CN113702971B - Radar beam width design method for synthetic aperture passive positioning system - Google Patents
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Abstract
The invention discloses a radar beam width design method for a synthetic aperture passive positioning system, which relates to the field of radar signal processing and comprises the following steps: receiving a transmitting signal of a signal source to obtain a receiving signal; the carrier frequency of the received signal is removed to obtain a first signal, and after a matching function is respectively constructed according to each preset distance, a focusing result of the first signal at each preset distance is obtained; determining a corresponding relation between a positioning error and a synthetic aperture length according to a focusing result, and determining a first beam width according to a preset positioning error; the radar beam width is taken as an independent variable, the azimuth bandwidth of a received signal is determined, and after the corresponding relation between the beam width and the azimuth resolution is determined according to the azimuth bandwidth, a second beam width is determined according to the preset resolution precision; and determining the beam width of the radar in the synthetic aperture passive positioning system according to the first beam width and the second beam width. The design mode can meet the requirements of high-precision and high-resolution positioning at the same time.
Description
Technical Field
The invention belongs to the field of radar signal processing, and particularly relates to a radar beam width design method for a synthetic aperture passive positioning system.
Background
At present, synthetic aperture passive positioning is a high-resolution positioning technology, in the process of flying the radar carrier along the azimuth direction, echo signals can be received to form a synthetic array, a very long virtual aperture is formed, and a high-resolution positioning result is obtained through azimuth focusing.
In synthetic aperture passive positioning techniques, the accuracy and resolution of positioning are two important parameters. The positioning accuracy is affected by the signal-to-noise ratio and the signal model, and because the focusing kernel function adopts the principle of azimuth secondary modulation matching, when the quadratic term assumption of the range history is not established, the too wide beam width can bring about the error of the signal model matching, thereby causing the error of the distance position. On the other hand, positioning resolution is affected by the virtual aperture length, which is proportional to the beam width, and too narrow a beam width results in reduced positioning resolution.
In the related art, a beam width design method for positioning resolution is provided, and a wide beam width is designed as far as possible through the preset resolution and combined with the requirement of large-range reconnaissance, without considering positioning model errors. In this design, since the beam width is far greater than that of SAR imaging, the second term of the range history is not assumed, and thus a large range positioning error is caused.
Therefore, the beam width design method in the related art cannot meet the requirements of high-precision positioning and high-resolution positioning at the same time.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention provides a radar beam width design method for use in a synthetic aperture passive positioning system. The technical problems to be solved by the invention are realized by the following technical scheme:
the invention provides a radar beam width design method for a synthetic aperture passive positioning system, which comprises the following steps:
receiving a transmitting signal of a signal source to obtain a receiving signal;
removing carrier frequency of the received signal to obtain a first signal, and respectively constructing a matching function according to each preset distance to obtain a focusing result of the first signal at each preset distance;
determining a corresponding relation between a positioning error and a synthetic aperture length according to the focusing result, and determining a first beam width according to a preset positioning error;
the radar beam width is taken as an independent variable, the azimuth bandwidth of the received signal is determined, and after the corresponding relation between the beam width and the azimuth resolution is determined according to the azimuth bandwidth, a second beam width is determined according to the preset resolution precision;
and determining the beam width of the radar according to the first beam width and the second beam width.
Optionally, the received signal is:
wherein t represents time, c represents light velocity, R (t) represents a received signal, s (t) represents a transmitted signal, R N An N-th Taylor expansion representing the range of the range between the signal source and the radar.
Optionally, the range history between the signal source and the radar is calculated according to the following steps:
determining the instantaneous position of the radar according to the running speed of the radar;
and calculating the slant range history between the signal source and the radar according to the instantaneous position.
Optionally, the step of removing carrier frequency from the received signal to obtain a first signal, and respectively constructing a matching function according to each preset distance to obtain a focusing result of the first signal at each preset distance comprises the following steps:
removing carrier frequency of the received signal to obtain a first signal, and respectively constructing a matching function according to each preset distance;
and multiplying the first signal with each matching function, and performing Fourier transformation to obtain focusing results of the first signal at each preset distance.
