CN112014813A - Sky-wave radar ionosphere pollution correction method and system - Google Patents
Sky-wave radar ionosphere pollution correction method and system Download PDFInfo
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Abstract
The invention relates to a sky-wave radar ionosphere pollution correction method and system. According to the method, a spline function is selected as a kernel function of parameterized time-frequency transformation according to the characteristics of ionospheric pollution, kernel function parameters are estimated according to signals after the ionospheric pollution, a pollution sequence is estimated by using the kernel function, and pollution correction is carried out. And for ionospheric pollution under the multimode propagation condition, the pollution is corrected by adopting a filtering mode after correction and iterating for multiple times. The sky-wave radar ionosphere pollution correction method and system provided by the invention can be suitable for pollution under the multimode condition, and improve the correction precision.
Description
Technical Field
The invention relates to the field of sky-wave radar ionosphere pollution correction, in particular to a sky-wave radar ionosphere pollution correction method and system.
Background
The sky wave over-the-horizon radar works in a short wave band (3-30MHz), and the over-the-horizon detection of air or sea/ground targets beyond thousands of kilometers is completed by utilizing the reflection effect of an ionosphere on short wave electromagnetic waves. Due to the 'look-down' mode of operation, sea/ground clutter interference is severe when detecting sea/ground targets. The sea/ground targets are slow moving, and to detect targets from strong sea/ground clutter, a long accumulation time is required to obtain sufficient doppler resolution to separate clutter and targets in the doppler domain. For the detection of sea/ground targets, the typical coherent integration time is 10-40 s. The ionospheric channels are fluctuating during this time frame. The fluctuation of the ionized layer causes the fluctuation of the phase of the short wave electric wave signal passing through the ionized layer, destroys the coherence between pulses, causes the Doppler frequency spectrum of clutter and targets to be widened, and thereby limits the detection of sky wave radar sea/ground targets.
Although the sky-wave radar can select frequency points with relatively small fluctuation to work under the support of the adaptive channel management subsystem of the sky-wave radar, the problem of ionospheric pollution can be relieved to a certain extent, but the pollution cannot be completely avoided. In order to ensure the successful target detection, the ionospheric contamination needs to be corrected. The most direct method for estimating and correcting ionospheric pollution is to arrange transponders in observation areas, but in practical application, the transponders are limited by environmental conditions and cannot be erected in all observation areas. To this end, one uses strong sea/ground clutter information to estimate and correct for ionospheric contamination. From the Doppler domain, the ground clutter is mainly concentrated near zero Doppler and can be used for ionospheric contamination correction, and the sea clutter is composed of a pair of first-order Bragg peaks and a plurality of second-order Bragg peaks. The position radar transmitting frequency of the sea clutter Bragg peak, the ionosphere state, the sea surface state, the geometric relation between the transceiver station and the like are related, and the first-order Bragg peak is strong and can be used for estimation and correction of ionosphere pollution.
Sky wave radar ionosphere phase pollution is represented as passenger interference in a slow time domain, and the change is nonlinear, and the conventional time-frequency filter can not be adopted for filtering. Therefore, various ionospheric contamination correction methods are proposed, which can basically comprise three steps: firstly, extracting a characteristic signal for ionospheric pollution correction, generally in a frequency domain, and mostly filtering out a Doppler spectrum peak after single-frequency component broadening by adopting band-pass filtering; secondly, extracting a pollution signal; and thirdly, constructing a correction operator to correct pollution. The current research mainly focuses on the second step, and the difference is mainly reflected in the step, and the two types are mainly different according to different implementation modes, namely, the instantaneous frequency is directly estimated by using the relation between the frequency and the phase, and a pollution phase sequence is obtained by integration, such as a phase gradient method, a WVD-based method and the like; secondly, data are segmented, the instantaneous frequency or phase of each segment is estimated, and then a phase pollution sequence is synthesized, such as a maximum entropy spectrum method, an estimation method based on singular value decomposition, a segmented polynomial phase modeling method and the like.
From the specific principle of various pollution correction methods, the phase gradient method, the method based on the WVD and the piecewise polynomial phase modeling method need to extract a doppler spectrum peak after single-frequency component broadening. The phase gradient method estimates the pollution signal by sequentially calculating the phase gradient based on the phase of the first data of the signal sequence, and the accuracy is higher only when the signal is a single-frequency signal. The method based on the WVD is a second-order time-frequency method, when a signal to be analyzed is a multi-component signal, cross terms can occur, so that the calculation precision is reduced rapidly, the segmented polynomial phase modeling method is also used for estimating polynomial coefficients of the segmented signal phase by using polynomial modeling aiming at the single-component signal, and the multiple segments are combined to complete the estimation and correction of pollution. The performance of the above algorithms is greatly compromised when the extracted signal is not a single component signal. The extraction of the characteristic signal is generally carried out in a Doppler domain, the characteristic signal is accurately extracted without introducing other interference, the bandwidth of a clutter filter needs to be carefully selected, and a clutter filter bandwidth self-adaptive selection algorithm based on minimum entropy is provided for accurately extracting the characteristic signal and the plum snow. Therefore, the correction effect of the pollution algorithm of the single component analysis class is difficult to guarantee due to the difficulty of accurately extracting the characteristic signal.
