Underwater sound time-varying channel prediction method based on kernel recursive least square

Abstract

The invention discloses an underwater acoustic time-varying channel prediction method based on kernel recursive least squares, and relates to the technical field of ocean communication, and the method comprises the steps: obtaining channel sample data, and constructing a gain training sample and a time delay training sample; and constructing a multipath gain prediction model and a multipath time delay prediction model of any path p by using a kernel recursion least square method, and training corresponding prediction models. And utilizing the trained corresponding prediction model to predict and obtain a multipath gain prediction value and a multipath time delay prediction value of the prediction moment T according to the historical sample sequences of a plurality of continuous moments before the prediction moment T. And integrating the multipath gain prediction values and the multipath time delay prediction values of all paths at the prediction time T to obtain a channel prediction value of the underwater sound time-varying channel at the prediction time T. According to the method, real-time tracking prediction can be carried out on the underwater sound time-varying channel in a complex and changeable underwater environment, and performance improvement of an underwater sound communication system is facilitated.

Description

Technical Field

[0001] The present application relates to the field of marine communication technology, and in particular to a method for predicting underwater acoustic time-varying channels based on kernel recursive least squares. Background Art

[0002] Acoustic waves are currently the only effective carrier for long-distance information transmission underwater. However, the complex time-varying characteristics of underwater acoustic channels seriously reduce the performance of underwater acoustic communication systems, especially for adaptive communication systems that require accurate channel information to optimize communication parameters. Accurately estimating the channel information at the next moment through reliable channel prediction methods can reduce the impact of underwater acoustic time-varying channels on communication system performance.

[0003] The kernel adaptive filter is an effective time series prediction method that can be applied to underwater acoustic time-varying channel prediction. The kernel adaptive filter method is a commonly used kernel method that can adaptively update the model through recursive increments as new samples are acquired. It is suitable for online prediction. With the help of the kernel function, the original input data is mapped into a high-dimensional kernel space, and complex nonlinear problems are converted into linear problems, which can reduce the complexity and delay of calculations.

[0004] At present, the kernel adaptive filter method has made good progress. Kernel Recursive Least Squares (KRLS), as a typical kernel adaptive filter method, has the advantages of fast convergence speed, low computational complexity, simple model, and online learning. However, the KRLS algorithm has weak tracking ability of the time series time-varying characteristics and anti-noise ability in dynamic environments during online prediction, and cannot adapt to the dynamically changing underwater acoustic time-varying channel environment. Summary of the invention

[0005] In view of the above problems and technical requirements, this application proposes a method for underwater acoustic time-varying channel prediction based on kernel recursive least squares. The technical solution of this application is as follows:

[0006] A method for predicting underwater acoustic time-varying channels based on kernel recursive least squares includes the following steps:

[0007] The kernel recursive least squares method is used to construct the multipath gain prediction model and the multipath delay prediction model of any path p in the underwater acoustic time-varying channel. The underwater acoustic time-varying channel includes N p Multipath, N p is an integer parameter;

[0008] Acquire channel sample data of an underwater acoustic time-varying channel at multiple consecutive sampling moments, and construct multiple gain training samples and multiple delay training samples for any path p, wherein the channel sample data of the underwater acoustic time-varying channel at any sampling moment includes the multipath gain and multipath delay of any path p in the underwater acoustic time-varying channel at the current sampling moment; any t-th training sample constructed for path p includes the signal measured data y(t) of path p at sampling moment t and the historical sample sequence x(t) at sampling moment t, wherein the historical sample sequence x(t) at sampling moment t includes a sequence composed of the signal measured data at all sampling moments before sampling moment t; the signal measured data y(t) in the gain training sample is the multipath gain, and the signal measured data y(t) in the delay training sample is the multipath delay, and the initial value of the integer parameter t is l;

[0009] The multipath gain prediction model of path p is trained using the gain training samples of path p, and the multipath delay prediction model of path p is trained using the delay training samples of path p. When the corresponding prediction model is trained using the training samples of path p:

