Direction of arrival estimation method and system based on Riemannian geometry

Abstract

The invention discloses a direction-of-arrival estimation method and system based on Riemannian geometry, and the method comprises the steps: constructing an array receiving signal observation model, carrying out the short-time Fourier transform of the array receiving signal observation model, obtaining the frequency domain data of an array antenna, and calculating the frequency domain data of the array antenna; fusing the array antenna frequency domain data to obtain fused array antenna data; obtaining a Riemannian manifold of a covariance matrix set according to the fused array antenna data; obtaining a Riemannian geometric mean value according to the Riemannian manifold of the covariance matrix set; and obtaining the direction of arrival of the expected signal source according to the steering vector and the Riemannian geometric mean value. According to the method, the calculation complexity is reduced, and meanwhile, the estimation precision and robustness in a complex signal environment are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication and array signal processing, and in particular relates to a method and system for estimating a direction of arrival based on Riemannian geometry. Background Art

[0002] In wireless communication systems, radar and sonar technology, Direction of Arrival (DOA) estimation is a key technology for determining the location of signal sources. Initial DOA estimation methods were mainly based on Fourier transform linear spectrum estimation methods, but these methods were limited by the Rayleigh limit, could not achieve ultra-high resolution performance, and had poor noise resistance. The subsequent maximum likelihood spectrum estimation method had high resolution performance and good robustness, but the computational complexity was extremely high. After the 1980s, the academic community proposed spectrum estimation methods based on matrix eigenvalue decomposition, such as the multiple signal classification (MUSIC) method and the rotationally invariant subspace (ESPRIT) method, which were based on the orthogonality of the signal subspace and the noise subspace and the rotational invariance of the signal subspace.

[0003] The above methods rely on the statistical characteristics of the signal or the signal subspace structure to varying degrees, and their performance is limited when dealing with non-ideal signal environments (such as multipath effects, signal coherence, etc.). They have problems such as low anti-interference performance and anti-clutter capabilities, and high computational complexity. Summary of the invention

[0004] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art and provide a method and system for estimating a direction of arrival based on Riemannian geometry, which reduces the computational complexity while significantly improving the estimation accuracy and robustness in a complex signal environment.

[0005] The object of the present invention is achieved through the following technical scheme: a wave direction estimation method based on Riemann geometry, comprising: constructing an array receiving signal observation model, using short-time Fourier transform to obtain array antenna frequency domain data of the array receiving signal observation model, fusing the array antenna frequency domain data to obtain fused array antenna data; obtaining the Riemann manifold of the covariance matrix set according to the fused array antenna data; obtaining the Riemannian geometry mean according to the Riemannian manifold of the covariance matrix set; and obtaining the wave direction of the expected signal source according to the steering vector and the Riemannian geometry mean.

[0006] In the above-mentioned DOA estimation method based on Riemannian geometry, the array receiving signal observation model is obtained by the following formula:

[0007]

[0008] Among them, z m (n) is the data observed by the mth receiving antenna, Indicates the jth 1 A source of expectation, For the jth 2 interference source, v m (n) is the noise of the mth receiving antenna, represents the mth receiving antenna for the jth 1 The receiving steering vector of the desired source, represents the mth receiving antenna for the jth 2 The receiving steering vector of the interference source, m is the number of the receiving antenna, n is the sampling snapshot index value, j is the receiving antenna number, 1 is the expected signal index value, N D is the expected number of radiation sources, j 2 is the interference signal index value, N I is the number of intermittent interference sources, d is the desired signal mark, and i is the interference signal mark.

[0009] In the above-mentioned DOA estimation method based on Riemannian geometry, the frequency domain data of the array antenna is obtained by the following formula:

[0010]

[0011] Among them, z m (l,k) is the frequency domain data of the array antenna, l is the window number, k is the frequency number, and m is the number of the receiving antenna. The expected signal The frequency domain representation of Receive the steering vector for the desired signal The frequency domain representation of Interference signal The frequency domain representation of Receive steering vector for interference signal The frequency domain representation of v m (l,k) is the noise term v m The frequency domain representation of (n), j 1 is the expected signal index value, N D is the expected number of radiation sources, j 2 is the interference signal index value, N I is the number of intermittent interference sources, i is the interference signal mark, and d is the desired signal mark.

