CN112180317A - DOA estimation algorithm of non-uniform over-complete dictionary based on priori knowledge - Google Patents
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Abstract
The invention relates to the technical field of signal processing, in particular to a DOA estimation algorithm of a non-uniform overcomplete dictionary based on priori knowledge, which can effectively avoid the defect of high calculation complexity of a traditional uniform overcomplete dictionary compressive sensing algorithm and greatly improve the accuracy of DOA estimation; the invention is composed of an antenna array, a sparse signal compression module and a signal reconstruction module.
Description
Technical Field
The invention relates to the technical field of signal processing, in particular to a DOA estimation algorithm of a non-uniform over-complete dictionary based on prior knowledge.
Background
Array signal processing is an important branch in the field of signal processing, and has been rapidly developed in recent 40 years, and the application of the array signal processing relates to a plurality of military and national economic fields such as radar, communication, sonar, earthquake, exploration, radio astronomy, biomedical engineering and the like.
As is well known, the time domain spectrum is an important concept in time domain processing, and the spatial spectrum is an important concept in array signal processing. The time domain spectrum represents the energy distribution of the signal at various frequencies, while the spatial spectrum represents the energy distribution of the signal in various directions in space. Therefore, if a "spatial spectrum" of a signal is available, the direction of arrival of the signal is obtained, and therefore, the spatial spectrum is generally referred to as a direction of arrival (DOA) estimate.
The DOA estimation algorithm takes subspace decomposition and subspace fitting algorithms as main flow algorithms, but the subspace decomposition and subspace fitting algorithms are based on accurate statistical characteristics, so that the DOA estimation algorithm often needs larger snapshot data. To solve the small snapshot situation, compressed sensing is a powerful means. The compressive sensing theory indicates that when a signal has a sparse characteristic, the signal can be mapped from a high-dimensional space to a low-dimensional space through linear observation, and the acquired low-dimensional sampling data contains most information in the original signal. And then accurately recovering the original signal from the observation data by a signal reconstruction method. In the process, the acquisition of the signals is not restricted by a Nyquist sampling law any more, so that the burden of a front-end system for acquiring the signals is greatly reduced. The application of the DOA algorithm in array signal processing is well developed, and researchers propose a plurality of DOA estimation algorithms based on compressed sensing (sparse recovery) thought, wherein the algorithms represented by comparison comprise SPICE (sparse representation and sparse Bayesian learning) and the like.
The compressed sensing theory can also be applied to underwater acoustic DOA estimation. The compressed sensing carries out sampling and compression simultaneously, so that the sampling data of the signals are greatly reduced, the redundancy of the measurement data meeting the Nyquist sampling theorem is greatly reduced, and the performance processing pressure of hardware equipment is greatly reduced.
Conventional compressed sensing is mainly based on a mesh, non-mesh and Bayesian compression framework method. But either framework is based on an overcomplete dictionary and involves optimization problems. If the data grid is too thin, the overcomplete dictionary is very large, the whole computation complexity is very high, and if the data grid is too thick, the DOA estimation precision is greatly reduced, and even errors occur. Therefore, the invention provides a non-uniform over-complete dictionary design method based on prior knowledge.
The basic idea of the method is to quickly obtain a relatively coarse DOA estimated value based on prior knowledge, for example, by using techniques such as MUSIC or ESPRIT under a small snapshot condition, and then generate a finer grid near the value and a coarser grid far away from the value (the grid is coarser as the distance from the value is larger), so as to generate a non-uniform overcomplete dictionary (the conventional overcomplete dictionaries are uniform grids). The non-uniform overcomplete dictionary has the advantages that the 'volume' of the overcomplete dictionary is greatly reduced, the DOA estimation precision can be guaranteed, and meanwhile, the calculation complexity can be greatly reduced.
Disclosure of Invention
In order to solve the technical problems, the invention provides the DOA estimation algorithm of the nonuniform overcomplete dictionary based on the priori knowledge, which can effectively avoid the defect of high calculation complexity of the traditional uniform overcomplete dictionary compressive sensing algorithm and greatly improve the accuracy of the DOA estimation.