[0010] (1) Using the lth training sample to initialize the model parameters of the prediction model at iteration number n = 1;

[0011] (2) Determine the characteristic matrix Φ(1) when the iteration number n=1 based on the historical sample sequence at sampling time l, and combine the characteristic matrix Φ(n) and use the prediction model of the nth iteration to obtain the channel prediction data at sampling time l+n-1 The channel prediction data when training the multipath gain prediction model is the multipath gain, and the channel prediction data when training the multipath delay prediction model is the multipath delay;

[0012] (3) Update the feature matrix Φ(n+1) based on the historical sample sequence at sampling time l+n, and combine the l+n-1th training sample and the channel prediction data at sampling time l+n-1 Update the model parameters of the prediction model at the n+1th iteration to obtain the prediction model at the n+1th iteration, and set n=n+1 and execute (2) again until the iteration condition is met to obtain the trained prediction model;

[0013] The multipath gain prediction value of path p at prediction time T is obtained by using the trained multipath gain prediction model of path p according to the multipath gain sequence of several consecutive times before prediction time T. The multipath delay prediction value of path p at the prediction time T is obtained by using the multipath delay sequence of several consecutive times before the prediction time T using the trained multipath delay prediction model of path p. The channel prediction value of the underwater acoustic time-varying channel at the prediction time T is obtained by combining the multipath gain prediction value and multipath delay prediction value of all paths at the prediction time T. τ is the time delay.

[0014] Its further technical solution is that the cost function of each prediction model at the nth iteration is x(i) is the historical sample sequence at sampling time i, the integer parameter is 1≤i≤n, the model parameters of each prediction model at the nth iteration include the kernel matrix K(n), the coefficient vector α(n) and the forgetting factor λ(n), and the model parameters of the prediction model initialized with the lth training sample at iteration number n=1 include:

[0015] Initialize the coefficient vector α(1)=K(1) using the measured signal data y(l) at sampling time l -1 y(l), the historical sample sequence x(l) at sampling time l to initialize the kernel matrix Kernel Function σ is the kernel function width parameter, and λ(1) is initialized to a value in the range of (0,1);

[0016] Among them, the forgetting factor λ(n) of the nth iteration indicates the weight of the historical sample sequence at the sampling time l+n-1 in the prediction model. The larger the value of the forgetting factor λ(n), the greater the weight of the historical sample sequence at the sampling time l+n-1.

[0017] A further technical solution is that the model parameters of the prediction model at the n+1th iteration are updated to include:

[0018] Calculate the channel sample data at sampling time l+n-1 and the channel prediction data at sampling time l+n-1 The prediction error ε(n) between the nth iteration and the forgetting factor λ(n+1) of the n+1th iteration are updated according to the prediction error ε(n) of the nth iteration;

[0019] According to the historical sample sequence at sampling time l+n, the updated feature matrix Φ(n+1) and the updated forgetting factor λ(n+1) are combined to update the kernel matrix K(n+1) of the n+1th iteration;

[0020] The coefficient vector α(n+1) of the n+1th iteration is updated according to the updated kernel matrix K(n+1).

[0021] A further technical solution is to update the forgetting factor λ(n+1)=λ of the n+1th iteration min +(λ max -λ min ) -βE(n) , where λ min is the minimum value of the forgetting factor, λ max is the maximum value of the forgetting factor, β is the decay constant that controls the convergence rate, and the error feedback function ε0 is the benchmark error, parameter k>0.

[0022] A further technical solution is to determine the characteristic matrix Φ(1) and update the characteristic matrix Φ(n+1) to include:

[0023] Map the historical sample sequence at sampling time l to the feature space to obtain the corresponding feature vector And initialize the feature matrix Φ(1) containing the feature vector

[0024] The correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is determined using the approximate linear correlation criterion;

[0025] If δ(n) is greater than the correlation threshold, it is determined that the historical sample sequence at sampling time l+n is linearly independent of the feature matrix Φ(n), and the historical sample sequence at sampling time l+n is mapped to the feature space to obtain the corresponding feature vector And add it to the feature matrix Φ(n), and update the feature matrix Φ(n+1);

[0026] If δ(n) is less than or equal to the correlation threshold, it is determined that the historical sample sequence at sampling time l+n is linearly correlated with the feature matrix Φ(n), and the updated feature matrix Φ(n+1)=Φ(n) is determined.

