A frequency domain sensing method for pulse signals based on narrowband feature extraction

Abstract

This invention provides a pulse signal frequency domain sensing method based on narrowband feature extraction. The method first initializes the sensing parameters of the pulse signal, then extracts the short-time power spectrum of the sampled data sequence of the pulse signal to be processed. Next, it calculates the local background noise extraction weights of the pulse signal to obtain the short-time narrowband feature parameters of the pulse signal. Finally, it calculates the short-time existence probability of the pulse signal to achieve automatic pulse signal sensing. This method fully utilizes the short-time narrowband features of the pulse signal in the frequency domain, achieving accurate pulse signal sensing with relatively low computational load. It has strong engineering practicality and is suitable for real-time sensing and processing of non-cooperative pulse signals.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and particularly relates to a pulse signal frequency domain sensing method based on narrowband feature extraction. Background Technology

[0002] With the development of sonar and underwater acoustic engineering technologies, human activities in areas such as marine resource exploration, underwater electronic warfare, and underwater acoustic communication are constantly deepening. Signal perception, as the first step in signal processing, determines the presence of target signals in the observed signal and is a crucial foundation for subsequent processing such as signal parameter extraction, noise estimation, and signal enhancement. Therefore, achieving accurate perception of underwater acoustic pulse signals under non-cooperative conditions is of great significance for applications such as underwater biological signal capture, underwater target detection, and underwater information transmission.

[0003] Existing pulse signal sensing methods mainly include: (1) energy detection method, which does not require any prior information about the signal. When the background noise is Gaussian white noise, the energy detection method is the best detection method for non-cooperative signals. However, when the background noise is non-stationary, it is difficult to select the threshold in the method, and the duration of the pulse signal is generally short, which makes the time gain that the energy detection method can obtain very limited; (2) Correlation detection method, which uses the difference in correlation between pseudo-random sequences and noise to distinguish signals and noise, to a certain extent makes it less sensitive to background noise, and even has good detection performance under low signal-to-noise ratio, but this method requires certain prior information, and is only of reference significance for pulse signal detection under non-cooperative conditions; (3) Higher-order spectrum cumulant detection method, since the higher-order spectrum contains more statistical information of random processes, this method has certain advantages, but the improvement of the ability of the higher-order spectrum cumulant detection method comes at the cost of greater computational load; (4) Cyclic spectrum detection method, which has the advantages of high resolution, ability to identify multiple non-cooperative signals from strong noise and interference, simple processing, and easy implementation, but this method is only advantageous for the detection of direct-sequence spread spectrum signals and frequency hopping signals; (5) Short-time Fourier transform detection method, which has low computational complexity, simple implementation, and clear physical meaning, but its time and frequency resolution cannot be obtained at the same time. Summary of the Invention

[0004] The purpose of this invention is to provide a pulse signal frequency domain sensing method based on narrowband feature extraction, so as to solve the technical problems of poor accuracy and robustness in pulse signal sensing.

[0005] Technical Solution: To solve the above-mentioned technical problems, this invention proposes a pulse signal frequency domain sensing method based on narrowband feature extraction, comprising the following steps:

[0006] Step 1: Obtain the pulse signal sampling data sequence x(n) to be processed, and initialize each sensing parameter of the pulse signal, setting the frame number l = 1;

[0007] Step 2: Extract the pulse signal sampling data sequence x of the current time frame using a sliding time window. l (n), and calculate the short-time power spectrum Y(l,k) of the pulse signal in the current frame;

[0008] Step 3: Extract the posterior signal-to-noise ratio γ(l,k) of the pulse signal in the current frame, and calculate the local background noise extraction weight h(l,k) of the pulse signal in the current frame;

[0009] Step 4: Extract the weight h(l,k) based on the local background noise of the pulse signal in the current frame, and calculate the short-time narrowband feature parameter ξ(l,k) of the pulse signal in the current frame;

[0010] Step 5: Based on the short-time narrowband characteristic parameter ξ(l,k) of the pulse signal, estimate the short-time existence probability P(l,k) of the pulse signal in the current frame;

[0011] Step 6: Determine whether the automatic signal sensing of all time frames of the pulse signal sampling data sequence x(n) to be processed has been completed. If the processing of all time frames has been completed, the processing ends; otherwise, set the time frame number l = l + 1 and return to step 2.

