CN112287517B - Design method and design device of one-dimensional multiple redundant sensor array structure - Google Patents
Design method and design device of one-dimensional multiple redundant sensor array structure Download PDFInfo
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Abstract
The invention discloses a design method and a device of a one-dimensional multiple redundant sensor array structure, wherein the method comprises the following steps: constructing a first sensor array structure according to a basic structure pattern; according to the distribution condition of the adjacent array element spacing of the first sensor array structure, iterating the parameters of the first sensor array structure to obtain a second sensor array structure; and calculating the structural parameters of the second sensor array according to the spacing distribution condition of adjacent array elements of the second sensor array structure to obtain a third sensor array structure. The method can solve the problem of large coverage of spatial frequency sampling under the condition that the number of damaged array elements is greater than or equal to 2, and provides guarantee for array robustness in array signal processing application.
Description
Technical Field
The invention relates to the technical field of array design and signal processing, in particular to a design method and a design device of a one-dimensional multiple redundant sensor array structure.
Background
In the field of array signal processing, a 'virtual' array structure with a larger caliber is obtained by utilizing a sparse structure and spatial frequency sampling distribution of a sensor array, so that spatial resolution higher than that of an original array structure is obtained. However, when the designer considers the reliability and robustness of the array signal processing system, especially in some severe working environments such as deep sea, space and the like, the integrity of the baseline coverage in a given spatial frequency sampling distribution area can still be ensured under the condition that any plurality of array elements are damaged (the number of damaged array elements is greater than or equal to 2). The existing low-redundancy sensor array structure cannot meet the requirement of base line coverage integrity in a spatial frequency sampling distribution area under the condition that the number of damaged array elements is greater than or equal to 2, and the reliability and robustness of an array signal processing system in the application environment are reduced; although the existing full-coverage sensor array structure can ensure the integrity of the baseline coverage, the full-coverage sensor array structure cannot achieve the performance of a system with higher spatial resolution.
Disclosure of Invention
The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.
Therefore, one object of the present invention is to provide a method for designing a one-dimensional multiple redundant sensor array structure, which solves the technical problems that the existing sensor array structure cannot give consideration to the complete coverage of the base line in the spatial frequency sampling distribution area and the realization of the performance of a high spatial resolution system when the number of damaged array elements is greater than or equal to 2.
Another objective of the present invention is to provide a design apparatus for a one-dimensional redundant sensor array structure.
In order to achieve the above object, an embodiment of an aspect of the present invention provides a method for designing a one-dimensional multiple redundant sensor array structure, including:
s1, constructing a first sensor array structure according to the basic structure mode;
s2, according to the distribution situation of the adjacent array element spacing of the first sensor array structure, iterating the parameters of the first sensor array structure to obtain a second sensor array structure;
and S3, calculating the second sensor array structure parameters according to the adjacent array element spacing distribution condition of the second sensor array structure to obtain a third sensor array structure.
In order to achieve the above object, another embodiment of the present invention provides a design apparatus for a one-dimensional multiple redundant sensor array structure, including:
a construction module for constructing a first sensor array structure according to a basic structure pattern;
the first design module is used for iterating parameters of the first sensor array structure according to the spacing distribution condition of adjacent array elements of the first sensor array structure to obtain a second sensor array structure;
and the second design module is used for calculating the parameters of the second sensor array structure according to the spacing distribution condition of adjacent array elements of the second sensor array structure to obtain a third sensor array structure.
