An iterative wideband weak target detection method based on hidden Markov model

Abstract

This invention discloses an iterative broadband weak target detection method based on a Hidden Markov Model (HMM). First, conventional beamforming is performed on the received data subbands of a broadband array to obtain a broadband frequency-azimuth spectrum. The azimuth variation of the broadband target is modeled as a first-order HMM. The parameters of the HMM model are calculated using the probability distribution characteristics of the conventional broadband FRAZ spectrum under pure noise and target presence conditions in a stochastic broadband signal model. Then, the Viterbi algorithm is used to obtain the azimuth of the broadband target at each frequency point. The power of the detected target signal and the contribution of the signal in that direction to the signal energy received by each beam are estimated. The beam energy distribution of the detected signal is subtracted, and the broadband FRAZ spectrum is updated. The next round of detection is then performed until a weak target is detected. Finally, the detected results are thresholded to remove false alarms caused by signal energy leakage. This method can detect the azimuth of broadband weak targets under strong interference conditions and is applicable to multi-target detection.

Description

Technical Field

[0001] This invention belongs to the field of signal detection technology, specifically relating to an iterative broadband weak target detection method based on a hidden Markov model. Background Technology

[0002] Ship-radiated noise is a primary target for passive sonar detection, and its radiated noise power spectrum mainly consists of broadband continuous spectrum and narrowband line spectrum components. With the rapid development of vibration reduction and noise reduction technologies, the radiation intensity of targets has been lowered, making narrowband line spectrum detection increasingly difficult. Broadband continuous spectrum, on the other hand, carries more target information and has strong anti-interference capabilities. Therefore, in practical applications, fully utilizing the information from multiple frequency points of broadband targets is crucial for improving system performance. However, traditional broadband energy detection methods accumulate noise and signal in the frequency dimension, making it difficult to detect weak targets and achieve high processing gain under low signal-to-noise ratio conditions. Reference 1, "Bono M, Shapo B, McCarty P, et al. Subband energy detection inpassive array processing[R]. ADA405484, 2000: 25-30," discloses a subband peak energy detection (SPED) algorithm. This algorithm utilizes the "spatial consistency" of signal peaks to accumulate peak values ​​in each subband from various directions, improving sonar visibility and enhancing weak target detection performance. However, this method assigns equal weight to the frequency components of both signal and noise within the processing band. Therefore, when faced with complex environments such as multiple targets, weak targets, and strong interference, the performance of this detection method rapidly deteriorates. Reference 2, “Xin Jirong, Luo Yuanlai. Pure azimuth trajectory detection method based on hidden Markov model. Systems Engineering and Electronics, 2016, 38(07):1496-1501,” discloses a pure azimuth detection algorithm based on hidden Markov model applicable to narrowband known line spectrum. This method models the change of azimuth angle as a first-order hidden Markov model, uses Gaussian distribution as model parameters, and detects the trajectory of narrowband known line spectrum over time azimuth history. However, ship radiated noise is a broadband random signal. Due to the limitations of computation time and the number of sub-bands, the number of snapshots used to obtain the frequency azimuth spectrum is insufficient to make it approximate a Gaussian distribution. Moreover, this method is only applicable to single targets. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, this invention provides an iterative broadband weak target detection method based on Hidden Markov Models (HMM), called the IBD-HMM method. First, conventional beamforming is performed on the received data subbands of the broadband array to obtain a broadband frequency-azimuth (FRAZ) spectrum. The azimuth angle variation of the broadband target is modeled as a first-order Hidden Markov Model (HMM). The parameters of the HMM model are calculated using the probability distribution characteristics of the conventional broadband FRAZ spectrum under pure noise and target presence conditions in a stochastic broadband signal model. Then, the Viterbi algorithm is used to obtain the azimuth angle of the broadband target at each frequency point. The power of the detected target signal and the contribution of the signal in that direction to the signal energy received by each beam are estimated. The beam energy distribution of the detected signal is subtracted, and the broadband FRAZ spectrum is updated. The next round of detection is then performed until a weak target is detected. Finally, the detected results are thresholded to remove false alarms caused by signal energy leakage. The method of this invention can detect the location of broadband weak targets under strong interference conditions, has higher processing gain than the methods disclosed in the prior art, and is applicable to multi-target detection.

