Non-Gaussian non-stationary signal detection method based on Riemannian manifold analysis
Through the Riemann manifold analysis method, the detector is constructed using the Gaussian window function and Riemann Gaussian distribution characteristics, which solves the problem of poor detection performance under the background of non-Gaussian non-stationary signals, and realizes efficient and universal signal detection.
Patent Information
- Application Number
- CN202510439640.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-09
- Publication Date
- 2025-07-22
AI Technical Summary
The existing signal detection methods have large performance losses in the context of non-Gaussian non-stationary signals, poor detection performance, and traditional methods are difficult to implement and have poor universality.
Using the Riemann manifold analysis method, the Hermitian positive definite matrix HPD manifold is constructed by receiving the signal and pre-processing it into a covariance matrix sequence using the Gaussian window function, and a generalized likelihood ratio detector is constructed using the Riemann Gaussian distribution characteristics to perform signal detection.
The detection performance is improved in the context of non-Gaussian non-stationary signals, the designed detector is universal, and the computing efficiency is improved through approximate optimization methods.
Smart Images
Figure CN120354046A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of signal detection, and specifically to a non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis. Background Art
[0002] The processing of non-Gaussian and non-stationary signals has always been a difficult problem in the field of signal processing. Most traditional signal detection methods are based on statistical hypothesis testing methods and design optimal detectors according to the Neyman-Pearson (NP) criterion. In Gaussian background noise, the matched filter is the optimal detector. However, signals in nature often do not have good stationarity, and at the same time, their statistical characteristics deviate from the Gaussian distribution. At this time, the optimal matched filter under Gaussian background will suffer great performance loss and the detection performance is poor. From the perspective of statistical models, the optimal detectors derived based on the probability density functions of non-Gaussian distributions often have relatively complex expressions and are difficult to implement in engineering; moreover, such methods need to be modeled separately for different scenarios and do not have universality. In order to propose a general signal detection method under the background of non-Gaussian and non-stationary signals, a feasible method is to consider the time-varying covariance structure of the signal, lift the detection problem to high-dimensional space for processing, and further explore its internal laws. Summary of the Invention
[0003] Aiming at the problem of poor detection performance of non-Gaussian and non-stationary signals in the background art, the present invention proposes a non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis, which solves the problems of large performance loss and poor detection performance of existing signal detection algorithms in the background noise of non-Gaussian and non-stationary signals. The technical solutions provided by the present invention are as follows:
[0004] A non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis includes the following steps:
[0005] Step 1, the receiver receives the signal to be detected and the reference noise signal, and preprocesses the signal into a covariance matrix sequence using a Gaussian window function;
[0006] Step 2, construct a Hermitian positive definite matrix HPD manifold, select the Fisher information matrix I(i,j) as the Riemannian metric on the HPD manifold, map the covariance matrix sequence to the HPD manifold, and obtain the RGD characteristics of the Riemannian Gaussian distribution using the parameter estimation method on the HPD manifold;
[0007] Step 3, according to the RGD characteristics on the HPD manifold, construct a generalized likelihood ratio detector based on the RGD characteristics, apply the detector to the covariance matrix sequence obtained by preprocessing the signal to be detected and the reference noise signal to obtain a detection statistic T, and compare the detection statistic T with a detection threshold η to make a detection decision.
[0008] Preferably, the specific process of step 1 is as follows:
[0009] In step 11, the signal received by the receiver is saved as a vector, denoted as x = [x(1), x(2),... x(T)] T ;
[0010] In step 12, a sequence of covariance matrices {Σ n , n = 1,..., N} is constructed, and the following parameters are selected: the time interval Δt of the covariance matrix, the sample accumulation time ΔT, and the dimension m of the covariance matrix;
[0011] In step 13, a Gaussian window function is constructed:
[0012]
[0013] This function is used to calculate the covariance matrix at time t = t0 + nΔt, where g is a scalar coefficient, and its vectorized representation is G = [G(1), G(2),... G(T)] T ;
[0014] In step 14, calculate y = x ⊙ G to obtain an m-dimensional covariance matrix as the element Σ of the covariance matrix sequence at time t = t0 + nΔt n .
