CN113203985B - Direct positioning method for shortwave same-frequency signals - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
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Abstract
The invention belongs to the technical field of short-wave radio positioning, and relates to a method for directly positioning short-wave same-frequency signals. The invention provides a method for directly positioning a short-wave co-frequency signal, which creatively provides a method for positioning the short-wave co-frequency signal under a multipath condition, namely, a single-antenna distributed sensor is used for synchronously collecting a target signal, and a state space model of short-wave signal propagation is established. By introducing a spatial frequency shift operator, the signal is converted from the time domain to the space domain and a random spatial spectrum is obtained. On the basis, the method is analyzed to have the spatial characteristics of restraining multipath and noise components, a spatial sparsification method is provided, and a k-means clustering method is adopted to realize the joint positioning method of a plurality of targets.
Description
Technical Field
The invention belongs to the technical field of short-wave radio positioning, relates to a direct positioning method of short-wave co-frequency signals, and particularly relates to a method for realizing joint positioning of a short-wave co-frequency emission source while restraining multipath interference by converting a space domain under the condition of time-frequency domain homogeneous aliasing.
Background
According to radio frequency division, short wave refers to electromagnetic waves having a frequency of 3MHz to 30MHz and a wavelength of 100m to 10m, and radio communication using a short wave band is called short wave communication. Because short-wave communication relies on ionosphere reflection as a transmission medium, long-distance communication can be realized without a relay station, and the construction and operation costs are relatively low, the method is widely applied to the fields of military, broadcasting, weather, business, external traffic and the like. Particularly, in recent years, with the continuous development of information technology, the automation and new service capacity of short-wave communication are enhanced, and a new system of a modern short-wave communication system is formed.
Advantages in long-range communication have led to many advances in short-wave communication, but there are also problems. Short wave signals are transmitted by means of ionosphere reflection, and the ionosphere is affected by the atmosphere and weather and shows different propagation characteristics under different seasons and different weather conditions. Thus, the transmission channel of short wave communication has time variability and uncertainty. And the multipath transmission, doppler frequency shift and the like cause the expansion of the short wave signals in the three-dimensional space of the time domain, the frequency domain and the space domain, and the effectiveness and the reliability of the short wave signal transmission can be affected. The electromagnetic environment is increasingly complex, short-wave frequency resources are extremely short, heterogeneous networks with various systems coexist and compete for limited frequency spectrum resources, and radio interference phenomenon in short-wave communication is increasingly increased, so that the communication quality is seriously affected. In addition, the advent of miniaturized mobile short wave transmitting stations and short wave communications of offshore mobile military targets have presented unprecedented challenges to radio monitoring.
The current short wave signal monitoring and positioning technology is mainly based on a national short wave monitoring network, and is realized by means of correlation interferometer technology or spatial spectrum direction finding and positioning. Traditional short wave positioning technology relies on the angle of arrival measurement of signals, and then targets are positioned by searching for the intersection areas of a plurality of direction finding lines. In order to improve the direction-finding precision, a super-resolution algorithm based on a spatial spectrum theory is widely applied. However, the conventional direction-finding system needs to be equipped with a medium-sized or large-sized antenna array and a matched multichannel signal acquisition device, so that the economic cost is high, the occupied area is large, and particularly in some economically developed areas, the worldwide problem of station resource shortage is faced. At the same time, the continuously deteriorating electromagnetic environment also causes a serious degradation of the performance of the direction finding system. Under the condition, a short-wave time difference positioning technology adopting distributed single antenna configuration is attracting attention gradually, the requirements of the mode on land and electromagnetic environment are relatively low, but due to the influence of factors such as time-varying ionosphere and co-frequency interference, accurate measurement of time difference of arrival (TDOA) parameters is difficult to realize, and the accuracy of target position estimation is further reduced. The algorithms all adopt a two-step method, namely, firstly, time delay parameter estimation is carried out, then positioning equation solution is carried out through an estimated value to obtain the position estimation of the target, and the parameter estimation and the positioning solution are two mutually independent parts. This approach does not guarantee consistency of observations, and in particular errors in parameter estimation in the case of low signal-to-noise ratios and short data can add up severely to the position estimate. The direct positioning method provided by the invention is based on the premise that the signals acquired by the receiving ends come from the same transmitting source, and the estimation result of the target position is directly acquired from the synchronously received I/Q data. The main research content is to organically combine a spatial spectrum theory method and a transform domain sparsification method, and provide a novel short wave positioning technology theory and method. The invention is based on the actual condition of short wave monitoring, the research result can enrich the theory and technology of short wave monitoring in China, break through the bottleneck, and greatly improve the positioning accuracy of the short wave emission source.