[0004] The technical solution adopted by this invention to solve its technical problem is as follows:

[0005] Step 1: Calculate the broadband frequency azimuth spectrum;

[0006] Step 2: Derive the precise probability distribution of random broadband signals in pure noise and with a target;

[0007] Step 3: Calculate the parameters of the hidden Markov model;

[0008] Step 4: Use the Viterbi algorithm to solve for the target azimuth value of the broadband frequency azimuth spectrum;

[0009] Step 5: Estimate the energy distribution of the detected signal beam and update the frequency azimuth spectrum;

[0010] Step 6: Eliminate false alarms caused by signal energy leakage.

[0011] Preferably, step 1 specifically comprises:

[0012] Consider a uniform linear array with M elements. Assume that H broadband sound sources arrive at the array in the far field as plane waves, with the wave direction of arrival being... , Then the time-domain signal received by the m-th array element for:

[0013]

[0014] in This represents the signal from the h-th sound source. This represents the time delay of the h-th sound source relative to the m-th array element. This represents superimposed Gaussian white noise. Let represent the azimuth angle of the h-th sound source incident array, and t represent the time-domain snapshot of the signal;

[0015] The broadband signal is segmented in the time domain, and a short-time Fourier transform is performed to divide the received data in the frequency domain into K non-overlapping sub-bands. Each sub-band satisfies the narrowband assumption. Then, the received data of each frequency domain array segment is:

[0016] ,

[0017] in, Given an H×1 dimensional source signal vector, Let H be a noise vector of dimension H. It is an M×H dimensional array manifold vector; This represents the k-th frequency point. A set representing the direction of a signal. This represents the frequency domain received signal at the k-th frequency point of the h-th sound source signal. This represents the background noise at the k-th frequency point of the h-th sound source signal;

[0018] Guide vector Represented as:

[0019]

[0020] Where c represents the speed of sound, M represents the number of array elements, and j represents the imaginary number;

[0021] Space of interest Discretize into Q azimuths, scan Q azimuths for each frequency point k, and weight vector. for:

[0022] ,

[0023] in, Indicates the azimuth value of the scan;

[0024] Calculate the covariance matrix of the data The resulting frequency azimuth spectrum is expressed as:

[0025]

[0026] in, Expressing expectations, This represents the frequency domain array receiving data at the k-th frequency point. This represents the weighted vector at the k-th frequency point.

[0027] Preferably, step 2 specifically comprises:

[0028] Considering a single target, the array receives data in two cases: when a signal is present, denoted as... When only noise exists, it is denoted as That is, it satisfies the binary hypothesis test:

[0029]

[0030] in, and Let be the signal and noise vectors at the k-th frequency and i-th azimuth, respectively. The array manifold vector representing the signal orientation. This indicates that the array is receiving signals;

[0031] Calculate separately and The frequency azimuth spectrum under the given conditions, the spectral value of the i-th azimuth at the k-th frequency point. They are respectively:

[0032]

[0033] This represents the beamforming weight vector at the k-th frequency and the i-th azimuth. express The conjugate transpose of;

[0034] and All are Gaussian white noise, following a complex Gaussian distribution with a mean of 0.

[0035] ,

[0036] in,

[0037] Under the condition, let ,but ,have to:

[0038]

[0039] make ,but Follows an exponential distribution:

[0040]

[0041] Under the condition, let ,but ,have to:

[0042]

[0043] make ,but Follows an exponential distribution:

[0044]

[0045] Therefore, the precise probability distribution of the frequency-azimuth spectrum of a random broadband signal in both pure noise and target conditions is:

[0046]

[0047] in, Indicates signal power. Indicates noise power. This represents an M-dimensional identity matrix.

[0048] Preferably, step 3 specifically comprises:

[0049] The azimuth variation in the frequency azimuth spectrum is modeled as a first-order hidden Markov process, with the hidden state being the azimuth angle, and the state at frequency point k defined as... ,Right now The state of frequency point k-1 is defined as , Follow the following state equations:

[0050]

[0051] in, This represents state noise, which follows a pattern with a mean of 0 and a variance of 0. Gaussian distribution;

[0052] Q scan positions correspond to Q states, where i is the state index, i.e. express The value is the i-th state. Assume that all states are independent and identically distributed.