[0012] In the above-mentioned DOA estimation method based on Riemannian geometry, the fused array antenna data is obtained by the following formula:

[0013] z(l,k)=H d (l,k)s d (l,k)+H i (l,k)s i(l,k)+v(l,k);

[0014] Among them, z(l,k) is the fused array antenna data, l is the window number, k is the frequency number, H d (l,k) is The matrix representation of Receive the steering vector for the desired signal The frequency domain representation of s d (l,k) is N D The matrix representation of the desired radiation source, H i (l,k) is The matrix representation of To receive the steering vector for the interference signal The frequency domain representation of s i (l,k) is N I The matrix representation of the interference signal, v(l,k) is the matrix representation of the noise term, i is the interference signal sign, and d is the desired signal sign.

[0015] In the above-mentioned DOA estimation method based on Riemannian geometry, obtaining the Riemannian manifold of the covariance matrix set according to the fused array antenna data includes: calculating the covariance matrix set of the fused array antenna data; and mapping the covariance matrix set to the Riemannian manifold to obtain the Riemannian manifold of the covariance matrix set.

[0016] In the above-mentioned method for estimating the direction of arrival based on Riemannian geometry, obtaining the direction of arrival of the desired signal source according to the steering vector and the Riemannian geometry mean value includes: obtaining the target function according to the steering vector and the Riemannian geometry mean value; performing a spectral peak search on the target function to obtain the angle that maximizes the target function, which is the direction of arrival of the desired signal source.

[0017] In the above-mentioned DOA estimation method based on Riemannian geometry, the objective function is obtained by the following formula:

[0018]

[0019] in, is the objective function, d(θ) is the steering vector, is the Riemannian geometric mean, and θ is the angle of the expected signal.

[0020] In the above-mentioned DOA estimation method based on Riemannian geometry, the angle that maximizes the objective function is obtained by the following formula:

[0021]

[0022] in, is the maximum angle of the objective function, is the objective function, is the Riemannian geometric mean, and θ is the angle of the expected signal.

[0023] A wave direction estimation system based on Riemannian geometry includes: a first module, used to construct an array receiving signal observation model, use short-time Fourier transform to obtain array antenna frequency domain data of the array receiving signal observation model, and fuse the array antenna frequency domain data to obtain fused array antenna data; a second module, used to obtain the Riemann manifold of a covariance matrix set according to the fused array antenna data; a third module, used to obtain the Riemannian geometry mean according to the Riemannian manifold of the covariance matrix set; and a fourth module, used to obtain the wave direction of a desired signal source according to a steering vector and the Riemannian geometry mean.

[0024] An electronic device comprises: a memory for storing computer-readable instructions; and a processor for running the computer-readable instructions to execute a method for estimating a direction of arrival based on Riemannian geometry.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] (1) Compared with the traditional beamforming algorithm, the Riemann mean of the present invention suppresses interference while maintaining the desired signal source, improves the accuracy of DOA estimation in complex signal environments, and enhances the robustness to multipath effects and signal coherence;

[0027] (2) The present invention integrates the advantages of the Riemannian geometric mean, does not need to calculate the rank of the covariance matrix in advance, and does not need to pre-estimate the number of desired signal sources and interference sources compared to subspace algorithms. It is not necessary to perform the eigenvalue solution process of the covariance matrix, which reduces the cost and computational complexity of the direction of arrival estimation and improves the real-time performance of the direction of arrival calculation.

[0028] (3) The present invention combines the potential geometric characteristics of Riemann manifolds and eliminates the need for parameter matching when performing multi-dimensional angle estimation, which makes up for the deficiency of conventional algorithms that require parameter matching. It uses Riemannian geometry theory to simplify the signal processing process and reduce the demand for computing resources, which has broad research significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0030] Figure 1 is a flow chart of a method for estimating a direction of arrival based on Riemannian geometry provided by an embodiment of the present invention;

[0031] Figure 2is a schematic diagram of a direction of arrival estimation scenario provided by an embodiment of the present invention;

[0032] Figure 3 is a flow chart of solving the Riemann mean provided by an embodiment of the present invention;

[0033] Figure 4 It is a spectrum diagram of direction of arrival estimation of a beamforming method in a traditional Euclidean space provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0034] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present disclosure and to be able to fully convey the scope of the present disclosure to those skilled in the art. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features described in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0035] Figure 1 It is a flow chart of a method for estimating a direction of arrival based on Riemannian geometry provided in an embodiment of the present invention.

