CN116203501B - Passive positioning method and equipment for mapping radiation source based on frequency domain mutual blurring function interpolation - Google Patents
Passive positioning method and equipment for mapping radiation source based on frequency domain mutual blurring function interpolation Download PDFInfo
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Abstract
The invention discloses a passive positioning method and device for a radiation source based on frequency domain mutual blurring function interpolation mapping, which solve the problems of low mapping accuracy and large calculated amount of the existing mutual blurring function; belonging to the field of passive positioning of radiation sources; comprising the following steps: based on the generated time-frequency difference lookup table, obtaining a grid point frequency difference value and a grid point time difference value corresponding to the received radiation source signal, and determining a time-frequency domain calculation range; taking the grid point frequency difference value as input, and outputting a model frequency difference coordinate, a model time difference coordinate and a frequency difference function value through a frequency domain mutual blurring function model; taking the model time difference coordinates, the frequency difference function values and the grid point time difference values as inputs, and outputting the time difference function values through an interpolation model constructed by the Sinc interpolation sub-model; and mapping the time difference function value to grid points of a time-frequency difference lookup table to form a radio frequency distribution map, and positioning to obtain the position coordinates of the radiation source. The invention avoids the precision loss of the intermediate parameter estimation; the operation amount is reduced, and the positioning speed and the positioning precision are high.
Description
Technical Field
The invention belongs to the technical field of passive positioning of radiation sources, and relates to a passive positioning method and device for mapping a radiation source based on frequency domain mutual blurring function interpolation.
Background
Under the countermeasure condition, the traditional active methods such as ground-based radar detection positioning and the like have the problems of high energy consumption, complex equipment, easy discovery and destruction by enemies and the like, and the research and exploration of reliable and efficient passive detection technology has important significance for supplementing and improving the situation awareness capability of an electromagnetic spectrum. In the prior art, a passive positioning method of a radiation source generally adopts a time-frequency difference two-step positioning method, namely, a mutual blurring function (Cross Ambiguity Function, CAF) is utilized to simultaneously estimate a time difference value and a frequency difference value of a received signal, and then the time-frequency difference value is substituted into a solution equation to calculate the position of the radiation source.
Time-frequency-difference two-step positioning methods are often used for positioning a single radiation source. In positioning multiple radiation sources, a cost function is generally constructed by using multiple signal classification (Multiple Signal Classification, MUSIC) or minimum variance distortion response (Minimum Variance Distortionless Response, MVDR) methods, which requires the introduction of angle information of an antenna array and a received signal, and the maximum number of radiation sources that can be positioned by an algorithm is limited by the number of receivers. In the case of space-based scenarios, several satellites need to face numerous radiation sources, and the above method is difficult to meet the positioning requirement of space-based radiation sources. While the us navy research laboratory has proposed a mutual blur function mapping method (CAF-MAP), which relies mainly on the basic principle that the main correlation peak of a stationary radiation source is exactly identical to all CAF amplitudes. All CAF amplitudes are mapped and combined in a common geographical frame to form an image similar to radio imaging. The mutual ambiguity function mapping (CAF-MAP) can skip the parameter estimation process and directly realize the position estimation of the radiation source. The method can realize direct positioning of multiple radiation sources and is not limited by the number of receivers.
The inventors found in the course of research that there are two problems with the mutual ambiguity function mapping method:
(1) data discretization errors. When the mutual ambiguity function value is mapped to the actual geographic map, the mutual ambiguity function value of the actual geographic position cannot be accurately obtained due to data discretization, and finally the positioning accuracy is affected. After data discretization, the time-frequency difference value corresponding to the grid point cannot find a completely consistent mapping in the calculated mutual blurring function under the limitation of sampling resolution. The mutual ambiguity function mapping method adopts a mode of searching nearest neighbors to determine the mutual ambiguity function amplitude corresponding to the time-frequency difference, and the method has errors to a certain extent. (2) The calculation process is complex. The algorithm needs a large amount of computation of the mutual blurring function, so that the algorithm processing speed is slower when the positioning problem of large sampled data volume, wide coverage range and high resolution requirement is faced. When the mutual blur function is calculated, the mutual blur function mapping method adopts a time domain mutual blur function calculation method. On the basis of the grid time difference range, the algorithm divides time difference sampling points according to the signal sampling rate, calculates the mutual ambiguity function value corresponding to the time difference offset according to the time difference sampling points, and obtains a complete mutual ambiguity function calculation result by circularly traversing all the time difference sampling points. This requires calculation of the sampling points in each time difference range, which increases with increasing signal sampling rate, and increases the calculation time significantly.