[0012] Furthermore, in step 1, the sampling data sequence x(n) of the pulse signal to be processed is obtained using the following method, and the sensing parameters of the pulse signal are initialized, specifically including the following steps:

[0013] Step 1.1: Obtain the pulse signal sampling data sequence x(n) to be processed: Receive real-time data from N sampling points of the sensor as the data sequence x(n) to be processed, or extract N sampling point data containing the entire pulse signal from the memory as the data sequence x(n) to be processed, where N = 2. p p is an integer greater than 10;

[0014] Step 1.2: Initialize the sensing parameters of the pulse signal, specifically including the initialization of the following parameters:

[0015] The short-time Fourier transform sliding window length K is initialized as follows: K = N / 2 a , where a is an integer 4 ≤ a ≤ 6;

[0016] The short-time Fourier transform sliding step M is initialized as follows: M = K / 2 b b is an integer 3 ≤ b ≤ 5;

[0017] The total number of time frames L of the pulse signal power spectrum is initialized as follows: where, int(·) represents the rounding operation;

[0018] The initial value of the local background noise extraction window length W1 is set to: an integer where 10 < W1 < 20;

[0019] The initial value of the local background noise splitting window length W2 is set to: an integer where 3 < W2 < 8;

[0020] The upper limit γ of the posterior signal-to-noise ratio of the pulse signal max is initialized to: 2 < γ max < a real number where 6;

[0021] The false alarm probability P of the pulse signal presence detection FA is initialized to: 0.001 < P FA < a real number where 0.1;

[0022] The lower limit η1 of the pulse signal continuity characteristic parameter is initialized to: a real number where 0.45 ≤ η1 ≤ 0.55;

[0023] The upper limit η2 of the pulse signal continuity characteristic parameter is initialized to: a real number where 0.9 ≤ η2 ≤ 1;

[0024] The decision threshold μ of the pulse signal presence is initialized to: a real number where 0.4 < μ < 0.6;

[0025] The smoothing factor α of the short-time narrowband characteristic parameter of the pulse signal is initialized to: a real number where 0.88 < α < 0.92.

[0026] Furthermore, in step 2, the following method is used to extract the pulse signal sampling data sequence x l (n) of the current l-th time frame by using a sliding time window, and calculate its short-time power spectrum Y(l,k), which specifically includes the following steps:

[0027] Step 2.1: Extract the pulse signal sampling data sequence x l (n) of the current l-th time frame by using a sliding time window:

[0028] x l (n) = x(n)w l (n - (l - 1)M), n = 1, 2,..., N

[0029] where, w l (n - (l - 1)M) is the sliding time window of the current l-th time frame, and it is expressed as:

[0030]

[0031] Step 2.2: For the pulse signal sampling data sequence x l(n) Perform a short-time Fourier transform to obtain the pulse signal spectrum y(l,k) of the current time frame l:

[0032]

[0033] Where k is the discrete frequency index;

[0034] Step 2.3: Based on the pulse signal spectrum y(l,k) of the current l-th time frame, calculate the short-time power spectrum Y(l,k) of the pulse signal in the current l-th time frame:

[0035]

[0036] Where k is the discrete frequency index, and || represents the modulo operation.

[0037] Step 2.4: Determine if l=1 is true. If true, proceed to step 2.5; otherwise, go to step 3.

[0038] Step 2.5: Initialize the noise power spectrum of the first time frame. for: k = 1, 2, ..., K. Initialize the local background noise power spectrum S(1, k) of the first time frame as: S(1, k) = Y(1, k), k = 1, 2, ..., K. Let the short-term existence probability P(1, k) of the pulse signal in the first time frame be: P(1, k) = 0.5, and proceed to step 6.

[0039] Furthermore, in step 3, the posterior signal-to-noise ratio γ(l,k) of the pulse signal in the current time frame l is extracted using the following method, and the background noise extraction weight h(l,k) of the pulse signal in the current time frame l is calculated. Specifically, the steps include:

[0040] Step 3.1: Determine if l > 2 is true. If true, proceed to step 3.2; otherwise, proceed to step 3.3.

[0041] Step 3.2: Estimate the noise power spectrum of each frequency point k = 1, 2, ..., K in the (l-1)th time frame.

[0042]

[0043] Where P(l-1,k) is the short-time existence probability of the pulse signal in the (l-1)th time frame, and Y(l-1,k) is the short-time power spectrum of the pulse signal in the (l-1)th time frame. The noise power spectrum of the (l-2)th frame;

[0044] Step 3.3: Calculate the posterior signal-to-noise ratio γ(l,k) of the pulse signals at each frequency point k = 1, 2, ..., K in the current time frame l:

[0045]

[0046] Step 3.4: Calculate the local background noise extraction weight h(l,k) for each frequency point k = 1, 2, ..., K of the pulse signal in the current time frame l:

[0047] h(l,k)=1+e -γ(l,k) .

[0048] Furthermore, in step 4, based on the obtained local background noise extraction weight h(l,k) of the pulse signal at each frequency point of the current time frame, the short-time narrowband feature parameter ξ(l,k) of the pulse signal of the current time frame is obtained using the following method, specifically including the following steps:

[0049] Step 4.1: Obtain the local background noise extraction split window Ω for each frequency point k = 1, 2, ..., K in the current time frame l. k :

[0050]

[0051] Step 4.2: Based on the posterior signal-to-noise ratio γ(l,k) of the pulse signal, extract the split window Ω for the local background noise of each frequency point k=1,2,…,K in the current l-th frame. k After correction, the corrected local background noise extraction split window Ω' is obtained. k The correction method is as follows:

[0052] Among them, Ω' k Ω k All impulse signals satisfying the posterior signal-to-noise ratio γ(l,k) < γ max The frequency point number, γ max The upper limit of the a posteriori signal-to-noise ratio of the pulse signal initialized in step 1.2, if Ω' k If the set is not empty, proceed to step 4.3; otherwise, proceed to step 4.4.

