Multi-component real sinusoidal signal detection method based on autoregression noise model

Abstract

The invention discloses a multi-component real sinusoidal signal detection method based on an autoregressive noise model. The method comprises the following steps: calculating a detection threshold gamma of constant false alarm binary hypothesis testing; fitting the power spectral density of the received signal, estimating an autoregressive noise coefficient, and constructing an autoregressive noise model; a Rao detector based on an autoregressive noise model is used for the current received signal, and if the obtained test statistic is smaller than gamma, estimation is stopped; otherwise, judging that a target signal exists, and performing coarse estimation on the frequency by using a grid search method; using an alternating minimization-Newton iteration method to obtain accurate estimation values of the frequency, the amplitude and the phase of the target signal; and rejecting the current estimated target signal from the current received signal, and returning the obtained residual signal as a new received signal for estimation. According to the method, the multi-source detection capability and the estimation precision under a complex noise background are remarkably improved on the premise of keeping relatively low calculation complexity.

Description

Technical Field

[0001] This invention relates to the field of signal processing, and in particular to a method for detecting multi-component real sinusoidal signals based on an autoregressive noise model. Background Technology

[0002] In the line spectrum estimation problem of signal processing, a series of advanced line spectrum estimation methods, such as the Welch method, maximum likelihood estimation method, and matched filter (MF) method, have been widely used in practical engineering due to their high resolution and theoretical resolvability. However, these methods are generally based on a series of idealized assumptions, especially treating noise as independent and identically distributed zero-mean white noise. Therefore, while the detector exhibits good robustness in the detection of electromagnetic wave signals on land, its performance degrades significantly in marine acoustic scenarios. When a detector based on the zero-mean white Gaussian noise assumption is directly applied to the detection of marine ships, the correlation of environmental noise will form significant interference peaks in specific frequency bands, leading to a coupled deterioration effect of decreased detection probability and increased false alarm rate. In fact, in complex marine acoustic environments, in practical applications with significant electromagnetic interference or equipment non-idealities, noise cannot always be modeled as zero-mean white Gaussian noise.

[0003] Specifically, actual received noise often exhibits significant correlations, primarily due to: noise correlation caused by inter-array element coupling effects, spatially correlated background noise resulting from ocean temperature and salinity variations, non-whitening or non-stationary noise processes generated by the equipment itself, and spurious signal aliasing caused by structural reflections or boundary multipath effects. Therefore, simplifying noise to Gaussian white noise has significant limitations in line spectrum estimation and detection tasks in marine environments, making the development of spectral detectors capable of effectively handling environmental noise correlations crucial.

[0004] In recent years, to address challenges such as insufficient signal coherence and snapshot quantity, novel methods such as sparse reconstruction and compressed sensing have emerged, demonstrating good robustness under low-sample conditions. However, these methods often default to white noise or highly simplified noise models in their model assumptions, making it difficult to effectively model and suppress correlated Gaussian noise in real-world environments. Therefore, it is urgent to structurally extend traditional subspace algorithms by introducing more universal noise modeling mechanisms, integrating spatiotemporal spectrum estimation methods, and adopting adaptive optimization strategies to improve the performance and robustness of signal detection systems under complex correlated Gaussian noise environments (especially under non-ideal conditions). Summary of the Invention

[0005] To address the problem of degraded detection and estimation quality in existing methods under low signal-to-noise ratio (SNR) environments, this invention proposes a multi-component real sinusoidal signal detection method based on an autoregressive noise model.

[0006] The specific technical solution is as follows:

[0007] A method for detecting multi-component real sinusoidal signals based on an autoregressive noise model includes the following steps:

[0008] S1: Set the false alarm rate and calculate the detection threshold for binary hypothesis testing based on the constant false alarm stopping criterion based on the chi-square threshold.

[0009] S2: Fit the power spectral density of the received signal to estimate the autoregressive noise figure and construct an autoregressive noise model;

[0010] S3: Apply a Rao detector based on an autoregressive noise model to the current received signal. If the obtained test statistic is greater than or equal to the detection threshold, it is determined that there is a target signal in the current received signal, and S4-S6 are continued; otherwise, the estimation process is terminated and all target signals are output; the target signal is the strongest sinusoidal signal in the current received signal.