Disclosure of Invention
The invention provides a passive positioning method and equipment for a radiation source based on frequency domain mutual blurring function interpolation mapping, which aims at the problems of low mutual blurring function mapping accuracy and large calculated amount in the current mutual blurring function mapping positioning method (CAF-MAP), and aims at solving the problems that the time-frequency domain calculation range of a radiation source signal covering grid points is not calculated in the whole time-frequency difference range when the mutual blurring function calculation is carried out, but the time-frequency domain calculation range of the radiation source signal covering the grid points is determined based on the grid point frequency difference value and the grid point time difference value, calculating the mutual blurring function according to the frequency difference value in the time-frequency domain calculation range, obtaining a series of discrete mutual blurring function slices, obtaining a frequency domain mutual blurring function interpolation model by utilizing a Sinc interpolation submodel, obtaining a time difference function value corresponding to the time difference value through the model, and finally mapping the time difference function value to the grid points to form a radio frequency distribution MAP. According to the method, the frequency domain mutual blurring function is calculated from the corresponding frequency difference value, and then the radiation source mapping and positioning are realized by interpolation, so that the positioning operation speed and accuracy are effectively improved.
The aim of the invention is realized by the following technical scheme:
the invention discloses a passive positioning method for a radiation source based on frequency domain mutual blurring function interpolation mapping, which comprises the following steps:
step one, based on the generated time-frequency difference lookup table, obtaining a grid point frequency difference value and a grid point time difference value in the time-frequency difference lookup table corresponding to a received radiation source signal, and determining a time-frequency domain calculation range of the radiation source signal covering the grid point based on the grid point frequency difference value and the grid point time difference value;
taking a grid point frequency difference value in a time-frequency domain calculation range as an input, discretizing the grid point frequency difference value through a constructed frequency domain mutual blurring function model, and outputting a model frequency difference coordinate, a model time difference coordinate and a frequency difference function value corresponding to the discretized grid point frequency difference value; corresponding the grid point frequency difference value with the model frequency difference coordinate through a frequency domain mutual blurring function model;
step three, taking the model time difference coordinates, the frequency difference function values and the grid point time difference values in the time-frequency domain calculation range as inputs, and outputting the time difference function values through an interpolation model constructed by the Sinc interpolation sub-model; the step corresponds the grid point time difference value to the model time difference coordinate through an interpolation model;
and fourthly, mapping the time difference function value to grid points of a time-frequency difference lookup table to form a radio frequency distribution map, and positioning to obtain the position coordinates of the radiation source.
In the first step, the method for generating the time-frequency difference lookup table comprises the following steps:
at least two receivers receive the radiation source signals;
performing grid division on a preset geographic coverage area to obtain a grid point set and a geographic coordinate set corresponding to the grid point set;
according to the geometric distribution relation between the grid point sets and the at least two receivers, calculating arrival time difference values and frequency difference values of the radiation source signals received by the at least two receivers corresponding to each grid point through the geographic coordinate sets corresponding to the grid point sets, and generating a time-frequency difference lookup table uniquely corresponding to the radiation source signals and the grid points based on the time difference values and the frequency difference values.
In the first step, the method for determining the time-frequency domain calculation range comprises the following steps:
obtaining maximum and minimum values of grid point time difference values in a time-frequency difference lookup table corresponding to the received radiation source signals, and determining a time domain calculation range through the maximum and minimum values of the grid point time difference values;
and obtaining the maximum value and the minimum value of the grid point frequency difference value in the time-frequency difference lookup table corresponding to the received radiation source signal, and determining the frequency domain calculation range through the maximum value and the minimum value of the grid point frequency difference value.
In the second step, the constructed frequency domain mutual ambiguity function model is as follows:
；
wherein,a frequency domain mutual blurring function model; />Time difference points discretized for time difference values; />Frequency difference points which are discretized for the frequency difference value; n is the number of sampling points, and the value range of N is from 0 to N-1; />Receiving a frequency domain sample of the radiation source signal for a first receiver; />Receiving frequency domain samples of the radiation source signal for a second receiver; />Receiving a conjugate of the frequency domain sampling result of the radiation source signal for the second receiver; k is a sampling point; />Is the sampling rate; e is a natural constant; j is the sign of the imaginary number.
In the second step, the model time difference coordinates output by the frequency domain mutual blurring function model are abscissa coordinates output by the frequency domain mutual blurring function model based on the start-stop time of receiving the radiation source signals and the sampling time in the receiving process of at least two receivers;
the frequency difference function value output by the frequency domain mutual blurring function model is the vertical coordinate output by the frequency domain mutual blurring function model, and is used as the input of the Sinc interpolation sub-model to participate in the construction of the interpolation model.