Disclosure of Invention
The invention aims to provide a direct positioning method for short-wave co-frequency signals, which aims to solve the problems in the prior art.
The core of the short wave same-frequency signal direct positioning method provided by the invention is a novel signal transformation domain method, so that the main path component of the short wave signal is enhanced, the multipath component is suppressed, further, the position estimation of a target is directly obtained in the transformation domain, and the problem that how to effectively extract useful information is needed to solve the core target is solved as follows:
(1) Collecting synchronous I/Q data;
(2) Converting the random position sample points of the time domain into the space domain;
(3) Multipath propagation and co-channel interference;
(4) Non-line-of-sight multipath suppression and low signal-to-noise ratio signal characteristic parameter extraction;
(5) Multi-parameter joint estimation of time-frequency domain aliasing signals;
(6) How to use the resulting data for target source localization.
The invention solves the technical problems by the following technical proposal:
the invention provides a method for directly positioning a short-wave co-frequency signal, which is a method for positioning a short-wave signal target source under co-frequency interference. By utilizing time delay information among a plurality of synchronous receiving station signals, a state space model is built by the receiving signals, the position coordinates of a transmitting source and the height parameters of a multidimensional ionization layer, and a random space spectrum method is provided, so that the signals are mapped from a time domain to a space domain. The method comprises the following steps:
step 1, short wave signals are transmitted through ionosphere reflection, one-hop or multi-hop mixed transmission is considered, and a short wave channel system function is established
The position coordinate vector of the normal service source is expressed as theta 1 ＝[x T ,y T ] T The superscript symbol T denotes the transpose, and the interference signal position coordinate vector is denoted as θ 2 ＝[x I ,y I ] T The receiving station position coordinate vector is expressed asp=1, 2,..p, where +.>Representing reference station position coordinates;
considering a mixed propagation mode of one and two hops, the target signal is transmitted to the receiving stationChannel system function h i (t) and channel System function g of interfering Signal to receiving station i (t) are respectively expressed as:
where j=1 represents one hop, j=2 represents two hops, a j,i Is the channel fading coefficient of the target signal to the receiving station, b j,i Is the channel fading coefficient of the interference signal to the receiving station, delta (·) represents the impulse function, t represents the discrete time sequence, D j,i Time delay sampling point and T representing target signal to receiving station j,i Representing the time delay sampling point of the interference signal to the receiving station, and obtaining:
wherein c is the speed of light, f s Representing the sampling rate of the signal, |·|| represents the vector 2 norm, h j,i Indicating the ionospheric virtual high on the jth path of the target signal to the ith receiving station,the ionosphere virtual height on the jth path of the interference signal to the ith receiving station is represented;
step 2, obtaining synchronous acquisition of same-frequency mixed signals of M distributed single-antenna receiving units
Channel system function h from the target signal obtained in step 1 to the receiving station i (t) and channel System function g of interfering Signal to receiving station i (t) obtaining the sampled signal r received by the receiver i (t) the signal is acquired by synchronous acquisition of M distributed single-antenna receiving units, and the output of the sampling signal received by the receiver is expressed as:
wherein,,representing convolution, s T (t) represents a target signal, s I (t) represents an interference signal, u i (t) represents a measured noise random variable, subject to zero-mean gaussian distribution;
for the received signal r i And (t) performing Fourier transformation to obtain:
R i (k)＝S T (k)H i (k)+S I (k)G i (k)+U i (k) (4)
where k=0, 1..k-1 is a frequency sequence, K represents the total sampling point number, S T (k) Representing the Fourier transform of the target signal S I (k) Representing the Fourier transform of the interfering signal, U i (k) Fourier transform representing noise sequence, H i (k) Fourier transform of channel system function representing target signal to receiving station, G i (k) Fourier transforms representing the channel system function of the interfering signal to the receiving station are:
wherein ΔD is j,i ＝D j,i -D 1,1 Representing the relative delay of the target signal, deltaT j,i ＝T j,i -T 1,1 Representing the relative delay of the interfering signal;
step 3, representing the emitting source coordinate sample points by random sample points, sampling by using prior probability distribution to obtain coordinates and height sample points, further obtaining time difference samples, and obtaining a random spatial spectrum of the receiving signal according to a spatial frequency shift operator