Optionally, determining a correspondence between a positioning error and a synthetic aperture length according to the focusing result, and determining a first beam width according to a preset positioning error, including:
determining a maximum value of a module value of the focusing result according to the focusing result of the first signal at each preset distance;
determining a preset distance corresponding to a focusing result with a maximum value of a module value as a first distance, and calculating a difference value between the first distance and the slant distance process to obtain a positioning error;
determining the corresponding relation between the positioning error and the synthetic aperture length according to the positioning error and the distance between the center of the positioning scene and the radar;
and calculating a first beam width corresponding to the preset positioning error according to the corresponding relation between the positioning error and the synthetic aperture length.
Optionally, the step of determining the azimuth bandwidth of the received signal by using the radar beam width as an argument, and determining the second beam width according to a preset resolution precision after determining the correspondence between the beam width and the azimuth resolution according to the azimuth bandwidth includes:
according to the running speed and carrier frequency wavelength of the radar, determining the azimuth bandwidth of the received signal by taking the radar beam width as an independent variable;
determining azimuth resolution according to azimuth bandwidth of the received signal, and obtaining a corresponding relation between beam width and azimuth resolution;
and acquiring a second beam width corresponding to the preset resolution precision.
Optionally, the step of determining the beam width of the radar according to the first beam width and the second beam width includes:
the first beam width is taken as an upper limit of the radar beam width, and the second beam width is taken as a lower limit of the radar beam width.
Optionally, the focusing result of the first signal at the respective preset distances is:
wherein,indicated at each preset distance R k A matching function of the construction, r 1 (T) represents a first signal, T represents a junctionThe length of time for receiving the signal, F (0; R k ) Representing the focusing result of the first signal at each preset distance.
Optionally, the correspondence between the positioning error and the synthetic aperture length is:
wherein ΔR represents a positioning error, L represents an aperture length, R represents a distance from a center to a radar in a positioning field, and a beam width
Optionally, the correspondence between the beam width and the azimuth resolution is:
wherein,λ represents carrier frequency wavelength, θ represents beam width, and ρ represents azimuth resolution.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a radar beam width design method for a synthetic aperture passive positioning system, which comprises the steps of after a received signal is carrier-removed to obtain a first signal, respectively constructing matching functions according to each preset distance, focusing the matching functions at different preset distances to obtain a functional relation between a positioning error and a synthetic aperture length, and further determining the upper limit of the synthetic aperture length, namely the first beam width, according to the preset positioning error; meanwhile, the functional relation between the positioning resolution and the aperture length is determined through analysis of the distance and azimuth two-dimensional resolution, so that the lower limit of the design of the synthetic aperture length parameter, namely the second beam width, is determined according to the requirement of the preset positioning resolution, and the radar beam width is arranged between the first beam width and the second beam width, so that the requirements of high-precision and high-resolution positioning can be met at the same time.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
FIG. 1 is a schematic flow chart of a radar beam width design method for use in a synthetic aperture passive positioning system according to an embodiment of the present invention;
FIG. 2 is a schematic illustration of a simulation of a method for designing radar beamwidth for use in a passive positioning system with synthetic apertures in accordance with an embodiment of the present invention;
fig. 3 is another simulation diagram of a radar beam width design method for use in a synthetic aperture passive positioning system according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but embodiments of the present invention are not limited thereto.
As shown in fig. 1, a radar beam width design method for a synthetic aperture passive positioning system according to an embodiment of the present invention includes:
s1, receiving a transmitting signal of a signal source to obtain a receiving signal;
s2, carrier frequency removal is carried out on the received signals to obtain first signals, and after matching functions are respectively constructed according to the preset distances, focusing results of the first signals at the preset distances are obtained;
step S3, determining a corresponding relation between a positioning error and a synthetic aperture length according to a focusing result, and determining a first beam width according to a preset positioning error;
s4, determining azimuth bandwidth of a received signal by taking radar beam width as an independent variable, and determining a second beam width according to preset resolution accuracy after determining a corresponding relation between the beam width and azimuth resolution according to the azimuth bandwidth;
and S5, determining the beam width of the radar according to the first beam width and the second beam width.