[0027] Its further technical solution is to determine the correlation between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) in, is the i-th eigenvector in the feature matrix Φ(n), and m is the total number of eigenvectors in the feature matrix Φ(n).

[0028] A further technical solution is that the kernel matrix K(n+1) of the n+1th iteration is updated to include:

[0029] When the correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is greater than the correlation threshold, it is determined

[0030] When the correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is less than or equal to the correlation threshold, it is determined that K(n+1)=K(n).

[0031] A further technical solution is that the coefficient vector α(n+1) of the n+1th iteration is updated to include:

[0032] When the correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is greater than the correlation threshold, the coefficient vector of the n+1th iteration is updated according to the updated kernel matrix K(n+1)

[0033]

[0034] Among them, the adaptive control amount z(n+1)=K(n) -1 h(n+1), adaptive control quantity The inner product of the historical sample sequence x(l+n) at sampling time l+n and the historical sample sequence from sampling time l to sampling time l+n-1 mapped to the feature space is h(n+1)=[k(x(l+n),x(l)),k(x(l+n),x(l+1)),...,k(x(l+n),x(l+n-1))] T , K(n)=Φ(n) T Φ(n), y(l+n) is the measured signal data at sampling time l+n, ε(n) is the prediction error, c is the regularization parameter, [] T Represents matrix transpose;

[0035] When the correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is less than or equal to the correlation threshold, the coefficient vector α(n+1) = α(n) + K(n+1) for the n+1th iteration is updated according to the updated kernel matrix K(n+1) -1 q(n+1)ε(n);

[0036] Among them, the increment vector Adaptive control amount γ(n+1)=(λ(n+1)) n+1 +z(n+1) T P(n)z(n+1), the inverse autocorrelation matrix of the coefficient vector α(n+1)

[0037]

[0038] A further technical solution is to obtain the multipath gain prediction value of path p at the prediction time T and multipath delay prediction value include:

[0039] For any prediction time T, calculate the inner product h of the historical sample sequence at the prediction time T and the historical sample sequence from the initial time T0 to the prediction time T-1 mapped to the feature space p (T)=[k(x(T),x(T0)),k(x(T),x(T0+1)),...,k(x(T),x(T-1))] T ;

[0040] Get the multipath gain prediction value of path p at the prediction time T Among them, α pA is the coefficient vector of the multipath gain prediction model of the trained path p; the multipath delay prediction value of path p at the prediction time T is obtained Among them, α pτ is the coefficient vector of the trained multipath delay prediction model for path p.

[0041] A further technical solution is that the underwater acoustic time-varying channel prediction method further includes:

[0042] In the process of performing channel prediction using the multipath gain prediction model and the multipath delay prediction model of each path obtained through training, channel sample data at each continuous prediction moment of the underwater acoustic time-varying channel is obtained;

[0043] The model parameters of each multipath gain prediction model and multipath delay prediction model obtained by training are updated respectively by using the channel sample data at each continuous prediction moment at every predetermined time interval.

[0044] The beneficial technical effects of this application are:

[0045] This application proposes a method for predicting underwater acoustic time-varying channels based on kernel recursive least squares. By using the kernel recursive least squares method to construct a prediction model for underwater acoustic time-varying channels and using channel sample data to train the prediction model, effective underwater acoustic time-varying channel prediction can be achieved. By adaptively updating the prediction model in a recursive form and combining the kernel function to transform complex nonlinear problems into linear problems, the problem of online prediction of multivariate time series of underwater acoustic time-varying channels can be effectively solved while reducing the computational complexity, and it has good generalization performance.