To construct H in step 2 i (k) And G i (k) Describing each unknown parameter by two random sets of spatial sample points, wherein the unknown parameters are represented by particles θ p ＝[x p ,y p ] T (p=1, 2,., P) to characterize the emission source coordinate sample points, P representing the number of coordinate sample points; by h q (q=1, 2,., Q) represents ionosphere virtual heightParticles, Q represents the number of high sample points; the coordinates and the height sample points are obtained through sampling the prior probability distribution, and the time difference sample is obtained through further calculation:
wherein f s Represents the sampling rate of the signal, index Q' =1, 2,..q,for the receiving station position coordinate vector in step 1, and (2)>Representing reference station position coordinates; each coordinate particle corresponds to Q 2 Different time difference sample values; obtaining a spatial frequency shift operator->The random spatial spectrum expression of the received signals of the ith base station and the reference station is given as:
wherein K represents the total sampling point number, R 1 (k) Representing the Fourier transform of the reference signal, R i (k) For fourier transformation of the received signal, symbol H represents conjugation; if the signals acquired by each receiving station are mutually independent, the multi-station joint random space spectrum is expressed as follows:
wherein M represents a distributed single antenna receiving unit, F i p,n Representing the random spatial spectrum of the signals received by the ith base station and the reference station;
step 4, establishing a spatial sparsification method to form spatial spectrum clusters, and obtaining the estimation of the same-frequency signal position through distinguishing a cluster center
Combining the multi-station joint random space spectrum F obtained in the step 3 p The value of (1) maps to [0,1 ]]In the interval, the contrast between strong and weak signals is effectively reduced under the condition of not increasing noise components, and the expression is as follows:
Φ p with |F p The increase of the i monotonically increases when the position sample point θ in step 3 p When appearing near the true value, then Φ p The closer to 1, if the sample point does not match the true position, Φ p The closer to 0; on the basis, a threshold T is given r When meeting phi p ＜T r When the coordinate sample is detected, the corresponding coordinate sample is removed;
for the co-existence of the same frequency signals, the coordinate sample is divided into two regions, E 1 And E is 2 Iterative calculation of the region centroid mu by k-means clustering algorithm for estimation of the position of the transmitting source 1 Sum mu 2 The method comprises the following steps:
wherein mu 1 Is area E 1 Centroid, mu 2 Is area E 2 Centroid, theta p To represent the source coordinate sample points in step 3,representing an estimate of the target signal position +.>An estimate representing the location of the interfering signal;
to further improve the positioning accuracy, the coordinate sample points are updated and (6) - (10) are repeated, then:
wherein P represents the number of coordinate sample points, w p Is superimposed random disturbance for improving the diversity of sample points, obeys the mean value to be 0 and variance to be 0Is a normal distribution of (2); thus, the joint positioning of the short wave same-frequency signals in the multipath environment is completed.
The invention provides a method for directly positioning a short-wave co-frequency signal, which organically and innovatively provides a method for positioning the short-wave co-frequency signal under a multipath condition, namely, a single-antenna distributed sensor is used for synchronously collecting a target signal, and a state space model of short-wave signal propagation is established. By introducing a spatial frequency shift operator, the signal is converted from the time domain to the space domain and a random spatial spectrum is obtained. On the basis, the method is analyzed to have the spatial characteristics of restraining multipath and noise components, a spatial sparsification method is provided, and a k-means clustering method is adopted to realize the joint positioning method of a plurality of targets. The system platform is flexible in station arrangement, easy to network, and capable of effectively saving station resources. Positioning accuracy in the case of both low signal-to-noise ratio and short data has significant advantages. The method effectively solves the problem of co-channel interference positioning in short wave monitoring, and has certain reference value for improving the technical level of radio monitoring and management.
The innovation point of the invention is that:
1. aiming at the practical problem of high difficulty in positioning the time difference of a short wave radiation source under the condition of a multipath/multi-hop mixed channel, a direct positioning method based on a random spatial spectrum theory is provided for the first time, a position sample and an ionization layer height sample are obtained through random sampling, and a direct corresponding relation between a received signal and multiple parameters is established. And performing energy matching in a three-dimensional space, and searching a position index of the maximum value of the spectrum amplitude of the space as an estimation of the position of the target emission source.