It should be understood that when the positioning of the signal source is realized by using the synthetic aperture technology, a synthetic array can be formed by the motion of the radar, and a long virtual aperture is obtained, and the initial phase of the signal received by the synthetic array at different moments is related to the slant range process between the signal source and the radar, so that the functional relationship between the azimuth frequency adjustment and the distance of the radiation source can be utilized to construct a focusing kernel function for distance and azimuth positioning, so as to obtain the positioning result of the signal source.
Specifically, in this embodiment, the radar receives the transmission signal of the signal source, and obtains the reception signal:
wherein t represents time, c represents light velocity, R (t) represents a received signal, s (t) represents a transmitted signal, R N N-th order Taylor expansion representing the range of the range between the signal source and the radar.
Optionally, the range history between the signal source and the radar is calculated according to the following steps:
determining the instantaneous position of the radar according to the running speed of the radar;
and calculating the pitch history between the signal source and the radar according to the instantaneous position.
In the step S2, the step of removing carrier frequency from the received signal to obtain a first signal, and respectively constructing a matching function according to each preset distance to obtain a focusing result of the first signal at each preset distance, includes:
carrier frequency removal is carried out on the received signals to obtain first signals, and matching functions are respectively constructed according to the preset distances;
and multiplying the first signal by each matching function, and performing Fourier transformation to obtain focusing results of the first signal at each preset distance.
Specifically, the carrier frequency of the received signal is removed, and the obtained first signal is:
r 1 (t)=r(t)exp(-j2πf c t)
wherein f c Representing the frequency of the carrier frequency.
Further, the wavelength of the received signal is determined:
λ=c/f c
constructing matching functions at each preset distance according to the wavelength of the received signalIllustratively, the distance R is preset k The matching function at this point is as follows:
multiplying the matching function with the first signal with carrier frequency removed, and performing Fourier transform to obtain focusing results of the first signal at each preset distance, namely:
wherein,R s representing the vertical distance between the signal source and the radar running direction,/->Representing higher-order phases of more than two times, < ->Indicated at each preset distance R k A matching function of the construction, r 1 (T) represents a first signal, T represents a time length of a received signal, F (0, R k ) Representing the focusing result of the first signal at each preset distance.
Optionally, in the step S3, determining a correspondence between the positioning error and the synthetic aperture length according to the focusing result, and determining the first beam width according to the preset positioning error includes:
determining a maximum value of a module value of the focusing result according to the focusing result of the first signal at each preset distance;
determining a preset distance corresponding to a focusing result with a maximum value of a module value as a first distance, and calculating a difference value between the first distance and an inclined distance process to obtain a positioning error;
determining the corresponding relation between the positioning error and the synthetic aperture length according to the positioning error and the distance between the center of the positioning scene and the radar;
and calculating a first beam width corresponding to the preset positioning error according to the corresponding relation between the positioning error and the synthetic aperture length.
Specifically, in this embodiment, the preset distance corresponding to the focusing result with the maximum value of the mode value is determined as the first distance, and the difference between the first distance and the pitch history is calculated, so as to obtain the positioning error.
Optionally, the maximum value of the module value of the focusing result is calculated by the following steps:
determining the range R between a signal source and a radar N Is exemplified by the taylor expansion of order N, N taking 4.
Where x represents the instantaneous position of the radar.
Neglecting constant phase not affecting modulusReplacing the focus result F (0; R k ) Is used, while the integration interval is defined by +.>Conversion to->The complex signal is converted into a real signal through an Euler formula, and the conversion result is as follows:
wherein k is λ =2π/λ。
Further, F' (0; R) is calculated k ) Is a modulus of:
wherein,f' (0; R) k ) Real part of->Is F' (0; R) k ) Is a virtual part of (c).