The design method and the device of the one-dimensional multiple redundant sensor array structure of the embodiment of the invention take a basic structure mode as a first sensor array structure; iterating the parameters of the first sensor array structure according to the spacing distribution condition of adjacent array elements of the first sensor array structure to obtain a second sensor array structure; and calculating the structural parameters of the second sensor array according to the distribution condition of the adjacent array element intervals of the second sensor array structure to obtain the optimal one-dimensional multiple redundant sensor array structure with any array element number and any redundant order. The obtained one-dimensional multiple redundant sensor array structure can realize the complete coverage of the base line in the space frequency sampling area under the condition that the number of the damaged array elements is more than or equal to 2, provides guarantee for the system reliability in array signal processing application, and can meet the system performance requirement of higher spatial resolution.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of a method for designing a one-dimensional multiple redundant sensor array structure according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a first sensor array configuration and baseline coverage within a spatial frequency sampling region in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of a second sensor array configuration and baseline coverage within a spatial frequency sampling region in accordance with an embodiment of the present invention;
FIG. 4 is a schematic diagram of a third sensor array configuration and baseline coverage within a spatial frequency sampling region for a given array element number and redundancy order in accordance with one embodiment of the present invention;
fig. 5 is a schematic structural diagram of a design apparatus of a one-dimensional multiple redundant sensor array structure according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The concept designed in the embodiments of the present invention is explained below.
N sensor array elements are given and arranged on a straight line to form a sensor array a, and a group of N different nonnegative integers a 1 ,a 2 ,…,a N Denotes the position of N sensor elements, and 0 ═ a 1 <a 2 <…<a N 。
The expression of the adjacent array element spacing of the sensor array a is as follows:
H＝{u 1 ,u 2 ,…,u N-1 }
wherein u is i ＝a i+1 -a i ,i＝1,2,…,N-1。
If u i ＝u i-1 I.e. the adjacent array element spacing v repeats twice, the adjacent array element spacing of sensor array a is expressed as:
H＝{u 1 ,u 2 ,…,u i-2 ,v 2 ,u i+1 ,…,u N-1 }。
if u i-3 ＝u i-2 ＝v 1 ,u i-1 ＝v 2 ,u i ＝u i+1 ＝v 1 ,u i+2 ＝v 2 I.e. groups of adjacent array element spacings
Repeating twice, and then representing the form of the adjacent array element spacing of the sensor array a as follows:
the distance between any two sensor array elements is the length d of a base line, and d belongs to [1, L ]]L denotes the maximum base length, L<a N -a 1 If for any base length d is equal to [1, L ]]All have beta to a i And a j (beta is not less than 3, i, j is 1,2, …, N) is equal to d, then the set of positive integers a 1 ,a 2 ,…,a N The sensor array representing the positions of the N sensor array elements is a one-dimensional multiple redundant sensor array, and β represents the redundancy order of the baseline.
The following describes a design method and apparatus for a one-dimensional multiple redundant sensor array structure according to an embodiment of the present invention with reference to the accompanying drawings.
First, a method for designing a one-dimensional multiple redundant sensor array structure according to an embodiment of the present invention will be described with reference to the accompanying drawings.
Fig. 1 is a flow chart of a design method of a one-dimensional multiple redundant sensor array structure according to an embodiment of the present invention.
As shown in fig. 1, the design method of the one-dimensional multiple redundant sensor array structure includes the following steps:
in step S1, a first sensor array structure is constructed according to the basic structure pattern.
Further, in the embodiment of the present invention, a basic structure mode is used as the first sensor array structure, and the basic structure mode is expressed as:
{1 β-1 ,p,1 β-1 ,p+β,1 p+β-2 }
wherein 1, p, p + beta represents the interval between adjacent array elements, 1 β-1 Represents the repetition of adjacent array elements with the distance of 1 for beta-1 times, 1 p+β-2 And the method represents that the adjacent array elements are repeated for p + beta-2 times with the distance of 1, wherein p and beta are positive integers, p is not less than 1, beta is not less than 3, p is a parameter, and beta is the redundancy order of the base line.
And step S2, according to the spacing distribution situation of adjacent array elements of the first sensor array structure, iterating the parameters of the first sensor array structure to obtain a second sensor array structure.
Further, in an embodiment of the present invention, S2 further includes:
s21, according to the distribution situation of different adjacent array element spacing in the first sensor array structure, determining the repeatable adjacent array element spacing group as (1) β-1 ,p+β)；
S22, setting a sensor array structure parameter m, representing the repetition times of the repeatable adjacent array element spacing group;
and S23, iterating the parameters of the first sensor array structure to obtain a second sensor array structure.