In the second step, the model frequency difference coordinate output by the frequency domain mutual blurring function model is the grid point frequency difference value in the input time-frequency domain calculation range, and is the ordinate output by the frequency domain mutual blurring function model.
In the third step, an interpolation model constructed through the Sinc interpolation sub-model is as follows:
；
wherein,is an interpolation model; />Interpolation sub-model for Sinc; />The weight value at the model time difference coordinate sample point i is obtained; x is the grid point time difference value in the frequency domain calculation range; and i is the model time difference coordinate.
In the third step, the Sinc interpolation submodel is:
；
wherein,interpolation sub-model for Sinc; />Is a frequency difference function value; />The weight value at the model time difference coordinate sample point i is obtained; x is the grid point time difference value in the frequency domain calculation range; and i is the model time difference coordinate.
In the fourth step, the time difference function value is mapped to grid points of the time-frequency difference lookup table to form a radio frequency distribution diagram, and the step of positioning to obtain the position coordinates of the radiation source comprises the following steps:
and mapping the time difference function value output by the interpolation model onto grid points of a time-frequency difference lookup table in a time-frequency domain calculation range, and generating a radio frequency distribution diagram in the time-frequency domain calculation range by accumulating a plurality of radiation source signal time periods based on the principle that the time difference function value is consistent when the same radiation source signal is received by receivers with different geometric configurations, wherein the peak value of the accumulated time difference function value in the radio frequency distribution diagram is the radiation source position coordinate obtained by positioning.
The invention also provides a passive positioning device for the radiation source based on frequency domain mutual blurring function interpolation mapping, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps of the method when executing the computer program.
The beneficial effects of the invention are as follows:
the method inputs the grid point frequency difference value in the time-frequency domain calculation range through the frequency domain mutual blurring function model, and outputs the model frequency difference coordinate, the model time difference coordinate and the frequency difference function value; the step corresponds the grid point frequency difference value and the model frequency difference coordinate through a frequency domain mutual blurring function model, so that the calculated amount is effectively reduced, and the corresponding relation between the grid point frequency difference value and the model frequency difference coordinate is ensured;
using the Sinc interpolation sub-model, taking the model time difference coordinates, the frequency difference function value and the grid point time difference value in the time-frequency domain calculation range as input, and outputting the time difference function value through an interpolation model constructed by the Sinc interpolation sub-model; the step corresponds the grid point time difference value to the model time difference coordinate through an interpolation model; the corresponding relation between the grid point time difference value and the model time difference coordinate is ensured, and the positioning precision is effectively improved.
The method and the device provided by the invention are used for carrying out passive positioning of the satellite to the ground radiation source, and have the following advantages:
1. the sampling signal is directly used as calculation input without measuring signal parameters, so that the precision loss of intermediate parameter estimation is avoided;
2. the operation amount of the existing mutual blurring function mapping method is reduced, and a positioning result can be obtained by rapid calculation when a large amount of data is faced;
3. the time difference function value mapping relation is improved, and the positioning accuracy of the target radiation source is effectively improved.
The invention does not need to calculate the mutual ambiguity function of the whole time-frequency difference lookup table, so that the calculation time is relatively shortened, and the memory requirement of a computer is reduced. Aiming at the problem that the calculation speed of the improved method is slower under the condition of low sampling rate, the multi-core computer is adopted for parallel calculation, so that the calculation speed is obviously improved.
Drawings
The invention is described in further detail below with reference to the drawings and examples.
Fig. 1 is a meshing schematic diagram.
Fig. 2 is a schematic diagram of a frequency domain cross-ambiguity function "slice" of a model frequency difference coordinate corresponding to a grid point frequency difference value in the frequency domain cross-ambiguity function model.
Fig. 3 is a schematic diagram of the Sinc function time domain spectrum.
Fig. 4 is a schematic diagram of the Sinc function frequency domain spectrum.
Fig. 5 is a schematic diagram of an example 8-point Sinc interpolation.
Fig. 6 is a schematic diagram of sample data.
Fig. 7 is a schematic diagram of the interpolated data.
Fig. 8 is a diagram illustrating a mapping distribution of the frequency domain mutual ambiguity function values at grid points.
Fig. 9 is an overview illustration of the positioning of rf signals according to an embodiment of the present invention.
Fig. 10 is an overview illustration of the radio frequency signal positioning results disclosed by the mutual ambiguity function mapping positioning method.