[0015] Preferably, the specific process of step 2 is as follows:
[0016] In step 21, the Riemannian Gaussian distribution of the sample Y on the HPD manifold Its probability density function is expressed as:
[0017]
[0018] where represents the Riemannian mean, σ represents the Riemannian standard deviation, represents the normalization factor, and its expression is:
[0019]
[0020] where C m is a constant related only to the dimension m, r is the polar coordinate Y(r, U) of the sample Y on the HPD manifold, is a real vector space;
[0021] In step 22, the Riemannian mean is iteratively solved using the Riemannian mean solving algorithm;
[0022] In step 23, for the samples {Y n , n = 1, 2,..., N} that follow the Riemannian Gaussian distribution, the average Riemannian distance is defined
[0023] Step 24, solve for the Riemannian standard deviation by minimizing the likelihood function
[0024] Step 25, obtain the bijective relationship between σ and by numerical solution
[0025] Preferably, the Riemannian mean solving algorithm is as follows:
[0026] Input the sample set {Y n , n = 1, 2,..., N}, set the threshold ε; initialize the Riemannian mean I is the identity matrix;
[0027] Calculate the projection transformation between the HPD manifold and the tangent space, and the calculation formula is:
[0028]
[0029] where represents projecting the point Y on the HPD manifold i onto the tangent space at ; represents projecting the point V in the tangent space at onto the HPD manifold;
[0030] Repeat the calculation until ||V||2 < ε, and output the Riemannian mean at this time
[0031] Preferably, the specific process of solving the bijective relationship between σ and is as follows:
[0032] Set the derivative of the likelihood function to zero to obtain:
[0033] Preferably, the specific process of constructing the generalized likelihood ratio detector based on RGD in step 3 is as follows:
[0034] Step 31, construct a binary hypothesis testing problem:
[0035]
[0036] where H0 represents no target, H1 represents having a target, represents that the covariance matrix sequence of the reference noise signal follows a Riemannian distribution;
[0037] Step 32, estimate the Riemannian mean and Riemannian standard deviation of the covariance matrix sequence {Σ n , n = 1,..., N} of the signal to be detected according to the method in step 2
[0038] Step 33. According to the probability density expression of the RGD manifold in Step 21, based on the distribution of the reference noise signal and the RGD estimation result of the signal to be detected Construct an RGD-GLRT detector, and the detection statistic is
[0039]
[0040] Preferably, an approximate calculation method is proposed for the RGD-GLRT detector in Step 3 to construct an RGD-AGLRT detector, which is embodied as the weighted sum of the difference between the distance from the sample to the means of the two distributions and the difference between the average dispersion distances of the two distributions.
[0041] Preferably, the specific process of the approximate calculation method is as follows:
[0042] Use a linear function to approximate as
[0043] Approximate as where a, b, and B are linear coefficients;
[0044] The approximate simplified detection statistic is:
[0045] A computer-readable storage medium stores a computer program thereon, and when the program is executed by a processor, it implements the steps in the above-mentioned method for detecting non-Gaussian and non-stationary signals based on Riemannian manifold analysis.
[0046] A computer device includes a processor, a memory, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the steps in the above-mentioned method for detecting non-Gaussian and non-stationary signals based on Riemannian manifold analysis.
[0047] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:
[0048] The present invention is applicable to signal detection under non-Gaussian and non-stationary background noise. The covariance matrix estimation method adopted is to continuously intercept the signal using a Gaussian window function, thereby estimating a series of covariance matrix sequences, and thus mapping to a series of points on the manifold. Compared with the existing detection methods, this method comprehensively considers the non-Gaussianity of the signal and its underlying non-stationary characteristics.
[0049] The present invention takes into account that the variance of the Riemannian Gaussian distribution can be different, and proposes a likelihood ratio test method. The designed RGD-GLRT detector based on the Riemannian manifold is universal and general.
[0050] Based on the proposed likelihood ratio detector, considering the problem of difficult calculation, the present invention performs approximate optimization on it to obtain another easily calculable RGD-AGLRT detector, thereby greatly improving the detection efficiency. BRIEF DESCRIPTION OF THE DRAWINGS
[0051] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention, but do not constitute a limitation to the present invention. In the drawings:
[0052] Figure 1 is the overall flowchart of the method of the present invention;
[0053] Figure 2 is the radar echo amplitude time-distance image of the IPIX Grimsby dataset used in the embodiment of the present invention;
[0054] Figure 3 is the schematic diagram of data preprocessing using a Gaussian window function, the signal amplitude waveform diagram, and the autocorrelation function image;
[0055] Figure 4 is the relationship schematic diagram of the parameters σ, and in the RGD manifold;
[0056] Figure 5 is the numerical solution image of when the dimension is 2, 4, 6, 8;
[0057] Figure 6 is the numerical solution image of the function when the dimension is 2, 4, 6, 8;
[0058] Figure 7 is the ROC curve of the comparative test made between the method of the present invention and the comparative method under the IPIX Grimsby dataset. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0059] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.
