in similar matrix form.
Step S400, judging whether the ionosphere basic parameters and the corresponding error covariance matrixes on all the range gates at all the moments in the set time period are fitted, if so, skipping to step S600; otherwise, skipping to the step S500;
in this embodiment, all the moments in a set time period are fitted to obtain the ionospheric basis parameters and the corresponding error covariance matrices at all the moments on each range gate, and if the fitting is not completed, the step S500 is skipped; otherwise, jumping to step S600, and further processing the ionospheric basis parameters and the corresponding error covariance matrix on each range gate at all the fitting moments.
Step S500, obtaining through a Bayesian filtering methodkTheoretical initial values of ionospheric base parameters at +1 time points and corresponding prior variances, and orderk= k+1, skipping to step S200;
in the present embodiment, it is assumed that the four ionospheric basis parameter vectors and the error covariance matrix at all range gates obtained at the previous time are expressed as:
Figure 909821DEST_PATH_IMAGE084
（4）
and constructing a parameter profile initial value required by fitting at the next moment by using the ionospheric parameters and the covariance matrix obtained at the previous moment as prior knowledge in combination with a related prior theory. Assuming unknown ionospheric base parametersxA priori value of
Figure 902048DEST_PATH_IMAGE022
Is true value, obtain parametersxThe problem of the theoretical initial value of (2) can be regarded as a linear inversion problem, and the linear mapping relation is
Figure 66313DEST_PATH_IMAGE085
The prior variance is
Figure 776780DEST_PATH_IMAGE086
Then, it can be expressed as the following linear relationship:
Figure 520745DEST_PATH_IMAGE087
（5）
in the above formula (5)
Figure 633058DEST_PATH_IMAGE022
Parameter vectors that can be fitted at a previous time
Figure 702645DEST_PATH_IMAGE088
Sum covariance matrix
Figure 900408DEST_PATH_IMAGE089
Instead. And introducing prior distribution with similar smooth property with the difference prior, namely weighting parameters on all range gates obtained at the previous moment so as to achieve the smoothness on the range gates. In addition, the
Figure 713643DEST_PATH_IMAGE085
、
Figure 680462DEST_PATH_IMAGE024
The maximum second order difference is expanded as follows:
Figure 920951DEST_PATH_IMAGE026
，
Figure 340431DEST_PATH_IMAGE090
（6）
wherein,
Figure 957357DEST_PATH_IMAGE091
、
Figure 778682DEST_PATH_IMAGE092
、
Figure 190072DEST_PATH_IMAGE030
respectively representing the prior variances of the zeroth, first, and second orders.
For each ionospheric parameter, the difference matrix of the zeroth order is an identity matrix, i.e.
Figure 99778DEST_PATH_IMAGE031
First and second order difference matrices
Figure 254816DEST_PATH_IMAGE093
、
Figure 196227DEST_PATH_IMAGE033
Are respectively as
Figure 44097DEST_PATH_IMAGE094
And
Figure 438170DEST_PATH_IMAGE035
is expressed as:
Figure 131319DEST_PATH_IMAGE095
，
Figure 927237DEST_PATH_IMAGE096
（7）
the error covariance matrices on all range gates obtained by fitting at the previous time can be used as a zeroth-order covariance matrix, so that first-order and second-order covariance matrices can be further derived, which are respectively:
Figure 680429DEST_PATH_IMAGE097
（8）
wherein,
Figure 561797DEST_PATH_IMAGE098
in order to take the diagonal line,
Figure 324217DEST_PATH_IMAGE041
in order to step the distance from the door by a spacing,
Figure 974641DEST_PATH_IMAGE099
for the relevant length of each parameter, proportional to the plasma level
Figure 633156DEST_PATH_IMAGE100
，
Figure 267399DEST_PATH_IMAGE044
Is constant by adjusting
Figure 302351DEST_PATH_IMAGE044
To maintain an effective smoothness of the parameter profile over distance. For different ionospheric parameters, such as electron density, electron temperature, ion temperature and plasma line-of-sight drift velocity,
Figure 72861DEST_PATH_IMAGE044
the settings are different.