[0053] Step 4.3: For each frequency point k = 1, 2, ..., K in the current time frame after correction, extract the split window Ω′ for its background noise. k The local background noise extraction weights h(l,ω) for all frequency points within the frame are normalized to obtain the normalized background noise extraction weights for each frequency point in the current time frame l.

[0054]

[0055] Step 4.4: Calculate the local background noise power spectrum S(l,k) for each frequency point k = 1, 2, ..., K in the current time frame l:

[0056]

[0057] Where S(l-1,k) is the local background noise power spectrum of the (l-1)th frame;

[0058] Step 4.5: Based on the local background noise power spectrum S(l,k) and the pulse signal power spectrum Y(l,k), calculate the short-time narrowband characteristic parameter ξ(l,k) of the pulse signal at each frequency point k = 1, 2, ..., K in the current time frame l:

[0059]

[0060] Furthermore, in step 5, the short-term existence probability P(l,k) of the pulse signal in the current time frame l is estimated using the following method, specifically including the following steps:

[0061] Step 5.1: Based on the short-time narrowband characteristic parameter ξ(l,k) of the pulse signal in the current time frame l, calculate the initial estimated short-time existence probability of the pulse signal at each frequency point k = 1, 2, ..., K in the time frame l.

[0062]

[0063] Among them, P FA Let λ = ξ(l,k) be the false alarm probability of pulse signal presence sensing. but Let be the probability distribution function of a non-central chi-square distribution with 2 degrees of freedom. Let be the probability density function of a non-central chi-square distribution with 2 degrees of freedom. Let t be the gamma function and t be the integration variable;

[0064] Step 5.2: For the current time frame l, based on the short-time narrowband feature parameter ξ(l-1,k) of the pulse signal in time frame l-1, extract the continuity feature parameter η(l,k) of the pulse signal:

[0065]

[0066] Step 5.3: Based on the continuity characteristic parameter η(l,k) of the pulse signal, make an initial estimate of the short-term existence probability of the pulse signal at each frequency point k = 1, 2, ..., K in the current time frame l. The corrected result is P(l,k):

[0067]

[0068] Where α is the smoothing factor of the short-time narrowband characteristic parameter of the pulse signal initialized in step 1.2, η1 and η2 are the lower limit and upper limit of the continuity characteristic parameter of the pulse signal initialized in step 1.2, respectively, and μ is the existence decision threshold of the pulse signal initialized in step 1.2.

[0069] Furthermore, in step 6, the following method is used to determine whether the automatic signal sensing of all time frames of the pulse signal sampling data sequence x(n) to be processed has been completed, specifically including the following steps:

[0070] Step 6.1: Determine whether the time frame number l = L is true. If it is true, the calculation of the short-term existence probability P(l,k) of the pulse signal ends. Otherwise, let the time frame number l = l + 1 and return to step 2.

[0071] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0072] 1. Based on the posterior signal-to-noise ratio of the signal to be processed, the present invention adaptively sets the extraction weight of local background noise, as shown in step 3, thereby achieving a better match between the extracted background noise and the actual background noise and improving the robustness of narrowband feature extraction of pulse signals.

[0073] 2. The present invention makes full use of the narrowband characteristics of the pulse signal spectrum. As shown in step 4, the extracted feature parameters have good distinguishability between pulse signals and background noise, and can still reflect the frequency domain distribution characteristics of pulse signals well at low signal-to-noise ratios, thereby improving the robustness and accuracy of pulse signal frequency domain sensing.

[0074] 3. This invention makes full use of the continuity characteristics of the pulse signal spectrum to correct the frequency domain perception results of the pulse signal based on narrowband feature extraction, as shown in the corresponding processing steps in step 5, thereby further improving the robustness and accuracy of pulse signal perception. Attached Figure Description

[0075] Figure 1 This is a schematic flowchart of the method of the present invention;

[0076] Figure 2 The short-time power spectrum of the simulated pulse signal in Example 1 is shown below.

[0077] Figure 3 This is a short-time narrowband characteristic parameter diagram of the simulated pulse signal in Example 1;

[0078] Figure 4 This is a short-time existence probability diagram of the simulated pulse signal in Example 1;

[0079] Figure 5 The short-time power spectrum of the simulated pulse signal in Example 2 is shown below.

[0080] Figure 6 This is a short-time narrowband characteristic parameter diagram of the simulated pulse signal in Example 2;

[0081] Figure 7 This is a short-time existence probability diagram of the simulated pulse signal in Example 2. Detailed Implementation

[0082] To better understand the purpose, structure, and function of this invention, the following detailed description of a pulse signal frequency domain sensing method based on narrowband feature extraction is provided in conjunction with the accompanying drawings.

