Passive target speed estimation algorithm based on sparse Bayesian learning cross spectrum

Abstract

The invention discloses a passive target speed estimation algorithm based on a sparse Bayesian learning cross spectrum, and belongs to the technical field of array signal processing. The method comprises the following steps: constructing a target cross-correlation field model, carrying out cross-spectrum on sound pressure and a delayed sound pressure channel to obtain cross-spectrum sound intensity flow, constructing a dictionary matrix according to target cross-spectrum frequency point features, establishing a joint probability density distribution function by virtue of a sparse Bayesian learning model, and finally estimating signal power according to maximum logarithm Bayesian evidence. And carrying out spectrum peak search on the signal power estimation value to realize speed estimation of the target. According to the method, the cross-spectrum sound intensity flow is used as input, all cross-spectrum frequency points are compensated, alignment of cross-spectrum results of different frequency points is achieved, the background noise suppression effect is achieved, and multi-frequency-point processing results are fused. Meanwhile, the method has good speed estimation precision, can maintain good performance under the condition of low signal-to-noise ratio, and has high engineering application value.

Description

Technical Field

[0001] The invention belongs to the technical field of array signal processing, and in particular relates to a passive target speed estimation algorithm based on sparse Bayesian learning cross spectrum. Background Art

[0002] The cross-spectrum method is one of the commonly used methods for estimating the radial velocity of hydroacoustic targets. How to ensure the performance of the algorithm under low signal-to-noise ratio conditions is the direction of continuous research on hydroacoustic target velocity measurement algorithms. Some methods introduce specific hydrological parameters and use waveguide invariants for ranging to achieve indirect velocity measurement. This method improves the velocity measurement accuracy but loses the advantage of the cross-spectrum method that it does not rely on hydrological information. In particular, when the hydrological data is mismatched, the velocity measurement performance will degrade sharply. Another method is to fuse the target radial velocity results solved at different frequencies through a show of hands or histogram statistics. Taking the histogram algorithm as an example, although it improves the performance under low signal-to-noise ratio conditions, its performance is affected by the histogram statistics and the width of each element of the histogram. Summary of the invention

[0003] (I) Purpose of the invention

[0004] The purpose of the present invention is to overcome the defects in the prior art and provide a passive target velocity estimation algorithm based on sparse Bayesian learning cross spectrum; the present invention enables the underwater acoustic target radial velocity estimation method to have good performance under high signal-to-noise ratio while improving the performance under low signal-to-noise ratio conditions, and the present invention can work normally under lower signal-to-noise ratio conditions.

[0005] (II) Technical solution

[0006] To achieve the above object, the present invention adopts the following technical solution: a sparse Bayesian target velocity passive estimation algorithm, comprising the following steps:

[0007] Step 1: The cross-spectrum of the scalar hydrophone sound pressure p(r) and the sound pressure p(r+Δr) after a certain delay is obtained to obtain the cross-spectrum sound intensity current I r,r+Δr ;

[0008] Step 2, based on the signal structure of the cross-spectral acoustic intensity flow, a sparse dictionary matrix is ​​established and a target cross-spectral signal model is constructed;

[0009] Step 3, construct a sparse Bayesian learning model based on the target cross-spectral signal model to obtain a probabilistic description of the target radial velocity;

[0010] Step 4, based on the sparse Bayesian model, alternately iteratively estimate the hyperparameters and the noise variance to obtain signal estimation values ​​at different speeds;

[0011] Step 5, terminating the iteration according to the convergence condition or the upper limit of the number of iterations, and the obtained hyperparameter is the target radial velocity estimation result;

[0012] The step 1 is specifically as follows:

[0013] According to the normal wave theory, for a point sound source of unit intensity and a horizontal constant waveguide, the sound source signal frequency is f, the depth is z, and the receiving depth is z. r Assuming that the target maintains a constant depth z and moves at a constant speed v0 on the horizontal plane, the radial velocity relative to the hydrophone in the horizontal direction is v r , then the sound pressure spectrum signals received at distances r and r+Δr are cross-correlated to obtain

[0014]

[0015] in, c p is the average phase velocity, Δk mn =k rm -k rn , is the average horizontal beam and

[0016] The step 2 is specifically as follows:

[0017] Step 2-1: Create a sparse dictionary matrix:

[0018] According to the sparse theory, the target speed Evenly divided into (2N+1) parts, we get an overcomplete dictionary matrix A(V,f l )=[A(v1,f l ),...,A(v N ,f l )], where the nth column element of the dictionary matrix is:

[0019]

[0020] Step 2-2: Construct a cross-spectral acoustic intensity flow signal model

[0021] At a certain time t, the target keeps the depth z unchanged and moves at a constant speed v0 on the horizontal plane. The radial velocity relative to the hydrophone in the horizontal direction is v r , the cross-correlation sound intensity flow can be expressed as a linear model:

[0022] I(f l )=A(V,f l )S(f l )+N(f l )

[0023] Among them, I(f l )=[I1(f l ),...,I M (fl )] T is an M*1 dimensional data vector, A(V,f l ) is a dictionary matrix of M*(2N+1) dimensions, S(f l ) is the target speed information of (2N+1)*1 dimension, N(f l ) is an M*1-dimensional noise matrix. The set {f1,...,f L} is the frequency point to be processed, with a total of L frequency points.

[0024] Step 4 is as follows:

[0025] Step 4-1: Solving for hyperparameter γ

[0026] After establishing the probability description of the target radial velocity in step 3, define the hyperparameter γ = [γ1,...,γ M ] to approximate the energy of the radial velocity of each target, and solve the hyperparameter γ by maximizing the logarithmic Bayesian evidence:

[0027]

[0028] Continuously iterate and update the hyperparameters to obtain the optimal parameter values. The current iteration round is recorded as k. The update formula obtained by the fixed-point iteration method is as follows:

[0029]

[0030] Step 4-2: Target radial velocity estimation

[0031] After updating the estimated value of the hyperparameter γ in the kth iteration, (k+1) Perform a peak search to determine the target radial velocity.

[0032] Step 4-3: Noise estimation

[0033] After obtaining the target radial velocity, the noise variance update formula is as follows:

[0034]

[0035] Where M is the number of observation channels, is the corresponding element of the target speed in the dictionary matrix,

[0036] Step 5 is as follows:

[0037] Assume ε min is the iteration termination threshold, and the iteration termination condition is:

[0038]

[0039] The iterative γ is the output result of the sparse Bayesian learning cross-spectral algorithm.

[0040] (III) Effective income

[0041] Compared with the prior art, the present invention has the following beneficial technical effects:

[0042] 1. The present invention utilizes the sparse characteristic of the target velocity in the cross-correlation spectrum, obtains the cross-spectral sound intensity flow through the cross-spectrum of the sound pressure and the sound pressure after a certain time delay, establishes a sparse Bayesian learning model for the target radial velocity estimation, and estimates the signal power and noise power of each radial velocity alternately and iteratively based on the model.

[0043] 2. The present invention adopts the cross-spectrum sound intensity flow as input, which overcomes the problem that the cross-spectrum algorithm cannot directly accumulate the solution results of each frequency, integrates all frequency point information and suppresses noise, and has good performance at high signal-to-noise ratio and maintains good accuracy under low signal-to-noise ratio conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a flow chart of the passive target speed estimation algorithm of the present invention;

[0045] Figure 2 This is a schematic diagram of the comparison of target radial velocity estimation results under -30dB signal-to-noise ratio conditions;

[0046] Figure 2 (a) is a schematic diagram of the radial velocity estimation result of the target in the example using the cross-spectrum algorithm under the condition of -30dB signal-to-noise ratio;

[0047] Figure 2 (b) is a schematic diagram of the radial velocity estimation result of the target in the example by the algorithm of the present invention under the condition of -30dB signal-to-noise ratio;

[0048] Figure 3 The radial velocity estimation results of the target in the example are obtained by the algorithm of the present invention and the cross-spectrum algorithm; the red line is the estimation result of the algorithm of the present invention; and the blue line is the estimation result of the cross-spectrum algorithm. DETAILED DESCRIPTION

[0049] The present invention is described clearly below in conjunction with the drawings and specific embodiments in the embodiments of the present invention. The description herein is only used to explain the present invention, but is not intended to be a limitation of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work, any modifications, equivalent substitutions, improvements, etc., should be included in the protection scope of the present invention.