[0053] The observed value of frequency point k is defined as ,in This represents the observation value at the i-th state on the k-axis spectrum;

[0054] Hidden Markov Model (HMM) parameters Let A be the state transition matrix, B be the observation probability matrix, and Π be the initial probability vector;

[0055] The initial probability vector Π is defined as:

[0056]

[0057] in, Represents probability;

[0058] In the initial stage, prior information about the target state is lacking, therefore... ;

[0059] State transition matrix element { } is defined as:

[0060] ,

[0061] in, Represents the determinant function. This represents the normalization factor, ensuring that the row sum of A is 1;

[0062] Observation probability matrix element { } is defined as:

[0063]

[0064] and Time observations The probability distributions are as follows:

[0065]

[0066]

[0067] get:

[0068] .

[0069] Preferably, step 4 specifically comprises:

[0070] The Viterbi algorithm is used to track the orientation of a target signal at various frequency points, and two metrics are defined. and :

[0071] The maximum state probability is defined as:

[0072]

[0073] state The maximum predecessor probability is defined as:

[0074]

[0075] (1) Initialization:

[0076] For all states, initialize:

[0077]

[0078] (2) Recursive metric:

[0079] frequency points For each state i, recursively calculate And store the predecessor state for:

[0080]

[0081] (3) Termination and backtracking:

[0082] After completing the recursion, the optimal state when k=K is obtained by the following equation:

[0083]

[0084] Then through backtracking To obtain the estimated state sequence:

[0085]

[0086] The obtained sequence The estimated azimuth of each frequency point is given. .

[0087] Preferably, step 5 specifically comprises:

[0088] Based on the estimated orientation Find the local peak direction where the error between each frequency point and the estimated value is minimized. The signal peak direction at frequency point k is denoted as... The noise power estimated when calculating HMM parameters As prior knowledge, estimate the power of the signal, denoted as . Approximately expressed as:

[0089]

[0090] in, for The weight vector of the beamformer corresponding to the direction. express The conjugate transpose of . for The azimuth spectral value corresponding to the direction, then The energy contribution of the direction signal to the signal received at each scanning azimuth. for:

[0091]

[0092] in, express directional array manifold vectors;

[0093] After obtaining the energy contribution of the signal, the broadband frequency azimuth spectrum is updated. The new broadband frequency azimuth spectrum for:

[0094]

[0095] Continue detection on the new broadband frequency azimuth spectrum until all preset H signals have been detected, denoted by the subscript h. , , , and The value of the h-th iteration is indicated by the superscript h, where h represents the value of other parameters in the h-th iteration. Parameters without h are constant parameters. The iteration process is as follows:

[0096] (1) Update the broadband frequency azimuth spectrum;

[0097]

[0098] (2) Calculate the parameters of the hidden Markov model;

[0099]

[0100] ,

[0101]

[0102] (3) The target azimuth value is obtained by using the Viterbi algorithm;

[0103] initialization:

[0104] frequency points For each state i, recursively calculate And store the predecessor state for:

[0105]

[0106] After completing the recursion, the optimal state when k=K is obtained by the following equation:

[0107]

[0108] Then through backtracking To obtain the estimated state sequence:

[0109]

[0110] The obtained sequence The estimated azimuth of each frequency point is given. .

[0111] (4) Estimate the beam energy distribution of the detected signal;

[0112]

[0113]

[0114] The detection results of H signal positions for:

[0115] .

[0116] Preferably, step 6 specifically comprises:

[0117] Define the azimuth difference detection between any two directions at the k-th frequency point. for:

[0118] ,

[0119] in, and These represent the detection azimuth of the p-th and q-th signals at the k-th frequency point, respectively.