[0083] like Figure 1 As shown, this invention proposes a pulse signal frequency domain sensing method based on narrowband feature extraction, comprising the following steps:

[0084] Step 1: Obtain the pulse signal sampling data sequence x(n) to be processed, and initialize each sensing parameter of the pulse signal, setting the frame number l = 1;

[0085] Step 2: Extract the pulse signal sampling data sequence x of the current time frame using a sliding time window. l (n), and calculate the short-time power spectrum Y(l,k) of the pulse signal in the current frame;

[0086] Step 3: Extract the posterior signal-to-noise ratio γ(l,k) of the pulse signal in the current frame, and calculate the local background noise extraction weight h(l,k) of the pulse signal in the current frame;

[0087] Step 4: Extract the weight h(l,k) based on the local background noise of the pulse signal in the current frame, and calculate the short-time narrowband feature parameter ξ(l,k) of the pulse signal in the current frame;

[0088] Step 5: Based on the short-time narrowband characteristic parameter ξ(l,k) of the pulse signal, estimate the short-time existence probability P(l,k) of the pulse signal in the current frame;

[0089] Step 6: Determine whether the automatic signal sensing of all time frames of the pulse signal sampling data sequence x(n) to be processed has been completed. If the processing of all time frames has been completed, the processing ends; otherwise, set the time frame number l = l + 1 and return to step 2.

[0090] Furthermore, in step 1, the sampling data sequence x(n) of the pulse signal to be processed is obtained using the following method, and the sensing parameters of the pulse signal are initialized, specifically including the following steps:

[0091] Step 1.1: Obtain the pulse signal sampling data sequence x(n) to be processed: Receive real-time data from N sampling points of the sensor as the data sequence x(n) to be processed, or extract N sampling point data containing the entire pulse signal from the memory as the data sequence x(n) to be processed, where N = 2. p p is an integer greater than 10;

[0092] Step 1.2: Initialize the sensing parameters of the pulse signal, specifically including the initialization of the following parameters:

[0093] The sliding window length K of the short-time Fourier transform is initialized as: K = N / 2 a , where a is an integer with 4 ≤ a ≤ 6;

[0094] The sliding step M of the short-time Fourier transform is initialized as: M = K / 2 b , where b is an integer with 3 ≤ b ≤ 5;

[0095] The total number of time frames L of the power spectrum of the pulse signal is initialized as: where int(·) represents the rounding operation;

[0096] The window length W1 for extracting the local background noise is initialized as: an integer with 10 < W1 < 20;

[0097] The splitting window length W2 of the local background noise is initialized as: an integer with 3 < W2 < 8;

[0098] The upper limit γ of the posterior signal-to-noise ratio of the pulse signal max is initialized as: 2 < γ max < 6, a real number;

[0099] The false alarm probability P for the detection of the presence of the pulse signal FA is initialized as:​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​(n-(l-1)M), n=1,2,...,N

[0107] Where, w l (n-(l-1)M) represents the sliding time window of the current l-th frame, which is expressed as:

[0108]

[0109] Step 2.2: Sample the pulse signal data sequence x of the current time frame l. l (n) Perform a short-time Fourier transform to obtain the pulse signal spectrum y(l,k) of the current time frame l:

[0110]

[0111] Where k is the discrete frequency index;

[0112] Step 2.3: Based on the pulse signal spectrum y(l,k) of the current l-th time frame, calculate the short-time power spectrum Y(l,k) of the pulse signal in the current l-th time frame:

[0113] Y(l,k)=|y(l,k)| 2 k = 1, 2, ..., K;

[0114] Where k is the discrete frequency index, and || represents the modulo operation.

[0115] Step 2.4: Determine if l=1 is true. If true, proceed to step 2.5; otherwise, go to step 3.

[0116] Step 2.5: Initialize the noise power spectrum of the first time frame. for: k = 1, 2, ..., K. Initialize the local background noise power spectrum S(1, k) of the first time frame as: S(1, k) = Y(1, k), k = 1, 2, ..., K. Let the short-term existence probability P(1, k) of the pulse signal in the first time frame be: P(1, k) = 0.5, and proceed to step 6.

[0117] Furthermore, in step 3, the posterior signal-to-noise ratio γ(l,k) of the pulse signal in the current time frame l is extracted using the following method, and the background noise extraction weight h(l,k) of the pulse signal in the current time frame l is calculated. Specifically, the steps include:

[0118] Step 3.1: Determine if l > 2 is true. If true, proceed to step 3.2; otherwise, proceed to step 3.3.

[0119] Step 3.2: Estimate the noise power spectrum of each frequency point k = 1, 2, ..., K in the (l-1)th time frame.

[0120]

[0121] Where P(l-1,k) is the short-time existence probability of the pulse signal in the (l-1)th time frame, and Y(l-1,k) is the short-time power spectrum of the pulse signal in the (l-1)th time frame. The noise power spectrum of the (l-2)th frame;

[0122] Step 3.3: Calculate the posterior signal-to-noise ratio γ(l,k) of the pulse signals at each frequency point k = 1, 2, ..., K in the current time frame l:

[0123]

[0124] Step 3.4: Calculate the local background noise extraction weight h(l,k) for each frequency point k = 1, 2, ..., K of the pulse signal in the current time frame l:

[0125] h(l,k)=1+e -γ(l,k) .

