CN115015832A - Large-scale array amplitude-phase error and target direction joint estimation method under non-uniform noise - Google Patents
Large-scale array amplitude-phase error and target direction joint estimation method under non-uniform noise Download PDFInfo
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Abstract
The invention provides a large-scale array amplitude-phase error and target direction joint estimation method under non-uniform noise, and belongs to the field of underwater acoustic array signal processing. The method and the device construct a variational Bayesian model based on background non-Gaussian noise and uniform linear array amplitude-phase characteristics, jointly estimate the noise power and array amplitude-phase deviation of each array element, modify an array flow pattern matrix and realize high-precision DOA estimation. Compared with the existing direction estimation method of the same type, the method has higher estimation precision and stronger adaptability.
Description
Technical Field
The invention relates to a large-scale array amplitude-phase error and target direction joint estimation method under non-uniform noise, belongs to the field of underwater acoustic array signal processing, and aims to solve the problems of amplitude and phase inconsistency and the like caused by bending, moving and the like of an underwater acoustic array during underwater installation.
Background
Direction of Arrival (DOA) estimation is a popular research Direction in array signal processing, and in the field of underwater acoustic detection, an underwater acoustic signal is observed and received by a plurality of hydrophones in an array, so that DOA estimation of an underwater acoustic target is realized. The traditional beam forming methods such as CBF (cone beam forming), MVDR (multifunction vehicle distance digital) and the like are limited in resolution and not enough to meet the high-precision requirement, and subspace type azimuth estimation methods such as MUSIC (multi-information scale) and ESPRIT (approximate least square) methods and the like can obtain a high-resolution azimuth estimation result, but need the number of information sources and the like as prior information.
Because the marine environment is more complicated and changeable, the hydrophone array can encounter the interference of seawater flow velocity, high pressure, heavy waves, installation, movement and the like caused by water flow when array arrangement operation is carried out underwater, the shape of the underwater acoustic array is deformed, the array amplitude and phase consistency is difficult to guarantee, the underwater array is usually longer and different from an ideal Gaussian noise environment, the noise environment where adjacent array elements are located is usually non-Gaussian noise and is not uniformly distributed, the direction-finding precision of the traditional method is reduced under the combined action of amplitude and phase inconsistency errors and non-Gaussian non-uniform noise, and an underwater target is difficult to accurately estimate. Although there are currently improved MUSIC methods for amplitude-phase error and gaussian uniform noise, respectively. However, in actual processing, extra source number estimation is often needed as a premise, and the DOA estimation requirement in the presence of both cases cannot be met.
Disclosure of Invention
The invention aims to provide a large-scale array amplitude-phase error and target direction combined estimation method under non-uniform noise, and solves the underwater DOA estimation problem under the environment of non-uniform amplitude-phase and non-Gaussian non-uniformly distributed noise.
The purpose of the invention is realized as follows: the method comprises the following steps:
the method comprises the following steps: the method comprises the following steps of building an underwater uniform long-line array, uniformly distributing the underwater uniform long-line array at a half-wavelength interval during distribution, and based on background non-Gaussian noise and uniform linear array amplitude-phase characteristics, enabling incident signal models received by each array element module to be as follows:
Y＝E p AX+V
step two: establishing prior distribution of each variable in the model; for array received signals, a complex gaussian distribution is constructed:
wherein Y is t Representing the received data vector at time t, X t Representing the desired signal vector at time t, the layered Gamma of the noise variance β is:
wherein: beta is a m Is the element with beta at the m-th array element, and c represents the noise variance beta m Shape parameter of d m Representing the variance beta of the noise at the m-th array element m The inverse scale parameter of (d);
the complex gaussian distribution of the desired signal is:
where α is the variance of the desired signal, x tn For received data of the nth spatial grid at time t, α n The variance of the expected signal at the nth scanning position;
the layered Gamma distribution of the desired signal variance α is:
wherein: a denotes the desired signal variance α n Shape parameter of (b) n Representing the variance α of the desired signal at the nth spatial grid n The inverse scale parameter of (d);
step three: initializing parameters; setting the initial value iter of the iteration number to be 1, initializing the maximum, N, a,
c，
and E p Maximum is the iteration maximum, N is the number of meshes divided by the whole space azimuth, a is the shape parameter of the variance of the expected signal distribution,
an inverse scale parameter for the variance of the desired signal distribution, c a shape parameter for the noise variance distribution,
as inverse scale parameter of the noise variance distribution, E p The initial value of the amplitude-phase characteristic of the array to be estimated is obtained;
step four: iterative computation, namely obtaining an iterative formula of each parameter according to the distribution in the step two, and updating;
step five: judging whether the iteration condition is met, if not, continuing the step four, and if so, jumping out of the iteration and outputtingGoes out mu x ；
Step six: searching a spectrum peak, and carrying out azimuth estimation according to the recovery signal:
wherein: i | · | purple wind 1 Representing a matrix-norm operation, | · | count non-woven phosphor ∞ Infinite norm operation representing a matrix;
step seven: outputting a bearing estimation result P VB (θ)。
The invention also includes such structural features:
1. the fourth step specifically comprises:
updating sigma x ：
Σ x ＝(A H E p H diag(<β>)EA+diag(<α>)) -1
Updating mu x ：
μ x ＝Σ x A H E p H diag(<β>)Y
Updating
Updating
Updating
Updating
Updating
Updating the mean of each variable, including:
let iter be iter + 1.