[0036] like Figure 1 As shown, the method includes:

[0037] Step 1: construct an array receiving signal observation model, use short-time Fourier transform to obtain array antenna frequency domain data, and fuse the array antenna frequency domain data to obtain fused array antenna data;

[0038] Step 2: Obtain the Riemann manifold of the covariance matrix set based on the fused array antenna data;

[0039] Step 3: Obtain the Riemannian geometric mean based on the Riemannian manifold of the covariance matrix set;

[0040] Step 4: Obtain the arrival direction of the desired signal source based on the steering vector and the Riemann geometry value.

[0041] In step one, (1) construct an array receiving signal observation model: determine the wave direction estimation scenario, and provide a receiving station observation signal model in an environment with interference and noise; the array signal reception model constructed by the present invention contains intermittent interference sources and noise, which poses a challenge to traditional DOA estimation. Being able to maintain the estimation accuracy of the wave direction in a complex environment with interference is a major problem that the present invention needs to solve; (2) use short-time Fourier transform (STFT) to process the received signal: through mathematical derivation and signal transformation processing, the present invention method converts the array receiving time domain data to the frequency domain for subsequent processing; (3) fuse the array antenna data to vectorize the received signal.

[0042] In step 2, (1) the covariance matrix of the data received by the array antenna is calculated: because the overall covariance is difficult to obtain and the computational complexity is high, the method of the present invention calculates the covariance matrix of the segmented samples; (2) the covariance matrix set is mapped to the Riemann manifold: based on the property that the covariance matrix has an Emitian positive definite matrix and the definition of the Riemannian geometric manifold, the Riemannian manifold of the covariance matrix set is constructed.

[0043] In step three, (1) the definition of the Riemannian geometric mean: based on the affine invariance of the metric and distance defined on the Riemannian manifold, the point with the smallest sum of distances from all points on the manifold is defined as the Riemannian mean; (2) solving the Riemannian geometric mean: first select the initial value of the iteration, based on which the Euclidean mean of the tangent plane is calculated, and then exponential mapping is performed to update the Riemannian mean, and determine whether the new Riemannian mean meets the convergence conditions. If so, the output is stopped, otherwise the iterative calculation continues.

[0044] In step 4, (1) the steering vector is calculated; (2) the objective function is calculated by combining the steering vector and the Riemann mean calculated in the previous step; (3) a spectrum peak search is performed on the objective function so that the angle at which the objective function is maximized is the direction of arrival of the desired signal source.

[0045] Specifically, the method comprises the following steps:

[0046] Step 101: Construct a model of array receiving signals in a complex environment.

[0047] (1) Construct an array receiving signal observation model.

[0048] like Figure 2 Schematic diagram of the wave direction estimation scenario. To simplify the description, this embodiment only considers estimating the one-dimensional wave direction of arrival angle in the two-dimensional plane. The same is true for the corresponding dimension of the three-dimensional plane. Assume that the receiving station is a linear array with M array elements. There are N in the far field of the receiving station. D There are stationary radiation sources of the desired signal, the number of radiation sources is N DIn unknown and complex signal scenarios, assuming an interference environment, the far field is accompanied by intermittent N I There are interference sources, which appear and disappear randomly, and the time of appearance and disappearance is unknown. The number is N I Unknown and not fixed. The signals radiated by each radiation source are unrelated to each other. The receiving station receives the signals radiated by the radiation source and processes them to estimate the angle of the radiation source.

[0049] Then the data received by the mth receiving antenna can be modeled as

[0050]

[0051] The number of sampling snapshots is N, n = 1, 2, ..., N, z m (n) is the data observed by the mth receiving antenna, Indicates the jth 1 A source of expectation, For the jth 2 interference source, v m (n) is the noise of the mth receiving antenna. We use represents the mth receiving antenna for the jth 1 The receiving steering vector of a desired source is the receiving response parameter of the antenna to the signal, which is mainly determined by the relative position relationship between the target radiation source and the receiving station. represents the mth receiving antenna for the jth 2 The receiving steering vector of the interference source. m is the number of the receiving antenna; n is the sampling snapshot number index value, indicating the nth sampling snapshot number; j 1 =1,2,…,N D is the expected signal index value, indicating the jth 1 Expected sources; N D is the expected number of radiation sources; j 2 =1,2,…,N I is the interference signal index value, indicating the jth 2 Interference sources; N I is the number of intermittent interference sources, d is the desired signal mark, and i is the interference signal mark.