The real part and the imaginary part are approximately calculated, and the calculation result is as follows:
wherein,
calculating an objective function G (R k ) For R k And let the derivative be 0, the derivative equation can be obtained:
will beAnd->Substituting the derivative equation and simplifying to obtain a third equation, at R k =R s The neighborhood of the radar aperture length L is approximated by a primary equation, and a solution of the primary approximation equation is calculated to obtain the corresponding relation between the positioning error delta R and the radar aperture length L as follows:
wherein Δr represents a positioning error, L represents an aperture length, and R represents a pitch history between a signal source and a radar. Due to radar beam widthThus, it is possible to obtain:
acquiring a preset positioning error delta e By means ofCalculating delta e A corresponding first beamwidth.
In the step S4, the step of determining the azimuth bandwidth of the received signal by using the beam width as an argument, determining the correspondence between the beam width and the azimuth resolution according to the azimuth bandwidth, and determining the second beam width according to the preset resolution accuracy, includes:
according to the running speed and carrier frequency wavelength of the radar, determining the azimuth bandwidth of a received signal by taking the radar beam width as an independent variable;
determining azimuth resolution according to azimuth bandwidth of a received signal, and obtaining a corresponding relation between beam width and azimuth resolution;
and acquiring a second beam width corresponding to the preset resolution precision.
Specifically, the azimuth bandwidth of the received signal is calculated from the operating speed v of the radar and the carrier wavelength λ using the radar beam width θ as an argument:
then, the azimuth resolution of the positioning is calculated according to the azimuth bandwidth of the received signal, and the corresponding relation between the beam width and the azimuth resolution is obtained:
wherein,
and acquiring the preset resolution precision, wherein the beam width corresponding to the preset resolution precision is the second beam width.
In this embodiment, after determining the first beam width and the second beam width, the first beam width is used as the upper limit of the radar beam width, and the second beam width is used as the lower limit of the radar beam width, so that the feasible range is [ θ ] when designing the radar beam width min ,θ max ]。
The method for designing the radar beam width in the synthetic aperture passive positioning system is further described below in connection with simulation experiments.
For the first beam width, if the positioning error delta is preset e The distances of the center of the scene irradiated by the beams are respectively 0.1, 0.3, 0.5 and 1, the simulation results are shown in fig. 2, the horizontal axis represents the positioning distance, the vertical axis represents the first beam width, and obviously, the upper limit of the first beam width, namely the radar beam width, is reduced along with the increase of the positioning distance.
For the second beam width, if the positioning resolution ρ is preset a 20, 40, 60 and 80, respectively, the wavelength of the received signal is from 0.01m to 0.3m, simulatedAs a result, as shown in fig. 3, the horizontal axis represents the wavelength of the received signal, and the vertical axis represents the second beam width, and it can be seen that the second beam width, i.e., the lower beam width limit, increases linearly with the increase in wavelength.
As shown in fig. 2-3, the higher the preset positioning error requirement, the farther the positioning distance, the lower the upper limit of the radar beam width design, the higher the preset positioning resolution requirement, the longer the wavelength, and the higher the lower limit of the radar beam width design. The radar beam width design method for the synthetic aperture passive positioning system can determine the feasible range of the radar beam width in the first beam width and the second beam width, and can simultaneously meet the requirements of positioning precision and resolution.
According to the above embodiments, the beneficial effects of the invention are as follows:
the invention provides a radar beam width design method for a synthetic aperture passive positioning system, which comprises the steps of after a received signal is carrier-removed to obtain a first signal, respectively constructing matching functions according to each preset distance, focusing the matching functions at different preset distances to obtain a functional relation between a positioning error and a synthetic aperture length, and further determining the upper limit of the synthetic aperture length, namely the first beam width, according to the preset positioning error; meanwhile, the functional relation between the positioning resolution and the aperture length is determined through analysis of the distance and azimuth two-dimensional resolution, so that the lower limit of the design of the synthetic aperture length parameter, namely the second beam width, is determined according to the requirement of the preset positioning resolution, and the radar beam width is arranged between the first beam width and the second beam width, so that the requirements of high-precision and high-resolution positioning can be met at the same time.
In the description of the present invention, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include one or more such feature. In the description of the present invention, the meaning of "a plurality" is two or more, unless explicitly defined otherwise.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Further, one skilled in the art can engage and combine the different embodiments or examples described in this specification.
Although the present application has been described herein in connection with various embodiments, other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed application, from a review of the figures, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the "a" or "an" does not exclude a plurality. A single processor or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.