The maximum entropy spectrum method, the estimation method based on singular value decomposition and the like do not need to extract characteristic signals in advance, the maximum entropy spectrum method is to segment signals to be polluted, perform spectrum analysis on all the signals by using a corrected Burg method, extract a spectrum peak of a maximum component, combine spectrum peak points of all the segments and perform interpolation calculation to estimate and correct pollution, but how to select the AR model order of spectrum estimation is a problem to be solved. The singular value decomposition-based method is characterized in that invariance of pollution frequency in a short time is utilized, a Hankel matrix is constructed by extracted characteristic signals to carry out singular value decomposition, rank reduction is carried out by reserving large singular values, noise components are inhibited, and extraction and correction of the pollution signals are realized after matrix blocking, characteristic decomposition and other operations.
In addition, because the doppler component of the received signal is increased in the multimode situation, the current pollution correction methods are all directed to the single-mode propagation situation, and are not applicable to the pollution in the multimode situation. The key problem of ionospheric pollution correction is analysis of the time-frequency structure of the pollution signal, and the difficulty is that analysis of the time-frequency structure of the pollution signal is influenced by multi-component signals and is difficult to analyze accurately.
Disclosure of Invention
The invention aims to provide a sky-wave radar ionospheric pollution correction method and a system, aiming at solving the problems that the existing pollution correction method aims at the situation of single-mode propagation, and the ionospheric pollution under the condition of multimode propagation is corrected in a filtering mode after correction, and the pollution correction is finished by iteration for many times. The sky-wave radar ionosphere pollution correction method and system provided by the invention can be suitable for pollution under the multimode condition, and improve the correction precision.
In order to achieve the purpose, the invention provides the following scheme:
a sky-wave radar ionospheric pollution correction method comprises the following steps:
acquiring a signal to be corrected of a sky wave radar slow time domain after ionosphere pollution;
selecting a spline function as a kernel function, initializing the kernel function, and determining the initialized kernel function;
performing generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function, and determining the time-frequency distribution of the signal to be corrected;
determining the time-frequency ridge position of the signal to be corrected based on the time-frequency distribution; the time-frequency ridge position is an estimated value of the time-frequency characteristic of the signal to be corrected;
performing curve fitting on the time-frequency ridge position by using a spline function, and taking a fitting curve as a kernel function of next transformation of the signal to be corrected;
judging whether iteration is terminated or not based on the kernel function of the next transformation and the initialized kernel function to obtain a first judgment result;
if the first judgment result shows that iteration is terminated, determining an estimated value of instantaneous frequency; the estimated value of the instantaneous frequency is a kernel function corresponding to the maximum time-frequency ridge position in the iteration process;
determining a pollution estimation value according to the estimation value of the instantaneous frequency;
determining a pollution-removing signal according to the pollution estimation value; the pollution-removing signal is a corrected ionospheric pollution signal;
and if the first judgment result indicates that the iteration is not terminated, taking the kernel function of the next transformation as an initialized kernel function, and returning to the step of performing generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function to determine the time-frequency distribution of the signal to be corrected.
Optionally, the performing generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function to determine the time-frequency distribution of the signal to be corrected specifically includes:
the time-frequency distribution of the signal to be corrected is as follows:
TF(t0,ω；Pi) Is t0Time-frequency distribution of signals to be corrected at a moment;
to transform the kernel parameter vector P in the ith iterationiDetermining a kernel function, i is the iteration number; t is t0Is the initial time; τ is an integral variable; x (tau) is the signal to be corrected; j isAn imaginary unit;
is an initialized kernel function; w is aσ(t) represents a window function determined by the parameter σ; ω is the angular frequency.
Optionally, the determining the position of the time-frequency ridge of the signal to be corrected based on the time-frequency distribution specifically includes:
the time-frequency ridge positions are as follows:
wherein the content of the first and second substances,
the position of a time-frequency ridge of the ith signal to be corrected; TFx(t,ω；Pi) The time-frequency distribution of the signal to be corrected at the time t.
Optionally, the determining whether iteration is terminated based on the kernel function of the next transformation and the initialized kernel function specifically includes:
the termination conditions are as follows:
wherein the content of the first and second substances,
the position of the time-frequency ridge of the signal to be corrected for the (i-1) th time is determined; ζ is a positive number below a first threshold; i.e. imaxIs the maximum number of iterations.
Optionally, the determining the pollution estimation value according to the estimation value of the instantaneous frequency specifically includes:
acquiring fixed frequency of clutter;
according to the formula
Determining foulingDye estimation value; wherein the content of the first and second substances,
is a pollution estimation value; IF (intermediate frequency) circuitl(t) is an estimated value of instantaneous frequency, l is iteration times, and l belongs to i; f. ofBIs a fixed frequency of the clutter.
Optionally, the determining a contamination resolution signal according to the estimated contamination value further includes:
ending the correction according to the correction ending condition;
the correction end condition is as follows:
A sky-wave radar ionospheric contamination correction system comprising:
the signal to be corrected acquisition module is used for acquiring a signal to be corrected of a slow time domain of the sky wave radar after ionosphere pollution;
the initialization module is used for selecting a spline function as a kernel function, initializing the kernel function and determining the initialized kernel function;
the time-frequency distribution determining module is used for carrying out generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function and determining the time-frequency distribution of the signal to be corrected;
a time-frequency ridge position determining module, configured to determine a time-frequency ridge position of the signal to be corrected based on the time-frequency distribution; the time-frequency ridge position is an estimated value of the time-frequency characteristic of the signal to be corrected;
the fitting module is used for performing curve fitting on the time-frequency ridge position by utilizing a spline function and taking a fitting curve as a kernel function of next transformation of the signal to be corrected;
the first judgment module is used for judging whether iteration is terminated or not based on the kernel function of the next transformation and the initialized kernel function to obtain a first judgment result;
the instantaneous frequency estimation value determining module is used for determining the instantaneous frequency estimation value if the first judgment result indicates that iteration is terminated; the estimated value of the instantaneous frequency is a kernel function corresponding to the maximum time-frequency ridge position in the iteration process;
the pollution estimation value determination module is used for determining a pollution estimation value according to the estimation value of the instantaneous frequency;
the pollution-removing signal determining module is used for determining a pollution-removing signal according to the pollution estimation value; the pollution-removing signal is a corrected ionospheric pollution signal;
and if the first judgment result indicates that the iteration is not terminated, taking the kernel function of the next transformation as an initialized kernel function, and returning to the step of performing generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function to determine the time-frequency distribution of the signal to be corrected.
