CN115826004B - Three-star cooperative direct positioning method based on two-dimensional angle and time difference combination - Google Patents
Three-star cooperative direct positioning method based on two-dimensional angle and time difference combination Download PDFInfo
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Abstract
The invention discloses a three-star collaborative direct positioning method based on two-dimensional angle and time difference combination, which belongs to the field of satellite positioning and comprises the following steps: step one: position estimation, namely determining a region to be searched; performing grid division on the area to be searched; step two: creating a model, namely: constructing an objective function implying the position of the radiation source by using a minimum variance undistorted response method according to the obtained covariance matrix; step four: calculating an objective function value of each grid point for the grids divided in the first step by using the objective function; step five: the method comprises the steps of drawing a spatial spectrum of a received signal according to an objective function value, searching a spectrum peak, determining the position of a radiation source, obtaining a directly positioned area to be searched by using a rough estimation result of single satellite direction finding positioning, reducing the searching range, reducing the calculated amount, realizing high-precision positioning under low signal-to-noise ratio, and simultaneously realizing high resolution when the radiation sources are closely spaced.
Description
Technical Field
The invention belongs to the technical field of satellite positioning, and particularly relates to a three-star collaborative direct positioning method based on two-dimensional angle and time difference combination.
Background
Passive positioning is an important research direction in civil and military fields, has long acting distance, can adapt to complex environments, has the advantage of good concealment because of no signal radiation, and is widely focused and valued by students in various countries.
The existing satellite positioning method mostly adopts a classical two-step method for positioning. The traditional two-step positioning method firstly extracts positioning parameters such as an arrival angle, arrival time difference, arrival frequency difference and the like from a received signal; and then, establishing and solving an equation by utilizing the relation between the positioning parameters and the positions of the radiation sources to realize positioning.
In recent decades, direct-Position-Determination (DPD) technology has been widely used in fields such as radar, navigation, sonar, and communication due to its superior performance. The direct positioning technology is also called one-step method positioning, which is used for directly processing an original sampling signal without estimating positioning parameters from a received signal, constructing an objective function related to a radiation source by utilizing implicit radiation source position information in the received signal, and realizing positioning by using a searching mode.
For the traditional two-step positioning, the estimation accuracy of positioning parameters directly influences the positioning accuracy, and the positioning error is large under the condition of low signal-to-noise ratio. There is a lot of research that the DPD can adapt to the environment with low signal to noise ratio, and the DPD does not need to estimate positioning parameters, so that the process of parameter correlation between different radiation sources is avoided. However, there is a disadvantage in the direct positioning, in which the direct positioning adopts a search method to perform the position estimation, the search range is large, and the number of grids is large, which results in a large calculation amount. It is therefore necessary to determine the search area in advance and to conduct an exhaustive search within a small range.
Disclosure of Invention
The invention aims to solve the problems, and provides a three-star cooperation based on two-dimensional angle-time difference combination, which can be used for high-precision positioning in an environment with low signal to noise ratio.
In order to achieve the above purpose, the invention adopts the following technical scheme: a three-star cooperative direct positioning method based on two-dimensional angle and time difference combination comprises the following steps:
step one: position estimation, namely positioning a radiation source by using a single satellite to measure the direction, positioning a rough position estimation value of the radiation source, and determining a region to be searched; performing grid division on the area to be searched;
step two: creating a model, namely performing segmented Fourier transform on all satellite received data to obtain a covariance matrix;
step three: constructing an objective function implying the position of the radiation source by using a minimum variance undistorted response method according to the obtained covariance matrix;
step four: calculating an objective function value of each grid point for the grids divided in the first step by using the objective function;
step five: and drawing a spatial spectrum of the received signal according to the objective function value, searching a spectrum peak, and determining the position of the radiation source.
As a further improvement of the above technical solution, the direction-finding positioning of the single satellite in the step one measures the two-dimensional angle by using the single satellite.
As a further improvement of the above technical solution, in the second step:
the model conditions are: q radiation sources, L satellites and L-shaped arrays used on the satellites are arranged in the space, and the number of array elements is 2M-1;
the signal model received by the first satellite is:
r l (t)＝γ l a l (p)s(t-τ l (p))+n l (t),0≤t≤T
wherein, gamma l Represents the signal attenuation factor, a, caused by path loss l (p) is the steering vector of the first satellite to the radiation source, l=1.. L is; s (t- τ) l (p)) is the signal s (t) delayed by a delay τ l The result of (p); n is n l (T) is zero-mean complex Gaussian noise, T is time, and T is observation duration;
wherein:
α q ,β q respectively representing the azimuth angle and the pitch angle of the q-th radiation source observed in the star coordinate system, d is the array element spacing, and lambda is the signal wavelength.