The invention relates to a DOA estimation algorithm of a nonuniform overcomplete dictionary based on prior knowledge, which comprises an antenna array, a sparse signal compression module and a signal reconstruction module; the DOA estimation algorithm comprises the following steps:
step 1: judging whether the incoming wave signal is a sparse signal or not according to the array receiving receipt;
step 2: when the signal has sparsity, applying a compressed sensing algorithm to the signal, wherein the number of information sources is M, the number of array elements is N, N is greater than M, and the value of M can be freely adjusted according to the actual situation;
and step 3: obtaining a DOA rough estimation value of an incoming wave signal by utilizing a ROOT-MUSIC, ESPRIT or other algorithms capable of quickly obtaining the DOA rough estimation value;
and 4, step 4: and (3) solving a non-uniform over-complete dictionary of the sparse signal, using the DOA rough estimation value quickly obtained in the step (3) as a weighing value, generating a finer grid near the value, generating a coarser grid at a position far away from the value, and changing the thickness of the specific grid according to the situation in the actual operation if the grid is thicker at a position far away from the value.
And 5: selecting a measurement matrix, such as a random Gaussian matrix which is independently and uniformly distributed is adopted as the measurement matrix;
step 6: and carrying out sparse reconstruction on the signals by adopting a reconstruction method so as to obtain the DOA estimation value.
The DOA estimation algorithm of the nonuniform over-complete dictionary based on the priori knowledge is characterized in that the signal is a sparse signal.
The DOA estimation algorithm of the nonuniform over-complete dictionary based on the priori knowledge is disclosed, wherein the noise is any noise.
The invention relates to a DOA estimation algorithm of a non-uniform overcomplete dictionary based on prior knowledge, wherein an antenna array is an arbitrary array flow pattern antenna.
Compared with the prior art, the invention has the beneficial effects that: the defect of high calculation complexity of a traditional uniform overcomplete dictionary compressed sensing algorithm can be effectively avoided, and the DOA estimation accuracy is greatly improved.
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FIG. 1 is a schematic diagram of an array receiving signal;
FIG. 2 is a schematic diagram of a DOA estimation method of compressed sensing of a non-uniform overcomplete dictionary based on prior knowledge;
FIG. 3 is a diagram of overcomplete dictionary effects for uniform distribution of sparse signals;
FIG. 4 is a diagram of a non-uniform overcomplete dictionary effect based on a priori knowledge.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
A DOA estimation algorithm of a nonuniform overcomplete dictionary based on prior knowledge comprises an antenna array, a sparse signal compression module and a signal reconstruction module; the DOA estimation algorithm comprises the following steps:
step 1: judging whether the incoming wave signal is a sparse signal or not according to the array receiving receipt;
step 2: when the signal has sparsity, applying a compressed sensing algorithm to the signal, wherein the number of information sources is M, the number of array elements is N, N is greater than M, and the value of M can be freely adjusted according to the actual situation;
and step 3: obtaining a DOA rough estimation value of an incoming wave signal by utilizing a ROOT-MUSIC, ESPRIT or other algorithms capable of quickly obtaining the DOA rough estimation value;
and 4, step 4: solving a non-uniform over-complete dictionary of the sparse signal; generating a finer grid near the DOA rough estimation value obtained in the step 3, generating a coarser grid far away from the DOA rough estimation value, and generating a non-uniform over-complete dictionary, wherein the grid is coarser the farther away from the DOA rough estimation value, and thus generating the non-uniform over-complete dictionary, wherein the incoming wave signal is 30 degrees, the rough DOA estimation value is obtained by using an ESPRIT algorithm, the grid is divided by 0.5 degrees at 31 degrees, the grid is divided by 5 degrees at the distance of 31 degrees, such as the vicinity of 60 degrees, and the grid is larger at the distance of 31 degrees from the rough DOA estimation value, so that the non-uniform over-complete dictionary based on the priori knowledge is formed;
and 5: selecting a measurement matrix, such as a random Gaussian matrix which is independently and uniformly distributed is adopted as the measurement matrix;
step 6: sparse reconstruction is carried out on the signals by adopting a reconstruction method, and then DOA estimated values are obtained;
the method can effectively avoid the defect of high calculation complexity of the traditional uniform over-complete dictionary compressed sensing algorithm, and simultaneously greatly improves the accuracy of DOA estimation.
