CN105911551B - A kind of Sound speed profile inversion method based on weighted aggregation Kalman filtering algorithm - Google Patents
A kind of Sound speed profile inversion method based on weighted aggregation Kalman filtering algorithm Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
- G01S15/88—Sonar systems specially adapted for specific applications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01H5/00—Measuring propagation velocity of ultrasonic, sonic or infrasonic waves, e.g. of pressure waves
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
- G01S7/52001—Auxiliary means for detecting or identifying sonar signals or the like, e.g. sonar jamming signals
Abstract
A kind of Sound speed profile inversion method based on Weighted EnKF algorithms, comprises the following steps:1) first marine site to be measured with source emission acoustical signal and with vertical hydrophone array gather sound pressure signal;2) the priori Sound speed profile obtained according to historical data, the marine site Sound speed profile is characterized using Empirical Orthogonal Function and its coefficient;3) state-space model is established using Empirical Orthogonal Function coefficient EVOLUTION EQUATION and acoustic pressure observational equation;4) inverting is carried out to Empirical Orthogonal Function coefficient with Weighted EnKF algorithms;5) the characterization formula of the inversion result combination Sound speed profile of time-varying is utilized, calculates the time-varying velocity of sound field in the marine site.Pass through simulation example, it is shown that the feasibility based on Weighted EnKF algorithm inverting Sound speed profiles, and inversion accuracy is demonstrated higher than the conventional Sound speed profile inversion method based on EnKF.
Description
Technical Field
The invention belongs to a marine environment parameter inversion method, and particularly relates to a sound velocity profile inversion method based on a Weighted ensemble Kalman filtering (Weighted-EnKF) algorithm.
Background
The sound wave is an effective carrier of ocean propagation information and is also an important means for detecting ocean environment information. How to detect marine environmental information using acoustic signals is widely studied. The propagation of sound waves in the ocean is closely related to the physical processes in the ocean. The sound transmission process contains abundant ocean temperature field and flow field distribution information. The parameter information is extracted by using the marine acoustic technology, so that the long-time and large-range dynamic real-time monitoring on the marine environment can be realized.
Compared with other inversion methods, the method for inverting the marine environment parameters by using the water acoustics is a method for efficiently and conveniently acquiring the marine environment. The method can be used for reproducing most of interested marine environment information by only arranging a plurality of sound sources and hydrophone arrays, and can realize long-time large-range real-time monitoring. The marine environment information obtained by inversion can provide estimation in a space and time average sense, which is difficult to obtain by the traditional direct measurement method.
In the traditional shallow sea acoustic velocity profile inversion method, commonly used algorithms include Extended Kalman Filtering (EKF), unscented Kalman (UKF), ensemble kalman (EnKF), and the like. The EnKF algorithm has better applicability in the field of acoustic velocity profile inversion due to the advantages of multivariate estimation, however, the EnKF graph based on Monte Carlo simulation uses a limited number of discrete samples to represent the quantity of continuous distribution, and problems can be encountered in practical application. In the conventional EnKF algorithm, the calculation of the mean of the aggregate samples does not take into account the distribution of the samples themselves. Such an estimation may not be accurate enough for highly non-linear models, resulting in deviations of the convergence direction from the true parameter values, and thus large errors in the inversion results. In order to overcome the defects, the Weighted-EnKF algorithm is provided, and the accuracy of the inversion result is obviously improved under the condition of increasing less operation amount.
Disclosure of Invention
The invention provides a Weighted-EnKF algorithm-based acoustic velocity profile inversion method, aiming at overcoming the defect that the inversion accuracy of the traditional simple EnKF algorithm-based shallow sea acoustic velocity profile inversion method is limited by a highly nonlinear ocean model, so that the accuracy and the resolution of acoustic velocity estimation are obviously improved.