Optionally, the time-frequency distribution of the signal to be corrected in the time-frequency distribution determining module is:
TF(t0,ω；Pi) Is t0Time-frequency distribution of signals to be corrected at a moment;
to transform the kernel parameter vector P in the ith iterationiDetermining a kernel function, i is the iteration number; t is t0Is the initial time; τ is an integral variable; x (tau) is the signal to be corrected; j is an imaginary unit;
is an initialized kernel function; w is aσ(t) represents a window function determined by the parameter σ; ω is the angular frequency.
Optionally, the time-frequency ridge position in the time-frequency ridge position determining module is:
wherein the content of the first and second substances,
the position of a time-frequency ridge of the ith signal to be corrected; TFx(t,ω；Pi) The time-frequency distribution of the signal to be corrected at the time t.
Optionally, the termination condition in the first determining module is:
wherein the content of the first and second substances,
the position of the time-frequency ridge of the signal to be corrected for the (i-1) th time is determined; ζ is a positive number below a first threshold; i.e. imaxIs the maximum number of iterations.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides a sky-wave radar ionosphere pollution correction method and system, wherein a spline function is selected as a kernel function of parameterized time-frequency transformation according to the characteristics of ionosphere pollution, kernel function parameters are estimated according to signals after the ionosphere pollution, and a pollution sequence is estimated by using the kernel function to correct the pollution. For ionospheric pollution under multimode propagation conditions, a mode of filtering after correction is adopted, pollution correction is completed through multiple iterations, and correction precision is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a sky-wave radar ionospheric contamination correction method according to the present invention;
FIG. 2 is a simplified ionospheric contamination correction flow diagram provided by the present invention;
FIG. 3 is a diagram of a sky-wave radar ionospheric contamination correction system according to the present invention;
fig. 4 is a diagram illustrating the effect of ionospheric contamination estimation and correction in the case of small-amplitude contamination (B ═ 1) according to the present invention; fig. 4(a) is a contamination phase estimation diagram in the case of small-amplitude contamination (B ═ 1), and fig. 4(B) is a contamination correction result diagram in the case of small-amplitude contamination (B ═ 1);
fig. 5 is a diagram illustrating the effect of ionospheric contamination estimation and correction in the case of large-amplitude contamination (B-5) provided by the present invention; FIG. 5(a) is a graph of contamination phase estimation, and FIG. 5(b) is a graph of contamination correction results;
FIG. 6 is a graph of absolute error estimates of contamination under different SNR, contamination amplitude and frequency conditions provided by the present invention; FIG. 6(a) is a graph of the effect of signal-to-noise ratio on absolute error, and FIG. 6(b) is a graph of the effect of contamination amplitude on absolute error; FIG. 6(c) is a graph of the effect of contamination frequency on absolute error;
FIG. 7 is a diagram illustrating the estimation and correction effects of simulated sub-sea clutter ionospheric contamination according to the present invention; fig. 7(a) is a simulated sea clutter pollution phase estimation diagram, and fig. 7(b) is a simulated sea clutter pollution correction result diagram;
FIG. 8 is a graph of absolute error estimates of pollution under different SNR, pollution amplitude and frequency conditions provided by the present invention; fig. 8(a) is a graph showing an influence of a simulated sea clutter lower noise ratio on an absolute error, fig. 8(b) is a graph showing an influence of a simulated sea clutter lower pollution amplitude on an absolute error, and fig. 8(c) is a graph showing an influence of a simulated sea clutter lower pollution frequency on an absolute error;
FIG. 9 is a chart illustrating ionospheric contamination correction under multimode conditions in accordance with the present invention; fig. 9(a) is a graph comparing the original signal and the contamination signal, and fig. 9(b) is a graph of the contamination correction result under the multimode condition.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a sky-wave radar ionosphere pollution correction method and system, which can be suitable for pollution under the multimode condition and improve the correction precision.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a flowchart of a sky-wave radar ionospheric pollution correction method provided by the present invention, and as shown in fig. 1, a sky-wave radar ionospheric pollution correction method includes:
step 101: and acquiring signals to be corrected of the slow time domain of the sky wave radar after ionosphere pollution.
In consideration of the multi-layer property of the ionosphere, the echo signal of slow time domain of sky wave radar in coherent accumulation time can be expressed as:
where T is 1, …, T denotes the slow time sequence of echo processing, c (T) denotes clutter echoes, n (T) denotes reception noise,
a pollution signal representing the M (M-1, …, M) th ionospheric propagation mode,
which represents the phase fluctuation of the corresponding propagation mode, and M represents the number of ionospheric propagation modes.
Phase fluctuation due to ionospheric contamination
The coherent integration time is long, such as 10-40s required for sea target detection, phase pollution nonlinear change, coherence between pulses is destroyed, and target and clutter Doppler spectrum are spread, which may result in target detection failure. The correction of ionospheric contamination is an estimate of the amount of phase fluctuation, noted
Constructing corresponding depollution sequences
And the pollution can be corrected by multiplying the corresponding components.