3.2. The method is characterized in that the iteration termination condition is as follows:
iter≥maxiter
or
Wherein tol is a set termination threshold, and the value of tol is 0.001; α is the iteratively calculated variance of the desired signal, defined as:
where < > represents the expectation of the variable to be solved.
Compared with the prior art, the invention has the beneficial effects that: the invention jointly considers the amplitude-phase inconsistency error and the non-Gaussian non-uniform noise, constructs a joint optimization model caused by the amplitude-phase error and the non-Gaussian non-uniform noise error, fully considers the influence brought by two conditions in the array received signal model, and jointly estimates the two conditions and the orientation, thereby compensating the array amplitude-phase deviation, reducing the influence of the non-Gaussian non-uniform noise and achieving the purpose of accurately estimating the orientation of the received signal of each array element. The method has higher resolution for the azimuth estimation of the target under the conditions of amplitude-phase inconsistent errors, noise in a complex environment and various array element disturbances, and has better adaptability to the environment with the amplitude-phase errors and non-Gaussian non-uniform noise.
Drawings
FIG. 1 is a schematic diagram of an array receive signal system according to the present invention;
FIG. 2 is a model of the noise and amplitude phase inconsistency joint modeling of the present invention;
FIG. 3 is a process flow diagram of joint position estimation of the present invention;
fig. 4(a) - (b) are graphs comparing the present invention (the joint DOA estimation method) with two other methods (the DOA method based on amplitude and phase errors, the DOA method based on gaussian noise): FIG. 4(a) the results of the orientation spectrum estimation of the respective methods; FIG. 4(b) Root Mean Square Error (RMSE) results for each method.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The steps of the invention are as follows with reference to the attached drawings:
(1) as shown in fig. 1, an M-element underwater uniform long-line array is built, the M-element underwater uniform long-line array is uniformly distributed at a half-wavelength interval during distribution, each array element receives an incident signal, and based on background non-gaussian noise and the amplitude-phase characteristics of the uniform linear array, an incident signal model received by each array element module is as follows:
Y＝E p AX+V
wherein,
a matrix of data received for the hydrophone array,
is the amplitude-phase error matrix for each channel of the array,
for the matrix of desired signals after sampling,
in the form of an array of flow pattern matrices,
the method is characterized in that a noise matrix at each array element of a hydrophone array is adopted, T is the length of data received by the array, and N is the grid number of division of a search azimuth space. The noise received by each hydrophone in the array is assumed to be Gaussian noise with different power, and the noise power follows non-uniform distribution and is independent of each other at each snapshot.
(2) Based on background non-Gaussian noise and the amplitude-phase characteristics of the uniform line array, a variation inference model shown in FIG. 2 is constructed.
(2.1) constructing a complex Gaussian distribution of the array received signal as follows:
wherein, Y t Representing the received data vector at time t, X t Representing a desired signal vector at the t-th moment, beta being a noise variance; the layered Gamma distribution of the noise variance β is constructed as:
wherein, beta m Is the element with beta at the m-th array element, and c represents the noise variance beta m Shape parameter of d m Represents the variance beta of the noise at the m-th array element m The inverse scale parameter of (d);
the complex gaussian distribution of the desired signal is constructed as:
where α is the variance of the desired signal, x tn For received data of the nth spatial grid at time t, α n The variance of the expected signal at the nth scanning position;
constructing a layered Gamma distribution of the variance α of the desired signal as
Where a represents the desired signal variance α n Shape parameter of b n Representing the variance α of the desired signal at the nth spatial grid n The inverse scale parameter of (d);
at this time, the joint distribution for the observed data and hidden variables can be expressed as:
p(Y m ,X,α,β m ；E pmm )＝p(Y m |X,β m ；E pmm )p(X|α)p(α)p(β m )
wherein E is pmm Is a parameter matrix E p The mth element of (1).