2. Aiming at the common-frequency-band interference problem frequently occurring in short-wave communication, a sparse representation method in a signal transformation domain is provided for the first time. According to the spatial independent characteristic of the position of the emission source, a spatial sparsification mathematical model is constructed by utilizing the proposed random spatial spectrum theory method, and a clustering algorithm is designed to obtain the estimation of the target position.
3. On the basis of breakthrough of key technology, the invention combines theoretical research results to finish upgrading and reforming the existing shortwave time difference positioning system platform, breaks through the barriers of the existing shortwave positioning technology, and realizes accurate positioning of shortwave signals of different modulation types.
Drawings
FIG. 1 is a general flow chart of positioning short-wave common-frequency signals provided by the invention;
FIG. 2 is a schematic representation of the reflection of signals through the ionosphere;
FIG. 3 is a block diagram of a positioning system setup;
fig. 4 is an amplitude waveform of a received signal of each receiving station;
fig. 5 is geographic coordinates of the results of positioning of the transmitting source and receiving station.
Detailed Description
The following describes the embodiments of the present invention further with reference to the drawings and technical schemes.
The positioning method based on the short-wave co-frequency signal under the multipath condition is convenient to operate and wide in application, synchronous I/Q data are collected, random sample points in a time domain are transferred to a space domain, and the obtained data are utilized to realize target source positioning of the short-wave signal.
Examples
As shown in fig. 1, the method for directly positioning the short-wave co-frequency signal under the multipath condition is realized by the following steps:
step 1, short wave signals are propagated through the ionosphere, as shown in FIG. 2, wherein A-D-B is the virtual height of the ionosphere of h=h 1 One-hop propagation path of A-E 1 -C-E 2 -B is ionosphere virtual height h=h 2 Is provided. As can be seen from electromagnetic mirror theory, the two-hop paths can be equivalently regarded as one-hop paths A-D' -B with different ionosphere virtual heights. Wherein, is normalThe position coordinate vector of the service information source is expressed as theta 1 ＝[x T ,y T ] T The superscript symbol T denotes the transpose, and the interference signal position coordinate vector is denoted as θ 2 ＝[x I ,y I ] T The receiving station position coordinate vector is expressed asp=1, 2,..p, where +.>Representing the reference station position coordinates. If more complex one-hop and two-hop mixed propagation modes are considered, the channel system function h of the target signal to the receiving station i (t) and channel System function g of interfering Signal to receiving station i (t) can be expressed as:
here, j=1 represents one hop, j=2 represents two hops, a j,i Is the channel fading coefficient of the target signal to the receiving station, b j,i Is the channel fading coefficient of the interference signal to the receiving station, delta (·) represents the impulse function, t represents the discrete time sequence, D j,i Time delay sampling point and T representing target signal to receiving station j,i The time delay sampling points representing the interference signals to the receiving station are obtained from the geometrical relationship of the Pythagorean theorem according to the signal-to-ionospheric reflection diagram of fig. 2:
here, c.apprxeq.3.times.10 8 m/s is the speed of light, f s Representing the sampling rate of the signal, |·|| represents the vector 2 norm, h j,i Indicating the ionospheric virtual high on the jth path of the target signal to the ith receiving station,indicating that the ionosphere on the jth path of the interfering signal to the ith receiving station is virtually high.
Step 2, channel system function h from the target signal obtained in step 1 to the receiving station i (t) and channel System function g of interfering Signal to receiving station i (t) obtaining the sampled signal r received by the receiver i (t) the signal is acquired by synchronous acquisition of M distributed single antenna receiving units, the sampled signal output received by the receiver can be expressed as:
wherein,,representing convolution, s T (t) represents a target signal, s I (t) represents an interference signal, u i And (t) represents a measurement noise random variable, and is subjected to zero-mean Gaussian distribution. Fourier transforming the received signal can result in:
R i (k)＝S T (k)H i (k)+S I (k)G i (k)+U i (k) (4)
where k=0, 1..k-1 is a frequency sequence, K represents the total sampling point number, S T (k) Representing the Fourier transform of the target signal S I (k) Representing the Fourier transform of the interfering signal, U i (k) Fourier transform representing noise sequence, H i (k) Fourier transform of channel system function representing target signal to receiving station, G i (k) Fourier transforms representing the channel system function of the interfering signal to the receiving station are:
here, Δd j,i ＝D j,i -D 1,1 Representing the relative delay of the target signal, deltaT j,i ＝T j,i -T 1,1 Representation ofThe relative delay of the interfering signal.