[0052] The array signal receiving model constructed by the present invention includes intermittent interference sources and noise, which poses a challenge to traditional DOA estimation. Being able to maintain the estimation accuracy of the direction of arrival in a complex environment with interference is a major problem that the present invention needs to solve.

[0053] (2) Use short-time Fourier transform (STFT) to process the received signal.

[0054] The signal received by the antenna in formula (1) is segmented and STFT is performed. We use express STFT of the kth frequency in the lth window. and v m The symbols of (l,k) are also defined similarly. Then, the received signal z is given by m (n) The STFT of the kth frequency in the lth window is as follows:

[0055]

[0056] Among them, z m (l,k) is the frequency domain data of the array antenna, l is the window number, k is the frequency number, and m is the number of the receiving antenna. The expected signal The frequency domain representation of Receive the steering vector for the desired signal The frequency domain representation of Interference signal The frequency domain representation of Receive steering vector for interference signal The frequency domain representation of v m (l,k) is the noise term v m The frequency domain representation of (n), j 1 =1,2,…,N D is the expected signal index value, indicating the jth 1 There are expectation sources, N D is the expected number of radiation sources, j 2 =1,2,…,N I is the interference signal index value, indicating the jth 2 There are interference sources, N I is the number of intermittent interference sources, i is the interference signal mark, and d is the desired signal mark.

[0057] Here, we assume that the number of samples is large enough and the length of the window is much larger than the number of array elements M.

[0058] (3) Fuse the array antenna data to vectorize the received signal.

[0059] We take the signals z received from all antennas m (l,k) are put together to obtain a column vector z(l,k)∈￡ of the received signal M×1

[0060] z(l,k)=[z 1 (l,k),…,z M (l,k)] T (3)

[0061] Its vector form expression is

[0062] z(l,k)=H d (l,k)s d (l,k)+H i (l,k)s i (l,k)+v(l,k) (4)

[0063] Among them, z(l,k) is the fused array antenna data, l is the window number, k is the frequency number, Steering vector for the desired signal source The matrix representation of N D The matrix representation of the desired radiation source is: The interference source steering vector The matrix representation of N I The matrix representation of the interference signal is: is the matrix representation of the noise term, i is the interference signal sign, and d is the desired signal sign.

[0064] Among them, s d (l,k) and s i (l, k) represent the STFT vector representation of the desired source and the interference source, respectively, that is,

[0065]

[0066] The noise term in formula (4) is expressed as

[0067] v(l,k)=[v 1 (l,k),…,v M (l,k)] T (6)

[0068] The steering vectors from the jth desired source and the jth interference source to the receiving array antenna are

[0069]

[0070] So as to obtain the steering vector matrix

[0071]

[0072] In order to simplify writing, in the present invention, the frequency segment l is focused on and the frequency index k is omitted. This process is applicable to narrowband signals and simplifies the received signal z(l,k) to z(l).

[0073] So far, the present invention has established an observation model for receiving signals in a complex array environment. The goal of the proposed method is to receive data z(l) through the array, l = 1, 2, ..., L STFT, to estimate the direction to the desired source, where L STFT is the number of STFT segments. In complex environments, the interference source is located at an unknown position and may have a high signal power. The ability to maintain the accuracy of the expected signal source direction of arrival while having a strong anti-interference ability and the ability to suppress clutter is one of the key issues that the method of the present invention focuses on solving.

[0074] Step 102: construct a Riemann manifold through the received signal covariance matrix set.

[0075] In order to transform the problem of estimating the direction of arrival of the desired signal into a problem of Riemannian manifold representation, inspired by the basic theory of Riemannian geometry, the method of the present invention considers combining the received data with the Riemannian manifold construction, constructing a Riemannian manifold using the set of covariance matrices calculated from the array received data, and estimating the direction of arrival in a complex environment by taking advantage of Riemannian geometry.

[0076] (1) Calculate the covariance matrix set of the array antenna received data.

[0077] The array received signal is processed and the overall covariance matrix is ​​calculated as follows

[0078]

[0079] Where Γ is the population covariance matrix, To calculate the mean representation in Euclidean space, z(l) is the received signal and l is the window number.