Using least squares thought calculation
Figure 902277DEST_PATH_IMAGE101
To a minimum, then from equation (5) one can derive:
Figure 758238DEST_PATH_IMAGE102
（9）
wherein,
Figure 862460DEST_PATH_IMAGE103
is a parameter profile after Bayesian filtering,
Figure 221897DEST_PATH_IMAGE104
is a covariance matrix after Bayesian filtering,Trepresenting a transpose; therefore, the theoretical initial value of the ionized layer parameter at the next moment after Bayesian filtering is based
Figure 484864DEST_PATH_IMAGE105
And corresponding a priori variance
Figure 562541DEST_PATH_IMAGE106
Respectively as follows:
Figure 204875DEST_PATH_IMAGE053
（10）
here, ,
Figure 949977DEST_PATH_IMAGE054
the time step interval, i.e. the integration time in the fitting process,
Figure 386775DEST_PATH_IMAGE055
is a constant value, and is characterized in that,
Figure 951748DEST_PATH_IMAGE107
for process noise variance, i.e. by adjustment
Figure 132194DEST_PATH_IMAGE055
The process noise variance is controlled such that the partial correlation priors introduced from one time instant to another preserve the correlation over time. Of course, for different ionospheric parameters,
Figure 731802DEST_PATH_IMAGE055
the settings are also different.
And step S600, performing recursive smoothing processing on the ionospheric basic parameters and the corresponding error covariance matrixes fitted on the range gates at all the moments in the set time period through a Bayes smoothing algorithm to obtain the final inverted ionospheric basic parameters.
In this embodiment, when the accumulation time is short enough, the plasma parameters change little between the previous time and the current time, and the fitted data is further smoothed by using a Rauch-Rung-Striebel (RTS) bayesian smoothing algorithm to obtain the final ionospheric parameters with high resolution, wherein the backward recursion equation of RTS is as follows:
Figure 605080DEST_PATH_IMAGE108
（11）
here, the
Figure 657350DEST_PATH_IMAGE109
And
Figure 375907DEST_PATH_IMAGE110
respectively the fitting parametric result at time k and the corresponding error covariance matrix,
Figure 830023DEST_PATH_IMAGE111
and
Figure 874202DEST_PATH_IMAGE112
respectively a theoretical initial value and a prior covariance matrix at the k +1 moment predicted after Bayesian filtering,
Figure 413768DEST_PATH_IMAGE113
and
Figure 201595DEST_PATH_IMAGE114
the parameter result and the error covariance matrix at the k moment after the Bayes smoothing are obtained,
Figure 510217DEST_PATH_IMAGE115
and
Figure 725297DEST_PATH_IMAGE116
for the parametric result and the error covariance matrix at the k +1 moment after Bayes smoothing,
Figure 486580DEST_PATH_IMAGE117
and the matrix is a dynamic prediction model matrix at the k moment. The ionospheric basic parameters at adjacent moments and the corresponding error covariance matrix are subjected to recursive smoothing by a Bayesian smoothing algorithm, and then the ionospheric basic parameters finally inverted at each moment are obtained.
In order to prove the effectiveness of the inversion method, the data are verified by the actually measured data of the triple incoherent scattering radar, which is detected by the alternating codes and the long pulses at 4 months and 14 days in 2021 at almost the same time. The alternating code parameter is 16-bit alternating code, one-third fractional order sampling, code element width is 30us, and sampling interval is 10us; the long pulse parameter is pulse width 480us, sample interval 10us.
As shown in fig. 4, the ionospheric parameters of electron density, electron temperature, ion temperature, and plasma line-of-sight drift velocity obtained by inverting the echo signal of the alternative code have a time resolution of 12s and a distance resolution of 4.5km.
FIG. 5 shows the ionospheric parameters of electron density, electron temperature, ion temperature and plasma line-of-sight drift velocity obtained by inversion of long pulse echo signals, with a time resolution of 18s, a distance resolution of 9km or less, a distance resolution of 18km or 200-400km, and a distance resolution of 24km or more.
As can be seen from fig. 4 and 5, the ionospheric parameter profiles obtained by inversion in the two encoding modes have higher time resolution, and the alternating codes can still obtain higher distance resolution after inversion even though the echo signals are very weak, which shows that the time and distance resolution of the incoherent scattering ionospheric parameter inversion can be greatly improved when the method is used for the incoherent scattering radar to detect.