The invention solves the problem that the TDOA and ionosphere virtual height are not required to be measured, and the time synchronization signal is received i (t) R obtained by Fourier transform i (k) Directly obtaining an estimate of the target signal location in (i=1, 2,., M)And an estimate of the position of the interfering signal ∈ ->
Step 3, H constructed by step 2 i (k) And G i (k) It is known that it is necessary to directly obtain a position estimate of the target signal from the received baseband signalAnd interference signal position estimation +.>The time difference is calculated. Because the coordinates of the emission source and the virtual height of the ionosphere in each path are unknown parameters, it is difficult to obtain an optimal solution for such an underdetermined mathematical problem.
The invention focuses on the location of the emission source and does not require an accurate solution for the virtual height of the ionosphere. In this case, for constructing H in step 2 i (k) And G i (k) The invention describes each unknown parameter by two random sets of spatial sample points, wherein particles theta are used for p ＝[x p ,y p ] T (p=1, 2,., P) to characterize the emission source coordinate sample points, P representing the number of coordinate sample points; by h q (q=1, 2,) Q represents ionospheric virtual high particles, Q represents the number of high sample points. The coordinates and the height sample points can be obtained through sampling the prior probability distribution, and the time difference samples can be further calculated as follows:
here, f s Represents the sampling rate of the signal, index Q' =1, 2,..q,for the receiving station position coordinate vector in step 1, and (2)>Representing the reference station position coordinates. Each coordinate particle may correspond to Q 2 Different time difference sample values. Obtaining a spatial frequency shift operator->The random spatial spectrum expression of the signals received by the ith base station and the reference station can be given as:
wherein K represents the total sampling point number, R 1 (k) Representing the Fourier transform of the reference signal, R i (k) For fourier transformation of the received signal, symbol H represents the conjugate. If the signals collected by each receiving station are independent of each other, the multi-station joint random space spectrum can be expressed as follows:
wherein M represents a distributed single antenna receiving unit, F i p,n Representing the random spatial spectrum of the signals received by the i-th base station and the reference station.
Step 4, step 3 obtains the multi-station joint random space spectrum, but because the space spectrum amplitude has direct relation with the transmitting power and the channel amplitude fading. If the target signal and the interference signal have difference in signal amplitude, the contrast between the weak signal and the noise is weakened after the spatial spectrum transformation, and the contrast between the weak signal and the strong signal is increased, so that the target signal and the interference signal are easy to statistically compareWeak signals and noise fall into one category and only strong signals are identified. In order to solve the problems, the invention adopts the multi-station joint random space spectrum F obtained in the step 3 p The value of (1) maps to [0,1 ]]In the interval, the contrast between strong and weak signals can be effectively reduced under the condition of not increasing noise components, and the expression is as follows:
it can be seen that Φ p With |F p The increase of the i monotonically increases when the position sample point θ in step 3 p When appearing near the true value, then Φ p The closer to 1, if the sample point does not match the true position, Φ p The closer to 0. On the basis, a threshold T is given r When meeting phi p ＜T r And eliminating the corresponding coordinate samples. After these processes, only samples near the true location of the target are saved. For the co-existence of the same-frequency signals, the coordinate sample is divided into two distinct regions, namely E 1 And E is 2 The estimation of the position of the transmitting source can iteratively calculate the centroid mu of the region through a k-means clustering algorithm 1 Sum mu 2 The method comprises the following steps:
wherein mu 1 Is area E 1 Centroid, mu 2 Is area E 2 Centroid, theta p To represent the source coordinate sample points in step 3,representing an estimate of the target signal position +.>Representing an estimate of the location of the interfering signal.
To further improve the positioning accuracy, the coordinate sample points need to be updated, and (6) - (10) are repeated, and then:
wherein P represents the number of coordinate sample points, w p Is superimposed random disturbance for improving the diversity of sample points, obeys the mean value to be 0 and variance to be 0Is a normal distribution of (c). Thus, the joint positioning of the short wave same-frequency signals in the multipath environment is completed.
Test case
In order to verify the feasibility of the invention, the invention establishes a practical system for positioning a short wave emission source, and single channel acquisition equipment and a single omni-directional antenna are respectively configured in five cities of western security, urufion, harbin, shenzhen, shanghai and the like, the system can synchronously acquire the short wave signals, and the obtained baseband I/Q data is transmitted to a data center for processing through a high-speed special wired network, and a system composition block diagram is shown in figure 3. The system uses the data received by the western security station as a reference signal.
