A Cramer-Rao bound analysis method for target depth estimation using reliable acoustic path matching beam intensity processing

Abstract

The present invention discloses a Cramer-Rao bound analysis method for reliable acoustic path matching beam intensity processing target depth estimation, comprising the following steps: step 1, determining the physical model of reliable acoustic path matching beam intensity processing, given a vertical receiving array arranged near the seabed in the deep sea, and calculating the peak beam intensity output by conventional beam forming, the broadband beam intensity fluctuation is the physical quantity to be matched; step 2, determining the observation data model, based on the frequency band of interest, obtaining independent data samples, and calculating the observed vertical array beam intensity data; step 3, calculating the likelihood ratio of the parameter to be estimated, and obtaining the likelihood function and log-likelihood function of the observation data; step 4, calculating the second-order derivative of the log-likelihood function. The present invention theoretically derives the Cramer-Rao bound of broadband matching beam intensity processing, which can reflect the theoretical optimal performance of the deep-sea reliable acoustic path passive target depth estimation algorithm.

Description

Technical field:

[0001] The invention relates to the field of deep-sea target depth estimation, and in particular to a Cramer-Rao bound analysis method for reliable acoustic path matching beam intensity processing target depth estimation. Background technology:

[0002] In recent years, experiments have observed that the background noise at the critical depth is 5dB to 20dB lower than the background noise at the critical depth. The propagation loss of the acoustic signal transmitted through the reliable acoustic path is 10dB to 20dB less than the propagation loss in the shallow sea at the same distance. These advantages enable the vertical array deployed at the critical depth to be used for the detection and positioning of deep-sea near-surface sound sources based on the reliable acoustic path (a combination of the direct path and the sea surface reflection path). Considering the correspondence between the target distance and the signal arrival pitch angle in the deep-sea reliable acoustic path mode, it is easy to estimate the target distance of the reliable acoustic path. Therefore, the research focus of domestic and foreign scholars in recent years has been on the research of target depth sounding methods and technologies using the interference characteristics of the sound field of the reliable acoustic path, and a large number of research results have been achieved.

[0003] McCargar, Zurk, Kniffin et al. (see literature [1] McCargar RK, Zurk L M. Depth-based signal separation with vertical line arrays in the deep ocean [J]. The Journal of the Acoustical Society of America, 2013, 133(4): EL320-EL325. Literature [2] McCargar R K, Zurk L M. Depth-based suppression of moving interference with vertical line arrays in the deep ocean[J].The Journal of the Acoustical Society ofAmerica,2012,132(3):2081-2081. Literature[3]Zurk LM,Boyle JK,Shibley J.Depth-basedpassive tracking of submerged sourced in the deep ocean using a vertical linearray[C] / / 2013Asilomar Conference on Signals,Systems and Computers. IEEE, 2013: 2130-2312. Reference [4] Kniffin GP, ​​Boyle JK, Zurk LM, Siderius M. Performance metrics for depth-based signal separation using deep vertical line arrays. The Journal of the Acoustical Society of America, 2016, 139: 418-425.) Using the interference fringes in the distance-depth plane caused by the superposition of the direct path and the sea surface reflection path (Lloyd's mirror interference), it is explained that for a narrowband signal, the signal energy is modulated by the depth of the sound source as a function of distance. This modulation change can be used to estimate the depth of the sound source. The generalized Fourier transform and zero-crossing detection method are used to estimate the target depth.

[0004] Yang et al. (see [5] Yang TC, Yoo K, Yates T. Matched-beam processing: Range tracking with vertical arrays in mismatched environments [J]. The Journal of the Acoustical Society of America, 1998, 104 (4): 2174-2188.) explained that the sound intensity is modulated by the depth of the sound source as a function of frequency, and estimated the depth of the sound source using the periodicity of the spectrum. Duan et al. (see [6] Duan R, Yang K, Ma Y, et al. Moving source localization with a single hydrophone using multipath time delays in the deep ocean [J]. The Journal of the Acoustical Society of America, 2014, 136 (2): EL159-EL165.) used an extended Kalman filter, used interference structure to estimate the depth of the sound source, and used a single hydrophone multipath structure to achieve the localization of the sound source.

[0005] ZHENG et al. (see reference [7] Zheng GY, Zhu F W. Difference Factor of Vertical Beam Pattern for Shallow-Water Source Depth Discrimination. Acoustics Australia, 2021, Vol. 49, No. 1, pp. 105-123.) applied incoherent matched beam processing to estimate the sound source depth. This method matches the time variation of the data beam peak with the time variation of the copy beam peak under the assumed sound source depth. The position where the copy beam best matches the data beam is the estimated sound source depth. Compared with the Fourier transform method, this method can obtain higher sound source depth estimation accuracy under the same distance and angle span, and is more suitable for estimating the depth of near-sea surface sound sources.

