CN114218777A - Polar region under-ice underwater acoustic channel estimation method - Google Patents

Polar region under-ice underwater acoustic channel estimation method Download PDF

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CN114218777A
CN114218777A CN202111493539.1A CN202111493539A CN114218777A CN 114218777 A CN114218777 A CN 114218777A CN 202111493539 A CN202111493539 A CN 202111493539A CN 114218777 A CN114218777 A CN 114218777A
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生雪莉
蔡晨阳
苍思远
董航
许静
殷敬伟
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Abstract

The invention discloses a polar region under-ice underwater acoustic channel estimation method, which comprises the following steps: introducing l to RLS algorithm cost function0Norm constraint yields l0-an RLS; to l0The RLS loss function introduces a Hampel three-stage re-reduction M-estimation function to obtain a loss function f (e), and the loss function f (e) is operated to obtain a weight function q (e); estimating and updating three thresholds set by a Hampel-three-section re-reduction M estimation function through estimation of variance of impulse noise; according to three estimated threshold value pair weight functions q (e) and a gain matrix k [ n ]]Updating is carried out; using updated weighting function q (e) and gain matrix k [ n ] according to transmitted signal and received signal]Performing channel estimation to obtain a channel estimation value
Figure DDA0003400131970000011
And judging whether the number of sampling points is reached, if so, ending, and otherwise, returning to the threshold value for updating. The invention improves the capability of inhibiting the impulse noise, reduces the possibility of influence of the large-amplitude ice crack impulse noise on the channel true value estimation under the condition of low signal-to-noise ratio, and improves the estimation performance of the channel amplitude.

Description

Polar region under-ice underwater acoustic channel estimation method
Technical Field
The invention belongs to the field of polar region acoustics and underwater acoustic signal processing, relates to a polar region under-ice underwater acoustic channel estimation method, and particularly relates to a polar region under-ice underwater acoustic channel estimation method based on a recursive least square algorithm (RLS).
Background
Due to the fact that the climate in the arctic region is abnormally cold, most water areas are covered by ice layers all the year round, a quite complex under-ice underwater acoustic environment is caused, due to the fact that relative motion exists among the ice layers, severe sea ice activity can be caused by melting and breaking of the ice layers caused by global warming, generated pulse noise is random, outlier points with abnormal amplitude exist in a time domain, and the second moment and the high-order moment of the pulse noise are infinite. The noise background of most channel estimation algorithms is gaussian noise, however, under the interference of impulse noise, due to the characteristics of the gaussian noise, the performance of the algorithms under the gaussian noise is seriously degraded. The Recursive Least Squares (RLS) algorithm is poorly robust to impulse noise, but when a robust cost function of the anomaly suppression method and/are introduced thereto0When the norm punishs the terms, the suppression capability of the algorithm on impulse noise is greatly improved.
Chinese patent CN112653640A, "a method for estimating an underwater acoustic channel by suppressing impulse noise using generalized approximate messaging-sparse bayes learning (GAMP-SBL)" proposes a method for performing underwater acoustic channel estimation by suppressing impulse noise using null subcarriers of OFDM signals in combination with GAMP-SBL, then subtracting the estimated impulse noise from baseband signals to suppress impulse noise, and performing underwater acoustic channel estimation using GAMP-SBL again after suppression. However, in this patent, the estimation effect of the modeling method is not good under low signal-to-noise, and in a polar environment, the probability, amplitude and event occurrence frequency of impulse noise are far greater than those of an open water area, and a low signal-to-noise ratio exists.
Disclosure of Invention
In view of the foregoing prior art, the technical problem to be solved by the present invention is to provide an RLS algorithm-based polar ice underwater acoustic channel estimation method capable of improving channel estimation performance in a polar environment at a low signal-to-noise ratio.