[0060] Next, the technical solutions provided by the present invention will be described in detail in conjunction with the drawings and specific embodiments:
[0061] Embodiment 1:
[0062] In this embodiment, the IPIX dataset, a measured sea clutter dataset, is taken as an example to illustrate a non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis proposed by the present invention. The IPIX dataset is sea clutter data collected and sorted by the team of McMaster University in Canada using the IPIX radar in 1993 and 1998. Sea clutter is a typical non-Gaussian and non-stationary signal, whose statistical characteristics deviate from the Gaussian distribution and vary with time. The IPIX radar is a shore-based fully coherent X-band radar, which can simultaneously transmit and receive electromagnetic waves of horizontal polarization (H-polarization) and vertical polarization (V-polarization). Each dataset contains data of four polarization modes, namely HH, VV, HV, and VH, collected simultaneously. Figure 2 Shows the radar echo amplitude time-distance images of File 2, File 16, and File 40 of the IPIX Grimsby dataset used for illustration. The radar signal accumulation time of the dataset used is 60 s, the Pulse Repetition Frequency (PRF) is 1000, and there are 28 range gates in total. A data matrix of size 28×60000 can be obtained by reading the original data file. Among them, the target range gate of File 2 is 7, and the affected range gates are 6 and 8; the target range gate of File 16 is 24, and the affected range gates are 23 and 25; the target range gate of File 40 is 7, and the affected range gates are 6 and 8.
[0063] A non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis provided by the present invention, as Figure 1 shown, includes the following steps:
[0064] Step 1, the receiver receives the signal to be detected and the reference noise signal, and preprocesses the signal into a covariance matrix sequence using a Gaussian window function. The specific operation steps are as follows:
[0065] Step 11, save the signal received by the receiver as a vector, denoted as x = [x(1), x(2),... x(T)] T ;
[0066] In this embodiment, the signal accumulation time for each segment is selected as 2 s, the PRF is 1000 at the same time, and there are 2000 points in each sample.
[0067] Step 12, construct a covariance matrix sequence {Σ n , n = 1,..., N}, and select the following parameters: the time interval Δt of the covariance matrix, the sample accumulation time ΔT, and the dimension m of the covariance matrix;
[0068] In this embodiment, the time interval of the covariance matrix is selected as 0.05 s, that is, the covariance matrix is estimated every 50 points; the accumulation time used for the covariance matrix is 1 s, that is, for each element in the covariance matrix sequence, 1000 points are used to estimate it; the dimension of the covariance matrix is selected as 8.
[0069] Step 13, construct a Gaussian window function:
[0070]
[0071] This function is used to calculate the covariance matrix at the moment of \(t = t_0 + n\Delta t\), where \(g\) is a scalar coefficient, and its vectorized representation is \(G=[G(1),G(2),...G(T)]\) T ;
[0072] Suppose it is necessary to estimate the covariance matrix at the moment of \(t_0\). The specific expression of the window function at this moment is selected as:
[0073]
[0074] Step 14, calculate \(y = x\odot G\), and obtain the \(m\)-dimensional covariance matrix as the element \(\sum\) of the covariance matrix sequence at the moment of \(t = t_0 + n\Delta t\) n . Here, the autocorrelation function is used to construct the autocovariance matrix as the estimated value of the covariance matrix. For example, as Figure 3 shown. Figure 3 (a) is an example of the Gaussian window function used; Figure 3 (b) is the signal used to estimate the covariance matrix after preprocessing; Figure 3 (c) is its autocovariance function, and an 8-dimensional Toeplitz matrix is constructed using the autocovariance function as the estimated value of the covariance matrix at this moment.
[0075] Step 2, construct the Hermitian positive definite matrix HPD manifold, and select the Fisher information matrix \(I(i,j)\) as the Riemannian metric on the HPD manifold. The HPD manifold has the following properties:
[0076] For the HPD manifold Regarding it as the covariance matrix of a zero-mean complex Gaussian distribution, for a complex Gaussian distribution Regarding both \(\mu\) and \(C\) as functions of \(\xi\), select the Fisher information matrix as the Riemannian metric. The Fisher information matrix is \(I(\xi)\), and its \(ij\)-th element is:
[0077]
[0078] Since the sea clutter signals are all zero-mean, the second term in the above formula can be discarded and simplified to:
[0079]
[0080] The line element on the manifold is expressed as Then, for a point Y on the HPD manifold, the Riemannian metric thereon is expressed as: ds 2 (Y) = tr(Y -1 dY) 2 .