[0126] Furthermore, in step 4, based on the obtained local background noise extraction weight h(l,k) of the pulse signal at each frequency point of the current time frame, the short-time narrowband feature parameter ξ(l,k) of the pulse signal of the current time frame is obtained using the following method, specifically including the following steps:

[0127] Step 4.1: Obtain the local background noise extraction split window Ω for each frequency point k = 1, 2, ..., K in the current time frame l. k :

[0128]

[0129] Step 4.2: Based on the posterior signal-to-noise ratio γ(l,k) of the pulse signal, extract the split window Ω for the local background noise of each frequency point k=1,2,…,K in the current l-th frame. k After correction, the corrected local background noise extraction split window Ω' is obtained. k The correction method is as follows:

[0130] Among them, Ω' k Ω k All impulse signals satisfying the posterior signal-to-noise ratio γ(l,k) < γ max The frequency point number, γ max The upper limit of the a posteriori signal-to-noise ratio of the pulse signal initialized in step 1.2, if Ω' k If the set is not empty, proceed to step 4.3; otherwise, proceed to step 4.4.

[0131] Step 4.3: For each frequency point k = 1, 2, ..., K in the current time frame after correction, extract the split window Ω′ for its background noise.k The local background noise extraction weights h(l,ω) for all frequency points within the frame are normalized to obtain the normalized background noise extraction weights for each frequency point in the current time frame l.

[0132]

[0133] Step 4.4: Calculate the local background noise power spectrum S(l,k) for each frequency point k = 1, 2, ..., K in the current time frame l:

[0134]

[0135] Where S(l-1,k) is the local background noise power spectrum of the (l-1)th frame;

[0136] Step 4.5: Based on the local background noise power spectrum S(l,k) and the pulse signal power spectrum Y(l,k), calculate the short-time narrowband characteristic parameter ξ(l,k) of the pulse signal at each frequency point k = 1, 2, ..., K in the current time frame l:

[0137]

[0138] Furthermore, in step 5, the short-term existence probability P(l,k) of the pulse signal in the current time frame l is estimated using the following method, specifically including the following steps:

[0139] Step 5.1: Based on the short-time narrowband characteristic parameter ξ(l,k) of the pulse signal in the current time frame l, calculate the initial estimated short-time existence probability of the pulse signal at each frequency point k = 1, 2, ..., K in the time frame l.

[0140]

[0141] Among them, P FA Let λ = ξ(l,k) be the false alarm probability of pulse signal presence sensing. but Let be the probability distribution function of a non-central chi-square distribution with 2 degrees of freedom. Let be the probability density function of a non-central chi-square distribution with 2 degrees of freedom. Let t be the gamma function and t be the integration variable;

[0142] Step 5.2: For the current time frame l, based on the short-time narrowband feature parameter ξ(l-1,k) of the pulse signal in time frame l-1, extract the continuity feature parameter η(l,k) of the pulse signal:

[0143]

[0144] Step 5.3: Based on the continuity characteristic parameter η(l,k) of the pulse signal, make an initial estimate of the short-time existence probability of the pulse signal at each frequency point k = 1, 2, ..., K in the current time frame l. The corrected result is P(l,k):

[0145]

[0146] Where α is the smoothing factor of the short-time narrowband characteristic parameter of the pulse signal initialized in step 1.2, η1 and η2 are the lower limit and upper limit of the continuity characteristic parameter of the pulse signal initialized in step 1.2, respectively, and μ is the existence decision threshold of the pulse signal initialized in step 1.2.

[0147] Furthermore, in step 6, the following method is used to determine whether the automatic signal sensing of all time frames of the pulse signal sampling data sequence x(n) to be processed has been completed, specifically including the following steps:

[0148] Step 6.1: Determine whether the time frame number l = L is true. If it is true, the calculation of the short-term existence probability P(l,k) of the pulse signal ends. Otherwise, let the time frame number l = l + 1 and return to step 2.

[0149] In the embodiments of the present invention, the simulated received pulse signal types are continuous wave (CW) signals and linear frequency modulated (LFM) signals. The simulated received CW signal model x1(t) is:

[0150]

[0151] The simulated LFM signal model x2(t) is:

[0152]

[0153] Where I represents the total number of CW sub-pulses in the simulated received CW signal, and J represents the total number of LFM sub-pulses in the simulated received LFM signal. To simulate the i-th CW sub-pulse of the received CW signal, The j-th LFM sub-pulse of the simulated received LFM signal is as follows:

[0154]

[0155]

[0156] Where T is the signal period, A is the signal amplitude, τ0 is the pulse start time, τ is the pulse width, and w(t) has a mean of zero and a variance of σ. 2 Gaussian white noise, variance σ 2 The size depends on the signal-to-noise ratio (SNR): SNR = 10log10 [A 2 / 2σ 2 f0 is the center frequency of the CW signal, f1 is the starting frequency of the LFM signal, and f2 is the ending frequency of the LFM signal;

[0157] With sampling frequency f s Discrete sampling is performed on the CW signal x1(t) and LFM signal x2(t) received in the above simulation to obtain the CW signal sampling data sequence x1(n) and the LFM signal sampling data sequence x2(n) as follows:

[0158]

[0159]

[0160] in, Let i be the sampled data sequence of the i-th CW sub-pulse. The sampled data sequence for the j-th LFM sub-pulse is as follows:

[0161]

[0162]

[0163] Where, n0 = int(τ0f s ), N0 = int(τf s ), N T =int(Tf s ).