In order to solve the technical problem, the polar ice underwater acoustic channel estimation method provided by the invention comprises the following steps of:
step 1: introduction of cost function l to RLS algorithm0Norm constraint yields l0-RLS；
Step 2: to l0Introducing a Hampel three-stage re-reduction M-estimation function into a loss function in the RLS to obtain a loss function f (e), and operating the loss function f (e) to obtain a weight function q (e);
and step 3: initializing impulse noise as mean 0 and variance σ2White gaussian noise of (1);
and 4, step 4: estimating and updating three thresholds set by a Hampel-three-section re-reduction M estimation function through estimation of variance of impulse noise;
and 5: updating the weight function q (e) and the gain matrix k [ n ] according to three estimated thresholds;
step 6: using updated weighting function q (e) and gain matrix k [ n ] according to transmitted signal and received signal]Performing channel estimation to obtain a channel estimation value
Figure BDA0003400131950000021
And judging whether the number of sampling points is reached, if so, ending, otherwise, returning to the step 4.
Further, step 1 l0-the RLS comprises:
the cost function is:
Figure BDA0003400131950000022
wherein lambda epsilon (0,1) is a forgetting factor,
Figure BDA00034001319500000213
in order to regularize the parameters of the process,
Figure BDA0003400131950000023
in the case of the regular term, the term,
Figure BDA0003400131950000024
comprises the following steps:
Figure BDA0003400131950000025
wherein, K is the number of channel sampling points, and eta is a constraint term constant.
Solving a cost function:
Figure BDA0003400131950000026
solving the result comprises:
Figure BDA0003400131950000027
Figure BDA0003400131950000028
Φ[n]-1＝λ-1(Φ[n-1]-1-k[n]u[n]TΦ[n-1]-1)
Figure BDA0003400131950000029
Figure BDA00034001319500000210
wherein u [ n ]]For the vector formed by the transmitted signals,
Figure BDA00034001319500000211
represents a conjugate transpose, e [ n ]]For instantaneous estimation error, k [ n ]]Is a gain matrix, q (e [ n ]]) As a function of the weight, phi n]-1Is a correlation matrix, vk[n]Representing constraint values at different sampling point numbers of the channel as constraint terms; initialization algorithm
Figure BDA00034001319500000212
m is a constant, f (e [ i ]])＝e[i]e[i]*，q(e[n])＝1。
Further, in step 2, p is0The loss function in the RLS is introduced into a Hampel three-stage re-reduction M-estimation function to obtain a loss function f (e), and the loss function f (e) is operated to obtain a weight function q (e) which comprises the following steps:
the loss function is:
Figure BDA0003400131950000031
calculating the loss function to obtain a weight function q (e):
Figure BDA0003400131950000032
where ξ, Δ, T are three thresholds set by the Hampel-three-segment re-reduction M estimation function.
Further, the estimating and updating of the three thresholds set by the Hampel-three-segment re-reduction M estimation function through the estimation of the variance of the impulse noise in step 4 includes:
the threshold expression is:
ξ＝2.45σ(n),(i.e.,Pr{|e|2＜ξ}＝0.95)
Δ＝2.72σ(n),(i.e.,Pr{|e|2＜Δ}＝0.975)
T＝3.03σ(n),(i.e.,Pr{|e|2＜T}＝0.99)
wherein σ2(n) is a noise variance representation:
σ2(n)＝0.5[σr 2(n)+ρi 2(n)]
wherein σr 2(n) is the variance of the real part of the noise, σi 2(n) is the variance of the imaginary noise part:
σr 2(n)＝λσσr 2(n-1)+c(1-λσ)med(ar(n))
σi 2(n)＝λσσi 2(n-1)+c(1-λσ)med(ai(n))
wherein λ isσIs a forgetting factor, ar(n)＝[er 2(n)...er 2(n-Nω+1)]TIs the real part of the a priori error signal, ai(n)＝[ei 2(n)...ei 2(n-Nω+1)]TIs the imaginary part of the a priori error signal, NωFor the channel estimation window length, med (-) is the median filter, and c is the effective sample correction factor that ensures the estimates are consistent.