[0120] Define neighborhood space for:

[0121]

[0122] in, The set threshold for detecting azimuth differences;

[0123] The judgment criteria are defined as follows:

[0124]

[0125] in, and express and The corresponding spectral value in the frequency azimuth spectrum;

[0126] The detection location is screened using decision criteria. If not within the preset neighborhood, then and Both signals will be retained, and the decision will come from different objectives; if Within the preset neighborhood, then and The results will be merged, and only the detection results with the larger corresponding spectral values ​​will be retained. The results with smaller spectral values ​​will be considered false alarms. The location after filtering will be the detection result.

[0127] An electronic device includes: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device performs the above-described iterative broadband weak target detection method based on a hidden Markov model.

[0128] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described iterative broadband weak target detection method based on a hidden Markov model.

[0129] A chip includes a processor for calling and running a computer program from a memory, causing a device equipped with the chip to perform the above-described iterative broadband weak target detection method based on a hidden Markov model.

[0130] A computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the above-described iterative broadband weak target detection method based on a hidden Markov model.

[0131] The beneficial effects of this invention are as follows:

[0132] The method of this invention can detect the location of broadband weak targets under strong interference conditions, has higher processing gain than the methods disclosed in the prior art, and is applicable to multi-target detection.

[0133] The method of this invention utilizes the "spatial consistency" of the frequency azimuth spectrum of a broadband target, and detects the target's azimuth by calculating a hidden Markov model under this condition, achieving excellent broadband high-gain performance, which is superior to the detection performance obtained in Reference 1. Compared to the method disclosed in Reference 2, it is applicable to broadband random signals and multi-target scenarios. Attached Figure Description

[0134] Figure 1 This is a schematic diagram of the horizontal uniform linear array used in the simulation of the embodiments of the present invention;

[0135] Figure 2 It is the original conventional FRAZ spectrum;

[0136] Figure 3 It is the FRAZ spectrum of the SPED algorithm in Reference 1;

[0137] Figure 4 It is the FRAZ spectrum of the parameterized likelihood energy orientation joint sequence detection algorithm in Reference 2;

[0138] Figure 5It is the FRAZ spectrum of the IBD-HMM detection algorithm;

[0139] Figure 6 This is the BTR graph of the CED algorithm;

[0140] Figure 7 This is the BTR diagram of the SPED algorithm in Reference 1;

[0141] Figure 8 This is the BTR diagram of the parameterized likelihood energy orientation joint sequence detection algorithm in Reference 2;

[0142] Figure 9 This is the BTR plot of the IBD-HMM detection algorithm. Detailed Implementation

[0143] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0144] This invention discloses an iterative broadband weak target detection method based on a hidden Markov model. For a broadband frequency azimuth spectrum, the precise probability distribution of a random broadband signal in pure noise and with a target is derived. The hidden Markov model under these parameters is then used to detect the target azimuth at each frequency point, achieving good broadband high-gain performance.

[0145] Step 1: Calculate the broadband frequency azimuth spectrum;

[0146] Consider a uniform linear array with M elements. Assume that H broadband sound sources arrive at the array in the far field as plane waves, with the wave direction of arrival being... , Then the time-domain signal received by the m-th array element for:

[0147]

[0148] in This represents the signal from the h-th sound source. This represents the time delay of the h-th sound source relative to the m-th array element. This represents superimposed Gaussian white noise. Let represent the azimuth angle of the h-th sound source incident array, and t represent the time-domain snapshot of the signal;

[0149] The broadband signal is segmented in the time domain, and a short-time Fourier transform is performed to divide the received data in the frequency domain into K non-overlapping sub-bands. Each sub-band satisfies the narrowband assumption. Then, the received data of each frequency domain array segment is:

[0150] ,

[0151] in, Given an H×1 dimensional source signal vector, Let H be a noise vector of dimension H. It is an M×H dimensional array manifold vector; This represents the k-th frequency point. A set representing the direction of a signal. This represents the frequency domain received signal at the k-th frequency point of the h-th sound source signal. This represents the background noise at the k-th frequency point of the h-th sound source signal;

[0152] Guide vector Represented as:

[0153]

[0154] Where c represents the speed of sound, M represents the number of array elements, and j represents the imaginary number;

[0155] Space of interest Discretize into Q azimuths, scan Q azimuths for each frequency point k, and weight vector. for:

[0156] ,

[0157] in, Indicates the azimuth value of the scan;

[0158] Calculate the covariance matrix of the data The resulting frequency azimuth spectrum is expressed as:

[0159]

[0160] in, Expressing expectations, This represents the frequency domain array receiving data at the k-th frequency point. This represents the weighted vector at the k-th frequency point.