[0011] S4: Use the grid search method to make a coarse estimate of the target signal frequency;

[0012] S5: Using the alternating minimization-Newton iteration method, accurate estimates of the target signal frequency, amplitude, and phase are obtained;

[0013] S6: Remove the currently estimated target signal from the current received signal, use the resulting residual signal as the new received signal, and return to S2.

[0014] Furthermore, in S1, the binary hypothesis testing problem based on the constant false alarm rate stopping criterion is: under the null hypothesis condition... Under the following conditions, the received signal equals the noise signal; under the alternative assumption... The received signal includes multiple sinusoidal signal components and noise signals, where each sinusoidal signal component has its own amplitude, frequency and phase parameters;

[0015] The Rao detector is a constant false alarm rate detector, and the detection threshold γ is the quantile value of the chi-square distribution with 2 degrees of freedom at a given false alarm rate.

[0016] The asymptotic probability density function of the Rao detector test statistic is: under the null hypothesis, it follows a chi-square distribution with 2 degrees of freedom; under the alternative hypothesis, it follows a non-centered chi-square distribution.

[0017] Further, in S2, the power spectral density of the received signal is fitted using the Yule-Walker equation to obtain an estimated autoregressive noise figure, which includes autoregressive coefficients and noise variance.

[0018] Based on the estimated autoregressive noise coefficient, construct p AR The autoregressive noise model of order 1 is: the current noise sample is equal to the sum of the linear weighted sum of the past p noise samples and the sum of the Gaussian white noise samples; where the linear weighting coefficients are the autoregressive coefficients.

[0019] Furthermore, the autoregressive noise figure includes autoregressive coefficients and noise variance. In S3, the test statistic of the Rao detector is calculated through equivalent time-domain operations, specifically: First, the received signal, a complex exponential reference signal, and a real cosine reference signal are filtered using the autoregressive coefficients estimated in S2, respectively; then, the cross-correlation between the filtered received signal and the filtered complex exponential reference signal is calculated, and the square of its magnitude is taken as the numerator; the denominator is the energy of the filtered real cosine reference signal, and it is normalized using the noise variance estimated in S2; the maximum value of the test statistic calculated at different frequency points is taken as the final detection statistic.

[0020] Furthermore, in step S4, the grid search method is used to coarsely estimate the frequency of the target signal as follows:

[0021] Within a preset frequency range, the search grid density is set to be inversely proportional to the signal length; the test statistic corresponding to each grid frequency point is calculated sequentially; the maximum value of the test statistic among all grid frequency points is compared with the detection threshold: if the maximum value is greater than or equal to the detection threshold, it is determined that there is a target signal in the current received signal, and the horizontal axis corresponding to the maximum value is taken as the coarse estimate of the target signal frequency.

[0022] Furthermore, in S5, the core of the alternating minimization-Newton iteration method lies in constructing and minimizing a cost function for signal parameters and noise parameters to measure the fitting error between the received signal and the currently estimated signal model; and using Newton's method to optimize the cost function to refine the frequency estimation.

[0023] The received signal includes a sinusoidal component and autoregressive noise. The autoregressive noise coefficient includes an autoregressive coefficient and a noise variance. The cost function is a function of the following four variables: the autoregressive coefficient, two intermediate parameters related to the amplitude and phase of the sinusoidal signal, and the frequency of the target signal to be estimated.

[0024] Furthermore, in step S5, the accurate estimate of the target signal frequency is obtained using the alternating minimization-Newton iteration method, specifically through the following sub-steps:

[0025] (5.1) Based on the coarse estimate of the target signal frequency obtained in S4, calculate the cost function required by the alternating minimization-Newton iteration method. The cost function is a least squares problem relative to the merging parameter vector b, specifically the ratio of the received signal vector x to the design matrix. The square of the Euclidean norm of the sum of the products of the merged parameter vector b; the optimal merged parameter vector solution that minimizes the cost function is obtained, and its value is the negative of the product of the pseudo-inverse of the design matrix and the received signal vector; the merged parameter vector to be optimized includes a set of autoregressive coefficients and two intermediate parameters related to the amplitude and phase of the sinusoidal signal.

[0026] (5.2) Fix other parameters: Substitute the obtained optimal merging parameter vector into the cost function, use the first and second derivatives of the cost function at the current frequency point to determine the search direction and step size, and obtain the frequency correction amount; subtract the frequency correction amount from the current frequency estimate to obtain the updated frequency estimate.