As a further improvement of the technical scheme, when the satellite and the radiation source are stationary in the observation period, the observation period [0, T ] is uniformly divided into J sections, and each section has a length of T/J;
when T/JThe fourier coefficients of the kth frequency point of the received signal in the jth period of time by the ith satellite can be expressed as:
wherein f k Is the kth frequency point of the fourier transform,respectively r l (t)，s(t)、n l (t) fourier coefficients at the kth frequency point of the jth segment;
definition of the definition
The above can be rewritten as:
combining signals received by different satellites:
γ[γ 1 ,...,γ L ] T ,
the method can obtain the following steps:
further, the method comprises the steps of,the writing is as follows:
wherein:
b represents the Kronecker product of the L x L identity matrix and the M x 1 full 1 vector, prescribing | γ||=1;
the covariance matrix of the received signal is expressed as:
as a further improvement of the above technical solution, the objective function constructed in the third step is:
wherein,is->Is lambda of the inverse matrix of lambda max {.cndot } represents a maximum eigenvalue operation.
As a further improvement of the above technical solution, in the first step, the specific method for determining the area to be searched is:
when the pitch angle and azimuth angle direction finding errors are sigma (rad) and the satellite orbit height is h (km), the radius range of the area to be searched is selected by the rough estimation value to be positioned, wherein the radius range is as follows:
h·3·σ(km)。
as a further improvement of the above technical solution, the two-dimensional angle includes an azimuth angle, a pitch angle, and a variance thereof.
The invention has the beneficial effects that:
1. the invention provides a three-star collaborative direct positioning method based on two-dimensional angle and time difference combination, which obtains a direct positioning area to be searched by using a rough estimation result of single satellite direction finding positioning, reduces the searching range and reduces the calculated amount.
2. Compared with the prior art, the method provided by the invention can realize high-precision positioning under the condition of low signal-to-noise ratio, and can realize high resolution ratio when the radiation sources are closely spaced.
3. The invention does not need iterative computation and signal sources are not known.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of single satellite direction finding positioning in a star coordinate system;
FIG. 3 is a view of a region to be searched determined by rough estimation of direction-finding positioning of a single satellite;
FIG. 4 is a thermodynamic diagram of a maximum likelihood estimate obtained from a simulation experiment in accordance with an embodiment of the present invention;
FIG. 5 is a signal space spectrum of a maximum likelihood estimate obtained by a simulation experiment in accordance with an embodiment of the present invention;
FIG. 6 is a thermodynamic diagram corresponding to the minimum variance without distortion obtained by a simulation experiment according to an embodiment of the present invention;
fig. 7 is a signal spatial spectrum corresponding to the minimum variance obtained by the simulation experiment of the embodiment of the present invention without distortion.
Wherein the above figures include the following reference numerals:
10. an array antenna on a satellite;
11. the position of the radiation source G on the ground;
12. a direction vector of the radiation source G in the star coordinate system;
120. azimuth angles of the radiation sources are observed in the star coordinate system;
121. observing a pitch angle of the radiation source in a star coordinate system;
13. the radius of the area to be searched in the direct positioning.
Detailed Description
In order that those skilled in the art may better understand the technical solutions of the present invention, the following detailed description of the present invention with reference to the accompanying drawings is provided for exemplary and explanatory purposes only and should not be construed as limiting the scope of the present invention.