Step 102: selecting a spline function as a kernel function, and initializing the kernel function to determine the initialized kernel function.
Step 103: and performing generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function, and determining the time-frequency distribution of the signal to be corrected.
The generalized parameterized time-frequency transform is defined as follows:
wherein
P denotes a vector of parameters of the transform kernel,
representing the frequency rotation operator associated with the kernel function,
represents t0Frequency translation operator, k, defined by a parameter P, for a period of time around the instantp(t)∈L2(R) represents a integrable kernel function, wσ(t) denotes a window function determined by the parameter σ.
For non-stationary signals, the effect of the frequency rotation operator is at t0Rotating the time-frequency ridge of the signal in a time window around the moment, i.e. subtracting k from the instantaneous frequency of the signalp(t), the frequency shift operator shifts the frequency spectrum of the signal in the time window, and the shifted frequency scale is kp(t0). From the definition of the transformation, the transformation is to make the original signal x (t) at t0Rotating, frequency shifting, windowing and then carrying out Fourier transform on a section near the moment, wherein the frequency resolution after the transform is determined by the window width and a kernel function kp(t) determining that when the difference between the kernel function and the time-frequency distribution of the original signal is a constant, the frequency resolution of the transform is determined only by the window width, and the time-frequency concentration is the best. When k ispWhen (t) is 0, the transform is degenerated to a short-time fourier transform.
Step 104: determining the time-frequency ridge position of the signal to be corrected based on the time-frequency distribution; and the time-frequency ridge position is an estimated value of the time-frequency characteristic of the signal to be corrected.
Step 105: and performing curve fitting on the time-frequency ridge position by using a spline function, and taking a fitting curve as a kernel function of next transformation of the signal to be corrected.
Step 106: and judging whether iteration is terminated or not based on the kernel function of the next transformation and the initialized kernel function, if so, executing the step 107, and if not, executing the step 110.
From the definition formula of the generalized parameterized time-frequency transformation, it can be seen that the more similar the transformation kernel function is to the time-frequency characteristics of the signal, the more concentrated the time-frequency distribution of the generalized parameterized time-frequency transformation of the signal is, and the more accurate the description of the time-frequency characteristics of the signal is. To make the time-frequency concentration of the transformation the best, the proper kernel function and kernel function parameters are selected according to the characteristics of the signal, so that the difference between the kernel function and the time-frequency distribution of the original signal is constant. The selection of the kernel function and the setting of the parameters thereof are to enable the kernel function to better approximate the time-frequency characteristics of the signal to be decomposed.
According to different signal time-frequency distribution characteristics, three forms of kernel functions are respectively given: polynomial function, spline function and Fourier series, and provides a corresponding kernel function parameter calculation method. For sky wave radar receiving signals after ionosphere pollution, due to the randomness of phase change, the time-frequency curve change of the receiving signals is complex, if a polynomial function is adopted, a high-order polynomial is needed, the high-order polynomial can generate a 'dragon' phenomenon in fitting, and numerical values are unstable, so that a spline function or a Fourier series is needed to be selected, the Fourier series is needed to better approximate randomly fluctuated pollution signals, a longer series is needed, more parameters are to be estimated, and the spline function is adopted here.
The kernel function parameters need to be estimated according to the time-frequency characteristics of the signals to be transformed, the accuracy of the characterization of the time-frequency characteristics of the signals to be transformed is related to the values of the kernel function parameters, the more appropriate the values are, the more concentrated the transformed time-frequency distribution is, the more accurate the characterization of the time-frequency characteristics is, and the more appropriate the estimated parameters are, and the repeated operation is repeated to form a cycle approximation process, so that the kernel function parameters are finally obtained. Taking the single component signal as an example, the estimation of the kernel function parameters can be summarized as:
(1) at the i (i ═ 1,2, …, i)max) In the sub-iteration, the time-frequency distribution of the signal is obtained by using generalized parameterized time-frequency transformation, i.e.
Wherein
Expressed by the parameter P in the ith iterationiA determined transformation kernel. Enabling kernel function k during initial transformationp(t) 0, namely, obtaining initial time-frequency distribution by adopting short-time Fourier transform;
(2) the peak value detection is carried out on the frequency along the time axis in the time frequency distribution to obtain the time frequency ridge position of the signal, and the time frequency ridge position is used as the time frequency characteristic of the signalEstimates of signs, i.e.
(3) Using spline function pairs
Performing curve fitting, and recording parameters obtained by fitting as
Fitting the resulting curve as a kernel function for the i +1 th transformation
(4) Judging whether the iteration is terminated or not, wherein the criterion is
Where ζ is a small positive number. When the value of i is 1, the value of i,
if the criterion is not satisfied, the steering is carried out to the step (1), and if the criterion is satisfied, the kernel function parameters are output.
Step 107: if the first judgment result shows that iteration is terminated, determining an estimated value of instantaneous frequency; and the estimated value of the instantaneous frequency is a kernel function corresponding to the maximum time-frequency ridge position in the iteration process.
Step 108: and determining a pollution estimation value according to the estimation value of the instantaneous frequency.
Step 109: determining a pollution-removing signal according to the pollution estimation value; and the pollution-removing signal is a corrected ionospheric pollution signal.
Step 110: and taking the kernel function of the next transformation as an initialized kernel function, and returning to the step of performing generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function to determine the time-frequency distribution of the signal to be corrected.