Fig. 11 is a schematic top view of a positioning result of a radio frequency signal according to an embodiment of the present invention.
Fig. 12 is a schematic top view of the rf signal positioning result disclosed by the mutual ambiguity function mapping positioning method.
Fig. 13 is a schematic diagram showing a result of positioning a radio frequency signal according to an embodiment of the present invention along a positive y-axis direction with a horizontal viewing angle.
Fig. 14 is a schematic diagram showing the result of horizontal viewing angle positioning of the radio frequency signal along the positive y-axis direction according to the mutual ambiguity function mapping positioning method.
Fig. 15 is a schematic diagram showing a result of positioning a radio frequency signal according to an embodiment of the present invention along an x-axis positive direction with a horizontal viewing angle.
Fig. 16 is a schematic diagram showing the result of horizontal viewing angle positioning of the rf signal along the positive x-axis direction according to the mutual ambiguity function mapping method.
Detailed Description
Example 1
The first embodiment of the invention provides a passive positioning method for a radiation source based on frequency domain mutual blurring function interpolation mapping, which comprises the following steps:
step one, based on the generated time-frequency difference lookup table, obtaining a grid point frequency difference value and a grid point time difference value in the time-frequency difference lookup table corresponding to a received radiation source signal, and determining a time-frequency domain calculation range of the radiation source signal covering the grid point based on the grid point frequency difference value and the grid point time difference value;
taking a grid point frequency difference value in a time-frequency domain calculation range as an input, discretizing the grid point frequency difference value through a constructed frequency domain mutual blurring function model, and outputting a model frequency difference coordinate, a model time difference coordinate and a frequency difference function value corresponding to the discretized grid point frequency difference value; corresponding the grid point frequency difference value with the model frequency difference coordinate through a frequency domain mutual blurring function model;
step three, taking the model time difference coordinates, the frequency difference function values and the grid point time difference values in the time-frequency domain calculation range as inputs, and outputting the time difference function values through an interpolation model constructed by the Sinc interpolation sub-model; the step corresponds the grid point time difference value to the model time difference coordinate through an interpolation model;
and fourthly, mapping the time difference function value to grid points of a time-frequency difference lookup table to form a radio frequency distribution map, and positioning to obtain the position coordinates of the radiation source.
As shown in fig. 1, in step one, the method for generating the time-frequency difference lookup table includes:
at least two receivers receive the radiation source signals;
performing grid division on a preset geographic coverage area to obtain a grid point set and a geographic coordinate set corresponding to the grid point set;
according to the geometrical distribution relation between the grid point sets and at least two receivers, the arrival time difference value TDOA (Time Difference of Arrival, TDOA) and the frequency difference value FDOA (Frequency Difference of Arrival, FDOA) of the radiation source signals received by at least two receivers corresponding to each grid point are calculated through the geographic coordinate sets corresponding to the grid point sets, and a time-frequency difference lookup table uniquely corresponding to the radiation source signals and the grid points is generated based on the time difference value and the frequency difference value.
According to the technical scheme disclosed by the embodiment of the invention, when a plurality of receivers are selected, the pairwise pairing mode can be selected to realize the technical scheme of the invention.
In the first step, the method for determining the time-frequency domain calculation range comprises the following steps:
obtaining maximum and minimum values of grid point time difference values in a time-frequency difference lookup table corresponding to the received radiation source signals, and determining a time domain calculation range through the maximum and minimum values of the grid point time difference values;
and obtaining the maximum value and the minimum value of the grid point frequency difference value in the time-frequency difference lookup table corresponding to the received radiation source signal, and determining the frequency domain calculation range through the maximum value and the minimum value of the grid point frequency difference value.
In specific calculation, the time domain mutual blurring function in the prior art can only be calculated according to integer times of sampling resolution, which leads to the limitation of the final result on the sampling resolution and the sampling point number, while the resolution of the frequency domain calculation range of the invention can be any value, and the resolution is not necessarily the integer times of the sampling period similar to the time domain calculation, so that the problem can be avoided.
In the second step, the constructed frequency domain mutual ambiguity function model is as follows:
；
wherein,a frequency domain mutual blurring function model; />Time difference points discretized for time difference values;frequency difference points which are discretized for the frequency difference value; n is the number of sampling points, and the value range of N is from 0 to N-1; />Receiving frequency domain samples of the radiation source signal for a first receiver, fourier transforming the received radiation source signal for the first receiver,，/>a time domain sampled signal received for a first receiver;receiving frequency domain samples of the radiation source signal for a second receiver, fourier transforming the received radiation source signal for the second receiver,/for the second receiver>，A time domain sampled signal received for a second receiver; />Receiving a conjugate of the frequency domain sampling result of the radiation source signal for the second receiver; * Representing to take conjugate; k is a sampling point; />Is the sampling rate; e is a natural constant; j is the sign of the imaginary number.