[0161] Step 2: Derive the precise probability distribution of random broadband signals in pure noise and with a target;

[0162] Considering a single target, the array receives data in two cases: when a signal is present, denoted as... When only noise exists, it is denoted as That is, it satisfies the binary hypothesis test:

[0163]

[0164] in, and Let be the signal and noise vectors at the k-th frequency and i-th azimuth, respectively. The array manifold vector representing the signal orientation. This indicates that the array is receiving signals;

[0165] Calculate separately and The frequency azimuth spectrum under the given conditions, the spectral value of the i-th azimuth at the k-th frequency point. They are respectively:

[0166]

[0167] This represents the beamforming weight vector at the k-th frequency and the i-th azimuth. express The conjugate transpose of;

[0168] and All are Gaussian white noise, following a complex Gaussian distribution with a mean of 0.

[0169] ,

[0170] in,

[0171] Under the condition, let ,but ,have to:

[0172]

[0173] make ,but Follows an exponential distribution:

[0174]

[0175] Under the condition, let ,but ,have to:

[0176]

[0177] make ,but Follows an exponential distribution:

[0178]

[0179] Therefore, the precise probability distribution of the frequency-azimuth spectrum of a random broadband signal in both pure noise and target conditions is:

[0180]

[0181] in, Indicates signal power. Indicates noise power. This represents an M-dimensional identity matrix.

[0182] Step 3: Calculate the parameters of the hidden Markov model;

[0183] The azimuth variation in the frequency azimuth spectrum is modeled as a first-order hidden Markov process, with the hidden state being the azimuth angle, and the state at frequency point k defined as... ,Right now The state of frequency point k-1 is defined as , Follow the following state equations:

[0184]

[0185] in, This represents state noise, which follows a pattern with a mean of 0 and a variance of 0. Gaussian distribution;

[0186] Q scan positions correspond to Q states, where i is the state index, i.e. express The value is the i-th state. Assume that all states are independent and identically distributed.

[0187] The observed value of frequency point k is defined as ,in This represents the observation value at the i-th state on the k-axis spectrum;

[0188] Hidden Markov Model (HMM) parameters Let A be the state transition matrix, B be the observation probability matrix, and Π be the initial probability vector;

[0189] The initial probability vector Π is defined as:

[0190]

[0191] in, Represents probability;

[0192] In the initial stage, prior information about the target state is lacking, therefore... ;

[0193] State transition matrix element { } is defined as:

[0194] ,

[0195] in, Represents the determinant function. This represents the normalization factor, ensuring that the row sum of A is 1;

[0196] Observation probability matrix element { } is defined as:

[0197]

[0198] and Time observations The probability distributions are as follows:

[0199]

[0200]

[0201] get:

[0202] .

[0203] Step 4: Use the Viterbi algorithm to solve for the target azimuth value of the broadband frequency azimuth spectrum;

[0204] The Viterbi algorithm is used to track the orientation of a target signal at various frequency points, and two metrics are defined. and :

[0205] The maximum state probability is defined as:

[0206]

[0207] state The maximum predecessor probability is defined as:

[0208]

[0209] (1) Initialization:

[0210] For all states, initialize:

[0211]

[0212] (2) Recursive metric:

[0213] frequency points For each state i, recursively calculate And store the predecessor state for:

[0214]

[0215] (3) Termination and backtracking:

[0216] After completing the recursion, the optimal state when k=K is obtained by the following equation:

[0217]

[0218] Then through backtracking To obtain the estimated state sequence:

[0219]

[0220] The obtained sequence The estimated azimuth of each frequency point is given. .