A second embodiment of the present invention provides a system for inverting incoherent scattering ionospheric parameters based on bayesian filtering, as shown in fig. 3, including: the system comprises a parameter initial value acquisition module 100, a theoretical autocorrelation calculation module 200, a parameter output module 300, a circulation judgment module 400, a Bayesian filtering module 500 and a Bayesian smoothing module 600;
the parameter initial value obtaining module 100 is configured to obtain the initial value according to the IRI ionosphere modelkTheoretical initial values of ionospheric basic parameters at all range gates and corresponding prior variances at all times;kwhen the time is initialized, the time is the actual time corresponding to the actually measured autocorrelation data adopted in the first fitting; the ionospheric basic parameters comprise electron density, electron temperature, ion temperature and plasma line-of-sight drift velocity;
the theoretical autocorrelation calculation module 200 is configured to be based onkCalculating a theoretical spectrum on each range gate through a scattering spectrum theoretical model according to a theoretical initial value of an ionospheric basic parameter on each range gate at any moment, and performing inverse Fourier transform on the theoretical spectrum on each range gate to obtain theoretical autocorrelation data;
the parameter output module 300 configured to perform nonlinear least square operation on the measured autocorrelation data and the theoretical autocorrelation data corresponding to each range gate to obtainkThe ionospheric basic parameters and the corresponding error covariance matrix are fitted on each range gate at the moment;
the loop judgment module 400 is configured to judge whether the ionospheric basis parameters and the corresponding error covariance matrices on the range gates at all times within a set time period are fitted, and if so, skip the bayesian smoothing module 600; otherwise, skipping to the Bayesian filtering module 500;
the Bayesian filtering module 500 is configured to obtain the Bayesian filtering methodkTheoretical initial values of ionospheric base parameters at +1 moment and their corresponding prior variances, and orderk= k+1, skipping the theoretical autocorrelation calculation module 200;
the bayesian smoothing module 600 is configured to perform recursive smoothing on the ionospheric basis parameters fitted to each range gate at all times within a set time period and the corresponding error covariance matrix through a bayesian smoothing algorithm to obtain final inverted ionospheric basis parameters.
It can be clearly understood by those skilled in the art that, for convenience and simplicity of description, reference may be made to the corresponding process in the foregoing method embodiment for the specific working process and related description of the system described above, and details are not described herein again.
It should be noted that, the incoherent scattering ionospheric parametric inversion system based on bayesian filtering provided in the foregoing embodiment is only illustrated by the division of the above functional modules, and in practical applications, the above functions may be allocated to different functional modules according to needs, that is, the modules or steps in the embodiment of the present invention are decomposed or combined again, for example, the modules in the foregoing embodiment may be combined into one module, or may be further split into multiple sub-modules, so as to complete all or part of the above described functions. The names of the modules and steps involved in the embodiments of the present invention are only for distinguishing the modules or steps, and are not to be construed as unduly limiting the present invention.
A storage device according to a third embodiment of the present invention stores therein a plurality of programs, which are adapted to be loaded by a processor and to implement the above-described method for incoherent scattering ionospheric parameter inversion based on bayesian filtering.
A processing apparatus according to a fourth embodiment of the present invention includes a processor, a storage device; a processor adapted to execute various programs; a storage device adapted to store a plurality of programs; the program is adapted to be loaded and executed by a processor to implement the above-described bayesian-filter-based incoherent scatter ionospheric parametric inversion method.
It can be clearly understood by those skilled in the art that, for convenience and simplicity of description, the specific working processes and related descriptions of the storage device and the processing device described above may refer to the corresponding processes in the foregoing method examples, and are not described herein again.
Referring now to FIG. 6, shown is a block diagram of a computer system suitable for use as a server for implementing embodiments of the present methods, systems, and apparatus. The server shown in fig. 6 is only an example, and should not bring any limitation to the functions and the use range of the embodiments of the present application.
As shown in fig. 6, the computer system includes a Central Processing Unit (CPU) 601, which can perform various appropriate actions and processes according to a program stored in a Read Only Memory (ROM) 602 or a program loaded from a storage section 608 into a Random Access Memory (RAM) 603. In the RAM603, various programs and data necessary for system operation are also stored. The CPU601, ROM 602, and RAM603 are connected to each other via a bus 604. An Input/Output (I/O) interface 605 is also connected to bus 604.