The parameter calculation process of the kernel function is actually a process of fitting the original signal time-frequency characteristics by using the kernel function. From another perspective, the calculated kernel function can be used as an estimate of the time-frequency curve of the original signal. When the signal received by the antenna radar is only a single-component signal (such as only ground clutter or a target signal) of single-mode propagation, the fixed component of the original signal is subtracted from the kernel function, and the kernel function is integrated to obtain an estimation value of the pollution phase sequence.
When the received signals of the antenna radar are multi-component (single-mode propagation sea clutter or multi-mode propagation) signals, and for the single-mode propagation situation, the ionospheric pollution of each component is the same, and then a kernel function corresponding to one component is estimated; for the case of multi-mode propagation, it is possible that ionospheric functions in each propagation mode are different, which causes different time-frequency distributions of corresponding components in different propagation modes, and therefore, the time-frequency distributions need to be estimated one by one and corrected one by one.
Ionospheric contamination correction can be summarized as follows:
(1) in the l (1, 2, …) -th correction, the received signal to be corrected is recorded as xl(t), the initial signal x (t) when l is 1, estimate xl(t) the transformation kernel function corresponding to the maximum component (i.e. the time-frequency ridge with the maximum peak value when extracting the time-frequency ridge) is taken as the estimation IF of the instantaneous frequencyl(t)；
(2) Subtracting the fixed frequency f of the clutter from the prior information of the clutterBAnd integrating to obtain the pollution estimation in the mode
Under ideal conditions, the contamination is accurately estimated, then
(3) The pollution-removing operation is carried out, and the signal after pollution removal is
(4) Filtering clutter from the signal after pollution removal by using the prior information of the clutter, and mixing the filtered clutter with the filtered signal
Multiply to avoid the influence of the current correction on the next pollution correction, will
As the signal to be corrected for the next correction, here
The estimation of the sea clutter main component obtained by using the prior information is shown, and is convenient to write into a signal subtraction form, and the actual operation is realized by adopting a filter;
(5) judging whether the correction is finished or not according to the criterion
If not, turning to (1).
It should be noted that, in terms of ionospheric contamination correction, in the estimation process of transforming kernel function parameters, not the parameters of the kernel function but the time series of the kernel function is concerned
Therefore, in the specific calculation of ionospheric pollution correction, pairs can be adopted
By means of interpolation
The steps of curve fitting and parameter calculation are omitted, and the calculation process is simplified. The whole ionospheric contamination correction flow is shown in fig. 2.
Correction of sky wave radar ionospheric contamination sharpens the doppler spectrum of the received signal for target detection and target parameter estimation after clutter suppression in the doppler domain. The ionospheric pollution correction process of fig. 2 is also a process of sea clutter suppression, wherein the suppression of sea clutter is performed based on the corrected clutter signal doppler domain characteristics. Reviewing the definition of the generalized parameterized time-frequency transform, neglecting the frequency shift factor and the window function, it is expressed as follows:
from the expression, in ionospheric pollution correction under multimode conditions, clutter filtering is equivalently performed after the transformation, that is, pollution solution operation is performed on signals according to estimated instantaneous pollution phase, and then Fourier transformation is performed. From the perspective of transformation, the depolluting operation is equivalent to rotating the polluted signal in the time-frequency domain, so that the instantaneous frequency of the signal is parallel to the time axis, even if the frequency of the signal does not change with time, and finally the signal can achieve the best accumulation effect in the frequency domain.
When the signal to be decontaminated contains the target signal, the formula can be rewritten as follows:
where s (t) represents the target signal. For sky wave radar, the target signal is generally small relative to the clutter, so pollution correction is not affected. Since the target prior information is generally unknown, after multiple corrections, clutter signals are filtered out, leaving only target and noise signals. In the calibration of fig. 2, in order to prevent the pollution of multiple propagation modes from interfering with each other, after a certain time of calibration and clutter filtering, the pollution factor is multiplied back, which results in that the target signal after clutter filtering is still the polluted signal, and ideally, the clutter is completely filtered, which is represented as follows:
further, the transform shown in the analysis formula shows that if the kernel function does not coincide with the instantaneous frequency of ionospheric contamination, the doppler after the transform is not concentrated. Therefore, the detection of the signal in the pollution can adopt formula conversion, and the instantaneous frequency of the pollution in each propagation mode estimated in the pollution correction is used as a kernel function to convert the instantaneous frequency, so that the target can be effectively accumulated, and the signal-to-noise ratio is improved. And performing joint detection on the signals after the plurality of propagation mode conversions, namely, more reliably detecting the target.
Fig. 3 is a structural diagram of a sky-wave radar ionospheric pollution correction system provided by the present invention, and as shown in fig. 3, a sky-wave radar ionospheric pollution correction system includes:
and a signal to be corrected acquisition module 301, configured to acquire a signal to be corrected of a slow time domain of a sky-wave radar after ionosphere contamination.
An initialization module 302, configured to select a spline function as a kernel function, perform initialization processing on the kernel function, and determine an initialized kernel function;
a time-frequency distribution determining module 303, configured to perform generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function, and determine time-frequency distribution of the signal to be corrected;
the time-frequency distribution of the signal to be corrected in the time-frequency distribution determining module 303 is:
TF(t0,ω；Pi) Is t0Time-frequency distribution of signals to be corrected at a moment;
to transform the kernel parameter vector P in the ith iterationiDetermining a kernel function, i is the iteration number; t is t0Is the initial time; τ is an integral variable; x (tau) is the signal to be corrected; j is an imaginary unit;
is an initialized kernel function; w is aσ(t) represents a window function determined by the parameter σ; ω is the angular frequency.