[0081] Suppose there are two points X and Y on the HPD manifold, and there is a differentiable curve c(t) connecting them, and c(0) = X and c(1) = Y. Then the length of c(t) can be defined as:
[0082]
[0083] The Riemannian distance between X and Y is obtained by taking the lower bound of the above formula:
[0084]
[0085] Taking the lower bound of the above formula gives the expression for the Riemannian distance:
[0086] d 2 (X, Y) = tr(X -1 Y) 2
[0087] The corresponding shortest curve is called a geodesic, and the expression is:
[0088] γ(t) = X -1 / 2 (X -1 / 2 YX -1 / 2 )tX 1 / 2 , t ∈ [0, 1].
[0089] The Riemannian volume element at a point Y on the HPD manifold is Using the method of eigenvalue decomposition, Y is represented in polar coordinates as Y(r, U) = U H diag[exp(r)]U; on the HPD manifold, for the function Integrating its Riemannian volume element dv[Y(r, U)] is expressed as:
[0090]
[0091] where C m is a constant related only to m.
[0092] Mapping the covariance matrix sequence to the HPD manifold, the RGD characteristics of the Riemannian Gaussian distribution are obtained by using the parameter estimation method on the HPD manifold. The specific process is as follows:
[0093] Step 21: Define the Riemannian Gaussian distribution on the HPD manifold Its probability density function is expressed as:
[0094]
[0095] Where denotes the Riemannian mean and σ denotes the Riemannian standard deviation.
[0096] denotes the normalization factor, and its derivation process is as follows:
[0097] Since the PDF needs to integrate to 1, we can obtain:
[0098]
[0099] For the congruence transformation under the action of the general linear group the HPD manifold has geometric invariant properties, which are manifested in the integral property as:
[0100]
[0101] So we can obtain:
[0102]
[0103] In polar coordinates, the integral transformation of the above formula is:
[0104]
[0105] The integral of the above formula is independent of U and can be simplified to:
[0106]
[0107] Step 22: For the Riemannian mean in the RGD manifold Use the Riemannian mean solving algorithm to iteratively solve it; before elaborating on the Riemannian mean solving algorithm, it is necessary to first specify the projection method between the HPD manifold and its tangent space. Use the exponential mapping and logarithmic mapping distributions to project points on the HPD manifold to its tangent space and project points on the tangent space to the HPD manifold. Their definitions are as follows:
[0108] L ogY (X) = Y 1 / 2 l og (Y -1 / 2 XY -1 / 2 )Y 1 / 2
[0109] E xpY (V) = Y 1 / 2 exp(Y -1 / 2 VY-1 / 2 )Y 1 / 2
[0110] Among them, Log Y (X) represents projecting a point X on the HPD manifold into the tangent space at point Y, and Exp Y (V) represents projecting a point V in the tangent space at point Y on the HPD manifold onto the HPD manifold.
[0111] The Riemann mean solving algorithm is summarized as follows:
[0112] Input the sample set {Y n , n = 1, 2,..., N}, and set the threshold ε;
[0113] Initialize the Riemann mean I is the identity matrix;
[0114] Repeatedly calculate the following formula:
[0115]
[0116] Until ||V||2 < ε, output the Riemann mean at this time
[0117] Step 33, for the samples {Y n , n = 1, 2,..., N} that follow the Riemann Gaussian distribution, define the average Riemann distance
[0118] Step 24, for the Riemann standard deviation σ, its likelihood function is:
[0119] Among them, the Riemann mean can already be calculated through the solving algorithm, so the Riemann standard deviation can be solved by minimizing the likelihood function
[0120] Step 25, obtain the bijective relationship between σ and through numerical solution for fast solution. The specific process is as follows:
[0121] To solve the minimization of the likelihood function, its derivative can be set to zero, thus obtaining:
[0122]
[0123] Regarding the relationship between σ, and is shown in Figure 4 .
[0124] For The calculation can obtain its numerical solution through the method of numerical integration. For the cases of dimensions 2, 4, 6, and 8, the images of the numerical solutions are shown in Figure 5 . Further, the bijective relationship between the numerically calculated σ and can be obtained, and the image is shown in Figure 6 .