[0046] For the time-varying characteristics of the underwater acoustic time-varying channel in a dynamic environment, the forgetting factor is introduced into the kernel recursive least squares method and adaptively adjusted to achieve real-time tracking of the historical sample data of the underwater acoustic time-varying channel and distinction of their importance, thereby ensuring the validity of the training sample data input into the prediction model, further improving the accuracy of the prediction model, and solving the problem that the traditional kernel recursive least squares method cannot track the time-varying nature of the underwater acoustic time-varying channel in real time.

[0047] Through the combination of offline training and online prediction, the prediction model obtained through training is used to perform online prediction within a predetermined time interval to obtain the channel sample data of the time interval, and the offline part uses the obtained channel sample data of the time interval to update the prediction model. This solves the problem that the time-consuming model update seriously affects the efficiency of online prediction, and can effectively prevent the prediction performance of the trained prediction model from decreasing after a period of time. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a flow chart of the underwater acoustic time-varying channel prediction method.

[0049] Figure 2 It is a flowchart for training a prediction model.

[0050] Figure 3 This is a framework diagram of the offline and online prediction method for underwater acoustic time-varying channels. DETAILED DESCRIPTION

[0051] The specific implementation of the present application is further described below in conjunction with the accompanying drawings.

[0052] This application discloses a method for predicting underwater acoustic time-varying channels based on kernel recursive least squares, which can be applied to the prediction of underwater acoustic time-varying channel impulse responses with multiple paths. Please refer to Figure 1 The flowchart shown in the figure has the following specific steps:

[0053] Step 1: The underwater acoustic time-varying channel contains N p multipaths, and pre-acquire channel sample data of multiple continuous sampling moments of the underwater acoustic time-varying channel. The channel sample data of the underwater acoustic time-varying channel at any sampling moment includes the multipath gain and multipath delay of any path p in the underwater acoustic time-varying channel at the current sampling moment. p An integer parameter.

[0054] For path p, multiple gain training samples and multiple delay training samples are constructed using the obtained channel sample data. Among them, any t-th training sample constructed includes the signal measured data y(t) obtained by actual measurement of path p at sampling time t and the historical sample sequence x(t) at sampling time t. The historical sample sequence x(t) at sampling time t includes a sequence composed of the signal measured data at all sampling times before sampling time t. The signal measured data y(t) in the gain training sample is the multipath gain, and the signal measured data y(t) in the delay training sample is the multipath delay. The initial value of the integer parameter t is l. In one example, the l-th training sample is an input-output data pair (x(l), y(l)). For the gain training sample, the input data is the multipath gain historical sample sequence x(l) at sampling time l = (A p (l-1),A p (l-2),...,A p (l0)), the expected output is the multipath gain y(l) = A at sampling time l p (l); For the delay training sample, the input data is the multipath delay history sample sequence x(l) = (τ p (l-1),τ p (l-2),...,τ p(l0)), the expected output is the multipath delay y(l) = τ at sampling time l p (l), the integer parameter l0 is the initial sampling time and l0 <l。

[0055] Step 2, use the kernel recursive least squares method to respectively construct a multipath gain prediction model and a multipath delay prediction model for any path p in the underwater acoustic time-varying channel. Input the constructed gain training samples of path p into the multipath gain prediction model of path p to train the multipath gain prediction model; input the constructed delay training samples of path p into the multipath delay prediction model of path p to train the multipath delay prediction model. When using the training samples of path p to train the corresponding prediction model, the training process of the multipath gain prediction model and the multipath delay prediction model are the same. You only need to replace the training samples with the corresponding training samples. Therefore, please refer to the training process of any prediction model. Figure 2 The specific process is as follows:

[0056] (1) Use the lth training sample to initialize the model parameters of the prediction model at iteration number n=1.