A time-frequency ridge position determining module 304, configured to determine a time-frequency ridge position of the signal to be corrected based on the time-frequency distribution; the time-frequency ridge position is an estimated value of the time-frequency characteristic of the signal to be corrected;
the time-frequency ridge position in the time-frequency ridge position determining module 304 is:
wherein the content of the first and second substances,
the position of a time-frequency ridge of the ith signal to be corrected; TFx(t,ω；Pi) The time-frequency distribution of the signal to be corrected at the time t.
A fitting module 305, configured to perform curve fitting on the time-frequency ridge position by using a spline function, and use a fitting curve as a kernel function of next transformation of the signal to be corrected;
a first determining module 306, configured to determine whether iteration is terminated based on the kernel function of the next transformation and the initialized kernel function, so as to obtain a first determining result;
the termination condition in the first determining module 306 is:
wherein the content of the first and second substances,
the position of the time-frequency ridge of the signal to be corrected for the (i-1) th time is determined; ζ is a positive number below a first threshold; i.e. imaxIs the maximum number of iterations.
An instantaneous frequency estimation value determination module 307, configured to determine an instantaneous frequency estimation value if the first determination result indicates that iteration is terminated; the estimated value of the instantaneous frequency is a kernel function corresponding to the maximum time-frequency ridge position in the iteration process;
a pollution estimation value determination module 308 for determining a pollution estimation value according to the estimation value of the instantaneous frequency;
a pollution-solution signal determining module 309, configured to determine a pollution-solution signal according to the pollution estimation value; the pollution-removing signal is a corrected ionospheric pollution signal;
and an iteration module 310, configured to, if the first determination result indicates that iteration is not terminated, take the kernel function of the next transformation as an initialized kernel function, and return to the step "perform generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function, and determine time-frequency distribution of the signal to be corrected".
The following numerical simulation experiments were designed to verify the effectiveness and robustness of the present invention:
Typical working parameters of the sky wave radar in a sea surface target detection mode are taken, the pulse interval is 0.2s, and the coherent accumulation time is 40 s. The working frequency is 18MHz, the sea surface incidence complementary angle is 25 degrees, the receiving and transmitting quasi-single base configuration is adopted, and the first-order Bragg peak frequency of the sea clutter
Where g denotes gravitational acceleration, Ψ denotes a complementary angle of incidence, and λ denotes a wavelength. To verify the performance of the algorithm, it is assumed that the sea clutter consists of only two first-order Bragg peaks and noise, i.e., x (t) -2 exp (j2 π f)B+t)+exp(j2πfB-t) + n (t), where fB+，fB-Respectively representing positive and negative first order Bragg peak frequencies, considering the situation of single-mode propagation, and adding a phase pollution signal
Wherein B is the pollution amplitude, representing the size of pollution fluctuation, fm1Representing the speed of pollution fluctuation for pollution frequency, and obtaining the signal-to-noise ratio of 30dB, fm1＝0.08，
The simulation results of the pollution phase estimation and the pollution correction of the small-amplitude pollution (B ═ 1) are shown in the figure, and two typical ionospheric pollution correction methods, namely a maximum entropy spectrum method and a method based on singular value decomposition, are provided for comparing the pollution correction performance. FIG. 4(b) shows the original signalThe signal spectrum is the uncorrupted signal spectrum, and the rest is the signal spectrum which is correspondingly corrected after adding pollution. From the results of small-amplitude pollution estimation and correction, the method based on singular value decomposition and the method based on singular value decomposition can better estimate and correct the pollution, the maximum entropy spectrum method has larger estimation error and poorer correction performance; the results of the pollution phase estimation and the pollution correction of the large-amplitude pollution (B ═ 5) are shown in fig. 5, in which the present invention can still estimate the pollution with higher accuracy, the method based on singular value decomposition is almost ineffective, and the maximum entropy spectroscopy performance is centered. A comparison of fig. 4 and 5 shows the robustness of the present invention to the magnitude of the pollution fluctuations. To further analyze the robustness of the present invention, FIG. 6 shows the absolute error of the pollution estimation under different SNR, pollution amplitude and frequency conditions
And (4) obtaining a simulation result. The standard parameter set taken in the simulation was: signal to noise ratio of 30dB, fm10.08 and 1, and one parameter is changed under different conditions. From the general trend of fig. 6(a) (b) (c) it can be seen that: (1) under the conditions of small-amplitude pollution and high signal-to-noise ratio, the method based on singular value decomposition is slightly superior to the method in performance because the structure of pollution change can be captured more accurately, but the stability is poor; (2) the performance of the maximum entropy spectrum method is slightly superior to that of the invention under the conditions of large signal-to-noise ratio and medium pollution frequency, as shown in figure 6(c), but the stability is poor; (3) the invention is insensitive to pollution amplitude and frequency change, shows good robustness, and only has the advantages that the error is obviously increased and the stability is poor when the signal-to-noise ratio is lower than 10dB, but in the case of sea clutter, the second-order Doppler peak of the sea clutter is usually 20-30dB lower than the first-order Bragg peak, and the performance of the invention is better in the region, so the phenomenon does not influence the applicability of the method.
The ionospheric contamination correction performance of the present invention is further verified for more realistic simulation of sea clutter. A sea clutter simulation method is adopted, and the influence of second-order and high-order spectral peaks is considered. In simulation, the sea surface wind speed is set to be 15m/s, the distance resolution is 7.5km, the semi-double base angle is 0, namely, the single baseIn the case of ground, the pulse interval is 0.2s and the coherent integration time is 40 s. The working frequency is 18MHz, and the sea surface incidence complementary angle is 25 degrees. Noise to noise ratio of 30dB, fm1＝0.08，
Under the condition of B being 5, the ionospheric phase pollution estimation and correction results are shown in fig. 7. It can be seen from the figure that the estimation performance of the phase pollution is somewhat reduced compared with that of fig. 5 due to the influence of the second-order and the higher-order spectrums of the sea clutter, but the pollution can still be better estimated and corrected by the method. The robustness and performance advantages of the present invention are further demonstrated by the trend of the absolute error of the pollution estimate under different noise to noise ratios, pollution amplitudes and frequencies in fig. 8.