The invention relates to a Weighted-EnKF-based sound velocity profile inversion algorithm, which is realized by the following technical scheme:
(1) Continuously transmitting an acoustic signal for a period of time by using an acoustic source in a sea area to be detected, and receiving an acoustic pressure signal by using an underwater vertical receiving array;
(2) Obtaining a prior sound velocity profile of a sea area to be measured by using historical data, and representing the sound velocity profile of the sea area by using an empirical orthogonal function and coefficients thereof;
(3) Establishing a state-space model by using an evolution equation of an empirical orthogonal function coefficient and a sound pressure observation equation;
(4) Inverting the empirical orthogonal function coefficient by using a Weighted-EnKF algorithm in combination with the sound pressure signal received by the vertical array;
(5) And calculating the sound velocity profile evolution condition of the sea area at the period of time by using the empirical orthogonal function coefficient obtained by inversion and combining the empirical orthogonal function.
The ocean sound velocity profile inversion method based on Weighted-EnKF algorithm comprises the following steps:
(1) In the technical scheme (1), a single sound source and a plurality of receiving array elements are required to be arranged in the sea area to be detected for receiving the sound signals, and the receiving arrays are vertically distributed at equal intervals. The sound source emits a signal for T time, if the signal received in T time is sampled to N t Group and N R N can be obtained by one receiving array element t ×N R A received signal.
(2) In the technical scheme (2), the sea area sound velocity profile is characterized by using an empirical orthogonal function and coefficients thereof, and is characterized as a formula c according to M prior sound velocity profiles 1 (z j ),c 2 (z j ),…,c M (z j ) J =1,2, \ 8230, where N is the number of discrete points in the depth direction, and sample points are combined to form a matrix C, i.e.
The sound velocity matrix is further decomposed into the sum of the average sound velocity profile and the sound velocity disturbance, and then the sound velocity disturbance is represented by calculating the covariance matrix of the disturbance quantity, which can be completed by the following steps.
Firstly, the average value of the sound velocity profiles of the M samples is obtained, and then the average sound velocity profile c is obtained 0 (z) that is
Wherein z = [ z ] 1 z 2 … z N ]Discrete points in the depth direction are represented. Using the data of the sound velocity profile of M samples and the mean value of the sound velocity profile samples just obtained to calculate a covariance matrix R,
wherein, Δ c i (z j )=c i (z j )-c 0 (z j ),j=1,2,…,N。
Carrying out eigenvalue decomposition on the sound velocity profile covariance matrix representing the uncertainty of the sound velocity fluctuation in the sea area to obtain N orthogonal eigenvectors, wherein the specific form is shown as a formula (4):
wherein λ n ,f n Respectively eigenvalues of the covariance matrix R and corresponding eigenvectors, i.e. the empirical orthogonal functions we discuss.
The obtained characteristic value is according to lambda 1 >λ 2 >…>λ N The order from large to small is arranged in sequence, and the eigenvectors (empirical orthogonal functions) corresponding to the first K eigenvalues are selected to represent the sound velocity profile, so that any sound velocity profile can be represented as:
wherein x l As an empirical orthogonal function f l (z) the corresponding undetermined coefficients.
(3) According to the technical scheme (3), the state-space model is established by using the evolution equation of the empirical orthogonal function coefficient and the sound pressure observation equation, and the two equations can be respectively expressed as
x k =x k-1 +v k-1 (6)
z k =h(x k )+w k (7)
Where h represents the nonlinear function of the acoustic propagation model, the state vector x k A coefficient vector consisting of empirical orthogonal function coefficients of order L, a measurement vector z k Is the sound pressure signal, v, received in step (1) k And w k Respectively process noise and measurement noise, and k is a time index.