The following components are connected to the I/O interface 605: an input portion 606 including a keyboard, a mouse, and the like; an output section 607 including a Cathode Ray Tube (CRT), a Liquid Crystal Display (LCD), and the like, a speaker, and the like; a storage section 608 including a hard disk and the like; and a communication section 609 including a Network interface card such as a LAN (Local Area Network) card, a modem, or the like. The communication section 609 performs communication processing via a network such as the internet. The driver 610 is also connected to the I/O interface 605 as needed. A removable medium 611 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, or the like is mounted on the drive 610 as necessary, so that the computer program read out therefrom is mounted in the storage section 608 as necessary.
In particular, according to an embodiment of the present disclosure, the processes described above with reference to the flowcharts may be implemented as computer software programs. For example, embodiments of the present disclosure include a computer program product comprising a computer program embodied on a computer readable medium, the computer program comprising program code for performing the method illustrated in the flow chart. In such an embodiment, the computer program may be downloaded and installed from a network through the communication section 609, and/or installed from the removable medium 611. More specific examples of a computer readable storage medium may include, but are not limited to, an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing Propagate or transport the program for use by or in connection with the instruction execution system, apparatus, or device. Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to: wireless, wire, fiber optic cable, RF, etc., or any suitable combination of the foregoing.
Computer program code for carrying out operations for aspects of the present application may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, smalltalk, C + + or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet service provider).
The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present application. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
The terms "first," "second," and the like are used for distinguishing between similar elements and not necessarily for describing or implying a particular order or sequence.
The terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
So far, the technical solutions of the present invention have been described in connection with the preferred embodiments shown in the drawings, but it is easily understood by those skilled in the art that the scope of the present invention is obviously not limited to these specific embodiments. Equivalent changes or substitutions of related technical features can be made by those skilled in the art without departing from the principle of the invention, and the technical scheme after the changes or substitutions can fall into the protection scope of the invention.

Claims (9)

1. A non-coherent scattering ionosphere parameter inversion method based on Bayesian filtering is characterized by comprising the following steps:
step S100, obtaining an IRI ionosphere modelkTheoretical initial values of ionospheric basic parameters at all range gates and corresponding prior variances at all times;kwhen the time is initialized, the time is the actual time corresponding to the actually measured autocorrelation data adopted in the first fitting; the ionospheric basic parameters comprise electron density, electron temperature, ion temperature and plasma line-of-sight drift velocity;
step S200 based onkCalculating a theoretical spectrum on each range gate through a scattering spectrum theoretical model according to a theoretical initial value of an ionosphere basic parameter on each range gate at any moment, and performing inverse Fourier transform on the theoretical spectrum on each range gate to obtain theoretical autocorrelation data;
step S300, for each range gate, carrying out nonlinear least square operation on the corresponding actual measurement autocorrelation data and theoretical autocorrelation data to obtainkThe ionospheric basic parameters and the corresponding error covariance matrix are fitted on each range gate at the moment;
step S400, judging whether the ionosphere basic parameters and the corresponding error covariance matrixes on all the range gates at all the moments in the set time period are fitted, if so, skipping to step S600; otherwise, skipping to the step S500;
step S500, obtaining through a Bayesian filtering methodkTheoretical initial values of ionospheric base parameters at +1 time points and corresponding prior variances, and orderk= k+1, skipping to step S200;
and step S600, performing recursive smoothing processing on the ionospheric basic parameters and the corresponding error covariance matrixes fitted on the range gates at all the moments in the set time period through a Bayes smoothing algorithm to obtain the final inverted ionospheric basic parameters.