Experiment 3
Still adopt the sea clutter simulation method in experiment 2, consider the situation of multimode propagation, for the sake of convenience, be equipped with two propagation modes, the Doppler frequency shift that the ionosphere brought between the two differs 0.2 Hz. The reason why the frequency shift caused by the ionosphere is not considered in experiments 1 and 2 is that the frequency shift only causes the translation of the frequency spectrum and does not cause the broadening effect, and the frequency shift is only carried out according to the symmetry of the sea clutter doppler spectrum with respect to the zero frequency after the broadening correction. In the simulation, the noise-to-noise ratio is 30dB, the pollution parameter of the propagation mode 1 is B-1, fm10.08, the contamination parameter of propagation mode 2 is B1, fm10.08. The simulated original signal and contamination signal are shown in fig. 9(a), and the contamination correction result is shown in fig. 9 (b). It can be seen from the figure that both types of contamination under propagation can be corrected according to the steps of fig. 2, demonstrating the effectiveness of the present invention. But the mutual influence between the two signals makes the correction result have a certain degree of expansion compared with the original signal.
The generalized parameterized time-frequency transformation method can be used for analyzing the time-frequency characteristics of the multi-component signals with high precision, has no influence of factors such as cross terms and the like, and is an excellent time-frequency analysis method. The invention applies the method to the ionospheric pollution estimation and correction of sky-wave radar. Selecting spline frequency modulation wavelets as a kernel function of parametric time-frequency transformation according to the characteristics of ionosphere pollution, estimating kernel function parameters aiming at signals after the ionosphere pollution, estimating a pollution sequence by using time-frequency characteristic quantity of the kernel function, and constructing a pollution correction operator to correct the pollution. And for ionospheric pollution under the multimode propagation condition, the pollution is corrected by adopting a filtering mode after correction and iterating for multiple times.
The pollution correction problem is essentially a multi-component signal time-frequency analysis problem, under a single-mode propagation condition, time-frequency structures of a plurality of components (in the case of sea clutter, the ground clutter is a single component, which is simple and not described herein) have similarity, and the distribution of different components on a time-frequency plane is relatively open, so that the components are relatively easy to separate and respectively estimate. Under the condition of multimode propagation, the time-frequency structures of a plurality of components do not have similarity, and are distributed on a time-frequency plane more densely and are difficult to separate and estimate, so that the pollution correction performance is poor. The invention corrects pollution in turn by iteration, and whether the propagation mode is multimode propagation does not affect the actual implementation of the invention.
In fact, the method adopted by the invention in the estimation of the transformation kernel parameters is a multi-component decomposition method based on the estimated parameters, the resolution of which depends on the length of the window function used. More accurate multi-component signal analysis method can adopt a method based on spectrum concentration, but the method needs multi-peak search on kernel function parameters and has larger calculation amount. On the one hand, the method can be adopted for pollution correction with higher precision or a better multi-component signal time-frequency analysis method is found, for example: empirical mode decomposition, empirical wavelet transform, differential mode decomposition and the like, and on the other hand, a nest socket for time-frequency analysis pollution correction can be skipped from the analysis of the formation mechanism of ionosphere pollution, and homomorphic filtering technology for inhibiting the interference of the nature can be adopted.
The invention introduces a generalized parameter time-frequency transformation method to analyze the sky wave radar receiving signals and provides a more effective and stable method for estimating and correcting the sky wave radar ionospheric pollution. The generalized parameterized time-frequency transformation constructs a matched kernel function aiming at a signal model, selects kernel function parameters, can accurately depict the time-frequency characteristics of non-stationary signals, and can effectively separate multi-component signals. When the generalized parametric time-frequency transformation is used for correcting the ionospheric pollution, spline frequency modulation wavelets are selected as a kernel function of the parametric time-frequency transformation according to the characteristics of the ionospheric pollution, kernel function parameters are estimated according to signals after the ionospheric pollution, a pollution sequence is estimated by using the time-frequency characteristic quantity of the kernel function, and a pollution correction operator is constructed to correct the pollution. The invention adopts a mode of filtering after correction to complete the correction of pollution by iteration for many times for ionospheric pollution under the condition of multimode propagation.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principle and the implementation mode of the invention are explained by applying a specific example, and the description of the embodiment is only used for helping to understand the method and the core idea of the invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A sky-wave radar ionospheric contamination correction method is characterized by comprising the following steps:
acquiring a signal to be corrected of a sky wave radar slow time domain after ionosphere pollution;
selecting a spline function as a kernel function, initializing the kernel function, and determining the initialized kernel function;
performing generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function, and determining the time-frequency distribution of the signal to be corrected;
determining the time-frequency ridge position of the signal to be corrected based on the time-frequency distribution; the time-frequency ridge position is an estimated value of the time-frequency characteristic of the signal to be corrected;
performing curve fitting on the time-frequency ridge position by using a spline function, and taking a fitting curve as a kernel function of next transformation of the signal to be corrected;
judging whether iteration is terminated or not based on the kernel function of the next transformation and the initialized kernel function to obtain a first judgment result;
if the first judgment result shows that iteration is terminated, determining an estimated value of instantaneous frequency; the estimated value of the instantaneous frequency is a kernel function corresponding to the maximum time-frequency ridge position in the iteration process;
determining a pollution estimation value according to the estimation value of the instantaneous frequency;
determining a pollution-removing signal according to the pollution estimation value; the pollution-removing signal is a corrected ionospheric pollution signal;
and if the first judgment result indicates that the iteration is not terminated, taking the kernel function of the next transformation as an initialized kernel function, and returning to the step of performing generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function to determine the time-frequency distribution of the signal to be corrected.