Claims (7)
1. A method for radar beam width design in a synthetic aperture passive positioning system, comprising:
receiving a transmitting signal of a signal source to obtain a receiving signal;
removing carrier frequency of the received signal to obtain a first signal, and respectively constructing a matching function according to each preset distance to obtain a focusing result of the first signal at each preset distance;
determining a corresponding relation between a positioning error and a synthetic aperture length according to the focusing result, and determining a first beam width according to a preset positioning error;
the radar beam width is taken as an independent variable, the azimuth bandwidth of the received signal is determined, and after the corresponding relation between the beam width and the azimuth resolution is determined according to the azimuth bandwidth, a second beam width is determined according to the preset resolution precision;
determining the beam width of a radar in a synthetic aperture passive positioning system according to the first beam width and the second beam width;
the received signal is:
wherein t represents time, c represents light velocity, R (t) represents a received signal, s (t) represents a transmitted signal, R N An N-th order Taylor expansion representing a range of the range between the signal source and the radar;
determining a corresponding relation between a positioning error and a synthetic aperture length according to the focusing result, and determining a first beam width according to a preset positioning error, wherein the method comprises the following steps:
determining a maximum value of a module value of the focusing result according to the focusing result of the first signal at each preset distance;
determining a preset distance corresponding to a focusing result with a maximum value of a module value as a first distance, and calculating a difference value between the first distance and the slant distance process to obtain a positioning error;
determining the corresponding relation between the positioning error and the SAR aperture length according to the positioning error and the distance from the center of the positioning scene to the radar;
calculating a first beam width corresponding to a preset positioning error according to the corresponding relation between the positioning error and the SAR aperture length;
the method for determining the azimuth bandwidth of the received signal by using the radar beam width as an independent variable comprises the steps of:
according to the running speed of the radar and the carrier frequency wavelength of the received signal, determining the azimuth bandwidth of the received signal by taking the radar beam width as an independent variable;
determining azimuth resolution according to azimuth bandwidth of the received signal, and obtaining a corresponding relation between beam width and azimuth resolution;
and acquiring a second beam width corresponding to the preset resolution precision.
2. The method for designing radar beam width in a passive positioning system with synthetic aperture according to claim 1, wherein the range of the range between the signal source and the radar is calculated by:
determining the instantaneous position of the radar according to the running speed of the radar;
and calculating the slant range history between the signal source and the radar according to the instantaneous position.
3. The method for designing radar beam width in a passive positioning system with synthetic aperture according to claim 2, wherein the step of removing carrier frequency from the received signal to obtain a first signal, and constructing a matching function according to each preset distance to obtain a focusing result of the first signal at each preset distance, comprises:
removing carrier frequency of the received signal to obtain a first signal, and respectively constructing a matching function according to each preset distance;
and multiplying the first signal with each matching function, and performing Fourier transformation to obtain focusing results of the first signal at each preset distance.
4. The method of claim 1, wherein the step of determining a beam width of the radar in the passive positioning system based on the first beam width and the second beam width comprises:
the first beam width is taken as an upper limit of the radar beam width, and the second beam width is taken as a lower limit of the radar beam width.
5. The method of claim 1, wherein the focusing of the first signal at the respective predetermined distances results in:
wherein,indicated at each preset distance R k A matching function of the construction, r 1 (T) represents a first signal, T represents a time length of a received signal, F (0, R k ) Representing the focusing result of the first signal at each preset distance.
6. The method for designing radar beam width in a passive positioning system of a synthetic aperture according to claim 1, wherein the correspondence between the positioning error and the synthetic aperture length is:
wherein Δr represents a positioning error, L represents an aperture length, R represents a center-to-radar distance in a positioning field, and a beam width
7. The method of claim 1, wherein the correspondence between the beam width and the azimuth resolution is:
wherein,λ represents carrier frequency wavelength, θ represents beam width, and ρ represents azimuth resolution.
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星载高分辨频率步进SAR成像技术;龙腾;丁泽刚;肖枫;王岩;李喆;;雷达学报(第06期);全文 * |
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