[0080] In practical applications, the overall covariance is difficult to obtain, and it is usually replaced by calculating the sample covariance matrix. In order to simplify the calculation, the sample covariance matrix is ​​calculated on multiple STFT windows. use To estimate the overall covariance matrix Γ. We divide the STFT of the signal into L s disjoint segments, each consisting of L w The continuous STFT window composition, namely L STFT =L s ·L w Then, the sample covariance matrix on each segment is calculated as follows

[0081]

[0082] in, is the sample covariance matrix on the segment, L w is the number of frequency domain windows. 1 is the segment index. In order to obtain a covariance matrix of full rank, the length of each STFT window is set to be greater than the dimension of the matrix (i.e., the number of antenna array elements), satisfying L w≥M.

[0083] (2) Map the covariance matrix set to a Riemann manifold.

[0084] From formula (10), according to the spectral theorem, for the covariance matrix, it represents the variability and linear correlation of the data received by each antenna unit. Since the variance of a random variable is always non-negative, the diagonal elements of the covariance matrix (i.e., the variance of the variable) are non-negative. At the same time, the covariance between the data received by the antenna units reflects the linear relationship between the variables, and these element values ​​are also non-negative, unless the two variables are completely linearly correlated (in this case, the covariance is zero). Therefore, all eigenvalues ​​of the covariance matrix are at least non-negative. In practical applications, we consider that the desired signal, the interference source signal, and the noise signal are all uncorrelated with each other. Because the elements of the covariance describe the statistical properties of the actual antenna received signal, the covariance matrix is ​​usually positive definite.

[0085] In summary, the covariance matrix is ​​an Emitian positive definite matrix. According to the definition of Riemann manifold, the set of Emitian positive definite matrices can form a Riemann manifold. Here, the Riemann manifold constructed by the set of covariance matrices is defined as

[0086] Step 103: Solve the Riemannian geometric mean

[0087] (1) Explore the definition of the Riemannian geometric mean.

[0088] The affine invariance property shows that the metrics and distances defined on the manifold are usually affine invariant. Usually, two matrices Γ are defined on the manifold. 1 and Γ 2 The distance between

[0089]

[0090] where ||g|| F It means to find the F norm.

[0091] Assume that Γ is A point on the manifold, Then the tangent space of Γ is defined as a vector space, and this vector space can be regarded as a local approximation of the manifold around the point Γ. For the quasi-positive definite matrix manifold, each The surrounding tangent spaces all represent vector spaces of Hermitian matrices of dimension n×n.

[0092] Point Collection The Riemann mean Γ R It is defined as the Frechet mean, which is the minimum sum of the distances from all points on the manifold to this point, expressed as

[0093]

[0094] The above formula indicates that the point with the smallest sum of distances from all points on the manifold to this point is the Riemann mean Γ R .

[0095] (2) Solve the Riemannian geometric mean.

[0096] Generally speaking, the Riemann mean formed by two or more matrices cannot be solved by a closed-form expression, but can be calculated by a corresponding iterative algorithm. The steps of calculating the Riemann mean by the method of the present invention are as follows: Figure 3 shown.

[0097] like Figure 3 In the calculation process of the Riemann mean, we first calculate the Euclidean mean of K eimitic positive definite matrices as the initial value of the Riemann mean iteration, that is,

[0098]

[0099] Among them, Γ R is the Riemann mean, K is the number of sample covariance matrices, For the i 1 The sample covariance matrix, i 1 It is the segment index value and also the covariance index value.

[0100] Based on the initial value of the Riemann mean, first calculate the Euclidean mean of the tangent plane

[0101]

[0102] in,

[0103] Based on the Euclidean mean Further update of the Riemann mean in, represents the tangent space from Γ to the vector The exponential mapping of

[0104]

[0105] judge The F-norm Is it small enough? If it is smaller than the threshold, stop the iteration and output the mean. If it is not satisfied, go back to the second step and continue the iteration.

[0106] So far, we have established the Riemann manifold of the covariance matrix set and calculated the corresponding Riemann mean. In the next step, we will use the calculated Riemann mean to perform beamforming and estimate the arrival angle of the desired signal.

[0107] Step 104: Estimate the direction of arrival of the source by combining beam forming with Riemannian geometry.