[0006] In the latest research results, ZHOU, ZHENG et al. (see reference [8] Zhou L, Zheng G, Yang TC. Target depth estimation by frequency interference matching for a deepvertical array. Applied Acoustics, 2022, Vol. 186, pp. 108493) proposed a depth estimation method based on peak beam intensity frequency interference structure matching based on narrowband matching beam intensity processing, which can be used for real-time or semi-real-time target depth estimation and identification.

[0007] Deep sea passive target depth estimation based on reliable acoustic path is to pick up target depth information by using the spatiotemporal characteristics of the sound field of the reliable acoustic path, which is a key issue in deep sea target detection. The Cramer-Rao lower bound describes the minimum value of the variance of the unbiased parameter estimation, which can reflect the theoretical optimal performance of the parameter estimation algorithm and plays an important role in parameter estimation theory. Therefore, it is meaningful to explore a Cramer-Rao bound analysis method for target depth estimation based on reliable acoustic path matching beam intensity processing. Summary of the invention:

[0008] The technical problem to be solved by the present invention is to provide a reliable Cramer-Rao bound analysis method for acoustic path matching beam intensity processing target depth estimation to achieve analysis of theoretical optimal performance.

[0009] The technical solution of the present invention is to provide a Cramer-Rao bound analysis method for reliable acoustic path matching beam intensity processing target depth estimation, comprising the following steps:

[0010] Step 1: determine the physical model of reliable acoustic path matching beam intensity processing, given a vertical receiving array deployed near the seabed in the deep sea, and calculate the peak beam intensity output by conventional beamforming, the broadband beam intensity fluctuation is the physical quantity to be matched;

[0011] Step 2, determine the observation data model, obtain independent data samples based on the frequency band of interest, and calculate the observed vertical array beam intensity data;

[0012] Step 3, calculate the likelihood ratio of the parameter to be estimated, and obtain the likelihood function and log-likelihood function of the observed data;

[0013] Step 4, calculate the second-order derivative of the log-likelihood function;

[0014] Step 5, according to the definition of Cramer-Rao bound, the Cramer-Rao bound of target depth estimation using reliable acoustic path matching beam intensity processing is obtained based on the inverse of Fisher information matrix J(θ), and the result is simulated by computer.

[0015] As a preferred embodiment, in step 1, given a vertical receiving array deployed near the seabed in the deep sea, the peak beam intensity of its conventional beamforming output is

[0016]

[0017] Where S(ω) represents the angular frequency, ω = 2πf, and k = k(ω) is the wave number and a function of the frequency. is the depth of the vertical array center position, is the elevation angle corresponding to the peak beam energy, z s is the target depth.

[0018] Preferably, in step 2, assuming that L independent data samples can be obtained for the frequency band of interest, the observed vertical array beam intensity data can be expressed as

[0019] B l (θ) = s l G(θ)+n l l=1,2,…,L (2)

[0020] Among them, s l =S H (ω)S(ω) is the amplitude term of the sound source spectrum, r l (θ) is an N×1 dimensional column vector, which is the data sample of N frequency points at the lth sampling time. describes the vertical array beam strength function used to match, n l is the observation noise vector within a given frequency band.

[0021] Preferably, in step 3, the likelihood function and log-likelihood function of the observed data are expressed as follows:

[0022]

[0023] L(θ,B)=ln p(B|θ)

[0024] The covariance matrix is

[0025]

[0026] Furthermore, in step 4, the Fisher information matrix J(θ) is expressed as follows,

[0027]

[0028] After derivation, the received signal model can be obtained as formula (2), and the Fisher information matrix when the noise model is a white noise model is:

[0029]

[0030] in,

[0031] is the signal-to-noise ratio term;

[0032] is the mean sensitivity of the beam strength function to the parameters to be estimated;

[0033] is the curvature of the sensitivity of the parameter to be estimated in the beam intensity function;

[0034]

[0035] Compared with the prior art, the present invention has the following advantages after adopting the above scheme:

[0036] Aiming at the problem of performance limit analysis of target depth estimation by broadband matched beam intensity processing in deep-sea reliable acoustic path, the present invention theoretically derives the Cramer-Rao bound of broadband matched beam intensity processing, and analyzes the relationship between factors such as signal-to-noise ratio, target position, processing bandwidth, pitch angle error and the Cramer-Rao bound of depth estimation based on simulation research, which can reflect the theoretical optimal performance of the passive target depth estimation algorithm by deep-sea reliable acoustic path. Description of the drawings:

[0037] Figure 1 Cramer-Rao bound solving process for target depth estimation for matching beam intensity;

[0038] Figure 2 is the variation of the lower bound of the depth estimation standard deviation with the signal-to-noise ratio;

[0039] Figure 3 is the distribution of the lower bound of the depth estimation standard deviation with the target spatial position;

[0040] Figure 4 The lower bound of the depth estimation standard deviation varies with target depth at different target distances;

[0041] Figure 5 The lower bound of the depth estimation standard deviation changes with the processing bandwidth when the signal-to-noise ratio is set to 5dB and the target distance is 5km, 15km, and 25km;

[0042] Figure 6 is the variation of the lower bound of the depth estimation standard deviation with the pitch angle estimation standard deviation. Specific implementation method:

[0043] The present invention will be further described below with reference to the accompanying drawings:

[0044] like Figure 1-6As shown, this embodiment provides a Cramer-Rao bound analysis method for reliable acoustic path matching beam intensity processing target depth estimation, comprising the following steps:

[0045] Step 1: Determine the physical model for reliable acoustic path matching beam intensity processing. Given a vertical receiving array deployed near the seabed in the deep sea, and calculating the peak beam intensity of the conventional beamforming output, the broadband beam intensity fluctuation is the physical quantity to be matched; the peak beam intensity of the beamforming output is

[0046]

[0047] Where S(ω) represents the angular frequency, ω = 2πf, and k = k(ω) is the wave number and a function of the frequency. is the depth of the vertical array center position, is the elevation angle corresponding to the peak beam energy. s is the target depth. The broadband beam intensity fluctuation is the physical quantity to be matched;

[0048] Step 2: Determine the observation data model, obtain independent data samples based on the frequency band of interest, and calculate the observed vertical array beam intensity data; assuming that for the frequency band of interest, L independent data samples can be obtained, the observed vertical array beam intensity data can be expressed as

[0049] B l (θ) = s l G(θ)+n l l=1,2,…,L (2)

[0050] Among them, s l =S H (ω)S(ω) is the amplitude term of the sound source spectrum, r l (θ) is an N×1 dimensional column vector, which is the data sample of N frequency points at the lth sampling time. describes the vertical array beam strength function used to match, n l is the observation noise vector within a given frequency band;

[0051] Step 3, calculate the likelihood ratio of the parameter to be estimated, and obtain the likelihood function and log-likelihood function of the observed data; in this step, the likelihood function and log-likelihood function of the observed data are expressed as follows:

[0052]

[0053] L(θ,B)=ln p(B|θ) (4)

[0054] The covariance matrix is

[0055]

[0056] Step 4: Calculate the second-order derivative of the log-likelihood function. In this step, the Fisher information matrix J(θ) is expressed as follows:

[0057]

[0058] After derivation, we can obtain the Fisher information matrix when the received signal model is formula x and the noise model is the white noise model:

[0059]

[0060] in,

[0061] is the signal-to-noise ratio term;

[0062] is the mean sensitivity of the beam strength function to the parameters to be estimated;

[0063] is the curvature of the sensitivity of the parameter to be estimated in the beam intensity function;

[0064]

[0065] Step 5, according to the definition of Cramer-Rao bound, the Cramer-Rao bound of target depth estimation using reliable acoustic path matching beam intensity processing is obtained based on the inverse of Fisher information matrix J(θ), and the result is simulated by computer.

[0066] in, Figure 1 The Cramer-Rao bound solution process for target depth estimation using matched beam intensity is given.

[0067] In a typical Munk deep-sea environment, with a target depth of 50m and a processing frequency band of 100Hz to 300Hz, the lower bound of the depth estimation standard deviation varies with the signal-to-noise ratio as follows: Figure 2 As shown. Figure 2 It can be seen that the signal-to-noise ratio has a significant impact on the depth estimation performance. When the signal-to-noise ratio changes from -20dB to 10dB, the lower bound of the depth estimation standard deviation decreases by two orders of magnitude. In addition, it is worth noting that when the target distance is 15km, the lower bound of the depth estimation standard deviation is always higher than the lower bound of the depth estimation standard deviation when the target depth is 5km, which shows that the performance of depth estimation is related to the target distance.