(2.2) utilizing a variational inference theory, sequentially substituting the distribution matrix constructed in the step (2.1) into the following formula to solve the posterior probability of each variable:
solving the variable X to obtain:
solving the variable beta to obtain:
for parameter E p And solving to obtain:
wherein q (-) represents the posterior probability of the variable (-) and ln (-) represents the logarithm,<·>expressing the expectation, p (. smallcircle.) represents the probability of the element therein, which can be obtained from (2.1), diag (. smallcircle.) represents the diagonal operation,
is a parameter matrix E p Represents the amplitude-phase error, mu, at the mth array element x Representing the mean value of the desired signal, sigma x Representing the variance of the desired signal.
(3) And (3) calculating the mean value and the variance of each variable according to the probability distribution of each variable obtained in the step (2).
(3.1) initializing parameters; setting the initial value iter of the iteration number to be 1, initializing the initial value maximum, N, a,
c，
and E p Maximum number of iterations, N the number of meshes divided for the entire spatial azimuth, a the shape parameter of the variance of the expected signal distribution,
an inverse scale parameter for the variance of the desired signal distribution, c a shape parameter for the noise variance distribution,
as inverse scale parameter of the noise variance distribution, E p The initial value of the amplitude-phase characteristic of the array to be estimated is obtained; then, according to the probability distribution of each variable obtained in the step (2), each parameter is sequentially subjected to iterative updating;
(3.2) updating the variance Σ of the desired signal in sequence x Mean value of μ x Sum array amplitude and phase error matrix
Updating sigma x ：
Σ x ＝(A H E p H diag(<β>)EA+diag(<α>)) -1
Updating mu x ：
μ x ＝Σ x A H E p H diag(<β>)Y
Updating
And (3.3) updating each distribution parameter according to the result of (3.2), wherein the updating comprises the following steps:
updating
Updating
Updating
Updating
(3.4) updating the mean value of each variable according to the result of (3.3), including:
the mean result of each variable is the result of the iteratively estimated variable, e.g. α ═<α n >The same applies otherwise.
(3.5) update iter:
iter＝iter+1
(4) judging whether an iteration termination condition is met, wherein the iteration termination condition is
iter is greater than or equal to maxiter or
Wherein tol is an upper line of a termination threshold, and the value is 0.001; α is the desired signal variance; when one of the above-mentioned iteration termination conditions is satisfied, the iteration is terminated and the mean value mu is output x Otherwise, continuing the iteration of (3.2) - (3.5);
(5): searching spectral peak, estimating direction according to the recovered signal to obtain
Wherein | · | purple sweet 1 Representing a matrix-norm operation, | · | count non-woven phosphor ∞ Representing an infinite norm operation of the matrix.
(6): outputting a bearing estimation result P VB (θ)。
Fig. 3 is a flow chart of the position estimation. The invention comprehensively considers the influence of amplitude-phase error and non-Gaussian non-uniform noise, thereby effectively making up the DOA estimation deviation and obtaining a better estimation result.
Simulation study of the invention:
simulation conditions are as follows:
two single-frequency pulse signals are used as incident sources, the incident directions are 5 degrees and 10 degrees respectively, and random amplitude deviation and phase deviation are applied to array receiving array elements. Wherein, the amplitude deviation of each array element is changed between [0.5 and 1], the phase deviation is changed between [0 degrees and 20 degrees ], the non-Gaussian non-uniform noise variance received by each array element is changed between [0 and 10], the snapshot number is 500, and the average received signal-to-noise ratio is 0 dB. The method is compared and analyzed with a DOA estimation method based on amplitude and phase errors and a DOA estimation method based on non-uniform noise.
Fig. 4(a) shows the estimation results of each method for the multi-target orientation, the dotted line is the DOA estimation method based on amplitude-phase errors, the dotted line is the DOA estimation method based on non-uniform noise, the solid line shows the joint DOA estimation method of the present invention, and the two vertical dense dotted lines show the set true target orientation. It can be found from the figure that the direction estimated by the method of the invention is consistent with the real target direction, which shows that the method of the invention can accurately estimate two target directions, while the other two methods can not accurately estimate two target directions, and the estimated single target has larger deviation.
Fig. 4(b) is a Root Mean Square Error (RMSE) variation curve of each method when changing with environmental parameters under the impulse noise environment, so that the SNR changes in the range of [ -10,20], the two target orientations are-30 ° and-15 ° respectively, and other parameters are kept consistent. From the results, it can be found that the joint DOA estimation method of the present invention is most stable and RMSE at > 0dB is minimal, which indicates that the method of the present invention has better robustness. If the target azimuth interval is reduced, the phenomenon of two targets being indistinguishable as shown in fig. 4(a) occurs, and the conventional method fails. Simulation proves that the method has higher target resolution and robustness, so that the method can reduce the influence of amplitude-phase errors and non-Gaussian non-uniform noise and obtain accurate DOA estimation.