Further, as an embodiment, the second sensor array structure is obtained by iterating the parameter of the first sensor array structure, and the second sensor array structure may be obtained by performing a plurality of first iteration operations on the first sensor array structure. Wherein the first iteration operation is to make the sensor array structure parameter m equal to m + 1.
Further, as another implementation, the second sensor array structure is obtained by iterating the parameter of the first sensor array structure, and the second sensor array structure may be obtained by performing a plurality of second iteration operations on the first sensor array structure. The second operation iteration is to make the sensor array structure parameter p equal to p + 1.
Further, as another implementation, the parameter of the first sensor array structure is iterated to obtain the second sensor array structure, and the second sensor array structure may also be obtained by simultaneously performing multiple first iteration operations and multiple second iteration operations on the first sensor array structure.
Further, the obtained representation of the adjacent array element spacing of the second sensor array structure is as follows:
{1 β-1 ,p,(1 β-1 ,p+β) m ,1 p+β-2 }
wherein 1, p, p + beta represents the interval between adjacent array elements, 1 β-1 Represents the repetition of adjacent array elements with the distance of 1 for beta-1 times, 1 p+β-2 Represents that the adjacent array elements are repeated for p + beta-2 times with the distance of 1, (1) β-1 ,p+β) m Representing groups of adjacent array element spacings (1) β-1 P + beta) is repeated m times, and p, beta and m are positive integers, p is more than or equal to 1, beta is more than or equal to 3, and m is more than or equal to 1.
The number of array elements N of the second sensor array structure is expressed as:
N＝p+(m+2)β-1
wherein p, beta and m represent structural parameters of the second sensor array, and are positive integers, p is more than or equal to 1, beta is more than or equal to 3, and m is more than or equal to 1;
the maximum baseline length L of the second sensor array structure is expressed as:
L＝(p+2β-1)m+2p+β-2
wherein p, beta and m represent structural parameters of the second sensor array, and are positive integers, p is more than or equal to 1, beta is more than or equal to 3, and m is more than or equal to 1;
the maximum baseline length a of the second sensor array structure is expressed as:
A＝L+β-1
wherein L represents the maximum base length of the second sensor array structure, beta represents a parameter of the second sensor array structure, and beta is a positive integer and is larger than or equal to 3.
And step S3, calculating the parameters of the second sensor array structure according to the distribution of the adjacent array element spacing of the second sensor array structure to obtain a third sensor array structure.
Further, S3 further includes:
s31, determining a design model form of the third sensor array structure, namely determining an optimal one-dimensional multiple redundancy sensor array structure design model giving any array element number and any redundancy order:
s.t.N＝p+(m+2)β-1,β≥3
wherein p and m are parameters of a second sensor array structure to be optimized, L represents the maximum baseline length of the sensor array structure, beta represents any given baseline redundancy order, N represents any given array element number, and p, beta and m are positive integers, p is more than or equal to 1, beta is more than or equal to 3, and m is more than or equal to 1;
s32, obtaining the optimal parameter p of the second sensor array structure according to the quadratic programming method * ,m * To obtain a third sensor array structure:
wherein the parameter m of the third sensor array structure * ,p * Expressed as:
wherein,
is shown and
the nearest integer, beta represents any given baseline redundancy order, N represents any given array element number, p and beta are positive integers, p is more than or equal to 1, and beta is more than or equal to 3;
the maximum baseline length L of the third sensor array structure is expressed as:
wherein m is * Representing a parameter of a third sensor array structure, wherein beta represents a given arbitrary baseline redundancy order, N represents a given arbitrary array element number, and p and beta are positive integers, p is more than or equal to 1, and beta is more than or equal to 3;
the bore length a of the third sensor array configuration is expressed as:
A＝L+β-1
wherein L represents the maximum baseline length of the third sensor array structure, beta represents any given baseline redundancy order, and beta is a positive integer and is more than or equal to 3.
The following describes the design method of the one-dimensional multiple redundant sensor array structure according to the present invention in detail with an embodiment.