[0027] (5.3) Determine whether the updated frequency estimate has converged. If not, repeat steps (5.1)-(5.2); if yes, end the iteration loop and obtain the accurate estimate of the target signal frequency.

[0028] Furthermore, in step S5, obtaining accurate estimates of the target signal amplitude and phase is specifically achieved through the following sub-steps:

[0029] In the process of calculating the accurate estimate of the target signal frequency, a set of optimal solutions containing autoregressive coefficients and other relevant parameters is obtained by least squares; from the optimal solution, the estimates of two key intermediate variables are extracted, wherein the first intermediate variable estimate is proportional to the product of the signal amplitude and the phase cosine value, and the second intermediate variable estimate is proportional to the negative product of the signal amplitude and the phase sine value.

[0030] The precise estimate of the target signal's amplitude is obtained by calculating the square root of the sum of the squares of the first and second intermediate variable estimates; the precise estimate of the target signal's phase is obtained by calculating the arctangent of the ratio of the inverse of the second intermediate variable estimate to the first intermediate variable estimate.

[0031] Furthermore, the received signal is the sum of a target signal component, a composite term including the remaining unprocessed sinusoidal signal component and background noise;

[0032] In step S6, the target signal is estimated by using the accurate estimates of the target signal frequency, amplitude and phase obtained in step S5; the target signal is estimated by using the OMP principle to remove the target signal from the current received signal: in the time domain, the target signal component is subtracted point by point from the original received signal sequence to obtain a new signal sequence, i.e., the residual signal.

[0033] The residual signal is used as the new round of received signal to be processed, and the target signal in it is estimated until no new sinusoidal signal can be detected in the received signal, that is, it does not contain the target signal and only contains background noise, and the iteration ends.

[0034] The beneficial effects of this invention are:

[0035] (1) This invention introduces an autoregressive noise model to model the noise signal, which makes the structure of the noise better represented and significantly enhances the algorithm's adaptability in complex noise environments.

[0036] (2) This invention combines Rao detector for coarse frequency estimation and alternating minimization-Newton iteration method to optimize target signal parameters, achieving high-precision sinusoidal signal parameter estimation with low computational complexity, overcoming the problem of insufficient accuracy of traditional matching pursuit method.

[0037] (3) The present invention uses a constant false alarm stopping criterion based on chi-square threshold, which can determine the number of target signals without pre-setting the number of target signals, thus avoiding the shortcomings of traditional methods that require pre-setting the number of sources or relying on threshold estimation. Attached Figure Description

[0038] Figure 1 This is a flowchart of a multi-component real sinusoidal signal detection method based on an autoregressive noise model in an embodiment of the present invention.

[0039] Figure 2 The diagram shows a comparison of the simulated detection performance of the present invention and other detection estimation algorithms when there are multiple signal components. (a) is the simulated detection performance result of the method of the present invention, and (b) is the simulated detection performance result of the matched filter method.

[0040] Figure 3 The diagram shows a comparison of the simulated detection performance of the present invention and other detection estimation algorithms when only one signal component remains. (a) is the simulated detection performance result of the method of the present invention, and (b) is the simulated detection performance result of the matched filter method.

[0041] Figure 4 The diagram shows a comparison of the simulation detection performance of the present invention and other detection estimation algorithms when only noise remains. In this diagram, (a) is the simulation detection performance result of the method of the present invention, and (b) is the simulation detection performance result of the matched filter method.

[0042] Figure 5 This is a performance comparison chart of the present invention and other detection and estimation algorithms under actual test data. Detailed Implementation

[0043] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The objectives and effects of the present invention will become clearer as a result. The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0044] This invention proposes a multi-component real sinusoidal signal detection method based on an autoregressive noise model, aiming to solve the problem of degraded detection and estimation quality in conventional matched filtering methods under low signal-to-noise ratio environments. This invention models background noise as an autoregressive noise model to better utilize the noise structure in the estimation and detection processes. Furthermore, the algorithm is used for coarse estimation with a Rao detector, which can be accelerated using Fast Fourier Transform (the calculation of the test statistic will be discussed later), reducing computational complexity and improving the speed of coarse frequency estimation. Simultaneously, the alternating minimization-Newton iteration method is used to improve the accuracy of the estimated parameters, avoiding bias caused by grid effects. Then, the OMP criterion is used to remove detected signal components from the received signal, and the residual energy is calculated for the next iteration. In addition, the algorithm uses a constant false alarm rate stopping criterion based on a chi-square threshold, eliminating the need to preset the number of signals, thus avoiding the shortcomings of traditional methods that require preset source numbers or rely on threshold estimation, improving the algorithm's universality and application flexibility.