[0050] Example 1

[0051] like Figure 1As shown, the sparse Bayesian target speed passive estimation algorithm provided by the present invention comprises the following steps:

[0052] Step 1: The cross-spectrum of the scalar hydrophone sound pressure p(r) and the sound pressure p(r+Δr) after a certain delay is obtained to obtain the cross-spectrum sound intensity current I r,r+Δr ;

[0053] Step 2, based on the signal structure of the cross-spectral acoustic intensity flow, a sparse dictionary matrix is ​​established and a target cross-spectral signal model is constructed;

[0054] Step 3, construct a sparse Bayesian learning model based on the target cross-spectral signal model to obtain a probabilistic description of the target radial velocity;

[0055] Step 4, based on the sparse Bayesian model, alternately iteratively estimate the hyperparameters and the noise variance to obtain signal estimation values ​​at different speeds;

[0056] Step 5: The iteration is terminated according to the convergence condition or the upper limit of the number of iterations, and the obtained hyperparameters are the target radial velocity estimation results.

[0057] The following is a detailed description.

[0058] The target keeps its depth constant and moves at a constant speed v0 on the horizontal plane. Its radial speed relative to the hydrophone is v r , then the cross-correlation sound intensity is:

[0059]

[0060] where f l ∈[f1,...,f L ] indicates the processing frequency, and there are L frequency points in total.

[0061] The cross-correlation sound intensity can be expressed as a linear model:

[0062] I(f l )=A(V,f l )S(f l )+N(f l )

[0063] Among them, I(f l )=[I1(f l ),...,I M (f l )] T is an M*1 dimensional data vector, A(V,f l ) is a dictionary matrix of M*(2N+1) dimensions, S(f l ) is the target speed information of (2N+1)*1 dimension, N(f l ) is an M*1-dimensional noise matrix. According to the sparse theory, the target speed Evenly divided into (2N+1) parts, we get an overcomplete dictionary matrix A(V,f l )=[A(v1,f l ),...,A(v N ,f l )], where the nth column element of the dictionary matrix is

[0064]

[0065] Taking advantage of the sparse characteristics of the signal in the frequency domain, we introduce the hyperparameter γ=[γ1,...,γ N ] T For S f Perform variational approximation, through hyperparameters γ and noise σ l 2 The target position estimation is achieved through alternating iterations.

[0066] If the signal and noise are uncorrelated, the likelihood of the data can be written as

[0067]

[0068] Let Γ = diag(γ1,…,γ N )=diag(γ), then we have a priori model

[0069]

[0070] Deriving Bayesian evidence from prior probability and likelihood under Gaussian assumption

[0071]

[0072] Among them, the covariance matrix

[0073] By maximizing the logarithmic Bayesian evidence to estimate the hyperparameter γ, we have the following formula:

[0074]

[0075] The hyperparameters γ and It can be updated by the last iteration. Using the fixed-point iteration method to update γ, we have the following formula:

[0076]

[0077] For different line spectrum frequencies of the same target, the spectrum of the cross-correlation sound intensity is the same. Therefore, the iterative formula under multiple frequencies is obtained:

[0078]

[0079] Assume that the noise is wide stationary noise Then there is

[0080]

[0081] Where M is the number of observation channels, is the corresponding element of the target speed in the dictionary matrix, Assume ε min is the iteration termination threshold, and the iteration termination condition is

[0082]

[0083] The iterative γ is the output result of the sparse Bayesian learning cross-spectral algorithm.

[0084] The effect of the above method is explained below through numerical simulation:

[0085] The surface target speed is set to 2.5m / s, starting from a position 5km away from the hydrophone, with a heading angle of 0°, a closest passing distance of 3km, and the sound source emits 69, 117, 183, 259, and 315Hz line spectrum signals. The cross-spectrum algorithm (CS) is added to the simulation as a comparison algorithm. Each simulation result is obtained through 1000 Monte Carlo experiments. The target radial velocity estimation is simulated based on the changes in algorithm performance under different signal-to-noise ratios.

[0086] Depend on Figure 2 a and Figure 2 b It can be seen that under low signal-to-noise ratio conditions, the method proposed in this patent has lower background noise and higher recognition. That is, the method proposed in this patent effectively suppresses background noise and has better performance under low signal-to-noise ratio conditions.

[0087] Depend on Figure 3 It can be seen that both methods have good accuracy at high signal-to-noise ratio. As the signal-to-noise ratio decreases, the accuracy of the method proposed in this patent decreases slowly. At the same time, it can work in a lower signal-to-noise ratio environment. The method proposed in this patent is completely superior to the CS algorithm in low signal-to-noise ratio conditions and has good accuracy under low signal-to-noise ratio conditions.