A three-star cooperative direct positioning method based on two-dimensional angle and time difference combination comprises the following steps:
step one: position estimation, namely positioning a radiation source by using a single satellite to measure the direction, positioning a rough estimation value of the radiation source, and determining a region to be searched; receiving a radiation source signal through a satellite, carrying out positioning parameter estimation measurement by utilizing the signal received by a single satellite, estimating and measuring a two-dimensional angle of the radiation source observed by the satellite under a satellite coordinate system, wherein the two-dimensional angle comprises an azimuth angle, a pitch angle and a variance thereof, and estimating the size of a direction finding error;
as shown in fig. 2, in a star coordinate system, the coordinate system is used for estimating the position of a radiation source by single satellite direction finding and positioning, the on-satellite array antenna 10 estimates positioning parameters through a two-step positioning method, namely, the azimuth angle 120 of the radiation source observed in the star coordinate system and the pitch angle 121 of the radiation source observed in the star coordinate system are obtained, and the coarse position estimation value of the radiation source G can be obtained through a single satellite direction finding and positioning algorithm;
when the pitch angle and azimuth angle direction finding errors are sigma (rad) and the satellite orbit height is h (km), the radius range of the area to be searched is selected by the rough estimation value to be positioned, wherein the radius range is as follows:
h·3·σ(km)，
reference is made to the radius 13 of the area to be searched in the direct positioning of fig. 3 of the description;
performing grid division on the area to be searched;
step two: creating a model, and carrying out segmented Fourier transform on all satellite receiving data to obtain a covariance matrix;
step three: constructing an objective function implying the position of the radiation source by using a minimum variance undistorted response method according to the obtained covariance matrix;
step four: calculating an objective function value of each grid point for the grids divided in the first step by using the objective function;
step five: and drawing a spatial spectrum of the received signal according to the objective function value, searching a spectrum peak, and determining the position of the radiation source.
Further optimizing on the basis of the embodiment: in step two:
the model conditions are: q radiation sources, L satellites and L-shaped arrays used on the satellites are arranged in the space, the number of array elements is 2M-1, M represents the number of array elements of uniform linear arrays on the x axis and the y axis,
reference is made to figure 2 of the accompanying drawings: the L-shaped array consists of two M-element uniform linear arrays on an x-y plane along an x axis and a y axis respectively;
the signal model received by the first satellite is:
r l (t)＝γ l a l (p)s(t-τ l (p))+n l (t),0≤t≤T
wherein, gamma l Represents the signal attenuation factor, a, caused by path loss l (p) is the steering vector of the first satellite to the radiation source, l=1.. L is; s (t- τ) l (p)) is the signal s (t) delayed by a delay τ l The result of (p); n is n l (t) complex Gaussian noise with zero meanSound, T is time, T is observation time;
wherein:
α q ,β q respectively representing the azimuth angle and the pitch angle of the q-th radiation source observed in the star coordinate system, d is the array element spacing, and lambda is the signal wavelength.
When the satellite and the radiation source are stationary in the observation time period, uniformly dividing the observation time period [0, T ] into J sections, wherein the length of each section is T/J;
when T/JThe fourier coefficients of the kth frequency point of the received signal in the jth period of time by the ith satellite can be expressed as:
wherein f k Is the kth frequency point of the fourier transform,respectively r l (t)，s(t)、n l (t) fourier coefficients at the kth frequency point of the jth segment;
definition of the definition
The above can be rewritten as:
combining signals received by different satellites:
γ[γ 1 ,...,γ L ] T ,
the method can obtain the following steps:
further, the method comprises the steps of,the writing is as follows:
wherein:
b represents the Kronecker product of the L x L identity matrix and the M x 1 full 1 vector, prescribing | γ||=1;
the covariance matrix of the received signal is expressed as:
further optimizing on the basis of the embodiment: the objective function constructed in the third step is:
wherein,is->Is lambda of the inverse matrix of lambda max {. The expression is operated by taking the maximum eigenvalue;
to increase the robustness of the method in step three, the covariance matrix inversion can be performed by adding a number to each element phase on the diagonal, which can be set to 0.01.
Specific examples:
the simulation experiment platform of the embodiment is performed in MATLAB R2022a in Windows 11 operating system. The simulation experiment conditions are as follows: the satellite positions of the 3 satellites with the orbit height of 1000km are imported by the STK, 15 array elements are arranged on each satellite, 7 array elements are placed on each axis, the observation time is divided into 20 sections, the number of Fourier transform points is 64, the corresponding frequency is 300MHz, the channel fading modeling mean value of each signal source and each array element is 0, and the variance is 0.1.
The method comprises the steps of establishing a northeast day coordinate system by taking the understar point of a main star A of 3 satellites as a coordinate origin, wherein the position of a radiation source is [ -0.5km,50km ], [1.5km,50km ], and when the signal-to-noise ratio changes, the position estimation result of the signal source is shown in the following table 1:
TABLE 1 estimation of the position of the various radiation sources at different signal-to-noise ratios
| Signal to noise ratio/dB | Radiation source 1 position/km | Radiation source 2 position/km |
| 10 | [-0.5，50] | [1.5，50] |
| 5 | [-0.5，50] | [1.5，50] |
| 0 | [-0.5，50] | [1.5，50] |
| -5 | [-0.5，50] | [1.5，50] |
It can be derived from table 1 that the radiation source position estimate is still accurate when the signal-to-noise ratio of the received signal is low.