[0125] Step 3: Based on the RGD characteristics on the HPD manifold, construct an RGD-based generalized likelihood ratio detector. Apply the detector to the covariance matrix sequence after preprocessing the received signal to obtain the detection statistic T. Compare the detection statistic T with the detection threshold η to make a detection decision.
[0126] Among them, the specific operation steps for constructing the RGD-based generalized likelihood ratio detector are as follows:
[0127] Step 31: Construct a binary hypothesis testing problem:
[0128]
[0129] Among them, H0 represents no target, and H1 represents having a target. indicates that the covariance matrix sequence of the reference noise signal follows a Riemannian distribution;
[0130] Step 32: Estimate the Riemannian mean and Riemannian standard deviation of the covariance matrix sequence {Σ n , n = 1,..., N} of the signal to be detected according to the method in Step 2.
[0131] Step 33: According to the probability density expression of the RGD manifold in Step 21, construct an RGD-GLRT detector based on the distribution of the reference noise signal and the RGD estimation result of the signal to be detected . The detection statistic is
[0132]
[0133] Furthermore, since the calculation of the parameters σ and is relatively difficult, this embodiment proposes an approximate calculation method, and then constructs an RGD-AGLRT detector, which is embodied as the weighted sum of the difference between the distance from the sample to the means of the two distributions and the difference between the average discrete distances of the two distributions. The specific process of the approximate calculation method is as follows:
[0134] Use a linear function to approximate as
[0135] Approximate as where a, b, and B are linear coefficients;
[0136] Substitute the approximate result into the formula in step 33, and the approximately simplified detection statistic is:
[0137]
[0138] For the preprocessed covariance matrix sequence {Σ n , n = 1, ..., N}, calculate the detection statistic T according to the RGD-AGLRT detector, determine the detection threshold η, and make a detection decision:
[0139] For the proposed RGD-AGLRT detector in this embodiment, compare the detection statistics calculated by it with those of the four methods of AR, MSR, KLD, and RD:
[0140] 1. The norm distance between the AR process coefficient of the signal to be detected and the reference noise signal;
[0141] 2. The KL divergence distance between the PDF of the signal to be detected and the PDF of the reference noise signal;
[0142] 3. The Riemannian distance between the overall covariance matrix of the signal to be detected and the overall covariance matrix of the reference noise signal;
[0143] 4. The average spectral radius of the signal to be detected.
[0144] The ROC curve is drawn using the results of the comparative experiment, as Figure 7 shown. The experimental results show that the proposed RGD-AGLRT detector has the best detection performance.
[0145] Embodiment 2: The computer-readable storage medium of this embodiment stores a computer program, and when the program is executed by a processor, it implements the steps in a non-Gaussian non-stationary signal detection method based on Riemannian manifold analysis in Embodiment 1.
[0146] The computer-readable storage medium of this embodiment can be the internal storage unit of the terminal, such as the hard disk or memory of the terminal; the computer-readable storage medium of this embodiment can also be the external storage device of the terminal, such as the plug-in hard disk, smart memory card, secure digital card, flash card, etc. equipped on the terminal; further, the computer-readable storage medium can also include both the internal storage unit and the external storage device of the terminal.
[0147] The computer-readable storage medium of this embodiment is used to store the computer program and other programs and data required by the terminal, and the computer-readable storage medium can also be used to temporarily store the data that has been output or will be output.
[0148] Embodiment 3: The computer device of this embodiment includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the method for detecting non-Gaussian non-stationary signals based on Riemannian manifold analysis in Embodiment 1.
[0149] In this embodiment, the processor may be a central processing unit, or may also be other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays, or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor, or the processor may also be any conventional processor, etc.; the memory may include a read-only memory and a random access memory, and provides instructions and data to the processor. A part of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.
[0150] Those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the above technical solution, in essence, or the part that contributes to the prior art can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.
[0151] The foregoing is only the preferred embodiment of the present invention and is not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.
Claims
1. A non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis, characterized in that Including the following steps: Step 1, the receiver receives the signal to be detected and the reference noise signal, and preprocesses the signals into a covariance matrix sequence using a Gaussian window function; Step 2, construct a Hermitian positive definite matrix HPD manifold, select the Fisher information matrix I(i,j) as the Riemannian metric on the HPD manifold, map the covariance matrix sequence onto the HPD manifold, and obtain the RGD characteristics of the Riemannian Gaussian distribution using a parameter estimation method on the HPD manifold; Step 3, based on the RGD characteristics on the HPD manifold, construct a generalized likelihood ratio detector based on the RGD characteristics, apply the detector to the covariance matrix sequence preprocessed from the signal to be detected and the reference noise signal to obtain a detection statistic T, compare the detection statistic T with a detection threshold η, and make a detection decision.
