DOA estimation method based on improved Gauss-Newton algorithm
阅读说明：本技术 一种基于改进高斯-牛顿算法的doa估计方法 (DOA estimation method based on improved Gauss-Newton algorithm ) 是由 陈海华 张玉成 周荣荣 韩义江 徐海成 王越 李涛 宋鹏 娄山关 李同滨 于 2020-07-14 设计创作，主要内容包括：本发明涉及信号处理的技术领域,特别是涉及一种基于改进高斯-牛顿算法的DOA估计方法,包括以下步骤：求接收信号的协方差矩阵；根据传统子空间拟合类算法求出推定信号的表达式；利用推定信号必须为非负定这一条件,反推出所有可能的信号源的方向构成限定解空间；在限定解空间内随机撒N个点作为初始化粒子；把相应的子空间拟合类算法的代价函数作为高斯-牛顿算法的评价标准函数；所有的初始粒子,针对代价函数分别进行常规高斯牛顿迭代；将N个粒子迭代计算的结果进行比较找出使得代价函数最小的估计值,确定为信号的波达方位估计,可以克服子空间拟合类DOA估计算法中应用高斯牛顿算法容易陷入局部最优解的问题。(The invention relates to the technical field of signal processing, in particular to a DOA estimation method based on an improved Gauss-Newton algorithm, which comprises the following steps: solving a covariance matrix of the received signal; solving an expression of the estimated signal according to a traditional subspace fitting algorithm; the method comprises the following steps of reversely deducing the directions of all possible signal sources to form a limited solution space by using the condition that an estimated signal is required to be non-negative; randomly scattering N points in a defined solution space to serve as initialization particles; taking the cost function of the corresponding subspace fitting algorithm as an evaluation standard function of the Gaussian-Newton algorithm; performing conventional Gauss-Newton iteration on all initial particles according to the cost function; the results of the N particle iterative computations are compared to find out an estimated value which enables the cost function to be minimum, the estimated value is determined as the direction of arrival estimation of the signal, and the problem that the local optimal solution is easy to fall into by applying a Gaussian Newton algorithm in a subspace fitting type DOA estimation algorithm can be solved.)
1. A DOA estimation method based on improved Gauss-Newton algorithm is characterized by comprising an Antenna Array (Antenna Array), a space-defining module and a Gauss-Newton algorithm module, and the DOA estimation method comprises the following steps:
step 1: solving a covariance matrix of the received signal;
step 2: solving an expression of the estimated signal according to a traditional subspace fitting algorithm;
and step 3: the method comprises the following steps of reversely deducing the directions of all possible signal sources to form a limited solution space by using the condition that an estimated signal is required to be non-negative;
and 4, step 4: randomly scattering N points in a defined solution space to serve as initialization particles;
and 5: taking the cost function of the corresponding subspace fitting algorithm as an evaluation standard function of the Gaussian-Newton algorithm;
step 6: performing conventional Gauss-Newton iteration on all initial particles in the step 4 according to the cost function in the step 5 until all the particles converge or reach the specified maximum iteration times;
and 7: and comparing the results of the N particle iterative computations to find an estimated value which enables the cost function to be minimum, and determining the estimated value as the direction of arrival estimation of the signal.
2. A DOA estimation method based on improved Gauss-Newton's algorithm in accordance with claim 1, characterized in that the applied algorithm is all algorithms related to multi-dimensional non-linear optimization in DOA estimation.
3. A DOA estimation method based on the modified gauss-newton algorithm as claimed in claim 1, wherein said signal is divided into: an arbitrary signal.
4. A DOA estimation method based on the modified gauss-newton algorithm as claimed in claim 1, wherein the noise score is: any noise.
5. A DOA estimation method based on the modified gauss-newton algorithm according to claim 1, wherein the number of signal sources is smaller than the number of array elements in the receiving array.
6. A DOA estimation method based on the modified gauss-newton algorithm as claimed in claim 1, wherein said antenna array is an arbitrary array flow pattern antenna.
Technical Field
The invention relates to the technical field of signal processing, in particular to a DOA estimation method based on an improved Gaussian-Newton algorithm.
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.
Early estimates of DOA were represented by Conventional Beamforming (CBF) beamforming. However, such algorithms are limited by the number of array elements and the spacing between the array elements, and the resolution is low. The high-resolution spectrum estimation algorithm represented by the Capon method and the maximum entropy method breaks through the above limitation to a certain extent.