2. The Bayesian filter-based incoherent scattering ionospheric parameter inversion method of claim 1, wherein a relationship between measured autocorrelation data and theoretical autocorrelation data is:
Figure DEST_PATH_IMAGE001
wherein,
Figure 504371DEST_PATH_IMAGE002
、
Figure DEST_PATH_IMAGE003
for the original complex signal echo sequence measured by the radar receiver,
Figure 831579DEST_PATH_IMAGE004
is a value of the time delay, and is,
Figure DEST_PATH_IMAGE005
the autocorrelation of the incoherent scattered echo signal, i.e. the measured autocorrelation data,
Figure 289105DEST_PATH_IMAGE006
in order to be the impedance of the radar receiver,
Figure DEST_PATH_IMAGE007
in order to transmit power for the radar,
Figure 648017DEST_PATH_IMAGE008
in order to transmit the pulse width of the pulse,
Figure DEST_PATH_IMAGE009
as is the distance from the radar antenna to the scattering point,
Figure 267218DEST_PATH_IMAGE010
in order to be a function of the delay ambiguity,
Figure DEST_PATH_IMAGE011
for a distance door
Figure 65409DEST_PATH_IMAGE012
Density of electrons in situ
Figure DEST_PATH_IMAGE013
Electron temperature, electron temperature
Figure 811779DEST_PATH_IMAGE014
Ion temperature
Figure DEST_PATH_IMAGE015
Plasma line-of-sight drift velocity
Figure 11817DEST_PATH_IMAGE016
The theoretical autocorrelation data of the determined plasma,
Figure DEST_PATH_IMAGE017
are system constants related to the radar antenna gain and the radar cross section.
3. The method for the parameter inversion of the incoherent scattering ionosphere based on the bayesian filter according to claim 1, wherein the non-linear least square operation is performed on the measured autocorrelation data and the theoretical autocorrelation data corresponding to each range gate to obtain the ionosphere basic parameters fitted on each range gate, and the method comprises the following steps:
and according to the set range gate stepping interval, carrying out nonlinear least square operation on the measured autocorrelation data and the theoretical autocorrelation data corresponding to each range gate one by one to obtain the ionospheric basic parameters fitted on each range gate.
4. The Bayesian filter-based incoherent scattering ionospheric parameter inversion method of claim 3, wherein in incoherent scattering radar detection, if an alternate code is used as a radar transmission signal, the minimum delay product at each detection distance of the delay profile matrix is removed, and the minimum delay product does not participate in fitting of a range gate of actually measured autocorrelation data.
5. The Bayesian filter-based incoherent scattering ionospheric parametric inversion method of claim 1, wherein the error covariance matrix corresponding to each range gate is obtained by:
Figure 801918DEST_PATH_IMAGE018
wherein,
Figure DEST_PATH_IMAGE019
in order to be the error covariance matrix,
Figure 103718DEST_PATH_IMAGE020
in order to fit the residual first-order partial derivatives,
Figure DEST_PATH_IMAGE021
for the variance of the measured autocorrelation data,Tindicating transposition.
6. The Bayesian filter based incoherent scattering ionospheric parameter inversion method of claim 5, wherein said obtaining is by a Bayesian filter methodkThe initial basic parameters of all the distance doors at the +1 moment are as follows:
if unknown ionospheric base parametersxA priori of
Figure 371888DEST_PATH_IMAGE022
True ionospheric base parametersxThe mapping relation of the theoretical initial value corresponding to the data is
Figure DEST_PATH_IMAGE023
The prior variance is
Figure 692011DEST_PATH_IMAGE024
Then the linear relationship between them is:
Figure DEST_PATH_IMAGE025
will be provided with
Figure 934904DEST_PATH_IMAGE026
、
Figure DEST_PATH_IMAGE027
Are respectively provided withMaximum second order difference form expansion:
Figure 973268DEST_PATH_IMAGE028
，
Figure DEST_PATH_IMAGE029
wherein,
Figure 58511DEST_PATH_IMAGE030
、
Figure DEST_PATH_IMAGE031
、
Figure 498719DEST_PATH_IMAGE032
respectively representing the prior variances of the zeroth order, the first order and the second order;
for each ionospheric base parameter, the difference matrix of the zeroth order is an identity matrix, i.e.