2. The sky-wave radar ionospheric contamination correction method according to claim 1, wherein the performing generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function to determine the time-frequency distribution of the signal to be corrected specifically includes:
the time-frequency distribution of the signal to be corrected is as follows:
TF(t0,ω；Pi) Is t0Time-frequency distribution of signals to be corrected at a moment;
to transform the kernel parameter vector P in the ith iterationiDetermining a kernel function, i is the iteration number; t is t0Is the initial time; τ is an integral variable; x (τ) is to be correctedA positive signal; j is an imaginary unit;
is an initialized kernel function; w is aσ(t) represents a window function determined by the parameter σ; ω is the angular frequency.
3. The sky-wave radar ionosphere pollution correction method according to claim 2, wherein the determining the time-frequency ridge position of the signal to be corrected based on the time-frequency distribution specifically includes:
the time-frequency ridge positions are as follows:
wherein the content of the first and second substances,
the position of a time-frequency ridge of the ith signal to be corrected; TFx(t,ω；Pi) The time-frequency distribution of the signal to be corrected at the time t.
4. The sky-wave radar ionospheric contamination correction method according to claim 3, wherein the determining whether iteration is terminated based on the kernel function of the next transformation and the initialized kernel function specifically includes:
the termination conditions are as follows:
wherein the content of the first and second substances,
the position of the time-frequency ridge of the signal to be corrected for the (i-1) th time is determined; ζ is a positive number below a first threshold; i.e. imaxIs the maximum number of iterations.
5. The sky-wave radar ionospheric contamination correction method according to claim 4, wherein said determining an estimate of contamination from the estimate of instantaneous frequency specifically comprises:
acquiring fixed frequency of clutter;
according to the formula
Determining a pollution estimation value; wherein the content of the first and second substances,
is a pollution estimation value; IF (intermediate frequency) circuitl(t) is an estimated value of instantaneous frequency, l is iteration times, and l belongs to i; f. ofBIs a fixed frequency of the clutter.
6. The sky-wave radar ionospheric contamination correction method according to claim 4, wherein said determining a solution-to-contamination signal from said contamination estimate further comprises:
ending the correction according to the correction ending condition;
the correction end condition is as follows:
7. A system for correcting ionospheric contamination of sky-wave radar, comprising:
the signal to be corrected acquisition module is used for acquiring a signal to be corrected of a slow time domain of the sky wave radar after ionosphere pollution;
the initialization module is used for selecting a spline function as a kernel function, initializing the kernel function and determining the initialized kernel function;
the time-frequency distribution determining module is used for carrying out generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function and determining the time-frequency distribution of the signal to be corrected;
a time-frequency ridge position determining module, configured to determine a time-frequency ridge position of the signal to be corrected based on the time-frequency distribution; the time-frequency ridge position is an estimated value of the time-frequency characteristic of the signal to be corrected;
the fitting module is used for performing curve fitting on the time-frequency ridge position by utilizing a spline function and taking a fitting curve as a kernel function of next transformation of the signal to be corrected;
the first judgment module is used for judging whether iteration is terminated or not based on the kernel function of the next transformation and the initialized kernel function to obtain a first judgment result;
the instantaneous frequency estimation value determining module is used for determining the instantaneous frequency estimation value if the first judgment result indicates that iteration is terminated; the estimated value of the instantaneous frequency is a kernel function corresponding to the maximum time-frequency ridge position in the iteration process;
the pollution estimation value determination module is used for determining a pollution estimation value according to the estimation value of the instantaneous frequency;
the pollution-removing signal determining module is used for determining a pollution-removing signal according to the pollution estimation value; the pollution-removing signal is a corrected ionospheric pollution signal;
and if the first judgment result indicates that the iteration is not terminated, taking the kernel function of the next transformation as an initialized kernel function, and returning to the step of performing generalized parameterized time-frequency transformation on the signal to be corrected based on the initialized kernel function to determine the time-frequency distribution of the signal to be corrected.
8. The system according to claim 1, wherein the time-frequency distribution of the signals to be corrected in the time-frequency distribution determination module is:
TF(t0,ω；Pi) Is t0Time-frequency distribution of signals to be corrected at a moment;
to transform the kernel parameter vector P in the ith iterationiDetermining a kernel function, i is the iteration number; t is t0Is the initial time; τ is an integral variable; x (tau) is the signal to be corrected; j is an imaginary unit;
is an initialized kernel function; w is aσ(t) represents a window function determined by the parameter σ; ω is the angular frequency.
9. The system of claim 2, wherein the time-frequency ridge locations in the time-frequency ridge location determination module are:
wherein the content of the first and second substances,
the position of a time-frequency ridge of the ith signal to be corrected; TFx(t,ω；Pi) The time-frequency distribution of the signal to be corrected at the time t.
10. The system according to claim 3, wherein the termination condition in the first determination module is:
wherein the content of the first and second substances,
the position of the time-frequency ridge of the signal to be corrected for the (i-1) th time is determined; ζ is a positive number below a first threshold; i.e. imaxIs the maximum number of iterations.
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