[0045] like Figure 1 As shown, a method for detecting multi-component real sinusoidal signals based on an autoregressive noise model includes the following steps:

[0046] S1: Set the false alarm rate (FAR) and calculate the detection threshold γ for the binary hypothesis test based on the constant false alarm rate stopping criterion.

[0047] The constant false alarm rate binary hypothesis testing problem is specifically represented as:

[0048]

[0049] In the formula, Indicates observation noise. Indicates the target signal component; The null hypothesis means that the received signal contains only observation noise. The alternative assumption is that the received signal contains both the target signal and observation noise.

[0050] The asymptotic probability density function of the Rao detector test statistic is:

[0051]

[0052] In the formula, This represents a chi-square distribution with 2 degrees of freedom and 0 non-central parameters. Let represent a chi-square distribution with 2 degrees of freedom and a non-central parameter λ.

[0053] As can be seen from the above formula, the Rao detector is a constant false alarm rate (CFAR) detector. Therefore, given a false alarm rate P... FA The detection threshold can be obtained as follows: , Let be the inverse right-tail probability function of the chi-square distribution.

[0054] S2: Fit the power spectral density (PSD) of the signal under test (received signal in this embodiment) to estimate the autoregressive (AR) noise figure and construct an autoregressive noise model; the autoregressive noise figure includes the autoregressive coefficient. (k=1,2,3,…,p) AR ) and noise variance p AR This represents the order of the autoregressive noise model. Specifically, it is achieved through the following operations:

[0055] p AR The general expression for an autoregressive noise model of order 1 is:

[0056]

[0057] In the formula, The autoregressive noise coefficient is unknown. This indicates that the mean is 0 and the variance is 0. Gaussian white noise.

[0058] Calculate the received signal The power spectral density is calculated using the following formula:

[0059]

[0060] In the formula, N is the length of the currently received signal, and f is the normalized frequency.

[0061] The power spectral density of the received signal was analyzed using the Yule-Walker equation. By performing a fitting, the estimated autoregressive noise coefficient is obtained. ,in, To estimate the obtained autoregressive coefficients, To estimate the noise variance, an autoregressive noise model is constructed based on the estimated autoregressive noise coefficients.

[0062] S3: Apply a Rao detector based on an autoregressive noise model to the currently received signal and compare the obtained test statistic with the detection threshold. If the test statistic is greater than or equal to the detection threshold, it is determined that a target signal exists in the currently received signal, and S4-S7 are continued; if the test statistic is less than the detection threshold, it is determined that the currently received signal contains only noise, the estimation process is terminated, and all target signals and their related parameters (frequency, amplitude, phase) are output.

[0063] The test statistic of the Rao detector based on the autoregressive noise model can be specifically expressed as:

[0064]

[0065]

[0066]

[0067] In the formula, M is the noise covariance matrix constructed based on the autoregressive coefficients; M is the signal steering matrix, which consists of two column vectors: the first column consists of the cosine function value of the product of an increasing integer sequence and the frequency to be detected, and the second column consists of the sine function value of the product of an increasing integer sequence and the frequency to be detected. The detection signal vector is composed of a series of time sampling points of the signal to be measured, arranged sequentially.

[0068] In actual calculations, due to Since it is an N×N matrix, it is difficult to invert. This invention simplifies the Rao detector described above, and the expression is:

[0069]

[0070]

[0071]

[0072] in, .

[0073] The test statistic is calculated using a Rao detector on the currently received signal. Specifically, in this embodiment, a grid search method is used for calculation: at the frequency... Draw a grid at the specified location with a grid density of 1. Found by grid search maximum value This is the test statistic calculated by the detector.