The calculation mode ensures that the accuracy of frequency difference calculation is not influenced by the sampling rate and the sampling point number, the time-frequency domain calculation range is determined by the grid points, and the time-domain mutual blurring function in the prior art can only be calculated according to the integral multiple of the sampling resolution, so that the defect that the final result is limited by the sampling resolution and the sampling point number is effectively overcome.
And step two, the frequency difference range of the whole time-frequency difference lookup table is not calculated, and the result is calculated through a frequency domain mutual blurring function model based on the grid point frequency difference value, so that the influence of insufficient frequency domain resolution is effectively eliminated, and the estimation problem of two-dimensional data points in the prior art is converted into the estimation problem of one-dimensional data points. Different from the prior art that the mutual blurring function is calculated to obtain a three-dimensional function diagram, the step of calculation finally obtains a series of frequency domain mutual blurring function slices. As shown in fig. 2.
The abscissa in fig. 2 corresponds to a time difference range, and is a model time difference coordinate, and is an abscissa outputted by a frequency domain mutual blurring function model based on the start-stop time of a received radiation source signal and sampling time in the receiving process of at least two receivers; the ordinate corresponds to the grid point frequency difference value, and the ordinate is the frequency difference function value. And the corresponding relation between the grid point frequency difference coordinates and the grid point frequency difference values in the mapping process is effectively ensured by corresponding the grid point frequency difference values and the model frequency difference coordinates through a frequency domain mutual blurring function model.
In the third step, an interpolation model constructed through the Sinc interpolation sub-model is as follows:
；
wherein,is an interpolation model; />Interpolation sub-model for Sinc; />The weight value at the model time difference coordinate sample point i is obtained; x is the grid point time difference value in the frequency domain calculation range; and i is the model time difference coordinate.
In the third step, the Sinc interpolation submodel is:
；
wherein,interpolation sub-model for Sinc; />Is a frequency difference function value; />The weight value at the model time difference coordinate sample point i is obtained; x is the grid point time difference value in the frequency domain calculation range; and i is the model time difference coordinate.
In data processing, it is often necessary to calculate unknown data points from currently known data, and this operation is called interpolation in numerical analysis. For any point x, interpolation may be achieved by convolution:
；
wherein,called interpolation factors or kernels, generally even functions with respect to x, i.e。/>Corresponding to the weight at sample point i. Function value of interpolation point x ∈>Is the interpolation of the intra-nuclear sample->And->The sum of the products, i.e. corresponds to the x-neighborhood samplesIs a weighted sum of (c).
The embodiment of the invention introduces a Sinc interpolation core, and an interpolation algorithm performed by using the Sinc interpolation core is a Sinc interpolation algorithm, also called a Shannon interpolation algorithm (whisttaker-shannon interpolation formula), is a method for constructing a time continuous band-limit function from discrete real signals, is an interpolation algorithm in signal processing, and is widely and very suitable for fitting most vibration signals and graphic signals; wherein the vibration is as follows: acoustic waves, seismic waves, etc. In the field of signal processing, a normalized Sinc function is generally used, defined as:
；
and the fourier transform of the Sinc function is:
；
the spectrum of the Sinc function can be obtained as a rectangular window, as shown in fig. 3 and 4.
As known from digital signal processing, the process of sampling a signal in the time domain is to perform cycle extension on the signal in the frequency domain. The original signal is recovered by the sampling point, and the extended spectrum is removed from the frequency domain, so that the filtering is performed by using a low-pass filter. In order to ensure that the frequency spectrum obtained by filtering is consistent with the frequency domain of the original signal, a filter with a rectangular window in the frequency domain is needed, and the corresponding function is a Sinc function in the time domain, so that the Sinc function is equivalent to a perfect low-pass filter. The time domain convolution is the product of the frequency domain, only the Sinc function and the sampling data are required to be convolved, and the convolution is actually the process of multiplication and summation, so thatChanging to the Sinc function, the Sinc interpolation submodel can be obtained as follows:
；
in order to accurately calculate the function value of a certain interpolation point, a convolution kernel is required to cover an infinite number of sampling points, which cannot be realized in practice. In general, to simplify the calculation process, the convolution kernel is truncated without unduly losing accuracy. According to the number of zero points in the frequency domain/time domain after the truncation, the embodiment can be divided into 4-point, 8-point and 16-point Sinc interpolation kernels. Including but not limited to other Sinc interpolation kernels that meet demand points. For the Gibbs phenomenon generated by truncation, a sharpening window, such as a keze (Kaiser) window, may be used to weight the interpolation kernel.