Further, the updating of the weighting function q (e) and the gain matrix k [ n ] according to the three estimated thresholds in step 5 includes:
the weighting function q (e) is:
Figure BDA0003400131950000041
the gain matrix k [ n ] is:
Figure BDA0003400131950000042
wherein, phi [ n ]]-1Initializing Φ (0) for the correlation matrix-1＝m-1IKAnd satisfies the following conditions:
Φ[n]-1＝λ-1(Φ[n-1]-1-k[n]u[n]TΦ[n-1]-1)
further, in step 6, updated weighting function q (e) and gain matrix k [ n ] are used according to the transmitted signal and the received signal]Performing channel estimation to obtain channel estimationValue of
Figure BDA0003400131950000043
The method comprises the following steps:
channel estimation value
Figure BDA0003400131950000044
Satisfies the following conditions:
Figure BDA0003400131950000045
wherein,
Figure BDA0003400131950000046
the invention has the beneficial effects that: the invention applies the recursive least square algorithm to channel estimation, introduces norm constraint and a modified Hampel three-section re-reduction M-estimation function to a cost function, and realizes steady channel estimation under the polar environment.
Compared with the traditional channel estimation method under the impulse noise background, the method of the invention uses the method0The norm constraint and the Hampel-three-segment re-reduction M estimation function improve the suppression capability of impulse noise, wherein the possibility of influence of large-amplitude ice crack impulse noise on channel truth estimation can be reduced at a low signal-to-noise ratio through three thresholds established by time domain sparsity of the impulse noise, and the estimation performance of channel amplitude is improved.
By adopting the polar region channel estimation method, the channel reconstruction coefficient of the estimation result of the arctic under-ice channel is higher, the problem of difficult channel estimation under low signal to noise ratio caused by the complex environment under the arctic under-ice is solved, the polar region under-ice channel estimation method can be well applied to the polar region under-ice channel estimation, and the sensing capability of the polar region under-ice acoustic environment is improved.
Drawings
Fig. 1 is an overall flow chart of the polar ice underwater acoustic channel estimation method of the present invention.
FIG. 2 is a drawing of0RLS and l0-mean square error curves simulated by monte carlo at different signal-to-noise ratios by RLM.
FIG. 3 is an impulse response function of Bellhop to model an ice channel using arctic ice-speed gradients.
FIG. 4 is a time domain plot of North Arctic Ice noise.
FIG. 5 is a arctic under-ice noise probability density fit.
FIG. 6 is a data processing flow of the ninth North Pole scientific research experiment.
FIG. 7 is a0-RLM algorithm channel estimation result.
Detailed Description
The invention is further described with reference to the drawings and the specific embodiments in the following description.
With reference to fig. 1, the present invention comprises the following steps:
step 1: introduction of cost function l to RLS algorithm0Norm constraint yields l0-RLS：
The cost function of the conventional RLS algorithm is represented as:
Figure BDA0003400131950000051
where λ e (0,1) is a forgetting factor, and e (i) y (i) -y (i-1) generates an error value for the received signal in each iteration.
Adding sparse constraint term on the basis of RLS algorithm cost function to utilize l0The norm is better estimated by considering a real non-negative loss function, denoted as f (e), for the purpose of mitigating errors caused by large-amplitude outlier interference due to impulse noise. Simultaneously express a scoring function of
Figure BDA0003400131950000052
The weighting function is q (e) ═ ψ (e)/e*。
The updated cost function is:
Figure BDA0003400131950000061
wherein lambda epsilon (0,1) is a forgetting factor,
Figure BDA0003400131950000062
in order to regularize the parameters of the process,
Figure BDA0003400131950000063
being a regular term, helps to speed up the convergence of the filter taps.
l0The norm is calculated below as:
Figure BDA0003400131950000064
the filter is a pair filter
Figure BDA0003400131950000065
L of0Complex expansion of norm, K being the number of sampling points of the channel, note JL0-RLSInstead of a convex cost function, η is a constraint term constant, and when η is close to 10 and ζ is chosen to be a sufficiently small value, the algorithm converges to a meaningful solution.
l0-the RLS cost function is solved by the equation:
Figure BDA0003400131950000066
the following equation summarizes the results:
Figure BDA0003400131950000067
Figure BDA0003400131950000068
Φ[n]-1＝λ-1(Φ[n-1]-1-k[n]u[n]TΦ[n-1]-1)
Figure BDA0003400131950000069
Figure BDA00034001319500000610
wherein u [ n ]]For the vector formed by the transmitted signals,
Figure BDA00034001319500000611
represents a conjugate transpose, e [ n ]]For instantaneous estimation error, k [ n ]]Is a gain matrix, q (e [ n ]]) As a function of the weight, phi n]-1Is a correlation matrix, vk[n]For the constraint term, the constraint value at different sampling points of the channel is expressed, and is a constant, and K is the sampling point of the channel.