[0074] Will Compare with the test threshold γ calculated by S1: If If so, it is determined that there is a sinusoidal signal component that meets the requirements in the currently received signal, and S4-S7 are continued; if If the current received signal contains only noise and no sine wave component that meets the requirements can be detected, the estimation process is terminated and all target signals and their related parameters are output.

[0075] To achieve multi-component real sinusoidal signal estimation, this method employs a greedy estimation strategy. In each detection loop, only the sinusoidal signal component with the strongest current energy that meets the requirements is considered the target signal to be detected, while the remaining sinusoidal signal components are treated as noise. Therefore, in each loop, the received signal model can be expressed as:

[0076]

[0077] In the formula, the first term is the target signal, and the second term is the remaining sinusoidal signal components plus background noise.

[0078] S4: Use the grid search method to make a coarse estimate of the target signal frequency.

[0079] The coarse frequency estimation process can be expressed as: if In S3 The corresponding horizontal axis represents a rough estimate of the target signal's frequency. .

[0080] S5: Using the alternating minimization-Newton iteration method, obtain accurate estimates of the target signal's frequency, amplitude, and phase. This is achieved through the following sub-steps:

[0081] (5.1) Calculate the cost function required by the alternating minimization-Newton iteration method, its expression is:

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] In the formula, x is the received signal vector, and x[p] corresponds to the value of the received signal at the p-th sampling time (p is the index); , which is the set of autoregressive coefficients; This is the frequency estimate for this iteration, with the initial value being the coarse frequency estimate. .

[0090] Take p in the above formula AR Therefore, the cost function can be rewritten as:

[0091]

[0092]

[0093] (5.2) After obtaining the cost function, the alternating minimization-Newton iteration method is performed. The specific process is as follows:

[0094] The least squares solution for b is obtained using the least squares method:

[0095]

[0096] Fixed b=b + By using Newton's method to differentiate the cost function with respect to f0, the first derivative is obtained. for:

[0097]

[0098] Second derivative result (Curvature) is:

[0099]

[0100]

[0101] The coarse frequency estimate is refined using Newton's method to obtain the optimized target signal frequency. for:

[0102]

[0103] (5.3) Using the optimized target signal frequency as the new coarse estimate, repeat steps (5.1)-(5.2) until the preset maximum number of iterations is reached, then end the iteration and obtain the fine estimate of the target signal frequency. and Detailed estimate This design improves accuracy through multiple iterative cycles.

[0104] (5.4) After the iterative optimization is completed, the amplitude and phase of the signal are estimated, as follows:

[0105] After obtaining the alternating minimization-Newton iteration method, we get optimal solution Thus, the autoregressive coefficients are obtained. as well as , The precise estimate of the value is then obtained, and thus the solution is obtained. and precise estimate , The precise estimates of the target signal's amplitude and phase are obtained through linear transformation, i.e.:

[0106]

[0107] In the formula, This is a precise estimate of the target signal amplitude. This is a precise estimate of the phase of the target signal.

[0108] S6: Using the OMP principle, remove the currently estimated target signal from the current received signal to obtain the residual signal, and use it as the new received signal. Return to execute S2 to start a new round of signal detection. The specific process is as follows:

[0109] After estimating the relevant parameters of the target signal Then, by subtracting the target signal from the time domain portion of the currently received signal, the residual signal can be obtained, i.e.:

[0110]

[0111] Will Treating it as a new received signal, continue processing S2 to S6 on the received signal until all sinusoidal signal components have been detected and estimated, leaving only background noise.

[0112] This invention utilizes simulation and marine field measurement data for testing, and compares it with the generalized matched filtering method and the FFT method.

[0113] Figure 2 To illustrate the simulation data detection, the target parameters are defined as follows:

[0114] Two receive signals are set. The parameters of signal one are set as follows: amplitude A=1, frequency f0=0.1Hz, and phase... The parameters for signal two are set as follows: amplitude A = 0.5, frequency f0 = 0.3 Hz, and phase... Set the order p of the autoregressive noise model. AR =2, the autoregressive coefficient and noise variance are... False alarm rate P FA =10 -4 Therefore, the detection threshold γ = 13.8155 was calculated. Figure 2The diagram shows the simulation results of two received signals using the method of this invention and the existing matched filter method. The comparison shows that under low signal-to-noise ratio conditions, the traditional matched filter method can no longer accurately detect and estimate the signal frequency; while the Rao detector used in this invention effectively suppresses noise interference by utilizing the mathematical structure of noise, successfully detecting the two target signals, and can autonomously terminate the detection process when the test statistic is less than the detection threshold.