[0108] Typically, the DoA estimate of the desired source is based on the output of a beamformer.

[0109] The present invention considers arbitrary indexing of antennas in the array and designates the first antenna of the array as the reference antenna. Let d(θ) denote the direction vector of the array relative to the first (reference) antenna to the direction θ, expressed as

[0110]

[0111] where φ m (θ) is the phase difference of the received signal of the mth antenna relative to the received signal of the first antenna. For uniform linear array index, calculate Where λ is the wavelength of the received signal and δ is the distance between the array antennas.

[0112] The objective function expression of the beamformer based on Euclidean space is:

[0113]

[0114] The Riemannian geometry is combined by transforming each covariance matrix is regarded as a point on the Emitian positive definite matrix manifold, and its Riemann mean is considered, denoted as It is expressed as:

[0115]

[0116] Based on the Riemann mean calculated in the previous step, Instead, the beamformer objective function of the joint Riemannian geometry is calculated

[0117]

[0118] in, is the objective function, d(θ) is the steering vector, is the Riemannian geometric mean, and θ is the angle of the expected signal.

[0119] The peak of the above objective function is searched, and the angle at which the objective function is the largest is The direction of arrival of the desired signal source

[0120]

[0121] In estimating N D In the case of N expected sources, according to the strongest N in the objective function D beams to estimate the source direction.

[0122] like Figure 1 The calculation process of the method of the present invention is shown in FIG.

[0123] Performance comparison analysis:

[0124] As a comparative analysis, we consider the traditional Euclidean space-based beamforming algorithm, which calculates the objective function based on the sample covariance matrix over the entire interval. That is, formula (16), where

[0125]

[0126] In the above formula is the Riemannian geometric mean The Euclidean counterpart of .

[0127] This embodiment assumes that the desired source is stationary and continuously radiates a single-carrier signal, while the interference source is intermittent. For this scenario, the above-mentioned Euclidean covariance matrix accumulates all sources, including the interference source. Therefore, the main lobe of the traditional Euclidean space-based beamforming algorithm may deviate from the direction of the desired source and focus on the direction of the interference source, which cannot accurately identify the desired signal source.

[0128] The Riemann mean of the method of the present invention attenuates intermittent interference while maintaining the desired signal source, so that no corresponding spectrum peak is formed in the direction of the interference source, no false capture occurs, and the desired signal is accurately identified. Figure 4 ,The simulation results show that compared with the traditional beamforming ,algorithm, the beamforming calculated by the method proposed in the ,presentation can achieve the effect of anti-interference.

[0129] By integrating the advantages of the Riemannian geometric mean, we do not need to calculate the rank of the covariance matrix in advance. Compared with the subspace algorithm, the method of the present invention does not need to pre-estimate the number of expected signal sources and interference sources, and does not need to perform the eigenvalue solution process of the covariance matrix, which reduces the cost of the direction of arrival estimation and improves the real-time performance of the direction of arrival calculation.

[0130] The DOA estimation method based on Riemannian geometry is suitable for a variety of scenarios due to its high accuracy and robustness in complex signal environments. The following are some potential application scenarios.

[0131] 1. Wireless communication systems: In mobile and cellular communications, smart antenna systems can use direction of arrival estimation technology to improve signal reception quality, reduce interference, and achieve spatial multiplexing, thereby increasing system capacity.

[0132] 2. Radar and sonar systems: In military and civilian radar systems, accurate direction of arrival estimation is essential for target detection, tracking and identification. Similarly, sonar systems also require accurate direction estimation capabilities for underwater communications and target detection.

[0133] 3. Multiple-Input Multiple-Output (MIMO) System: MIMO system can optimize channel estimation and signal transmission through direction of arrival estimation, thereby improving data rate and system reliability.

[0134] 4. Autonomous driving and automated navigation: In driverless cars and other autonomous systems, environmental perception and obstacle avoidance require accurate direction estimation technology for safe navigation.

[0135] 5. Satellite communications: In geosynchronous orbit or low-Earth orbit satellite communications, direction of arrival estimation can help the satellite point to the ground station more accurately and improve communication quality.

[0136] 6. Internet of Things (IoT) devices: With the surge in the number of IoT devices, the positioning and communication of these devices in urban and industrial environments require efficient direction estimation techniques to overcome multipath effects and signal obstruction problems.