Initialization algorithm
Figure BDA00034001319500000612
m is a very small constant, IkIs an identity matrix when f (e [ i ]])＝e[i]e[i]*，q(e[n]) When 1, the above formula algorithm is l0RLS if
Figure BDA00034001319500000613
At this time, the algorithm becomes the RLS algorithm.
Step 2: based on l0The RLS introduces a modified Hampel three-section re-reduction M-estimation function, and the weight function is modified by setting a threshold value to obtain l0RLM, improving robustness to impulse noise.
Introduce l based on this algorithm0Norm and the Hampel three-part re-reduction M estimation function is modified to conform to the selected negative gradient operator, the time index is deleted for easy labeling, and the loss function is expressed as:
Figure BDA0003400131950000071
where ξ,. DELTA.T, are thresholds for suppression of outliers,. DELTA.. gtY2Is a two-norm, the loss function is calculated to obtain a weight function,expressed as:
Figure BDA0003400131950000072
as can be seen from the above formula, when | e2When the amplitude is less than the threshold xi, the algorithm sum is0The RLS algorithm is the same. And in l0In the RLS algorithm, if the amplitude becomes large due to the occurrence of large impulse noise in the system, l is caused0The performance of the RLS algorithm adaptation is greatly reduced, so that impulse noise suppression of abnormal amplitudes is achieved by setting the threshold.
The weight function can be obtained by comparing the error with the threshold value, the weight function changes in each iteration, the gain matrix changes accordingly, and the channel estimation value
Figure BDA0003400131950000073
Updated and of good robustness, it is desirable to describe a method of threshold estimation, which will be described in detail in the next step.
And step 3: and estimating three thresholds set by the Hampel-three-section re-reduction M estimation function through the prior probability of the impulse noise.
The selection of three threshold parameters for suppressing impulse noise greatly affects the estimation performance of the algorithm, and we need to describe an estimation method for the three threshold parameters in the impulse noise interference background, the selection of the threshold parameter values depends on the prior distribution probability of the impulse noise, the impulse noise is assumed to be mean 0 by the initial value, and the variance is σ2White Gaussian noise, such that the white light passes through | e-2Is segmented and estimated by the probability that the error is less than a threshold. Calculating the variance of the real part of the noise by using a median operator:
σr 2(n)＝λσρr 2(n-1)+c(1-λσ)med(a(n))
wherein λσAs a forgetting factor, a (n) ═ er 2(n)...er 2(n-Nω+1)]TIs the real part of the a priori error signal, NωFor the channel estimation window length, which determines the complexity of the algorithm and the averaging capability for impulse noise suppression, med (-) is a median filter, which acts to suppress the impact of transient impulse noise outliers. c is 1.483(1+ 5/(N)ω-1)) is a valid sample correction factor that ensures that the estimates are consistent. The imaginary variance of the baseband noise is calculated in the same way:
σi 2(n)＝λσσi 2(n-1)+c(1-λσ)med(a(n))
where a (n) ═ ei 2(n)...ei 2(n-Nω+1)]T；
The final noise variance is expressed as:
σ2(n)＝0.5[σr 2(n)+σi 2(n)]
parameter | e ∞ with baseband noise variance2Using the rayleigh distribution to obtain a threshold expression under a certain probability:
ξ＝2.45σ(n),(i.e.,Pr{|e|2＜ξ}＝0.95)
Δ＝2.72σ(n),(i.e.,Pr{|e|2＜Δ}＝0.975)
T＝3.03σ(n),(i.e.,Pr{|e|2＜T}＝0.99)
three thresholds are selected at each time0And updating the variance when the RLM channel is updated so as to update the threshold, thereby updating the weight function and the gain matrix and obtaining a channel estimation result through continuous iteration. The threshold is set up so that the robustness is good when large impulse noise occurs and the signal-to-noise ratio is low, and the modified Hampel three-part re-reduction M-estimation function enables the estimation of the channel to be more accurate in amplitude.