1) The first sensor array is constructed according to the basic structural pattern shown below:
{1 β-1 ,p,1 β-1 ,p+β,1 p+β-2 }
wherein 1, p, p + beta represents the interval between adjacent array elements, 1 β-1 Represents the repetition of adjacent array elements with the distance of 1 for beta-1 times, 1 p+β-2 The method represents that the adjacent array elements are repeated for p + beta-2 times with the distance of 1, and p and beta are positive integers, p is more than or equal to 1, and beta is more than or equal to 3.
Selecting the first sensor array structure parameters as follows: (β, p) ═ 3,4, the obtained representation of the adjacent array element spacing for the first sensor array structure is of the form:
{1 2 ,4,1 2 ,7,1 5 }
the array structure and the baseline coverage are as shown in fig. 2, and it can be seen that the array element number of the first sensor array structure is N — 12; the redundancy order is beta-3; the maximum base length in the sense of this redundancy order (i.e. β -3) is L-18; the array aperture length is A-20.
2) And iterating the sensor array structure parameters according to the adjacent array element spacing distribution of the first sensor array structure in fig. 2 to obtain a second sensor array structure.
Obtaining a second sensor array structure comprises the steps of:
observing the distribution of different adjacent array element intervals in the first sensor array structure, and determining a repeatable adjacent array element interval group as (1) 2 ,7)。
Introducing a sensor array structure parameter m representing the number of repetitions of a repeatable set of adjacent array element spacings, the first sensor array structure being represented as:
{1 2 ,4,(1 2 ,7) m＝1 ,1 5 }
if a first iteration is performed on the first sensor array structure: namely, the structural parameter m of the sensor array is equal to m +1, and the process is repeated for 1 time:
{1 2 ,4,(1 2 ,7) 1 ,1 5 }→{1 2 ,4,(1 2 ,7) 2 ,1 5 }
let the sensor array structure parameter m equal to m +1, repeat 2 times:
{1 2 ,4,(1 2 ,7) 1 ,1 5 }→{1 2 ,4,(1 2 ,7) 3 ,1 5 }
if a second iteration is performed on the first sensor array structure: namely, the structural parameter p of the sensor array is equal to p +1, and the process is repeated for 1 time:
{1 2 ,4,(1 2 ,7) 1 ,1 5 }→{1 2 ,5,(1 2 ,8) 1 ,1 6 }
repeat 2 times:
{1 2 ,4,(1 2 ,7) 1 ,1 5 }→{1 2 ,6,(1 2 ,9) 1 ,1 7 }
by carrying out first iteration operation or second iteration operation or simultaneously carrying out the first iteration operation and the second iteration operation on the first sensor array structure, a new second sensor array structure can be obtained, and the general expression form of the adjacent array element spacing is as follows:
{1 β-1 ,p,(1 β-1 ,p+β) m ,1 p+β-2 }
wherein 1, p, p + beta represents the interval between adjacent array elements, 1 β-1 Represents the repetition of adjacent array elements with the distance of 1 for beta-1 times, 1 p+β-2 Represents that the adjacent array elements are repeated for p + beta-2 times with the distance of 1, (1) β-1 ,p+β) m Representing groups of adjacent array element spacings (1) β-1 P + beta) is repeated m times, and p, beta and m are positive integers, p is more than or equal to 1, beta is more than or equal to 3, and m is more than or equal to 1.
Performing 2 first iteration operations and 2 second iteration operations on the first sensor array structure in fig. 2, and obtaining the adjacent array element spacing of the second sensor array structure as follows:
{1 2 ,6,(1 2 ,9) 3 ,1 7 }
the array structure and the baseline coverage are shown in fig. 3, and it can be known that the second sensor array structure parameter is (β, p, m) ═ 3,6, 3; the number of array elements is N-20; the redundancy order is beta-3; the maximum base length in the sense of this redundancy order (i.e. β -3) is L-46; the aperture length of the array is A-48.
3) And calculating the structural parameters of the second sensor array according to the distribution condition of the spacing between the adjacent array elements of the second sensor array structure to obtain a third sensor array structure, namely the optimal one-dimensional multiple redundant sensor array structure with any given array element number and any given redundant order.