Beginning in the 70's of the 20 th century, multiple signal classification (MUSIC) algorithms and rotation invariant subspace (ESPRIT) algorithms were proposed. The two subspace decomposition type algorithms greatly improve the DOA estimation precision. Subspace fitting algorithms such as a late maximum likelihood algorithm (ML), a Weighted Subspace Fitting (WSF) and the like are also provided, and the DOA estimation accuracy is high, and the DOA estimation method can be rapidly developed because the DOA estimation accuracy is high, the orientation information of a plurality of signals can be detected simultaneously, and coherent signals can be processed. However, the subspace fitting algorithm relates to a multidimensional nonlinear optimization problem, so that a large amount of calculation is required to obtain a solution (i.e., the direction of a signal source), and the real-time performance is poor, which is not favorable for application in practical engineering practice.
The gauss-newton algorithm is a classic algorithm aiming at a multi-dimensional nonlinear optimization problem, but the traditional gauss-newton algorithm has the problem that the traditional gauss-newton algorithm is easy to fall into a local optimal solution after iteration.
Disclosure of Invention
Technical problem to be solved
Aiming at the defects of the prior art, the invention provides the DOA estimation method based on the improved Gauss-Newton algorithm, which can overcome the problem that the applied Gauss-Newton algorithm in the subspace fitting type DOA estimation algorithm is easy to fall into the local optimal solution.
(II) technical scheme
In order to achieve the purpose, the invention provides the following technical scheme: a DOA estimation method based on improved Gauss-Newton algorithm comprises an Antenna Array (Antenna Array), a space-defining module and a Gauss-Newton algorithm module, and comprises the following steps:
step 1: solving a covariance matrix of the received signal;
step 2: solving an expression of the estimated signal according to a traditional subspace fitting algorithm;
and step 3: the method comprises the following steps of reversely deducing the directions of all possible signal sources to form a limited solution space by using the condition that an estimated signal is required to be non-negative;
and 4, step 4: randomly scattering N points in a defined solution space to serve as initialization particles;
and 5: taking the cost function of the corresponding subspace fitting algorithm as an evaluation standard function of the Gaussian-Newton algorithm;
step 6: performing conventional Gauss-Newton iteration on all initial particles in the
and 7: and comparing the results of the N particle iterative computations to find an estimated value which enables the cost function to be minimum, and determining the estimated value as the direction of arrival estimation of the signal.
Preferably, the algorithms applied are all algorithms in DOA estimation involving multi-dimensional non-linear optimization.
Preferably, the signal is divided into: an arbitrary signal.
Preferably, the noise score is: any noise.
Preferably, the number of signal sources is less than the number of array elements in the receiving array.
Preferably, the antenna array is an arbitrary array flow pattern antenna.
(III) advantageous effects
Compared with the prior art, the invention provides a DOA estimation method based on an improved Gauss-Newton algorithm, which has the following beneficial effects: the DOA estimation method based on the improved Gaussian-Newton algorithm can effectively avoid the defects that the traditional Gaussian-Newton algorithm excessively depends on the initial value and is easy to fall into the local optimal value, and can reduce the calculation complexity of the subspace fitting algorithm to a certain extent.
Drawings
FIG. 1 is a schematic diagram of an array receiving signal;
FIG. 2 is a schematic diagram of an application of the modified Gaussian-Newton algorithm in an example of the SML algorithm;
FIG. 3 is a comparison graph of the computational complexity effect of the improved Gaussian-Newton algorithm applied in the example of the SML algorithm;
fig. 4 is a graph comparing the accuracy effect of the improved gaussian-newton algorithm applied in the SML algorithm as an example.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-4, a DOA estimation method based on improved gauss-newton algorithm includes an Antenna Array (Antenna Array), a solution space defining module, and a gauss-newton algorithm module, including the following steps:
step 1: solving a covariance matrix of the received signal;
step 2: solving an expression of the estimated signal according to a traditional subspace fitting algorithm;
and step 3: the method comprises the following steps of reversely deducing the directions of all possible signal sources to form a limited solution space by using the condition that an estimated signal is required to be non-negative;
and 4, step 4: randomly scattering N points in a defined solution space as initialization particles (note: the size of N can be freely adjusted according to the actual situation, and is generally recommended to be 5);
and 5: taking the cost function of the corresponding subspace fitting algorithm as an evaluation standard function of the Gaussian-Newton algorithm;
step 6: performing conventional gauss-newton iteration on all initial particles in the
and 7: and comparing the results of the N particle iterative computations to find an estimated value which enables the cost function to be minimum, and determining the estimated value as the direction of arrival estimation of the signal.
In summary, according to the DOA estimation method based on the improved Gauss-Newton algorithm, a solution space is defined according to the condition that an estimation signal is not negative, the estimation range is narrowed, a plurality of points are scattered randomly in the defined solution space at the same time to serve as initial particles, then Gauss-Newton iteration is carried out on all the particles at the same time, and finally a global solution is determined through comparison, so that the defects that the traditional Gauss-Newton algorithm depends on the initial values excessively and is easy to fall into local optimal values can be effectively avoided, and the calculation complexity of a subspace fitting algorithm can be reduced to a certain extent.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, 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.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.