For the truncated Sinc kernel function, normalization processing is needed to ensure that the sum of weights of the Sinc kernel function on sampling points is equal to 1, namely the following operation is performed, and an interpolation model is constructed through a Sinc interpolation sub-model, wherein the interpolation model is obtained as follows:
；
and carrying out interpolation operation after selecting 8-point Sinc interpolation kernels, wherein the obtained result is shown in fig. 5.
As can be seen from fig. 5, the 8-point Sinc interpolation can effectively recover the required raw data points from the sampled data. The above completes the derivation of the Sinc interpolation, which is applied to the positioning method of the present invention below.
In the fields of digital signal communication, SAR image restoration and reconstruction, etc., it is often necessary to obtain values at non-integer points by interpolation. In the second step, corresponding the grid point frequency difference value with the model frequency difference coordinate through a frequency domain mutual blurring function model; after ensuring the corresponding relation between grid points and the frequency difference coordinates of the mutual blurring function, the step three is to correspond the grid point time difference value with the model time difference coordinates through an interpolation model by applying a Sinc interpolation method; and constructing a corresponding relation between the grid point time difference value and the model time difference coordinate, and finally realizing more accurate function value mapping.
As in fig. 6, the dots are sampling points, and the triangles are time differences of the grid points. It is apparent from fig. 6 that the time difference value of the grid point cannot directly find the corresponding function value. Aiming at the situation, an interpolation model constructed by the introduced Sinc interpolation sub-model is utilized to obtain a time difference function value corresponding to the grid point time difference. As shown in fig. 7, the dots connected by the dotted lines in fig. 7 are time difference function values. Considering the balance of the calculated amount and the accuracy, an 8-point Sinc interpolation kernel is selected for interpolation operation. And mapping the time difference function value obtained by interpolation to the grid point, and finally obtaining a more accurate positioning result.
As shown in fig. 8 and 9, in the fourth step, the method for mapping the time difference function value to the grid points of the time-frequency difference lookup table to form the radio frequency distribution map and obtaining the position coordinates of the radiation source by positioning includes:
in the time-frequency domain calculation range, the time difference function value output by the interpolation model is mapped to grid points of a time-frequency difference lookup table, the radiation source is relatively static in a scene, and when the receiver moves, a radio frequency distribution diagram is generated in the time-frequency domain calculation range through accumulation of a plurality of radiation source signal time periods based on the principle that the time difference function value is consistent when the same radiation source signal is received by receivers with different geometric configurations, and the peak value of the accumulated time difference function value in the radio frequency distribution diagram is the radiation source position coordinate obtained through positioning.
The following provides a simulation verification test, and the detailed description of the method provided by the invention is as follows:
the simulation test is used for verifying the effectiveness of the positioning algorithm. The scenario is set forth below, where the first receiver A and the second receiver B are located at (5000,0,7500) m and (15000,5000,7500) m, respectively, the radiation source E is located at (30000,70000,0) m, the first receiver A and the second receiver B are moving along the X-axis at a speed of 150m/s, and the radiation source E is stationary. The generated signal is a linear frequency modulation pulse signal, the positioning range is 40km multiplied by 40km, and the grid point spacing is 1km. The positioning result obtained by the technical scheme disclosed by the invention is shown in fig. 9, 11, 13 and 15.
As shown in fig. 9, a distinct peak is obtained near (3000,7000) m, which coincides with the initially set radiation source coordinates, indicating that the present invention can effectively perform radiation source positioning. Fig. 10 is a result obtained by calculating the mutual blur function mapping and positioning method under the same condition, fig. 9 and fig. 10 are an overview of the calculation results of the method and the mutual blur function mapping and positioning method disclosed by the invention, and compared with the result that the peak value obtained by calculating the method disclosed by the invention can be found to be more concentrated and sharp.