And 4, step 4: using l according to the transmitted signal and the received signal0The RLM algorithm performs channel estimation.
The polar ice underwater acoustic channel estimation technology based on the robust recursive least square algorithm and the beneficial effects thereof are further described in detail below by combining with specific embodiments.
Fig. 1 is an overall flow diagram of a polar sub-ice channel estimation technique based on a robust recursive least squares algorithm.
FIG. 2 is a drawing proposed by the present invention0RLM and l0The mean square error curve under monte carlo simulation by RLS, fig. one shows that the proposed modified Hampel-three-segment re-reduction M estimation function has good suppression capability on impulse noise, and the RMSE of L0-RLM algorithm is only about 0.07 at signal-to-noise ratio of-5 dB, obviously, the proposed method has robust channel estimation performance at low signal-to-noise ratio.
Fig. 3 is an impulse response obtained by Bellhop processing of the sound velocity gradient in the ninth arctic scientific test data.
Fig. 4 and 5 are processing results of the noise under ice at the north pole, and it can be seen from the time domain diagram that the noise under ice has pulse noise characteristics and outlier points with abnormal amplitudes, and meanwhile, fig. 5 can be well fitted with an S α S pulse noise model by probability density fitting, and the noise-to-noise ratio of the test noise at this section is obtained by estimation to be 6.8 dB.
Fig. 6 is a processing flow chart of experimental data of the ninth north pole scientific investigation, and due to the randomness of the generation of the impulse noise and the influence of experimental conditions and the like, it cannot be determined that the impulse noise is generated by the ice layer movement in the time from the signal transmission to the signal reception of the receiver, and in order to improve the validity and the reliability of the north pole experimental verification algorithm, the experimental data processing is performed according to the flow chart of fig. 6.
FIG. 7 shows0And the RLM algorithm carries out a final channel estimation result according to the flow of the figure five, and accurately estimates the amplitude and the time delay of the ice channel.
Table 1 correlation coefficient of channel estimation for three algorithms
Figure BDA0003400131950000091
In conclusion, the invention provides a method based on recursive least square algorithm, and introduces l0Norm constraint and modified Hampel-three-segment channel of M estimation functionThe estimation technology can achieve 98.73% of channel reconstruction capability under the polar environment. The invention belongs to the field of underwater acoustic signal processing. The invention has the advantages that: three thresholds are set to suppress impulse noise, and the thresholds are updated along with the change of the variance when the thresholds are updated in each iteration, so that the robustness of the impulse noise is ensured to the greatest extent, the channel estimation performance cannot be influenced by outliers with abnormal amplitudes, and the robust channel estimation capability is realized in the environment of the extremely strong ice source impulse noise.

Claims (6)

1. A polar region under ice underwater acoustic channel estimation method is characterized by comprising the following steps:
step 1: introduction of cost function l to RLS algorithm0Norm constraint yields l0-RLS；
Step 2: to l0Introducing a Hampel three-stage re-reduction M-estimation function into a loss function in the RLS to obtain a loss function f (e), and operating the loss function f (e) to obtain a weight function q (e);
and step 3: initializing impulse noise as mean 0 and variance σ2White gaussian noise of (1);
and 4, step 4: estimating and updating three thresholds set by a Hampel-three-section re-reduction M estimation function through estimation of variance of impulse noise;
and 5: updating the weight function q (e) and the gain matrix k [ n ] according to three estimated thresholds;
step 6: using updated weighting function q (e) and gain matrix k [ n ] according to transmitted signal and received signal]Performing channel estimation to obtain a channel estimation value
Figure FDA0003400131940000011
And judging whether the number of sampling points is reached, if so, ending, otherwise, returning to the step 4.
2. The polar region under-ice underwater acoustic channel estimation method according to claim 1, characterized in that: 1 said0-the RLS comprises:
the cost function is:
Figure FDA0003400131940000012
wherein lambda epsilon (0,1) is a forgetting factor,
Figure FDA0003400131940000013
in order to regularize the parameters of the process,
Figure FDA0003400131940000014
in the case of the regular term, the term,
Figure FDA0003400131940000015
comprises the following steps:
Figure FDA0003400131940000016
wherein, K is the number of channel sampling points, and eta is a constraint term constant.