The positions of the emitting sources are respectively near the Xishan and the Shijia, the ground distance of the emitting sources exceeds 800km, the modulation mode is AM, the center frequency is 8.69MHz, the signal bandwidths are all 8kHz, and the emitting power is consistent. Each receiver performs time service synchronization through GPS, acquires zero intermediate frequency baseband I/Q data, and has a sampling rate of 16kHz and acquisition time of 1s. Fig. 4 shows a time-domain amplitude waveform of a primary sampling signal, which is a waveform obtained by superimposing a target signal and an interference signal.
In the actual measurement process, 100 times of data recording are performed every time signals are acquired at intervals of 20 seconds. And setting parameters according to simulation conditions, and averaging the positioning results to obtain a co-channel transmitting source position estimation result, as shown in fig. 5, wherein the positioning error of the target transmitting source is about 40km, and the positioning of the interference signal is about 55km. The actual measurement result shows that the algorithm is effective for the joint positioning of the short-wave co-frequency signals.
In summary, the short wave emission source direct positioning technology provided by the invention innovates and develops a nonlinear parameter estimation method under the conditions of multiple modes, non-line-of-sight and underdetermined in theory, greatly enriches short wave monitoring and positioning technical means, particularly provides a series of direct positioning theoretical methods based on random spatial spectrum and the like, fully suppresses the influence of signal multipath propagation, common-frequency interference, mobile emission sources and the like on positioning precision, and realizes the joint positioning of the short wave common-frequency emission sources while establishing the inhibition of multipath interference. Compared with the traditional short wave direction finding positioning technology, the system platform is flexible in station arrangement and easy to network, and station resources are effectively saved. Compared with the existing short-wave time difference positioning two-step method, the method can obtain higher estimation accuracy under the conditions of low signal-to-noise ratio and small amount of data. The method is provided according to actual requirements, is particularly suitable for calculating the random spatial spectrum by utilizing the received time synchronization I/Q data under the condition of the same frequency signal under the conditions of low signal-to-interference ratio and signal-to-noise ratio, and directly obtains the estimation of the target position through three-dimensional search. The short wave monitoring and positioning technical means are greatly enriched, and the technical upgrading of the short wave emission source positioning means by a radio management department can be promoted. Plays a positive role in maintaining social stability, guaranteeing the life and property safety of people and the like, and has important practical significance and value.
The description of the exemplary embodiments presented above is merely illustrative of the technical solution of the present invention and is not intended to be exhaustive or to limit the invention to the precise form described. Obviously, many modifications and variations are possible in light of the above teaching to those of ordinary skill in the art. The exemplary embodiments were chosen and described in order to explain the specific principles of the invention and its practical application to thereby enable others skilled in the art to understand, make and utilize the invention in various exemplary embodiments and with various alternatives and modifications. It is intended that the scope of the invention be defined by the following claims and their equivalents.
Claims (1)
1. The method for directly positioning the short-wave same-frequency signals is characterized by comprising the following steps of:
step 1, short wave signals are transmitted through ionosphere reflection, one-hop or multi-hop mixed transmission is considered, and a short wave channel system function is established:
the position coordinate vector of the normal service source is expressed as theta 1 ＝[x T ,y T ] T The superscript symbol T denotes the transpose, and the interference signal position coordinate vector is denoted as θ 2 ＝[x I ,y I ] T The receiving station position coordinate vector is expressed asp=1, 2,..p, where +.>Representing reference station position coordinates;
considering a mixed propagation mode of one and two hops, the channel system function h of the target signal to the receiving station i (t) and channel System function g of interfering Signal to receiving station i (t) are respectively expressed as:
where j=1 represents one hop, j=2 represents two hops, a j,i Is the channel fading coefficient of the target signal to the receiving station, b j,i Is the channel fading coefficient of the interference signal to the receiving station, delta (·) represents the impulse function, t represents the discrete time sequence, D j,i Time delay sampling point and T representing target signal to receiving station j,i Representing the time delay sampling point of the interference signal to the receiving station, and obtaining:
wherein c is the speed of light, f s Representing the sampling rate of the signal, |·|| represents the vector 2 norm, h j,i Indicating the ionospheric virtual high on the jth path of the target signal to the ith receiving station,the ionosphere virtual height on the jth path of the interference signal to the ith receiving station is represented;