[0137] 7. Biomedical imaging: In some biomedical imaging techniques, such as ultrasound imaging, direction estimation can be used to improve image resolution and penetration.

[0138] 8. Environmental monitoring: In atmospheric science and oceanographic research, directional estimation techniques can be used to monitor the diffusion paths of pollutants or ocean flow patterns.

[0139] These application scenarios highlight the broad potential value of DOA estimation methods based on Riemannian geometry in future communications, navigation, monitoring, and imaging technologies. With further development and optimization of the technology, these methods are expected to play an even more important role in practical systems.

[0140] Example

[0141] The embodiment adopts a stationary uniform linear array receiving station with M=12 array elements. The distance between adjacent sensors of each receiving station is half a wavelength. The direction of the desired radiation source is θ D =110°, interference radiation source direction θ I1 =50°θ I2 =150°, assuming that the desired radiation source and the interference radiation source are uncorrelated and both are located in the far field of the receiving station.

[0142] Assuming the signal-to-noise ratio SNR = 5 dB, the interference-to-signal ratio INR = 10 dB, the receiving station samples the received signal for K = 64 times, and obtains the beam spectrum of the method of the present invention and the traditional Euclidean spatial beamforming algorithm as follows: Figure 4As shown by Figure 4 It can be seen that the horizontal coordinate angle corresponding to the beam spectrum peak of the method of the present invention is 110°, that is, the estimated direction of arrival of the desired signal This is consistent with the actual desired source setting angle, verifying the accuracy of the direction of arrival estimation of the method of the present invention in the presence of interference.

[0143] like Figure 4 As shown in the figure, the method of the present invention is compared with the traditional Euclidean beamforming algorithm. It can be seen that under the same signal-to-noise ratio and interference-to-noise ratio conditions, the method of the present invention can accurately measure the direction of arrival of the desired source, while the traditional Euclidean beamforming algorithm forms beam spectrum peaks in the direction of both the desired source and the interference source. From the comparative analysis, it can be seen that the direction of arrival estimation method based on Riemannian geometry of the present invention has anti-interference ability and is superior to the traditional algorithm based on Euclidean space.

[0144] This embodiment also provides a wave direction estimation system based on Riemannian geometry, which includes: a first module, used to construct an array received signal observation model, use short-time Fourier transform on the array received signal observation model to obtain array antenna frequency domain data, and fuse the array antenna frequency domain data to obtain fused array antenna data; a second module, used to obtain the Riemann manifold of the covariance matrix set based on the fused array antenna data; a third module, used to obtain the Riemannian geometry mean based on the Riemannian manifold of the covariance matrix set; and a fourth module, used to obtain the wave direction of the desired signal source based on the steering vector and the Riemannian geometry mean.

[0145] This embodiment also provides an electronic device, including: a memory: used to store computer-readable instructions; and a processor: used to run the computer-readable instructions to execute a method for estimating a direction of arrival based on Riemannian geometry.

[0146] Compared with the traditional beamforming algorithm, the Riemann mean of this embodiment suppresses interference while maintaining the desired signal source, improves the accuracy of DOA estimation in complex signal environments, and enhances the robustness to multipath effects and signal coherence; this embodiment integrates the advantages of the Riemann geometric mean, does not need to calculate the rank of the covariance matrix in advance, and compared with the subspace algorithm, does not need to pre-estimate the number of desired signal sources and interference sources, and does not need to perform the eigenvalue solution process of the covariance matrix, which reduces the cost and computational complexity of the direction of arrival estimation and improves the real-time performance of the direction of arrival calculation; this embodiment combines the potential geometric characteristics of the Riemann manifold, and does not need to perform parameter matching when performing multi-dimensional angle estimation, which makes up for the deficiency of conventional algorithms that require parameter matching, simplifies the signal processing process by using Riemannian geometry theory, reduces the demand for computing resources, and has broad research significance.

[0147] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for estimating the direction of arrival based on Riemannian geometry, characterized in that include: An array receiving signal observation model is constructed, the array receiving signal observation model is subjected to short-time Fourier transform to obtain frequency domain data of array antennas, and the frequency domain data of array antennas are fused to obtain fused array antenna data; The Riemann manifold of the covariance matrix set is obtained according to the fused array antenna data; The Riemannian geometric mean is obtained according to the Riemannian manifold of the covariance matrix set; The arrival direction of the desired signal source is obtained based on the steering vector and Riemann geometry.