Solving a cost function:
Figure FDA0003400131940000017
solving the result comprises:
Figure FDA0003400131940000021
Figure FDA0003400131940000022
Φ[n]-1＝λ-1(Φ[n-1]-1-k[n]u[n]TΦ[n-1]-1)
Figure FDA0003400131940000023
Figure FDA0003400131940000024
wherein u [ n ]]For the vector formed by the transmitted signals,
Figure FDA0003400131940000028
represents a conjugate transpose, e [ n ]]For instantaneous estimation error, k [ n ]]Is a gain matrix, q (e [ n ]]) As a function of the weight, phi n]-1Is a correlation matrix, vk[n]Representing constraint values at different sampling point numbers of the channel as constraint terms; initialization algorithm
Figure FDA0003400131940000025
m is a constant, f (e [ i ]])＝e[i]e[i]*，q(e[n])＝1。
3. The polar region under-ice underwater acoustic channel estimation method according to claim 2, characterized in that: step 2 said pair l0The loss function in the RLS is introduced into a Hampel three-stage re-reduction M-estimation function to obtain a loss function f (e), and the loss function f (e) is operated to obtain a weight function q (e) which comprises the following steps:
the loss function is:
Figure FDA0003400131940000026
calculating the loss function to obtain a weight function q (e):
Figure FDA0003400131940000027
where ξ, Δ, T are three thresholds set by the Hampel-three-segment re-reduction M estimation function.
4. The polar region under-ice underwater acoustic channel estimation method according to claim 3, characterized in that: step 4, the estimation and updating of the three thresholds set by the Hampel-three-segment re-reduction M estimation function through the estimation of the variance of the impulse noise comprises the following steps:
the threshold expression is:
ξ＝2.45σ(n),(i.e.,Pr{|e2|＜ξ}＝0.95)
Δ＝2.72σ(n),(i.e.,Pr{|e2|＜Δ}＝0.975)
T＝3.03σ(n),(i.e.,Pr{|e|2＜T}＝0.99)
wherein σ2(n) is a noise variance representation:
σ2(n)＝0.5[σr 2(n)+σi 2(n)]
wherein σr 2(n) is the variance of the real part of the noise, σi 2(n) is the variance of the imaginary noise part:
σr 2(n)＝λσσr 2(n-1)+c(1-λσ)med(ar(n))
σi 2(n)＝λσσi 2(n-1)+c(1-λσ)med(ai(n))
wherein λ isσIs a forgetting factor, ar(n)＝[er 2(n)...er 2(n-Nω+1)]TIs the real part of the a priori error signal, ai(n)＝[ei 2(n)...ei 2(n-Nω+1)]TIs the imaginary part of the a priori error signal, NωFor the channel estimation window length, med (-) is the median filter, and c is the effective sample correction factor that ensures the estimates are consistent.
5. The polar ice underwater acoustic channel estimation method according to claim 4, characterized in that: step 5, updating the weighting function q (e) and the gain matrix k [ n ] according to the three estimated thresholds comprises:
the weighting function q (e) is:
Figure FDA0003400131940000031
the gain matrix k [ n ] is:
Figure FDA0003400131940000032
wherein, phi [ n ]]-1Initializing Φ (0) for the correlation matrix-1＝m-1IKAnd satisfies the following conditions:
Φ[n]-1＝λ-1(Φ[n-1]-1-k[n]u[n]TΦ[n-1]-1)
6. the polar ice underwater acoustic channel estimation method according to claim 5, characterized in that: step 6, updated weighting function q (e) and gain matrix k [ n ] are utilized according to the transmitting signals and the receiving signals]Performing channel estimation to obtain a channel estimation value
Figure FDA0003400131940000041
The method comprises the following steps:
channel estimation value
Figure FDA0003400131940000042
Satisfies the following conditions:
Figure FDA0003400131940000043
wherein,
Figure FDA0003400131940000044
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