And then respectively observing from different angles, wherein fig. 11 and fig. 12 are top views of the calculation results of the method and the mutual ambiguity function mapping positioning method disclosed by the invention, and the center point of the result of the method disclosed by the invention is closer to the real point of the radiation source coordinates;
FIGS. 13 and 14 are schematic views showing the calculated results of the disclosed method and the mutual ambiguity function mapping method, respectively, along the positive y-axis direction, with the center point of the result of the disclosed method being closer to 30000m of the abscissa of the real point of the radiation source coordinate and the peaks being more concentrated;
FIGS. 15 and 16 are schematic diagrams of the calculated results of the method and the mutual ambiguity function mapping method according to the present invention, respectively, showing a horizontal viewing angle along the positive x-axis direction, where the center point of the result of the method disclosed by the present invention is closer to the ordinate 70000m of the real point of the radiation source coordinate, and the peak value is more concentrated;
the position calculation time is mainly affected by the signal sampling rate. Taking into account the number of signal samplesNUnder the condition that the sampling rates are respectively 50MHz, 200MHz and 1GHz, and the parameters of signal power, carrier frequency, bandwidth and modulation type are the same, the average calculation time of a CAF-MAP method of a mutual ambiguity function mapping positioning method in the prior art and the average calculation time of the method disclosed by the invention are shown in a table 1:
TABLE 1
Compared with the prior art, the peak value of the simulation test result of the technical scheme disclosed by the invention is more obvious. The invention does not need to calculate the mutual ambiguity function of the whole time-frequency difference lookup table, so that the calculation time is relatively shortened, and the memory requirement of a computer is reduced. Aiming at the problem that the calculation speed of the improved method is slower under the condition of low sampling rate, the parallel calculation is carried out by adopting a multi-core computer, for example, the parallel calculation can be carried out by using the parcor command of matlab, so that the calculation speed is obviously improved.
According to the simulation verification test disclosed by the invention, when facing the technical problem of positioning a plurality of radiation sources, the person in the art only needs to arrange the plurality of radiation sources in the grid points, and the positions of the plurality of radiation sources can be positioned by utilizing the technical scheme disclosed by the invention.
Example two
The second embodiment of the invention provides a passive positioning device for a radiation source based on frequency domain mutual blurring function interpolation mapping, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps of the passive positioning method for the radiation source based on the frequency domain mutual blurring function interpolation mapping when executing the computer program.
In addition, the embodiment of the invention also provides a computer readable storage medium, which stores a computer program, and the computer program realizes the steps of a passive positioning method for mapping a radiation source based on frequency domain mutual blurring function interpolation when being executed by a processor.
The embodiment of the invention has the beneficial effects that:
the method inputs the grid point frequency difference value in the time-frequency domain calculation range through the frequency domain mutual blurring function model, and outputs the model frequency difference coordinate, the model time difference coordinate and the frequency difference function value; the step corresponds the grid point frequency difference value and the model frequency difference coordinate through a frequency domain mutual blurring function model, so that the calculated amount is effectively reduced, and the corresponding relation between the grid point frequency difference value and the model frequency difference coordinate is ensured;
using the Sinc interpolation sub-model, taking the model time difference coordinates, the frequency difference function value and the grid point time difference value in the time-frequency domain calculation range as input, and outputting the time difference function value through an interpolation model constructed by the Sinc interpolation sub-model; the step corresponds the grid point time difference value to the model time difference coordinate through an interpolation model; the corresponding relation between the grid point time difference value and the model time difference coordinate is ensured, and the positioning precision is effectively improved.
The method and the device provided by the invention are used for carrying out passive positioning of the satellite to the ground radiation source, and have the following advantages:
1. the sampling signal is directly used as calculation input without measuring signal parameters, so that the precision loss of intermediate parameter estimation is avoided;
2. the operation amount of the existing mutual blurring function mapping method is reduced, and a positioning result can be obtained by rapid calculation when a large amount of data is faced;
3. the time difference function value mapping relation is improved, and the positioning accuracy of the target radiation source is effectively improved.
The invention does not need to calculate the mutual ambiguity function of the whole time-frequency difference lookup table, so that the calculation time is relatively shortened, and the memory requirement of a computer is reduced. Aiming at the problem that the calculation speed of the improved method is slower under the condition of low sampling rate, the multi-core computer is adopted for parallel calculation, so that the calculation speed is obviously improved.