2. The method for estimating the direction of arrival based on Riemannian geometry according to claim 1, characterized in that: The array receiving signal observation model is obtained by the following formula: Among them, z m (n) is the data observed by the mth receiving antenna, represents the j1th expected source, is the j2th interference source, v m (n) is the noise of the mth receiving antenna, represents the receiving steering vector of the mth receiving antenna to the j1th desired source, represents the receiving steering vector of the mth receiving antenna to the j2th interference source, where m is the number of the receiving antenna, n is the sampling snapshot index value, j1 is the expected signal index value, and N D is the expected number of radiation sources, j2 is the interference signal index value, N I is the number of intermittent interference sources, d is the desired signal mark, and i is the interference signal mark.

3. The method for estimating the direction of arrival based on Riemannian geometry according to claim 1, characterized in that: The frequency domain data of the array antenna is obtained by the following formula: Among them, z m (l,k) is the frequency domain data of the array antenna, l is the window number, k is the frequency number, and m is the number of the receiving antenna. The expected signal The frequency domain representation of Receive the steering vector for the desired signal The frequency domain representation of Interference signal The frequency domain representation of Receive steering vector for interference signal The frequency domain representation of v m (l,k) is the noise term v m (n) is the frequency domain representation, j1 is the expected signal index value, N D is the expected number of radiation sources, j2 is the interference signal index value, N I is the number of intermittent interference sources, i is the interference signal mark, and d is the desired signal mark.

4. The method for estimating the direction of arrival based on Riemannian geometry according to claim 1, characterized in that: The fused array antenna data is obtained by the following formula: z(l,k)=H d (l,k)s d (l,k)+H i (l,k)s i (l,k)+v(l,k); Among them, z(l,k) is the fused array antenna data, l is the window number, k is the frequency number, H d (l,k) is The matrix representation of Receive the steering vector for the desired signal The frequency domain representation of s d (l,k) is N D The matrix representation of the desired radiation source, H i (l,k) is The matrix representation of To receive the steering vector for the interference signal The frequency domain representation of s i (l,k) is N I The matrix representation of the interference signal, v(l,k) is the matrix representation of the noise term, i is the interference signal sign, and d is the desired signal sign.

5. The method for estimating the direction of arrival based on Riemannian geometry according to claim 1, characterized in that: The Riemann manifold of the covariance matrix set obtained based on the fused array antenna data includes: Calculate the covariance matrix set of the fused array antenna data; Mapping the covariance matrix set to the Riemann manifold obtains the Riemann manifold of the covariance matrix set.

6. The method for estimating the direction of arrival based on Riemannian geometry according to claim 1, characterized in that: The arrival direction of the desired signal source obtained based on the steering vector and Riemann geometry includes: The objective function is obtained according to the steering vector and the Riemann geometry; The peak of the objective function is searched to obtain the angle that maximizes the objective function, which is the direction of arrival of the desired signal source.

7. The method for estimating the direction of arrival based on Riemannian geometry according to claim 6, characterized in that: The objective function is obtained by the following formula: in, is the objective function, d(θ) is the steering vector, is the Riemannian geometric mean, and θ is the angle of the expected signal.

8. The method for estimating the direction of arrival based on Riemannian geometry according to claim 6, characterized in that: The angle that maximizes the objective function is obtained by the following formula: in, is the maximum angle of the objective function, is the objective function, is the Riemannian geometric mean, and θ is the angle of the expected signal.

9. A direction of arrival estimation system based on Riemannian geometry, characterized in that include: The first module is used to construct an array receiving signal observation model, use short-time Fourier transform to obtain array antenna frequency domain data, and fuse the array antenna frequency domain data to obtain fused array antenna data; The second module is used to obtain the Riemann manifold of the covariance matrix set according to the fused array antenna data; The third module is used to obtain the Riemannian geometric mean according to the Riemannian manifold of the covariance matrix set; The fourth module is used to obtain the arrival direction of the desired signal source according to the steering vector and the Riemann geometry mean value.

10. An electronic device, characterized in that: include: Memory: used to store computer-readable instructions; and Processor: used to run the computer-readable instructions to perform the method according to any one of claims 1 to 8.

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