In conclusion, the invention provides a large-scale array amplitude-phase error and target direction joint estimation method under non-uniform noise, and belongs to the field of underwater acoustic array signal processing. The invention constructs a variational Bayesian inference model based on background non-Gaussian noise and uniform linear array amplitude-phase characteristics, jointly estimates the noise power and array amplitude-phase deviation of each array element, corrects an array flow pattern matrix, and finally realizes high-precision DOA estimation. Compared with the existing direction estimation method of the same type, the method has higher estimation precision and stronger adaptability. The simulation research result verifies the effectiveness and feasibility of the invention.
In summary, the invention provides a large-scale array amplitude-phase error and target orientation joint estimation method under non-uniform noise aiming at the characteristics of amplitude and phase inconsistency caused by bending, moving and the like of an underwater acoustic array during underwater installation, and belongs to the field of underwater acoustic array signal processing. The method and the device construct a variational Bayesian model based on background non-Gaussian noise and uniform linear array amplitude-phase characteristics, jointly estimate the noise power and array amplitude-phase deviation of each array element, modify an array flow pattern matrix and realize high-precision DOA estimation. Compared with the existing direction estimation method of the same type, the method has higher estimation precision and stronger adaptability.
Claims (3)
1. A large-scale array amplitude-phase error and target azimuth joint estimation method under non-uniform noise is characterized by comprising the following steps:
the method comprises the following steps: the method comprises the following steps of constructing an underwater uniform long-line array, uniformly distributing the underwater uniform long-line array at half-wavelength intervals during distribution, and based on background non-Gaussian noise and uniform linear array amplitude-phase characteristics, wherein incident signal models received by each array element module are as follows:
Y＝E p AX+V
step two: establishing prior distribution of each variable in the model; for the array received signal, a complex gaussian distribution is constructed:
wherein, Y t Representing the received data vector at time t, X t Representing the desired signal vector at time t, the layered Gamma of the noise variance β is:
wherein: beta is a m Is the element with beta at the m-th array element, and c represents the noise variance beta m Shape parameter of d m Representing the variance beta of the noise at the m-th array element m The inverse scale parameter of (d);
the complex gaussian distribution of the desired signal is:
where α is the variance of the desired signal, x tn For received data of the nth spatial grid at time t, α n For the period when scanning the nth azimuthThe variance of the inspection signal;
the layered Gamma distribution of the desired signal variance α is:
wherein: a denotes the desired signal variance α n Shape parameter of b n Representing the variance α of the desired signal at the nth spatial grid n The inverse scale parameter of (d);
step three: initializing parameters; setting the initial value iter of the iteration number to be 1, initializing the maximum, N, a,
c，
and E p Maximum is the iteration maximum, N is the number of meshes divided by the whole space azimuth, a is the shape parameter of the variance of the expected signal distribution,
an inverse scale parameter for the variance of the desired signal distribution, c a shape parameter for the noise variance distribution,
as inverse scale parameter of the noise variance distribution, E p The initial value of the amplitude-phase characteristic of the array to be estimated is obtained;
step four: iterative computation, namely obtaining an iterative formula of each parameter according to the distribution in the step two, and updating;
step five: judging whether the iteration condition is met, if not, continuing the step four, and if so, jumping out of the iteration and outputting mu x ；
Step six: searching a spectrum peak, and carrying out azimuth estimation according to the recovery signal:
wherein: i | · | purple wind 1 Representing a matrix-norm operation, | · | count non-woven phosphor ∞ Infinite norm operation of the representation matrix;
step seven: outputting a bearing estimation result P VB (θ)。
2. The method for jointly estimating the amplitude-phase error and the target orientation of the large-scale array under the nonuniform noise according to claim 1, wherein the fourth step specifically comprises:
updating sigma x ：
Σ x ＝(A H E p H diag(β)EA+diag(<α>)) -1
Updating mu x ：
μ x ＝Σ x A H E p H diag(<β>)Y
Updating
Updating
Updating
Updating
Updating
Updating the mean of the variables, including:
let iter be iter + 1.
3. The method for jointly estimating the amplitude-phase error and the target azimuth of the large-scale array under the nonuniform noise according to claim 1, wherein the iteration termination condition is as follows:
iter≥maxiter
or
Wherein tol is a set termination threshold, and the value of tol is 0.001; α is the iteratively calculated variance of the desired signal, defined as:
where < > represents the expectation of the variable to be solved.
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