[0088] The present invention utilizes the sparse characteristic of the target velocity in the cross-correlation spectrum, obtains the cross-spectrum sound intensity flow through the cross-spectrum of the sound pressure and the sound pressure after a certain time delay, establishes a sparse Bayesian learning model for the target radial velocity estimation, and estimates the signal power and noise power of each radial velocity alternately and iteratively based on the model. The algorithm uses the cross-spectrum sound intensity flow as input, overcomes the problem that the cross-spectrum algorithm cannot directly accumulate the solution results of each frequency, integrates all frequency point information and suppresses noise, and has good performance at high signal-to-noise ratio, and maintains good accuracy under low signal-to-noise ratio conditions.

[0089] The above contents are further detailed descriptions of the present invention in combination with specific implementation methods, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A passive target velocity estimation algorithm based on sparse Bayesian learning cross spectrum, characterized in that: The following steps are involved: Step 1: The cross-spectrum of the scalar hydrophone sound pressure p(r) and the sound pressure p(r+Δr) after a certain delay is obtained to obtain the cross-spectrum sound intensity current I r,r+Δr ; Step 2, based on the signal structure of the cross-spectral acoustic intensity flow, a sparse dictionary matrix is ​​established and a target cross-spectral signal model is constructed; Step 3, construct a sparse Bayesian learning model based on the target cross-spectral signal model to obtain a probabilistic description of the target radial velocity; Step 4, based on the sparse Bayesian model, alternately iteratively estimate the hyperparameters and the noise variance to obtain signal estimation values ​​at different speeds; Step 5, terminating the iteration according to the convergence condition or the upper limit of the number of iterations, and the obtained hyperparameter is the radial velocity estimation result of the underwater acoustic target; The step 1 is specifically as follows: For a point sound source of unit intensity and a horizontal constant waveguide, the sound source signal frequency is f, the depth is z, and the receiving depth is z r ; Assume that the target maintains a constant depth z and moves at a constant speed v0 on the horizontal plane. The radial velocity relative to the hydrophone in the horizontal direction is v r , then the sound pressure spectrum signals received at distances r and r+Δr are cross-correlated to obtain in, c p is the average phase velocity, Δk mn =k rm -k rn , is the average horizontal beam and The step 2 is specifically as follows: Step 2-1: Create a sparse dictionary matrix: Set the target speed Evenly divided into (2N+1) parts, we get an overcomplete dictionary matrix A(V,f l )=[A(v1,f l ),...,A(v N ,f l )], where the nth column element of the dictionary matrix is: Step 2-2: Construct a cross-spectral acoustic intensity flow signal model At a certain time t, the target keeps the depth z unchanged and moves at a constant speed v0 on the horizontal plane. The radial velocity relative to the hydrophone in the horizontal direction is v r , the cross-correlation sound intensity flow can be expressed as a linear model: I(f l )=A(V,f l )S(f l )+N(f l ) Among them, I(f l )=[I1(f l ),...,I M (f l )] T is an M*1 dimensional data vector, A(V,f l ) is a dictionary matrix of M*(2N+1) dimensions, S(f l ) is the target speed information of (2N+1)*1 dimension, N(f l ) is an M*1-dimensional noise matrix; the set {f1,...,f L } is the frequency point to be processed, with a total of L frequency points; Step 4 is as follows: Step 4-1: Solving for hyperparameter γ After establishing the probability description of the target radial velocity in step 3, define the hyperparameter γ = [γ1,...,γ M ] to approximate the energy of the radial velocity of each target, and solve the hyperparameter γ by maximizing the logarithmic Bayesian evidence: Iteratively update the hyperparameters to obtain the optimal parameter values. The current iteration round is denoted as k. The update formula obtained by the fixed-point iteration method is as follows: Step 4-2: Target radial velocity estimation After updating the estimated value of the hyperparameter γ in the kth iteration, (k+1) Perform spectrum peak search to determine the target radial velocity; Step 4-3: Noise estimation After obtaining the target radial velocity, the noise variance update formula is as follows: Where M is the number of observation channels, is the corresponding element of the target speed in the dictionary matrix, Step 5 is as follows: Assume ε min is the iteration termination threshold, and the iteration termination condition is: The iterative γ is the output result of the sparse Bayesian learning cross-spectral algorithm.

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