For example, given an array element number N of 30 and a redundancy order β of 4, obtaining a third sensor array structure comprises the steps of:
determining an optimal one-dimensional multiple redundancy sensor array structure design model giving any array element number and any redundancy order:
s.t.N＝p+(m+2)β-1,β≥3
and p and m represent a second sensor array structure parameter to be optimized, L represents the maximum baseline length of the sensor array structure, beta is 4 to represent any given baseline redundancy order, N is 30 to represent any given array element number, and p and m are positive integers, p is larger than or equal to 1, and m is larger than or equal to 1.
Obtaining optimal array structure parameter p according to quadratic programming method * ,m * ：
The third sensor array structure obtained is represented as:
{1 3 ,11,(1 3 ,15) 3 ,1 13 }
the array structure and baseline coverage are shown in FIG. 4, and the second sensor array structure parameter is (β, p) * ,m * ) (4,11, 3); the number of array elements is N-20; the redundancy order is beta-4; the maximum baseline length in the sense of this redundancy order (i.e., β -4) is L-78; the array aperture length is a 81.
In the embodiment provided by the invention, all the obtained sensor array structures can cover the base line in a given spatial frequency sampling area to a greater extent under the condition of any beta-1 (more than or equal to 2) array elements; the third sensor array structure provided by the invention can cover the baseline in the given spatial frequency sampling region to a greater extent under the condition of any beta-1 (more than or equal to 2) array elements, and can also ensure the high resolution performance requirement of the system, so that the array signal processing system has higher reliability.
According to the design method of the one-dimensional multiple redundant sensor array structure provided by the embodiment of the invention, firstly, a basic structure mode is used as a first sensor array structure; iterating the parameters of the first sensor array structure according to the spacing distribution condition of adjacent array elements of the first sensor array structure to obtain a second sensor array structure; and calculating the structural parameters of the second sensor array according to the distribution condition of the adjacent array element intervals of the second sensor array structure to obtain the optimal one-dimensional multiple redundant sensor array structure with any array element number and any redundant order. The obtained one-dimensional multiple redundant sensor array structure can realize complete coverage of the base line in the spatial frequency sampling region under the condition that the number of the damaged array elements is greater than or equal to 2, provides guarantee for system reliability in array signal processing application, and can meet the system performance requirement of higher spatial resolution.
Next, a design apparatus of a one-dimensional multiple redundant sensor array structure according to an embodiment of the present invention will be described with reference to the drawings.
Fig. 5 is a schematic structural diagram of a design apparatus of a one-dimensional multiple redundant sensor array structure according to an embodiment of the present invention.
As shown in fig. 5, the design device of the one-dimensional multiple redundant sensor array structure includes: a construction module 501, a first design module 502, and a second design module 503.
A construction module 501 for constructing a first sensor array structure according to a basic structural pattern.
The first design module 502 is configured to iterate parameters of the first sensor array structure according to a distribution of adjacent array element intervals of the first sensor array structure to obtain a second sensor array structure.
And a second design module 503, configured to calculate a second sensor array structure parameter according to a distribution of adjacent array element intervals of the second sensor array structure to obtain a third sensor array structure.
It should be noted that the foregoing explanation of the method embodiment is also applicable to the apparatus of this embodiment, and is not repeated herein.
According to the design device of the one-dimensional multiple redundant sensor array structure provided by the embodiment of the invention, firstly, a basic structure mode is used as a first sensor array structure; iterating the parameters of the first sensor array structure according to the spacing distribution condition of adjacent array elements of the first sensor array structure to obtain a second sensor array structure; and calculating the structural parameters of the second sensor array according to the distribution condition of the adjacent array element intervals of the second sensor array structure to obtain the optimal one-dimensional multiple redundant sensor array structure with any array element number and any redundant order. The obtained one-dimensional multiple redundant sensor array structure can realize complete coverage of the base line in the spatial frequency sampling region under the condition that the number of the damaged array elements is greater than or equal to 2, provides guarantee for system reliability in array signal processing application, and can meet the system performance requirement of higher spatial resolution.