The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any person skilled in the art will readily recognize that variations or substitutions are within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (9)
1. A passive positioning method of a radiation source based on frequency domain mutual blurring function interpolation mapping is characterized by comprising the following steps:
step one, based on the generated time-frequency difference lookup table, obtaining a grid point frequency difference value and a grid point time difference value in the time-frequency difference lookup table corresponding to a received radiation source signal, and determining a time-frequency domain calculation range of the radiation source signal covering the grid point based on the grid point frequency difference value and the grid point time difference value;
taking a grid point frequency difference value in a time-frequency domain calculation range as an input, discretizing the grid point frequency difference value through a constructed frequency domain mutual blurring function model, and outputting a model frequency difference coordinate, a model time difference coordinate and a frequency difference function value corresponding to the discretized grid point frequency difference value;
step three, taking the model time difference coordinates, the frequency difference function values and the grid point time difference values in the time-frequency domain calculation range as inputs, and outputting the time difference function values through an interpolation model constructed by the Sinc interpolation sub-model;
mapping the time difference function value to grid points of a time-frequency difference lookup table to form a radio frequency distribution map, and positioning to obtain the position coordinates of the radiation source; the method specifically comprises the following steps: and mapping the time difference function value output by the interpolation model onto grid points of a time-frequency difference lookup table in a time-frequency domain calculation range, and generating a radio frequency distribution diagram in the time-frequency domain calculation range by accumulating a plurality of radiation source signal time periods based on the principle that the time difference function value is consistent when the same radiation source signal is received by receivers with different geometric configurations, wherein the peak value of the accumulated time difference function value in the radio frequency distribution diagram is the radiation source position coordinate obtained by positioning.
2. The method of claim 1 wherein in step one, the method of generating the time-frequency difference look-up table comprises:
at least two receivers receive the radiation source signals;
performing grid division on a preset geographic coverage area to obtain a grid point set and a geographic coordinate set corresponding to the grid point set;
according to the geometric distribution relation between the grid point sets and the at least two receivers, calculating arrival time difference values and frequency difference values of the radiation source signals received by the at least two receivers corresponding to each grid point through the geographic coordinate sets corresponding to the grid point sets, and generating a time-frequency difference lookup table uniquely corresponding to the radiation source signals and the grid points based on the time difference values and the frequency difference values.
3. The method according to claim 1 or 2, wherein in the step one, the method for determining the time-frequency domain calculation range includes:
obtaining maximum and minimum values of grid point time difference values in a time-frequency difference lookup table corresponding to the received radiation source signals, and determining a time domain calculation range through the maximum and minimum values of the grid point time difference values;
and obtaining the maximum value and the minimum value of the grid point frequency difference value in the time-frequency difference lookup table corresponding to the received radiation source signal, and determining the frequency domain calculation range through the maximum value and the minimum value of the grid point frequency difference value.
4. The method of claim 1, wherein in the second step, the constructed frequency domain mutual ambiguity function model is:
；
wherein,a frequency domain mutual blurring function model; />Time difference points discretized for time difference values; />Frequency difference points which are discretized for the frequency difference value; n is the number of sampling points, and the value range of N is from 0 to N-1; />Receiving a frequency domain sample of the radiation source signal for a first receiver; />Receiving frequency domain samples of the radiation source signal for a second receiver; />Receiving a conjugate of the frequency domain sampling result of the radiation source signal for the second receiver; k is a sampling point;is the sampling rate; e is a natural constant; j is the sign of the imaginary number.
5. The method according to claim 1 or 4, wherein in the second step, the model time difference coordinates outputted by the frequency domain mutual blur function model are abscissa outputted by the frequency domain mutual blur function model based on the start-stop time of the received radiation source signal and the sampling time in the receiving process of at least two receivers;
the frequency difference function value output by the frequency domain mutual blurring function model is the vertical coordinate output by the frequency domain mutual blurring function model, and is used as the input of the Sinc interpolation sub-model to participate in the construction of the interpolation model.
6. The method as claimed in claim 1 or 4, wherein in the second step, the model frequency difference coordinates outputted by the frequency domain mutual blurring function model are grid point frequency difference values in a range calculated for the inputted time-frequency domain, and are ordinate outputted by the frequency domain mutual blurring function model.
7. The method of claim 1, wherein in step three, the interpolation model constructed by the Sinc interpolation sub-model is:
；
wherein,is an interpolation model; />Interpolation sub-model for Sinc; />The weight value at the model time difference coordinate sample point i is obtained; x is the grid point time difference value in the frequency domain calculation range; and i is the model time difference coordinate.
8. The method of claim 1 or 7, wherein in step three, the Sinc interpolation submodel is:
；
wherein,interpolation sub-model for Sinc; />Is a frequency difference function value; />The weight value at the model time difference coordinate sample point i is obtained; x is the grid point time difference value in the frequency domain calculation range; and i is the model time difference coordinate.
9. A passive positioning device for mapping a radiation source based on frequency domain mutual blur function interpolation, comprising a memory storing a computer program and a processor implementing the steps of the method according to any one of claims 1 to 8 when the computer program is executed by the processor.
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