[0221] Step 5: Estimate the energy distribution of the detected signal beam and update the frequency azimuth spectrum;

[0222] Based on the estimated orientation Find the local peak direction where the error between each frequency point and the estimated value is minimized. The signal peak direction at frequency point k is denoted as... The noise power estimated when calculating HMM parameters As prior knowledge, estimate the power of the signal, denoted as . Approximately expressed as:

[0223]

[0224] in, for The weight vector of the beamformer corresponding to the direction. express The conjugate transpose of . for The azimuth spectral value corresponding to the direction, then The energy contribution of the direction signal to the signal received at each scanning azimuth. for:

[0225]

[0226] in, express directional array manifold vectors;

[0227] After obtaining the energy contribution of the signal, the broadband frequency azimuth spectrum is updated. The new broadband frequency azimuth spectrum for:

[0228]

[0229] Continue detection on the new broadband frequency azimuth spectrum until all preset H signals have been detected, denoted by the subscript h. , , , and The value of the h-th iteration is indicated by the superscript h, where h represents the value of other parameters in the h-th iteration. Parameters without h are constant parameters. The iteration process is as follows:

[0230] (1) Update the broadband frequency azimuth spectrum;

[0231]

[0232] (2) Calculate the parameters of the hidden Markov model;

[0233]

[0234] ,

[0235]

[0236] (3) The target azimuth value is obtained by using the Viterbi algorithm;

[0237] initialization:

[0238] frequency points For each state i, recursively calculate And store the predecessor state for:

[0239]

[0240] After completing the recursion, the optimal state when k=K is obtained by the following equation:

[0241]

[0242] Then through backtracking To obtain the estimated state sequence:

[0243]

[0244] The obtained sequence The estimated azimuth of each frequency point is given. .

[0245] (4) Estimate the beam energy distribution of the detected signal;

[0246]

[0247]

[0248] The detection results of H signal positions for:

[0249] .

[0250] Step 6: Eliminate false alarms caused by signal energy leakage.

[0251] Define the azimuth difference detection between any two directions at the k-th frequency point. for:

[0252] ,

[0253] in, and These represent the detection azimuth of the p-th and q-th signals at the k-th frequency point, respectively.

[0254] Define neighborhood space for:

[0255]

[0256] in, The set threshold for detecting azimuth differences;

[0257] The judgment criteria are defined as follows:

[0258]

[0259] in, and express and The corresponding spectral value in the frequency azimuth spectrum;

[0260] The detection location is screened using decision criteria. If not within the preset neighborhood, then and Both signals will be retained, and the decision will come from different objectives; if Within the preset neighborhood, then and The results will be merged, and only the detection results with the larger corresponding spectral values ​​will be retained. The results with smaller spectral values ​​will be considered false alarms. The location after filtering will be the detection result.

[0261] Example:

[0262] Consider a 32-element uniform linear array with an element spacing of 1.5m. The element coordinates are as follows: Figure 1 As shown. Broadband target 1 has an incident direction varying from 60° to 80° with a signal-to-noise ratio (SNR) of -20dB; broadband target 2 has an incident direction varying from 75° to 55° with a SNR of -15dB; and broadband target 3 has an incident direction of 120° with a SNR of -5dB. The signal is broadband Gaussian white noise, and the noise is an isotropic noise field. The SNR is defined as the ratio of signal energy to noise energy within the same bandwidth. The speed of sound is 1500m / s, the frequency range is [200Hz, 400Hz], the sub-band spacing is 10Hz, and the integration time is 1s.

[0263] for Figure 1 The array shown in Reference 1 uses the SPED algorithm, which only extracts and accumulates local peaks from sub-bands. It leverages the "spatial consistency" of the continuous local peaks of the signal across frequencies, while the random local peaks of noise enhance the visibility of weak targets. However, the SPED algorithm assigns equal weight to each sub-band and indiscriminately accumulates directional spectrum peaks, resulting in a still relatively high background noise level. Figure 3 , Figure 7 As shown. Reference 2's parameterized likelihood-energy-orientation joint sequence detection fails to detect weak targets due to model mismatch, such as... Figure 4 , Figure 8 As shown. The IBD-HMM detection algorithm proposed in this invention calculates the parameters of the HMM model through the probability distribution characteristics of broadband random signals, uses the Viterbi algorithm to solve for the azimuth angle of the broadband target at each frequency point, estimates the power of the detected target signal and the contribution of the signal in that direction to the signal energy received by each beam, subtracts the beam energy distribution of the detected signal, updates the broadband FRAZ spectrum, and then performs the next round of detection. Figure 5 , Figure 9 It can be observed that the IBD-HMM detection algorithm effectively distinguishes between signal peaks and spurious peaks of background noise from the FRAZ spectrum, clearly displaying the trajectory of weak targets.