step 2, obtaining synchronous acquisition co-frequency mixed signals of M distributed single-antenna receiving units:
channel system function h from the target signal obtained in step 1 to the receiving station i (t) and channel System function g of interfering Signal to receiving station i (t) obtaining the sampled signal r received by the receiver i (t) the signal is acquired by synchronous acquisition of M distributed single-antenna receiving units, and the output of the sampling signal received by the receiver is expressed as:
wherein,,representing convolution, s T (t) represents a target signal, s I (t) represents an interference signal, u i (t) represents a measured noise random variable, subject to zero-mean gaussian distribution;
for the received signal r i And (t) performing Fourier transformation to obtain:
R i (k)＝S T (k)H i (k)+S I (k)G i (k)+U i (k) (4)
where k=0, 1..k-1 is a frequency sequence, K represents the total sampling point number, S T (k) Representing the Fourier transform of the target signal S I (k) Representing the Fourier transform of the interfering signal, U i (k) Fourier transform representing noise sequence, H i (k) Representing a target signal to a receiving stationFourier transform of channel system function, G i (k) Fourier transforms representing the channel system function of the interfering signal to the receiving station are:
wherein ΔD is j,i ＝D j,i -D 1,1 Representing the relative delay of the target signal, deltaT j,i ＝T j,i -T 1,1 Representing the relative delay of the interfering signal;
step 3, representing the coordinate sample points of the transmitting source by using random sample points, sampling by using prior probability distribution to obtain coordinates and height sample points, further obtaining a time difference sample, and obtaining a random spatial spectrum of the receiving signal according to a spatial frequency shift operator:
to construct H in step 2 i (k) And G i (k) Describing each unknown parameter by two random sets of spatial sample points, wherein the unknown parameters are represented by particles θ p ＝[x p ,y p ] T To characterize the emission source coordinate sample points, p=1, 2,..p, P represents the number of coordinate sample points; by h q Representing ionospheric virtual high particles, q=1, 2,..q, Q represents the number of high sample points; the coordinates and the height sample points are obtained through sampling the prior probability distribution, and the time difference sample is obtained through further calculation:
wherein f s Represents the sampling rate of the signal, index Q' =1, 2,..q,for the receiving station position coordinate vector in step 1, and (2)>Representing reference station position coordinates; each coordinate particle corresponds to Q 2 Different time difference sample values; to obtain the empty spaceInter-frequency shift operatorThe random spatial spectrum expression of the received signals of the ith base station and the reference station is given as:
wherein K represents the total sampling point number, R 1 (k) Representing the Fourier transform of the reference signal, R i (k) For fourier transformation of the received signal, symbol H represents conjugation; if the signals acquired by each receiving station are mutually independent, the multi-station joint random space spectrum is expressed as follows:
wherein M represents a distributed single antenna receiving unit, F i p,n Representing the random spatial spectrum of the signals received by the ith base station and the reference station;
step 4, establishing a spatial sparsification method to form spatial spectrum clusters, and obtaining the estimation of the same-frequency signal position through distinguishing a cluster center:
combining the multi-station joint random space spectrum F obtained in the step 3 p The value of (1) maps to [0,1 ]]In the interval, the contrast between strong and weak signals is effectively reduced under the condition of not increasing noise components, and the expression is as follows:
Φ p with |F p The increase of the i monotonically increases when the position sample point θ in step 3 p When appearing near the true value, then Φ p The closer to 1, if the sample point does not match the true position, Φ p The closer to 0; on the basis, a threshold T is given r When meeting phi p ＜T r When in use, the corresponding sitting position is removedA target sample;
for the co-existence of the same frequency signals, the coordinate sample is divided into two regions, E 1 And E is 2 Iterative calculation of the region centroid mu by k-means clustering algorithm for estimation of the position of the transmitting source 1 Sum mu 2 The method comprises the following steps:
wherein mu 1 Is area E 1 Centroid, mu 2 Is area E 2 Centroid, theta p To represent the source coordinate sample points in step 3,representing an estimate of the target signal position +.>An estimate representing the location of the interfering signal;
to further improve the positioning accuracy, the coordinate sample points are updated and (6) - (10) are repeated, then:
wherein P represents the number of coordinate sample points, w p Is superimposed random disturbance for improving the diversity of sample points, obeys the mean value to be 0 and variance to be 0Is a normal distribution of (2); thus, the joint positioning of the short wave same-frequency signals in the multipath environment is completed.
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