The following is an experiment at a signal to noise ratio of 0 dB:
as shown in fig. 4 and 5, which show the signal space spectrum of the maximum likelihood estimation, it can be seen that there are many clutter peaks, which have an effect on the position estimation.
As shown in fig. 6 and 7, which show the signal spatial spectrum corresponding to the minimum variance without distortion, it can be seen that there are two sharp spectral peaks, i.e. estimated radiation source positions.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to facilitate an understanding of the method of the present invention and its core ideas. The foregoing is merely illustrative of the preferred embodiments of this invention, and it is noted that there is objectively no limit to the specific structure disclosed herein, since numerous modifications, adaptations and variations can be made by those skilled in the art without departing from the principles of the invention, and the above-described features can be combined in any suitable manner; such modifications, variations and combinations, or the direct application of the inventive concepts and aspects to other applications without modification, are contemplated as falling within the scope of the present invention.
Claims (5)
1. A three-star cooperative direct positioning method based on two-dimensional angle and time difference combination is characterized by comprising the following steps of: the method comprises the following steps:
step one: position estimation, namely positioning a radiation source by using a single satellite to measure and position, positioning a rough estimation value of the position of the radiation source, and determining a region to be searched; performing grid division on the area to be searched;
the specific method for determining the area to be searched is as follows: when the pitch angle and azimuth angle direction finding errors are sigma (rad) and the satellite orbit height is h (km), the radius range of the area to be searched is selected by the rough estimation value to be positioned, wherein the radius range is as follows:
h·3·σ(km)；
step two: creating a model, namely performing segmented Fourier transform on all satellite received data to obtain a covariance matrix;
the model conditions are: q radiation sources, L satellites and L-shaped arrays used on the satellites are arranged in the space, and the number of array elements is 2M-1;
the signal model received by the first satellite is:
r l (t)＝γ l a l (p)s(t-τ l (p))+n l (t),0≤t≤T
wherein, gamma l Represents the signal attenuation factor, a, caused by path loss l (p) is the steering vector of the first satellite to the radiation source, l=1.. L is; s (t- τ) l (p)) is the signal s (t) delayed by a delay τ l The result of (p); n is n l (t) is zero-mean complexGaussian noise, T is time, and T is observation time;
wherein:
α q ,β q respectively representing the azimuth angle and the pitch angle of a q-th radiation source observed in a star coordinate system, wherein d is the array element spacing, and lambda is the signal wavelength;
step three: constructing an objective function implying the position of the radiation source by using a minimum variance undistorted response method according to the obtained covariance matrix;
step four: calculating an objective function value of each grid point for the grids divided in the step one by using the objective function;
step five: and drawing a spatial spectrum of the received signal according to the objective function value, searching a spectrum peak, and determining the position of the radiation source.
2. The three-star collaborative direct positioning method based on two-dimensional angle and time difference combination according to claim 1, which is characterized in that: the single satellite direction-finding positioning in the first step is to measure a two-dimensional angle by using a single satellite.
3. The three-star collaborative direct positioning method based on two-dimensional angle and time difference combination in claim 1 is characterized in that:
when the satellite and the radiation source are stationary in the observation time period, uniformly dividing the observation time period [0, T ] into J sections, wherein the length of each section is T/J;
when (when)The fourier coefficients of the kth frequency point of the received signal in the jth period of time by the ith satellite can be expressed as:
wherein f k Is the kth frequency point of the fourier transform,respectively r l (t)，s(t)、n l (t) fourier coefficients at the kth frequency point of the jth segment;
definition of the definition
The above can be rewritten as:
combining signals received by different satellites:
the method can obtain the following steps:
further, the method comprises the steps of,the writing is as follows:
wherein:
b represents the Kronecker product of the L x L identity matrix and the M x 1 full 1 vector, prescribing | γ||=1;
the covariance matrix of the received signal is expressed as:
4. the three-star collaborative direct positioning method based on two-dimensional angle and time difference combination in claim 3 is characterized in that: the objective function constructed in the third step is:
wherein,is->Is lambda of the inverse matrix of lambda max {.cndot } represents a maximum eigenvalue operation.
5. The three-star collaborative direct positioning method based on two-dimensional angle and time difference combination according to claim 2, which is characterized in that; the two-dimensional angle includes azimuth, pitch, and variance thereof.
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