(4) According to the technical scheme (4), inversion is carried out by utilizing a Weighted-EnKF algorithm according to the state-space model established in the step (3) and the sound pressure signal received in the step (1), and the inversion has the following properties:
when calculating the average value of the set samples, adding a likelihood function according to normalization as a sample weightNamely, it is
C k (f j )=E[z k (f j )z k (f j ) T ] (10)
Wherein, the first and the second end of the pipe are connected with each other,is the weight of the ith sample, n p Is the aggregate sample size, n h Is the number of hydrophones, n f Is the number of frequencies, tr is the matrix tracing, C k (f j )=E[z k (f j )z k (f j ) T ]Is a spectral density function, phi j (x k ) I.e. the Bartlett Power objective function. And then inversion is carried out by combining the traditional EnKF algorithm. The experience of obtaining the section of the time sound velocity profile of the sea area is positiveAnd (4) coefficient of the cross function.
The Weighted-EnKF algorithm flow is as follows:
(5) In the step (5), the inversion result obtained in the step (4) is obtained, namely Wherein t is k The time corresponding to the time index k is represented, and the sound velocity profile evolution condition of the time in the sea area is calculated, namely
The invention has the advantages that: the parameter estimation performance of the traditional inversion method under the condition of a strong nonlinear model is improved, and the accuracy of the inversion result is improved by the improved algorithm under the condition of increasing a small amount of calculated amount.
Drawings
FIG. 1 shows an algorithmic flow chart of the present invention
FIG. 2 shows a simulated marine environment and placement of array elements
FIG. 3 shows a prior sound velocity profile change of a certain sea area in a certain period of time
FIG. 4 shows an average sound velocity profile and a first third order empirical orthogonal function obtained from a prior sound velocity profile
FIG. 5 shows the inversion result of the empirical orthogonal function coefficient of the time acoustic velocity profile of the sea area obtained by the Weighted-EnKF algorithm.
FIG. 6 shows the evolution situation of the sound velocity profile of the sea area at the time period calculated by combining the empirical orthogonal function coefficient obtained by Weighted-EnKF algorithm inversion with the empirical orthogonal function.
Detailed Description
The invention is further described below in conjunction with the figures and the specific examples to verify the effectiveness of the invention. FIG. 1 shows a work flow chart of an ocean sound velocity profile inversion method based on Weighted-EnKF algorithm, and the specific implementation process is as follows:
(1) And carrying out an ocean sound velocity profile inversion experiment for a certain period of time in a certain sea area to estimate the sound velocity profile. The marine environment is a shallow sea channel with the depth of 80 meters, and a sound source and a receiving array are arranged at two nodes with the distance of 3 kilometers. The sound source distribution depth is 30 meters, and the radiation frequency is 255Hz. The receiving array is arranged at the position 3 kilometers away from a transmitting sound source in a sea area to be detected, the depth is 8.2 meters to 64.45 meters, the interval is 3.75 meters, and 16 hydrophones are total. The ocean acoustic velocity profile inversion environment is shown in FIG. 2, wherein the depth of the sedimentary layer is 20 meters, and the density, attenuation coefficient and acoustic velocity are 1.6g/cm respectively 3 0.673dB/km,1610m/s, a substrate density, an attenuation coefficient and a sound velocity of 2g/cm respectively 3 ,0.51dB/km,1740m/s。
(2) Fig. 3 shows the change of the sound velocity profile in the region over time, which is taken as the prior sound velocity profile. And calculating the average sound velocity profile and the sound velocity fluctuation condition of the region to obtain the first 3-order empirical orthogonal function of the sea area, as shown in fig. 4.
(3) The sound source emits 255Hz single-frequency signals, sound pressure signals sent by the sound source within 2 days are continuously collected on the receiving array, and the sound pressure signals with corresponding frequencies are extracted. Then, the coefficient evolution equation and the sound pressure observation equation establish a state-space model as shown in equation (6) and equation (7).