[0115] Figure 3 This chart compares the performance of the proposed method with traditional matched filter and FFT methods under actual marine noise conditions. The measured data includes a simulated signal with a frequency of f0 = 210 Hz, and the signal-to-noise ratio gradually decreases as the signal length increases (i.e., over time). Figure 3 It can be seen that the method of the present invention has a significantly better detection effect than the matched filter method and the FFT method under low signal-to-noise ratio.

[0116] This invention, by introducing an autoregressive noise model, alternating minimization-Newton iterative optimization, and a constant false alarm rate (CFAR) iterative stopping criterion, maintains low computational complexity while suppressing the influence of noise correlation and improving estimation accuracy. This significantly enhances the robustness and practicality of detecting multiple sinusoidal signals in complex environments. Simulation and experimental results both demonstrate that this invention has higher detection accuracy and better adaptability to correlated Gaussian noise compared to existing methods.

[0117] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for detecting multi-component real sinusoidal signals based on an autoregressive noise model, characterized in that, Includes the following steps: S1: Set the false alarm rate and calculate the detection threshold for binary hypothesis testing based on the constant false alarm stopping criterion based on the chi-square threshold. S2: Fit the power spectral density of the received signal to estimate the autoregressive noise figure and construct an autoregressive noise model; S3: Apply a Rao detector based on an autoregressive noise model to the current received signal. If the obtained test statistic is greater than or equal to the detection threshold, it is determined that there is a target signal in the current received signal, and S4-S6 are continued; otherwise, the estimation process is terminated and all target signals are output; the target signal is the strongest sinusoidal signal in the current received signal. S4: Use the grid search method to make a coarse estimate of the target signal frequency; S5: Using the alternating minimization-Newton iteration method, accurate estimates of the target signal frequency, amplitude, and phase are obtained; S6: Remove the currently estimated target signal from the current received signal, use the resulting residual signal as the new received signal, and return to S2.

2. The method for detecting multi-component real sinusoidal signals based on an autoregressive noise model according to claim 1, characterized in that, In S1, the binary hypothesis testing problem based on the constant false alarm rate stopping criterion is: under the null hypothesis condition... Under the following conditions, the received signal equals the noise signal; under the alternative assumption... The received signal includes multiple sinusoidal signal components and noise signals, where each sinusoidal signal component has its own amplitude, frequency and phase parameters; The Rao detector is a constant false alarm rate detector, and the detection threshold γ is the quantile value of the chi-square distribution with 2 degrees of freedom at a given false alarm rate. The asymptotic probability density function of the Rao detector test statistic is: under the null hypothesis, it follows a chi-square distribution with 2 degrees of freedom; under the alternative hypothesis, it follows a non-centered chi-square distribution.

3. The method for detecting multi-component real sinusoidal signals based on an autoregressive noise model according to claim 1, characterized in that, In step S2, the power spectral density of the received signal is fitted using the Yule-Walker equation to obtain the estimated autoregressive noise figure, which includes the autoregressive coefficient and the noise variance. Based on the estimated autoregressive noise coefficient, construct p AR The autoregressive noise model of order 1 is: the current noise sample is equal to the sum of the linear weighted sum of the past p noise samples and the sum of the Gaussian white noise samples; where the linear weighting coefficients are the autoregressive coefficients.

4. The method for detecting multi-component real sinusoidal signals based on an autoregressive noise model according to claim 1, characterized in that, The autoregressive noise figure includes autoregressive coefficients and noise variance. In S3, the test statistic of the Rao detector is calculated through equivalent time-domain operations, specifically: First, the received signal, a complex exponential reference signal, and a real cosine reference signal are filtered using the autoregressive coefficients estimated in S2; then, the cross-correlation between the filtered received signal and the filtered complex exponential reference signal is calculated, and the square of its magnitude is taken as the numerator; the denominator is the energy of the filtered real cosine reference signal, which is normalized using the noise variance estimated in S2; the maximum value of the test statistic calculated at different frequency points is taken as the final detection statistic.