Claims

1. An iterative broadband weak target detection method based on a hidden Markov model, characterized in that, Includes the following steps: Step 1: Calculate the broadband frequency azimuth spectrum; Step 2: Derive the precise probability distribution of random broadband signals in pure noise and with a target; Step 3: Calculate the parameters of the hidden Markov model; The azimuth variation in the frequency azimuth spectrum is modeled as a first-order hidden Markov process, where the hidden state is the azimuth angle, and the state at frequency point k is defined as follows: ,Right now The state of frequency point k-1 is defined as , Follow the following state equations: ； in, This represents state noise, which follows a pattern with a mean of 0 and a variance of 0. Gaussian distribution; Q scan positions correspond to Q states, where i is the state index, i.e. express The value is the i-th state. Assume that all states are independent and identically distributed. The observed value of frequency point k is defined as ,in This represents the observation value at the i-th state on the k-axis spectrum; Hidden Markov Model (HMM) parameters Let A be the state transition matrix, B be the observation probability matrix, and Π be the initial probability vector; The initial probability vector Π is defined as: ； in, Represents probability; In the initial stage, prior information about the target state is lacking, therefore... ; State transition matrix element { } is defined as: ， ； in, Represents the determinant function. This represents the normalization factor, ensuring that the row sum of A is 1; Observation probability matrix element { } is defined as: ； and Time observations The probability distributions are as follows: ； ； get: ； Step 4: Use the Viterbi algorithm to solve for the target azimuth value of the broadband frequency azimuth spectrum; Step 5: Estimate the energy distribution of the detected signal beam and update the frequency azimuth spectrum; Step 6: Eliminate false alarms caused by signal energy leakage.

2. The iterative broadband weak target detection method based on a hidden Markov model according to claim 1, characterized in that, Step 1 specifically involves: Consider a uniform linear array with M elements. Assume that H broadband sound sources arrive at the array in the far field as plane waves, with the wave direction of arrival being... , Then the time-domain signal received by the m-th array element for: ； in This represents the signal from the h-th sound source. This represents the time delay of the h-th sound source relative to the m-th array element. This represents superimposed Gaussian white noise. Let represent the azimuth angle of the h-th sound source incident array, and t represent the time-domain snapshot of the signal; The broadband signal is segmented in the time domain, and a short-time Fourier transform is performed to divide the received data in the frequency domain into K non-overlapping sub-bands. Each sub-band satisfies the narrowband assumption. Then, the received data of each frequency domain array segment is: ， ； in, Let H×1 be the source signal vector. Let H be a noise vector of dimension H. It is an M×H dimensional array manifold vector; This represents the k-th frequency point. A set representing the direction of a signal. This represents the frequency domain received signal at the k-th frequency point of the h-th sound source signal. This represents the background noise at the k-th frequency point of the h-th sound source signal; Guide vector Represented as: ； Where c represents the speed of sound, M represents the number of array elements, and j represents the imaginary number; Space of interest Discretize into Q azimuths, scan Q azimuths for each frequency point k, and weight vector. for: ， ； in, Indicates the azimuth value of the scan; Calculate the covariance matrix of the data The resulting frequency azimuth spectrum is expressed as: ； in, Expressing expectations, This represents the frequency domain array receiving data at the k-th frequency point. This represents the weighted vector at the k-th frequency point.