Furthermore, the terms "first", "second" and "first" 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 defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean 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 invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer 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. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
Claims (8)
1. A design method of a one-dimensional multiple redundant sensor array structure is characterized by comprising the following steps:
s1, constructing a first sensor array structure according to a basic structure mode, wherein the basic structure mode of the first sensor array is as follows:
{1 β-1 ，p，1 β-1 ，p+β，1 p+β-2 }
wherein 1, p, p + beta represents the interval between adjacent array elements, 1 β-1 Represents the repetition of adjacent array elements with the distance of 1 for beta-1 times, 1 p+β-2 Representing the repetition p + beta-2 times with the adjacent array element spacing of 1, wherein p and beta are positive integers, p is more than or equal to 1, beta is more than or equal to 3, p is a parameter, and beta is the redundancy order of a base line;
s2, according to the distribution condition of the adjacent array element spacing of the first sensor array structure, iterating the parameters of the first sensor array structure to obtain a second sensor array structure, wherein the adjacent array element spacing of the second sensor array structure is represented by the following form:
{1 β-1 ，p，(1 β-1 ，p+β) m ，1 p+β-2 }
wherein 1, p, p + beta represents the interval between adjacent array elements, 1 β-1 Represents the repetition of adjacent array elements with the distance of 1 for beta-1 times, 1 p+β-2 Represents that the adjacent array elements are repeated for p + beta-2 times with the distance of 1, (1) β-1 ，p+β) m Representing groups of adjacent array element spacings (1) β-1 P + beta) is repeated for m times, and p, beta and m are positive integers, p is more than or equal to 1, beta is more than or equal to 3, and m is more than or equal to 1;
s3, calculating the second sensor array structure parameters according to the adjacent array element spacing distribution condition of the second sensor array structure to obtain a third sensor array structure, wherein the design model form of the third sensor array structure is as follows:
s.t.N＝p+(m+2)β-1，β≥3
wherein p and m are parameters of a second sensor array structure to be optimized, L represents the maximum baseline length of the sensor array structure, beta represents any given baseline redundancy order, N represents any given array element number, and p, beta and m are positive integers, p is larger than or equal to 1, beta is larger than or equal to 3, and m is larger than or equal to 1.
2. The method according to claim 1, wherein the S2 further comprises:
s21, determining repeatable adjacent array element spacing group as (1) according to the distribution of different adjacent array element spacings in the first sensor array structure β-1 ，p+β)；
S22, setting a sensor array structure parameter m, representing the repetition times of the repeatable adjacent array element spacing group;
and S23, iterating the parameters of the first sensor array structure to obtain a second sensor array structure.
3. The method according to claim 2, wherein the S23 further comprises:
performing a plurality of first iteration operations on the first sensor array structure to obtain a second sensor array structure;
the first iteration is operated such that the first sensor array structure parameter m is equal to m + 1.
4. The method according to claim 2, wherein the S23 further comprises:
performing a plurality of second iterative operations on the first sensor array structure to obtain a second sensor array structure;
the second iterative operation is to make the first sensor array structure parameter p equal to p + 1.
5. The method according to claim 3 or 4, wherein the S23 further comprises:
and carrying out multiple first iteration operations and multiple second iteration operations on the first sensor array structure to obtain the second sensor array structure.
6. The method of claim 1, wherein the number of array elements N of the second sensor array structure is expressed as:
N＝p+(m+2)β-1
wherein p, beta and m represent structural parameters of the second sensor array, and are positive integers, p is more than or equal to 1, beta is more than or equal to 3, and m is more than or equal to 1;
the maximum baseline length L of the second sensor array structure is expressed as:
L＝(p+2β-1)m+2p+β-2
wherein p, beta and m represent structural parameters of the second sensor array, and are positive integers, p is more than or equal to 1, beta is more than or equal to 3, and m is more than or equal to 1;
the maximum baseline length a of the second sensor array structure is expressed as:
A＝L+β-1
wherein L represents the maximum base length of the second sensor array structure, beta represents a parameter of the second sensor array structure, and beta is a positive integer and is larger than or equal to 3.