2. The non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis according to claim 1, characterized in that, The specific process of Step 1 is as follows: Step 11, save the signal received by the receiver as a vector, expressed as x = [x(1), x(2),... x(T)] T ; Step 12, construct a sequence of covariance matrices \(\{\Sigma_{ n}, n = 1,\cdots,N\}\), and select the following parameters: the time interval \(\Delta t\) of the covariance matrix, the sample accumulation time \(\Delta T\), and the dimension \(m\) of the covariance matrix; n ,n = 1,\cdots,N\}, select the following parameters: the time interval \(\Delta t\) of the covariance matrix, the sample accumulation time \(\Delta T\), and the dimension \(m\) of the covariance matrix; Step 13, construct a Gaussian window function: This function is used to calculate the covariance matrix at time \(t = t_0 + n\Delta t\), where \(g\) is a scalar coefficient, and its vectorized representation is \(G=[G(1),G(2),\cdots,G(T)]\). T ; Step 14, calculate y = x⊙G to obtain an m-dimensional covariance matrix as the element Σ of the covariance matrix sequence at the moment t = t0 + nΔt n .
3. A non-Gaussian non-stationary signal detection method based on Riemannian manifold analysis according to claim 2, characterized in that, The specific process of Step 2 is as follows: Step 21, the Riemannian Gaussian distribution of sample Y on the HPD manifold Its probability density function is expressed as: where denotes the Riemann mean, and σ denotes the Riemann standard deviation, denotes the normalization factor, and its expression is: where C m is a constant related only to dimension m, r is the polar coordinates Y(r, U) of sample Y on the HPD manifold, is a real vector space; Step 22, use the Riemannian mean solution algorithm to iteratively solve the Riemannian mean; Step 23, for samples {Y n , n = 1, 2, ..., N} that follow the Riemann Gaussian distribution, define the average Riemannian distance Step 24, solve for the Riemannian standard deviation by minimizing the likelihood function Step 25, obtain the bijective relationship between σ and by means of numerical solution 4. A non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis according to claim 3, characterized in that, The Riemannian mean solution algorithm is: Input sample set {Y n , n = 1, 2, ..., N}, set a threshold ε; initialize the Riemann mean I is the identity matrix; Calculate the projection transformation between the HPD manifold and the tangent space, and the calculation formula is: Among them represents projecting the point Y on the HPD manifold i onto the tangent space at; represents projecting the point V in the tangent space at onto the HPD manifold; Repeat the calculation until ||V||2 < ε, and output the Riemann mean at this time 5. A non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis according to claim 3, characterized in that The specific process of solving the bijective relationship between σ and is as follows: Set the derivative of the likelihood function to zero, and we get:
6. The non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis according to claim 3, characterized in that The specific process of constructing the generalized likelihood ratio detector based on RGD in Step 3 is as follows: Step 31, construct a binary hypothesis testing problem: Among them, H0 indicates no target, and H1 indicates there is a target. It indicates that the sequence of covariance matrices of the reference noise signals follows a Riemannian distribution. Step 32, estimate the Riemannian mean and Riemannian standard deviation of the covariance matrix sequence {Σ n , n = 1, ..., N} of the signal to be detected according to the method in Step 2 Step 33: According to the probability density expression of the RGD manifold in Step 21, based on the distribution of the reference noise signal and the RGD estimation result of the signal to be detected Construct an RGD-GLRT detector, and the detection statistic is 7. A non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis according to claim 6, characterized in that Propose an approximate calculation method for the RGD-GLRT detector in Step 3, and construct an RGD-AGLRT detector, which is embodied as the weighted sum of the difference between the distances from the sample to the means of the two distributions and the difference between the average dispersion distances of the two distributions.
8. A non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis according to claim 7, characterized in that The specific process of the approximate calculation method is as follows: Using a linear function, approximate as Approximate as where a, b, and B are linear coefficients; The approximately simplified detection statistic is as follows:
9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, it implements the steps in a non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis as described in any one of claims 1-8.
10. A computer device, comprising a processor, a memory, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in a non-Gaussian and non-stationary signal detection method based on Riemannian manifold analysis as described in any one of claims 1-8.