Figure DEST_PATH_IMAGE033
First and second order difference matrices
Figure 630623DEST_PATH_IMAGE034
、
Figure DEST_PATH_IMAGE035
Are respectively as
Figure 907015DEST_PATH_IMAGE036
And
Figure DEST_PATH_IMAGE037
expressed as:
Figure 782567DEST_PATH_IMAGE038
，
Figure DEST_PATH_IMAGE039
wherein,
Figure 77282DEST_PATH_IMAGE040
representing the number of distance gates;
the error covariance matrixes on all range gates obtained by fitting at the previous moment can be used as a zeroth-order covariance matrix, so that first-order and second-order covariance matrixes can be further deduced, namely the first-order and second-order covariance matrixes are respectively
Figure DEST_PATH_IMAGE041
Wherein,
Figure 396399DEST_PATH_IMAGE042
in order to take the diagonal line out,
Figure DEST_PATH_IMAGE043
in order to step the interval from the door,
Figure 409355DEST_PATH_IMAGE044
for the relevant length of each parameter, proportional to the plasma level
Figure DEST_PATH_IMAGE045
，
Figure 636068DEST_PATH_IMAGE046
Is a constant value, and is characterized in that,
Figure DEST_PATH_IMAGE047
to representkAt the first moment
Figure 939617DEST_PATH_IMAGE040
A covariance matrix of range gates;
using least squares thought calculations
Figure 147744DEST_PATH_IMAGE048
To a minimum, then the equation for the linear relationship described above yields:
Figure DEST_PATH_IMAGE049
wherein,
Figure 913575DEST_PATH_IMAGE050
is a parameter profile after Bayesian filtering,
Figure 616083DEST_PATH_IMAGE051
is a covariance matrix after Bayes filtering,Trepresenting a transposition; therefore, the method is based on the theoretical initial value of the basic parameters of the ionized layer at the next moment after Bayesian filtering
Figure 619811DEST_PATH_IMAGE052
And corresponding a priori variance
Figure DEST_PATH_IMAGE053
Are respectively as
Figure 811889DEST_PATH_IMAGE054
Wherein,
Figure DEST_PATH_IMAGE055
the time step interval, i.e. the integration time in the fitting process,
Figure 65016DEST_PATH_IMAGE056
is a constant value, and is characterized in that,
Figure DEST_PATH_IMAGE057
is the process noise variance.
7. A non-coherent scattering ionospheric parametric inversion system based on Bayesian filtering, characterized in that the system comprises: the system comprises a parameter initial value acquisition module, a theoretical autocorrelation calculation module, a parameter output module, a circulation judgment module, a Bayesian filtering module and a Bayesian smoothing module;
the parameter initial value acquisition module is configured to acquire parameters according to the IRI ionosphere modelkTheoretical initial values of ionospheric basic parameters at all range gates and corresponding prior variances at all times;kwhen the time is initialized, the time is the actual time corresponding to the actually measured autocorrelation data adopted in the first fitting; the ionospheric essential parameters include electron density, electron temperature, ion temperature and plasma line-of-sight drift velocity;
the theoretical autocorrelation calculating module is configured to be based onkCalculating a theoretical spectrum on each range gate through a scattering spectrum theoretical model according to a theoretical initial value of an ionospheric basic parameter on each range gate at any moment, and performing inverse Fourier transform on the theoretical spectrum on each range gate to obtain theoretical autocorrelation data;
the parameter output module is configured to perform nonlinear least square operation on the corresponding measured autocorrelation data and theoretical autocorrelation data of each range gate to obtainkThe ionospheric basic parameters and the corresponding error covariance matrix are fitted on each range gate at the moment;
the loop judgment module is configured to judge whether the ionospheric basic parameters and the corresponding error covariance matrixes on the distance gates at all moments in a set time period are fitted or not, and if yes, the Bayesian smoothing module is skipped; otherwise, skipping the Bayesian filtering module;
the Bayesian filtering module is configured to obtain through a Bayesian filtering methodkTheoretical initial values of ionospheric base parameters at +1 moment and their corresponding prior variances, and orderk= k+1, skipping the theoretical autocorrelation calculation module;
and the Bayesian smoothing module is configured to perform recursive smoothing on the ionospheric basis parameters and the corresponding error covariance matrix fitted on each range gate at all moments in a set time period through a Bayesian smoothing algorithm to obtain final inverted ionospheric basis parameters.
8. A storage device having stored therein a plurality of programs, wherein said programs are applied for loading and execution by a processor to implement the bayesian filter based incoherent scatter ionospheric parametric inversion method of any one of claims 1 to 6.
9. A processing device comprising a processor, a storage device; a processor adapted to execute programs; a storage device adapted to store a plurality of programs; wherein the program is adapted to be loaded and executed by a processor to implement the Bayesian filter based incoherent scattering ionospheric parametric inversion method of any of claims 1-6.
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