[0068] The signal-to-noise ratio is 5dB, the processing frequency band is 100Hz~300Hz, and the distribution of the lower bound of the depth estimation standard deviation with the target spatial position is as follows Figure 3As shown. It can be seen that the farther the target is, the larger the lower bound of the depth estimation standard deviation is. The reason is that the farther the target is, the smaller the pitch angle (sine) of the acoustic signal is, and the Fisher information matrix is ​​positively correlated with the pitch angle (sine) of the acoustic signal. Therefore, the lower bound of the depth estimation standard deviation is inversely correlated with the pitch angle (sine) of the acoustic signal, that is, it is positively correlated with the change in target distance. The physical reason is that the smaller the pitch angle (sine) of the acoustic signal, the slower the broadband change of the beam intensity, and the fewer the number of cycles, resulting in poor depth estimation performance of the matching frequency domain interference structure.

[0069] Under different distance slice conditions, the lower bound of the depth estimation standard deviation varies with the target depth as follows: Figure 4 As shown, it can be seen that when the target depth is less than 10m, there is a peak in the lower bound of the depth estimation standard deviation. When the target depth is greater than 50m, the lower bound of the depth estimation standard deviation of the target at a close distance remains almost unchanged, and the lower bound of the depth estimation standard deviation of the target at a long distance has certain fluctuations.

[0070] When the signal-to-noise ratio is 5dB and the target depth is 50m, the lower bound of the depth estimation standard deviation varies with the processing bandwidth at different target distances, such as Figure 5 As shown in Figure 2, it can be seen that as the processing bandwidth increases, the lower bound of the depth estimation standard deviation gradually decreases, and the depth estimation performance improves.

[0071] When the target depth is 50m and the target distance is 5km, 15km, and 25km, the lower bound of the depth estimation standard deviation changes with the pitch angle standard deviation as shown below: Figure 6 As shown in Figure 2, it can be seen that the larger the standard deviation of the pitch angle estimation, the larger the lower bound of the depth estimation standard deviation, and the worse the depth estimation performance.

[0072] The above is only an explanation of the preferred embodiments of the present invention, which should not be construed as a limitation on the claims. Any equivalent structure or equivalent process changes made using the present invention specification are included in the patent protection scope of the present invention.

Claims

1. A Cramer-Rao bound analysis method for reliable acoustic path matching beam intensity processing target depth estimation, characterized by: The following steps are included: Step 1: determine the physical model of reliable acoustic path matching beam intensity processing, given a vertical receiving array deployed near the seabed in the deep sea, and calculate the peak beam intensity output by conventional beamforming, the broadband beam intensity fluctuation is the physical quantity to be matched; Step 2, determine the observation data model, obtain independent data samples based on the frequency band of interest, and calculate the observed vertical array beam intensity data; Step 3, calculate the likelihood ratio of the parameter to be estimated, and obtain the likelihood function and log-likelihood function of the observed data; Step 4, calculate the second-order derivative of the log-likelihood function; Step 5, according to the definition of Cramer-Rao bound, based on the inverse of Fisher information matrix J(θ), the Cramer-Rao bound of target depth estimation using reliable acoustic path matching beam intensity processing is obtained, and the result is simulated by computer; wherein, In step 1, given a vertical receiving array deployed near the seabed in the deep sea, the peak beam intensity of its conventional beamforming output is Where S(ω) represents the angular frequency, ω = 2πf, and k = k(ω) is the wave number and a function of the frequency. is the depth of the vertical array center position, is the elevation angle corresponding to the peak beam energy, z s is the target depth; In step 2, assuming that L independent data samples are available for the frequency band of interest, the observed vertical array beam intensity data can be expressed as B l (θ)=s l G(θ)+n l l=1,2,…,L (2) Among them, s l =S H (ω)S(ω) is the amplitude term of the sound source spectrum, r l (θ) is an N×1 dimensional column vector, which is the data sample of N frequency points at the lth sampling time. describes the vertical array beam strength function used to match, n l is the observation noise vector within a given frequency band.

2. The Cramer-Rao bound analysis method for target depth estimation by reliable acoustic path matching beam intensity processing according to claim 1 is characterized in that: In step 3, the likelihood function and log-likelihood function of the observed data are expressed as follows: L(θ,B)=ln p(B|θ) The covariance matrix is 3. The Cramer-Rao bound analysis method for target depth estimation by reliable acoustic path matching beam intensity processing according to claim 1, characterized in that: In step 4, the Fisher information matrix J(θ) is expressed as follows, After derivation, the received signal model can be obtained as formula (2), and the Fisher information matrix when the noise model is a white noise model is: in, is the signal-to-noise ratio term; is the mean sensitivity of the beam strength function to the parameters to be estimated; is the curvature of the sensitivity of the parameter to be estimated in the beam intensity function;

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