5. The method for detecting multi-component real sinusoidal signals based on an autoregressive noise model according to claim 1, characterized in that, In step S4, the grid search method is used to coarsely estimate the frequency of the target signal, as follows: Within a preset frequency range, the search grid density is set to be inversely proportional to the signal length; the test statistic corresponding to each grid frequency point is calculated sequentially; the maximum value of the test statistic among all grid frequency points is compared with the detection threshold: if the maximum value is greater than or equal to the detection threshold, it is determined that there is a target signal in the current received signal, and the horizontal axis corresponding to the maximum value is taken as the coarse estimate of the target signal frequency.

6. The method for detecting multi-component real sinusoidal signals based on an autoregressive noise model according to claim 1, characterized in that, In S5, the core of the alternating minimization-Newton iteration method is to construct and minimize a cost function for signal parameters and noise parameters to measure the fitting error between the received signal and the currently estimated signal model; and to use Newton's method to optimize the cost function to refine the frequency estimation. The received signal includes a sinusoidal component and autoregressive noise. The autoregressive noise coefficient includes an autoregressive coefficient and a noise variance. The cost function is a function of the following four variables: the autoregressive coefficient, two intermediate parameters related to the amplitude and phase of the sinusoidal signal, and the frequency of the target signal to be estimated.

7. The method for detecting multi-component real sinusoidal signals based on an autoregressive noise model according to claim 6, characterized in that, In step S5, the accurate estimate of the target signal frequency is obtained using the alternating minimization-Newton iteration method, specifically through the following sub-steps: (5.1) Based on the coarse estimate of the target signal frequency obtained in S4, calculate the cost function required by the alternating minimization-Newton iteration method. The cost function is a least squares problem relative to the merging parameter vector b, specifically the ratio of the received signal vector x to the design matrix. The square of the Euclidean norm of the sum of the products of the merged parameter vector b; the optimal merged parameter vector solution that minimizes the cost function is obtained, and its value is the negative of the product of the pseudo-inverse of the design matrix and the received signal vector; the merged parameter vector to be optimized includes a set of autoregressive coefficients and two intermediate parameters related to the amplitude and phase of the sinusoidal signal. (5.2) Fix other parameters: Substitute the obtained optimal merging parameter vector into the cost function, use the first and second derivatives of the cost function at the current frequency point to determine the search direction and step size, and obtain the frequency correction amount; subtract the frequency correction amount from the current frequency estimate to obtain the updated frequency estimate. (5.3) Determine whether the updated frequency estimate has converged. If not, repeat steps (5.1)-(5.2); if yes, end the iteration loop and obtain the accurate estimate of the target signal frequency.

8. The method for detecting multi-component real sinusoidal signals based on an autoregressive noise model according to claim 7, characterized in that, In step S5, obtaining accurate estimates of the target signal amplitude and phase is achieved through the following sub-steps: In the process of calculating the accurate estimate of the target signal frequency, a set of optimal solutions containing autoregressive coefficients and other relevant parameters is obtained by least squares; from the optimal solution, the estimates of two key intermediate variables are extracted, wherein the first intermediate variable estimate is proportional to the product of the signal amplitude and the phase cosine value, and the second intermediate variable estimate is proportional to the negative product of the signal amplitude and the phase sine value. The precise estimate of the target signal's amplitude is obtained by calculating the square root of the sum of the squares of the first and second intermediate variable estimates; the precise estimate of the target signal's phase is obtained by calculating the arctangent of the ratio of the inverse of the second intermediate variable estimate to the first intermediate variable estimate.

9. The method for detecting multi-component real sinusoidal signals based on an autoregressive noise model according to claim 1, characterized in that, The received signal is the sum of a target signal component, a composite term including the remaining unprocessed sinusoidal signal component and background noise; In step S6, the target signal is estimated by using the accurate estimates of the target signal frequency, amplitude and phase obtained in step S5; the target signal is estimated by using the OMP principle to remove the target signal from the current received signal: in the time domain, the target signal component is subtracted point by point from the original received signal sequence to obtain a new signal sequence, i.e., the residual signal. The residual signal is used as the new round of received signal to be processed, and the target signal in it is estimated until no new sinusoidal signal can be detected in the received signal, that is, it does not contain the target signal and only contains background noise, and the iteration ends.

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