[0164] Example 1:

[0165] The simulated pulse signal type is a CW signal, and the signal parameters are set as follows: signal amplitude A = 1, signal pulse width τ = 1s, signal start time τ0 = 2s, signal period T = 10s, number of sub-pulses I = 10, signal center frequency f0 = 400Hz, and sampling frequency f s =5000Hz, signal-to-noise ratio (SNR) = -3dB.

[0166] The following section describes frequency domain sensing of the simulated pulse signal:

[0167] Based on step 1, extract 500,000 sampling points containing the entire pulse signal from the memory as the data sequence x(n) to be processed, and initialize the sensing parameters of the pulse signal: set the short-time Fourier transform sliding window length K to 2048, the short-time Fourier transform sliding step M to 256, the local background noise extraction window length W1 to 15, the local background noise splitting window length W2 to 5, and the upper limit of the posterior signal-to-noise ratio γ of the pulse signal. max The false alarm probability P of pulse signal presence sensing is 5. FAThe lower limit η1 of the pulse signal continuity characteristic parameter is 0.01, the upper limit η2 of the pulse signal continuity characteristic parameter is 1, the pulse signal existence decision threshold μ is 0.5, and the smoothing factor α of the pulse signal short-time narrowband characteristic parameter is 0.9.

[0168] Based on step 2, the pulse signal sampling data sequence x of the current time frame is extracted using a sliding time window. l (n), and calculate its short-time power spectrum Y(l,k);

[0169] Based on step 3, extract the posterior signal-to-noise ratio γ(l,k) of the pulse signal in the current frame, and calculate the local background noise extraction weight h(l,k) of the pulse signal in the current frame.

[0170] Based on step 4, calculate the short-time narrowband characteristic parameter ξ(l,k) of the pulse signal in the current frame;

[0171] Based on step 5, estimate the short-term existence probability P(l,k) of the pulse signal in the current frame;

[0172] Based on step 6, determine whether the automatic sensing of the signal of all time frames of the pulse signal sampling data sequence x(n) to be processed has been completed. If the processing of all time frames has been completed, the processing ends; otherwise, set the time frame number l = l + 1 and return to step 2.

[0173] The calculated short-time power spectrum Y(l,k) of the pulse signal for all time frames is as follows: Figure 2 As shown;

[0174] The calculated short-time narrowband characteristic parameters ξ(l,k) of the pulse signal for all time frames are as follows: Figure 3 As shown;

[0175] The estimated short-time existence probability P(l,k) of the pulse signal in all time frames is as follows: Figure 4 As shown;

[0176] Detection probability P of pulse signal sensing D And the false positive probability P F They are respectively:

[0177]

[0178]

[0179] Where Ψ1 is the set of all time-frequency points where pulse signals exist, Ψ0 is the set of all time-frequency points where pulse signals do not exist, M1 is the total number of time-frequency points where pulse signals exist, and M0 is the total number of time-frequency points where pulse signals do not exist.

[0180] Example 2:

[0181] The simulated pulse signal type is an LFM signal, and the signal parameters are set as follows: signal amplitude A = 1, signal pulse width τ = 1s, signal start time τ0 = 1s, signal period T = 10s, number of sub-pulses J = 10, signal start frequency f1 = 530Hz, signal end frequency f2 = 580Hz, and sampling frequency f s =5000Hz, signal-to-noise ratio (SNR) = -6dB.

[0182] The following section describes frequency domain sensing of the simulated pulse signal:

[0183] Based on step 1, extract 500,000 sampling points containing the entire pulse signal from the memory as the data sequence x(n) to be processed, and initialize the sensing parameters of the pulse signal: set the short-time Fourier transform sliding window length K to 2048, the short-time Fourier transform sliding step M to 256, the local background noise extraction window length W1 to 15, the local background noise splitting window length W2 to 5, and the upper limit of the posterior signal-to-noise ratio γ of the pulse signal. max The false alarm probability P of pulse signal presence sensing is 5. FA The lower limit η1 of the pulse signal continuity characteristic parameter is 0.01, the upper limit η2 of the pulse signal continuity characteristic parameter is 1, the pulse signal existence decision threshold μ is 0.5, and the smoothing factor α of the pulse signal short-time narrowband characteristic parameter is 0.9.