As a preferred technical scheme, the DOA estimation algorithm of the nonuniform overcomplete dictionary based on the priori knowledge comprises an antenna array, a sparse signal compression module and a signal reconstruction module; the DOA estimation algorithm comprises the following steps:
step 1: judging whether the incoming wave signal is a sparse signal or not according to the array receiving receipt;
step 2: when the signal has sparsity, applying a compressed sensing algorithm to the signal, wherein the number of information sources is M, the number of array elements is N, N is greater than M, and the value of M can be freely adjusted according to the actual situation;
and step 3: obtaining a DOA rough estimation value of an incoming wave signal by utilizing a ROOT-MUSIC, ESPRIT or other algorithms capable of quickly obtaining the DOA rough estimation value;
and 4, step 4: solving a non-uniform over-complete dictionary of the sparse signal; generating a finer grid near the DOA rough estimation value obtained in the step 3, generating a coarser grid far away from the DOA rough estimation value, and generating a non-uniform over-complete dictionary, wherein the grid is coarser the farther away from the DOA rough estimation value, and the grid is coarser the farther away from the DOA rough estimation value, wherein the incoming wave signal is 30 degrees, the rough DOA estimation value is obtained by using an ESPRIT algorithm, the grid is divided at intervals of 0.5 degrees near 31 degrees, the grid is divided at intervals of 5 degrees near 60 degrees as near 31 degrees, and the intervals of the divided grid are larger the farther away from the DOA rough estimation value, so that the non-uniform over-complete dictionary based on the priori knowledge is formed;
and 5: selecting a measurement matrix, such as a random Gaussian matrix which is independently and uniformly distributed is adopted as the measurement matrix;
step 6: and carrying out sparse reconstruction on the signals by adopting a reconstruction method so as to obtain the DOA estimation value.
As a preferred technical scheme, the DOA estimation algorithm of the nonuniform overcomplete dictionary based on the priori knowledge comprises an antenna array, a sparse signal compression module and a signal reconstruction module; the DOA estimation algorithm comprises the following steps:
step 1: judging whether the incoming wave signal is a sparse signal or not according to the array receiving receipt;
step 2: when the signal has sparsity, applying a compressed sensing algorithm to the signal, wherein the number of information sources is M, the number of array elements is N, N is greater than M, and the value of M can be freely adjusted according to the actual situation;
and step 3: obtaining a DOA rough estimation value of an incoming wave signal by utilizing a ROOT-MUSIC, ESPRIT or other algorithms capable of quickly obtaining the DOA rough estimation value;
and 4, step 4: solving a non-uniform over-complete dictionary of the sparse signal; generating a finer grid near the DOA rough estimation value obtained in the step 3, and generating a coarser grid far away from the DOA rough estimation value, and the coarser grid is the farther away from the DOA rough estimation value, so as to generate a non-uniform over-complete dictionary, wherein the incoming wave signal is 30 degrees, for example, the rough DOA estimation value is obtained by using an ESPRIT algorithm, the grid is divided at intervals of 0.5 degrees near 31 degrees, the grid is divided at intervals of 5 degrees near 60 degrees far away from 31 degrees, and the intervals of the divided grids are larger at 31 degrees far away from the rough DOA estimation value, so that the non-uniform over-complete dictionary based on priori knowledge is formed;
and 5: selecting a measurement matrix, such as a random Gaussian matrix which is independently and uniformly distributed is adopted as the measurement matrix;
step 6: sparse reconstruction is carried out on the signals by adopting a reconstruction method, and then DOA estimated values are obtained;
wherein the signal is a sparse signal.
As a preferred technical scheme, the DOA estimation algorithm of the nonuniform overcomplete dictionary based on the priori knowledge comprises an antenna array, a sparse signal compression module and a signal reconstruction module; the DOA estimation algorithm comprises the following steps:
step 1: judging whether the incoming wave signal is a sparse signal or not according to the array receiving receipt;
step 2: when the signal has sparsity, applying a compressed sensing algorithm to the signal, wherein the number of information sources is M, the number of array elements is N, N is greater than M, and the value of M can be freely adjusted according to the actual situation;
and step 3: obtaining a DOA rough estimation value of an incoming wave signal by utilizing a ROOT-MUSIC, ESPRIT or other algorithms capable of quickly obtaining the DOA rough estimation value;
and 4, step 4: solving a non-uniform over-complete dictionary of the sparse signal; generating a finer grid near the DOA rough estimation value obtained in the step 3, and generating a coarser grid far away from the DOA rough estimation value, and the coarser grid is the farther away from the DOA rough estimation value, so as to generate a non-uniform over-complete dictionary, wherein the incoming wave signal is 30 degrees, for example, the rough DOA estimation value is obtained by using an ESPRIT algorithm, the grid is divided at intervals of 0.5 degrees near 31 degrees, the grid is divided at intervals of 5 degrees near 60 degrees far away from 31 degrees, and the intervals of the divided grids are larger at 31 degrees far away from the rough DOA estimation value, so that the non-uniform over-complete dictionary based on priori knowledge is formed;
and 5: selecting a measurement matrix, such as a random Gaussian matrix which is independently and uniformly distributed is adopted as the measurement matrix;
step 6: sparse reconstruction is carried out on the signals by adopting a reconstruction method, and then DOA estimated values are obtained;
wherein the noise is arbitrary noise.