7. The method according to claim 1, wherein the S3 further comprises: obtaining an optimal parameter p of the second sensor array structure according to a quadratic programming method * ，m * To obtain the third sensor array structure:
wherein the parameter m of the third sensor array structure * ，p * Expressed as:
wherein,
is shown and
the nearest integer, beta represents any given baseline redundancy order, N represents any given array element number, p and beta are positive integers, p is more than or equal to 1, and beta is more than or equal to 3;
the maximum baseline length L of the third sensor array structure is expressed as:
wherein m is * Representing a parameter of a third sensor array structure, wherein beta represents a given arbitrary baseline redundancy order, N represents a given arbitrary array element number, and p and beta are positive integers, p is more than or equal to 1, and beta is more than or equal to 3;
the aperture length a of the third sensor array structure is expressed as:
A＝L+β-1
wherein L represents the maximum baseline length of the third sensor array structure, beta represents any given baseline redundancy order, and beta is a positive integer and is more than or equal to 3.
8. A design device of a one-dimensional multiple redundant sensor array structure is characterized by comprising:
a construction module for constructing a first sensor array structure according to a basic structure pattern, the basic structure pattern of the first sensor array being:
{1 β-1 ，p，1 β-1 ，p+β，1 p+β-2 }
wherein 1, p, p + beta represents the interval between adjacent array elements, 1 β-1 Represents the repetition of adjacent array elements with the distance of 1 for beta-1 times, 1 p+β-2 Representing the repetition p + beta-2 times with the adjacent array element spacing of 1, wherein p and beta are positive integers, p is more than or equal to 1, beta is more than or equal to 3, p is a parameter, and beta is the redundancy order of a base line;
the first design module is used for iterating parameters of the first sensor array structure according to the distribution condition of the adjacent array element spacing of the first sensor array structure to obtain a second sensor array structure, and the adjacent array element spacing of the second sensor array structure is represented in the form of:
{1 β-1 ，p，(1 β-1 ，p+β) m ，1 p+β-2 }
wherein 1, p, p + beta represents the interval between adjacent array elements, 1 β-1 Represents the repetition of adjacent array elements with the distance of 1 for beta-1 times, 1 p+β-2 Represents that the adjacent array elements are repeated for p + beta-2 times with the distance of 1, (1) β-1 ，p+β) m Representing groups of adjacent array element spacings (1) β-1 P + beta) is repeated for m times, and p, beta and m are positive integers, p is more than or equal to 1, beta is more than or equal to 3, and m is more than or equal to 1;
the second design module is used for calculating the second sensor array structure parameters according to the adjacent array element spacing distribution condition of the second sensor array structure to obtain a third sensor array structure, and the design model form of the third sensor array structure is as follows:
s.t.N＝p+(m+2)β-1，β≥3
wherein p and m are parameters of a second sensor array structure to be optimized, L represents the maximum baseline length of the sensor array structure, beta represents any given baseline redundancy order, N represents any given array element number, and p, beta and m are positive integers, p is larger than or equal to 1, beta is larger than or equal to 3, and m is larger than or equal to 1.
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| CN106785485A (en) * | 2016-12-29 | 2017-05-31 | 华中科技大学 | A kind of one-dimensional dual redundant aerial array and building method |
| CN109932681A (en) * | 2019-04-04 | 2019-06-25 | 哈尔滨工程大学 | A kind of drop redundancy nested array setting method based on Space-Time information |
| CN110726967A (en) * | 2019-10-25 | 2020-01-24 | 北京理工大学 | Unilateral sparse nested array design method for one-dimensional array direction finding |
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| CN106785485A (en) * | 2016-12-29 | 2017-05-31 | 华中科技大学 | A kind of one-dimensional dual redundant aerial array and building method |
| CN109932681A (en) * | 2019-04-04 | 2019-06-25 | 哈尔滨工程大学 | A kind of drop redundancy nested array setting method based on Space-Time information |
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