(4) And (3) performing tracking inversion on the empirical orthogonal function coefficient of the 3 th order according to the Weighted-EnKF algorithm flow and the established state-space model. FIG. 5 shows the result of the Weighted-EnKF algorithm tracking inversion of empirical orthogonal function coefficients of the sound velocity profile in 2 days in the region and the empirical orthogonal function coefficients of the actually measured sound velocity profile. As can be seen from FIG. 5, the empirical orthogonal function coefficient of Weighted-EnKF algorithm tracking inversion is basically consistent with the empirical orthogonal function coefficient of the measured sound velocity profile except for a small part of time when the algorithm starts to enter tracking. Therefore, the feasibility of the Weighted-EnKF algorithm in the method for inverting the sound velocity profile is verified.
(5) FIG. 6 shows that the empirical orthogonal function coefficients obtained by Weighted-EnKF algorithm inversion are combined with the empirical orthogonal function to calculate the sound velocity profile evolution situation of the sea area at the time, and through comparison calculation with an actually measured sound velocity profile, the time average root mean square error is 0.39m/s, which is 0.59m/s (obtained through simulation calculation) superior to the time average root mean square error of the inversion result of the traditional EnKF algorithm. Therefore, the sea sound velocity profile inversion method based on the Weighted-EnKF algorithm can obviously improve the accuracy of sound velocity profile inversion.
Claims (1)
1. A sound velocity profile inversion method based on Weighted-EnKF algorithm comprises the following steps:
(1) Continuously transmitting an acoustic signal for a period of time by using an acoustic source in a sea area to be detected, and receiving an acoustic pressure signal by using an underwater vertical receiving array;
(2) Acquiring a prior sound velocity profile of a sea area to be measured by using historical data, and representing the sound velocity profile of the sea area by using an empirical orthogonal function and coefficients thereof;
(3) Establishing a state-space model by using an evolution equation of the empirical orthogonal function coefficient and a sound pressure observation equation;
(4) Inverting the empirical orthogonal function coefficient by using a Weighted-EnKF algorithm in combination with the sound pressure signal received by the vertical array;
(5) Calculating the sound velocity profile evolution condition of the sea area at the period of time by using the empirical orthogonal function coefficient obtained by inversion and combining the empirical orthogonal function;
in the step (3), an empirical orthogonal function is obtained by utilizing the prior sound velocity profile, and the previous L-order empirical orthogonal function is selected to approximately represent the sound velocity profile, namely
Wherein c is 0 (z) is the mean of the sound velocity profile, z = [ z ] 1 z 2 … z N ]Discrete points, x, representing the depth direction l As an empirical orthogonal function f l (z) the corresponding undetermined coefficients;
in the step (3), a state-space model is established by using an evolution equation of the empirical orthogonal function coefficient and a sound pressure observation equation, wherein the two equations are respectively expressed as:
x k =x k-1 +v k-1 (6)
z k =h(x k )+w k (7)
where h represents the nonlinear function of the acoustic propagation model, the state vector x k A coefficient vector consisting of empirical orthogonal function coefficients of order L, a measurement vector z k Is the sound pressure signal, v, received in step (1) k And w k Respectively process noise and measurement noise, and k is a time index;
in the step (4), inversion is carried out by using a Weighted-EnKF algorithm according to the state-space model established in the step (3) and the sound pressure signal received in the step (1), and the inversion has the following properties:
when calculating the average value of the set samples, adding a likelihood function according to normalization as a sample weightNamely, it is
C k (f j )=E[z k (f j )z k (f j ) T ] (10)
Wherein, the first and the second end of the pipe are connected with each other,is the weight of the ith sample, n p Is the aggregate sample size, n h Is the number of hydrophones, n f Is the number of frequencies, tr is the matrix tracing, C k (f j )=E{z k (f j )z k (f j ) T ]Is a function of spectral density, phi j (x k ) Namely a Bartlett Power objective function; then, inversion is carried out by combining a traditional EnKF algorithm to obtain an empirical orthogonal function coefficient of the sound velocity profile of the sea area at the period of time;
in the step (5), the inversion result obtained in the step (4) is usedWherein t is k The time corresponding to the time index k is represented, and the sound velocity profile evolution condition of the time in the sea area is calculated, namely
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