3. The iterative broadband weak target detection method based on a hidden Markov model according to claim 2, characterized in that, Step 2 specifically involves: Considering a single target, the array receives data in two cases: when a signal is present, denoted as... When only noise exists, it is denoted as That is, it satisfies the binary hypothesis test: ； in, and Let be the signal and noise vectors at the k-th frequency and i-th azimuth, respectively. The array manifold vector representing the signal orientation. Indicates that the array receives signals; Calculate separately and The frequency azimuth spectrum under the given conditions, the spectral value of the i-th azimuth at the k-th frequency point. They are respectively: ； This represents the beamforming weight vector at the k-th frequency and the i-th azimuth. express The conjugate transpose of; and All are Gaussian white noise, following a complex Gaussian distribution with a mean of 0. ， ； in, Under the condition, let ,but ,have to: ； make ,but Follows an exponential distribution: ； Under the condition, let ,but ,have to: ； make ,but Follows an exponential distribution: ； Therefore, the precise probability distribution of the frequency-azimuth spectrum of a random broadband signal in both pure noise and target conditions is: ； in, Indicates signal power. Indicates noise power. This represents an M-dimensional identity matrix.

4. The iterative broadband weak target detection method based on a hidden Markov model according to claim 3, characterized in that, Step 4 specifically involves: The Viterbi algorithm is used to track the orientation of a target signal at various frequency points, and two metrics are defined. and : The maximum state probability is defined as: ； state The maximum precursor probability is defined as: ； (1) Initialization: For all states, initialize: ； (2) Recursive metric: frequency points For each state i, recursively calculate And store the predecessor state for: ； (3) Termination and backtracking: After completing the recursion, the optimal state when k=K is obtained by the following equation: ； Then through backtracking To obtain the estimated state sequence: ； The obtained sequence The estimated azimuth of each frequency point is given. .

5. The iterative broadband weak target detection method based on a hidden Markov model according to claim 4, characterized in that, Step 5 specifically involves: Based on the estimated orientation Find the local peak direction where the error between each frequency point and the estimated value is minimized. The signal peak direction at frequency point k is denoted as... The noise power estimated when calculating HMM parameters As prior knowledge, estimate the power of the signal, denoted as . Approximately expressed as: ； in, for The weight vector of the beamformer corresponding to the direction. express The conjugate transpose of . for The azimuth spectral value corresponding to the direction, then The energy contribution of the direction signal to the signal received at each scanning azimuth. for: ； in, express directional array manifold vectors; After obtaining the energy contribution of the signal, the broadband frequency azimuth spectrum is updated. The new broadband frequency azimuth spectrum for: ； Continue detection on the new broadband frequency azimuth spectrum until all preset H signals have been detected, denoted by the subscript h. , , , and The value of the h-th iteration is indicated by the superscript h, where h represents the value of other parameters in the h-th iteration. Parameters without h are constant parameters. The iteration process is as follows: (1) Update the broadband frequency azimuth spectrum; ； (2) Calculate the parameters of the hidden Markov model; ； ， ； ； (3) The target azimuth value is obtained by using the Viterbi algorithm; initialization: ; frequency points For each state i, recursively calculate And store the predecessor state for: ； After completing the recursion, the optimal state when k=K is obtained by the following equation: ； Then through backtracking To obtain the estimated state sequence: ； The obtained sequence The estimated azimuth of each frequency point is given. ; (4) Estimate the beam energy distribution of the detected signal; ； ； The detection results of H signal positions for: 。 6. The iterative broadband weak target detection method based on a hidden Markov model according to claim 5, characterized in that, Step 6 specifically involves: Define the azimuth difference detection between any two directions at the k-th frequency point. for: ， ； in, and These represent the detection azimuth of the p-th and q-th signals at the k-th frequency point, respectively. Define neighborhood space for: ； in, The set threshold for detecting azimuth differences; The judgment criteria are defined as follows: ； in, and express and The corresponding spectral value in the frequency azimuth spectrum; The detection location is screened using decision criteria. If not within the preset neighborhood, then and Both signals will be retained, and the decision will come from different objectives; if Within the preset neighborhood, then and The results will be merged, and only the detection results with the larger corresponding spectral values ​​will be retained. The results with smaller spectral values ​​will be considered false alarms. The location after filtering will be the detection result.

7. An electronic device, characterized in that, include: Processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to cause the electronic device to perform the method as described in any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 6.

9. A chip, characterized in that, include: A processor for retrieving and running a computer program from memory, causing a device on which the chip is mounted to perform the method as described in any one of claims 1 to 6.

Images