As a preferred technical scheme, the DOA estimation algorithm of the nonuniform overcomplete dictionary based on the priori knowledge comprises an antenna array, a sparse signal compression module and a signal reconstruction module; the DOA estimation algorithm comprises the following steps:
step 1: judging whether the incoming wave signal is a sparse signal or not according to the array receiving receipt;
step 2: when the signal has sparsity, applying a compressed sensing algorithm to the signal, wherein the number of information sources is M, the number of array elements is N, N is greater than M, and the value of M can be freely adjusted according to the actual situation;
and step 3: obtaining a DOA rough estimation value of an incoming wave signal by utilizing a ROOT-MUSIC, ESPRIT or other algorithms capable of quickly obtaining the DOA rough estimation value;
and 4, step 4: solving a non-uniform over-complete dictionary of the sparse signal; generating a finer grid near the DOA rough estimation value obtained in the step 3, and generating a coarser grid far away from the DOA rough estimation value, and the coarser grid is the farther away from the DOA rough estimation value, so as to generate a non-uniform over-complete dictionary, wherein the incoming wave signal is 30 degrees, for example, the rough DOA estimation value is obtained by using an ESPRIT algorithm, the grid is divided at intervals of 0.5 degrees near 31 degrees, the grid is divided at intervals of 5 degrees near 60 degrees far away from 31 degrees, and the intervals of the divided grids are larger at 31 degrees far away from the rough DOA estimation value, so that the non-uniform over-complete dictionary based on priori knowledge is formed;
and 5: selecting a measurement matrix, such as a random Gaussian matrix which is independently and uniformly distributed is adopted as the measurement matrix;
step 6: and carrying out sparse reconstruction on the signals by adopting a reconstruction method so as to obtain the DOA estimation value.
Wherein the antenna array is an arbitrary array flow pattern antenna.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (4)
1. A DOA estimation algorithm of a nonuniform overcomplete dictionary based on prior knowledge is characterized by comprising an antenna array, a sparse signal compression module and a signal reconstruction module; the DOA estimation algorithm comprises the following steps:
step 1: judging whether the incoming wave signal is a sparse signal or not according to the array receiving receipt;
step 2: when the signal has sparsity, applying a compressed sensing algorithm to the signal, wherein the number of information sources is M, the number of array elements is N, N is greater than M, and the value of M can be freely adjusted according to the actual situation;
and step 3: obtaining a DOA rough estimation value of an incoming wave signal by utilizing a ROOT-MUSIC, ESPRIT or other algorithms capable of quickly obtaining the DOA rough estimation value;
and 4, step 4: and (3) solving a non-uniform over-complete dictionary of the sparse signal, using the DOA rough estimation value quickly obtained in the step (3) as a weighing value, generating a finer grid near the value, generating a coarser grid at a position far away from the value, and changing the thickness of the specific grid according to the situation in the actual operation if the grid is thicker at a position far away from the value.
And 5: selecting a measurement matrix, such as a random Gaussian matrix which is independently and uniformly distributed is adopted as the measurement matrix;
step 6: and carrying out sparse reconstruction on the signals by adopting a reconstruction method so as to obtain the DOA estimation value.
2. The a priori knowledge based DOA estimation algorithm for a non-uniform overcomplete dictionary as set forth in claim 1, wherein said signal is a sparse signal.
3. The a priori knowledge based non-uniform overcomplete dictionary DOA estimation algorithm as recited in claim 1, wherein the noise is arbitrary noise.
4. The DOA estimation algorithm based on the non-uniform overcomplete dictionary of prior knowledge as set forth in claim 1, wherein the antenna array is an arbitrary array flow pattern antenna.
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