[0184] Based on step 2, the pulse signal sampling data sequence x of the current time frame is extracted using a sliding time window. l (n), and calculate its short-time power spectrum Y(l,k);

[0185] Based on step 3, extract the posterior signal-to-noise ratio γ(l,k) of the pulse signal in the current frame, and calculate the local background noise extraction weight h(l,k) of the pulse signal in the current frame.

[0186] Based on step 4, calculate the short-time narrowband characteristic parameter ξ(l,k) of the pulse signal in the current frame;

[0187] Based on step 5, estimate the short-term existence probability P(l,k) of the pulse signal in the current frame;

[0188] Based on step 6, determine whether the automatic sensing of the signal of all time frames of the pulse signal sampling data sequence x(n) to be processed has been completed. If the processing of all time frames has been completed, the processing ends; otherwise, set the time frame number l = l + 1 and return to step 2.

[0189] The calculated short-time power spectrum Y(l,k) of the pulse signal for all time frames is as follows: Figure 5 As shown;

[0190] The calculated short-time narrowband characteristic parameters ξ(l,k) of the pulse signal for all time frames are as follows: Figure 6 As shown;

[0191] The estimated short-time existence probability P(l,k) of the pulse signal in all time frames is as follows: Figure 7 As shown;

[0192] Detection probability P of pulse signal sensing D And the false positive probability P F They are respectively:

[0193]

[0194]

[0195] Where Ψ1 is the set of all time-frequency points where pulse signals exist, Ψ0 is the set of all time-frequency points where pulse signals do not exist, M1 is the total number of time-frequency points where pulse signals exist, and M0 is the total number of time-frequency points where pulse signals do not exist.

[0196] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A pulse signal frequency domain sensing method based on narrowband feature extraction, characterized in that, It includes the following steps: Step 1: Obtain the sampled data sequence x(n) of the pulse signal to be processed, and initialize each sensing parameter of the pulse signal, and set the number of time frames l = 1; Step 2: Extract the pulse signal sampling data sequence of the current time frame using a sliding time window. And calculate the short-time power spectrum Y(l,k) of the pulse signal in the current frame, where k is the discrete frequency index; Step 3: Extract the a posteriori signal-to-noise ratio of the pulse signal in the current frame. Calculate the local background noise extraction weight h(l,k) of the pulse signal in the current frame; Step 4: Extract weight h(l,k) based on the local background noise of the pulse signal in the current frame, and calculate the short-time narrowband feature parameters of the pulse signal in the current frame. ; Step 5: Based on the short-time narrowband characteristic parameters of the pulse signal The short-term existence probability P(l,k) of the pulse signal in the current frame is estimated. Step 6: Determine whether the automatic sensing of the signals in all time frames of the sampled data sequence x(n) of the pulse signal to be processed is completed. If the processing of all time frames is completed, the processing ends; otherwise, let the number of time frames l = l + 1, and return to Step 2; In step 3, the current number is extracted using the following method. Posterior signal-to-noise ratio of pulse signals in time frames And calculate the current number. Weighting of background noise extraction from pulse signal of time frame Specifically, it includes the following steps: Step 3.1, Judgment Check if the condition is met. If it is met, proceed to step 3.2; otherwise, proceed to step 3.

3. Step 3.2, estimate the first Noise power spectrum at each frequency point k = 1, 2, ..., K of the time frame : ； in, Let be the probability of the pulse signal existing for a short time in the (l-1)th time frame. This is the short-time power spectrum of the pulse signal in the (l-1)th time frame. The noise power spectrum of the (l-2)th frame; Step 3.3: Calculate the posterior signal-to-noise ratio of the pulse signal at each frequency point k=1,2,…,K in the current time frame l. : ； Step 3.4: Calculate the local background noise extraction weights for each frequency point k=1,2,…,K of the pulse signal in the current time frame l. : ； In step 4, the weights h(l,k) are extracted based on the local background noise of the pulse signal at each frequency point of the current time frame l. The following method is used to obtain the weights h(l,k) of the current time frame l. Short-time narrowband characteristic parameters of pulse signals in time frames Specifically, it includes the following steps: Step 4.1: Obtain the current number. Local background noise extraction split window for each frequency point k =1,2,…,K of the time frame. : ； Among them, W1 is the window length for extracting local background noise; Step 4.2: Based on the a posteriori signal-to-noise ratio of the pulse signal To obtain the current number Local background noise extraction split window for each frequency point k=1,2,…,K of the time frame. After correction, a corrected local background noise extraction split window is obtained. The correction method is as follows: in, for All pulse signals that satisfy the posterior signal-to-noise ratio The frequency point number, γ max The upper limit of the posterior signal-to-noise ratio of the pulse signal initialized in step 1.2, if If the set is not empty, proceed to step 4.3; otherwise, proceed to step 4.

4. Step 4.3: For the corrected current [number]th [item]... For each frequency point k=1,2,…,K of the time frame, a split window is extracted for its background noise. Weighting of local background noise at all frequencies Perform normalization to obtain the current number. Background noise extraction and normalization weights at each frequency point of the time frame : ； Step 4.4: Calculate the current number. Local background noise power spectrum at each frequency point k = 1, 2, ..., K of the time frame : ； in, The local background noise power spectrum of the (l-1)th frame; Step 4.5: Based on the local background noise power spectrum and short-time power spectrum of pulse signal Calculate the current number Short-time narrowband characteristic parameters of pulse signals at each frequency point k = 1, 2, ..., K of the time frame : ； In step 5, the current i-th digit is estimated using the following method. The probability of short-term existence of pulse signals in time frames Specifically, it includes the following steps: Step 5.1: Based on the short-time narrowband characteristic parameters of the current l-th frame pulse signal Calculate the initial short-time existence probability of the pulse signal at each frequency point k = 1, 2, ..., K in the l-th frame. : ； Among them, P FA Let λ = ξ(l,k) be the false alarm probability of pulse signal presence sensing, and x = ,but Let be the probability distribution function of a non-central chi-square distribution with 2 degrees of freedom. Let be the probability density function of a non-central chi-square distribution with 2 degrees of freedom. Let t be the gamma function and t be the integration variable; Step 5.2: For the current time frame l, based on the short-time narrowband characteristic parameters of the pulse signal in time frame (l-1)... Extracting the continuity feature parameters of pulse signals : ； Step 5.3: Based on the continuity characteristic parameters of the pulse signal For the current number Frequency points of time frame Initial estimation of the short-term existence probability of the pulse signal Corrected : ； in, The smoothing factor for the short-time narrowband characteristic parameters of the initialized pulse signal. and These are the lower and upper limits of the initial pulse signal continuity characteristic parameters, respectively, and μ is the initial pulse signal existence decision threshold.

2. The pulse signal frequency domain sensing method based on narrowband feature extraction according to claim 1, characterized in that, In Step 1, the following method is used to obtain the sampled data sequence x(n) of the pulse signal to be processed and initialize each sensing parameter of the pulse signal, which specifically includes the following steps: Step 1.1: Obtain the pulse signal sampling data sequence x(n) to be processed: Receive real-time data from N sampling points of the sensor as the data sequence x(n) to be processed, or extract N sampling point data containing the entire pulse signal from the memory as the data sequence x(n) to be processed. p is an integer greater than 10; Step 1.2: Initialize each sensing parameter of the pulse signal, which specifically includes the initialization of the following parameters: The short-time Fourier transform sliding window length K is initialized as follows: , a is Integers; The short-time Fourier transform sliding step M is initialized as follows: ,b is Integers; The total number of time frames L of the pulse signal power spectrum is initialized as follows: ,in, This represents rounding to the nearest integer. The window length W1 for extracting local background noise is initialized as an integer where 10 < W1 < 20; The window length W2 for splitting local background noise is initialized as an integer where 3 < W2 < 8; Upper limit of posterior signal-to-noise ratio γ of pulse signal max Initialized as: 2 < γ max Real numbers less than 6; False alarm probability P of pulse signal presence sensing FA Initialized to: 0.001 <P FA Real numbers less than 0.1; Lower limit of pulse signal continuity characteristic parameter Initialize to: real numbers; Upper limit of pulse signal continuity characteristic parameter Initialize to: real numbers; The pulse signal existence determination threshold μ is initialized as follows: real numbers; Smoothing factor of short-time narrowband characteristic parameters of pulse signal Initialize to: The real number.

3. The pulse signal frequency domain sensing method based on narrowband feature extraction according to claim 2, characterized in that, In step 2, the following method is used to extract the current time frame using a sliding time window. Time frame pulse signal sampling data sequence And calculate its short-time power spectrum. Specifically, it includes the following steps: Step 2.1: Extract the current time using a sliding time window. Time frame pulse signal sampling data sequence : ； in, For the current number The sliding time window of a time frame is represented as follows: ； Step 2.2, for the current... Time frame pulse signal sampling data sequence Perform a short-time Fourier transform to obtain the pulse signal spectrum of the current time frame l. : ； Among them, k is the discrete frequency index; Step 2.3: Based on the pulse signal spectrum of the current l-th time frame. Calculate the short-time power spectrum of the pulse signal in the current time frame l. : ； Where k is the discrete frequency index. Represents modulo operation; Step 2.4: Determine whether l = 1 holds. If it holds, execute Step 2.5; otherwise, transfer to Step 3; Step 2.5: Initialize the noise power spectrum of the first time frame. for: Let k = 1, 2, ..., K, and initialize the local background noise power spectrum of the first frame. for: =Y(1,k), k =1,2,…,K, let the short-time existence probability of the pulse signal in the first time frame be Y(1,k), k =1,2,…,K. for: Proceed to step 6.

4. The pulse signal frequency domain sensing method based on narrowband feature extraction according to claim 1, characterized in that, In step 6, the following method is used to determine whether the sampling data sequence of the pulse signal to be processed has been completed. The automatic sensing of signals across all real-time frames includes the following steps: Step 6.1: Determine the number of time frames. Does this hold true? If so, what is the probability that the pulse signal exists for a short time? Calculation complete; otherwise, set the time frame number. Return to step 2.

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