[0057] This application introduces a forgetting factor based on the traditional kernel recursive least squares model to distinguish historical sample data at different sampling times to ensure the effectiveness of the selected training samples, thereby improving the accuracy of the prediction model. In one embodiment, the cost function of each prediction model at the nth iteration is constructed as follows: x(i) is the historical sample sequence at sampling time i, and the integer parameter is 1≤i≤n. The purpose of model training is to find the model parameters that minimize the cost function through iterative updates. The model parameters of each prediction model at the nth iteration include the kernel matrix K(n), the coefficient vector α(n) and the forgetting factor λ(n). The forgetting factor λ(n) of the nth iteration indicates the weight of the historical sample sequence at sampling time l+n-1 in the prediction model. The larger the value of the forgetting factor λ(n), the larger the weight of the historical sample sequence at sampling time l+n-1. λ(1) is initialized to a value in the range of (0,1].

[0058] Initialize the coefficient vector α(1)=K(1) using the measured signal data y(l) at sampling time l -1 y(l), the kernel matrix is ​​initialized using the historical sample sequence x(l) at sampling time l The kernel function The Mercer kernel function method can be used to map the historical sample sequence at sampling time l to the feature vector corresponding to the feature space The inner product between Converted into the calculation of the kernel function, the kernel function is calculated σ is the kernel function width parameter, and exp() is the e exponent. Converting the inner product calculation between feature vectors in the feature space into a simple e exponential calculation can effectively reduce the computational complexity and improve the computational efficiency.

[0059] (2) Determine the characteristic matrix Φ(1) when the iteration number n=1 based on the historical sample sequence at sampling time l, and combine the characteristic matrix Φ(n) and use the prediction model of the nth iteration to obtain the channel prediction data at sampling time l+n-1 The feature matrix Φ(n) is composed of the feature vector corresponding to the historical sample sequence at the sampling time corresponding to the nth iteration mapped to the feature space. In an example, when n=1, the initial feature matrix The channel prediction data at sampling time l is obtained by using the prediction model parameters initialized in the first iteration Channel prediction data at sampling time l+n-1 The corresponding expected output is the measured signal data y(l+n-1) at sampling time l+n-1. For the multipath gain prediction model, the multipath gain at sampling time l+n-1 is predicted using the historical sample sequence of multipath gain at sampling time l; for the multipath delay prediction model, the multipath delay at sampling time l+n-1 is predicted using the historical sample sequence of multipath delay at sampling time l.

[0060] (3) Update the feature matrix Φ(n+1) based on the historical sample sequence at sampling time l+n, and combine the l+n-1th training sample and the channel prediction data at sampling time l+n-1 Update the model parameters of the prediction model at the n+1th iteration. The model parameters of the n+1th iteration include the kernel matrix K(n+1), the coefficient vector α(n+1) and the forgetting factor λ(n+1). The specific process of updating the model parameters according to the correlation between each model parameter is:

[0061] First, calculate the channel sample data at sampling time l+n-1 and the channel prediction data at sampling time l+n-1. The prediction error ε(n) between the nth iterations is calculated, and the forgetting factor λ(n+1) of the n+1th iteration is updated according to the prediction error ε(n) of the nth iteration. The specific calculation relationship of the forgetting factor for the prediction error can be customized according to the data form of the actual application. In the prior art, there is a form of using the log(ε(n)) function. In this application, the forgetting factor updated in each iteration is adaptively adjusted in the form of the e exponent. Specifically, the updated forgetting factor λ(n+1) of the n+1th iteration is = λ min +(λ max -λ min ) -βE(n) , where λmin is the minimum value of the forgetting factor, λ max is the maximum value of the forgetting factor, usually set to 0.9-1; β is the attenuation constant that controls the convergence rate. The larger β is, the faster the convergence speed is; error feedback function When ε(n)<ε0, the ratio of ε(n) to ε0 is reduced by the kth power, the parameter k>0, k is generally 2 or 4, and λ(n+1) quickly approaches λ max ; When ε(n)>ε0, the ratio of ε(n) to ε0 will be further amplified, thus accelerating the approach of λ(n+1) to λ min speed, ε0 is the reference error.

[0062] Map the historical sample sequence at sampling time l to the feature space to obtain the corresponding feature vector And initialize the feature matrix Φ(1) containing the feature vector Update the feature matrix Φ(n+1) according to the initialized feature matrix. In order to further improve the accuracy of the prediction model, the training data input to the prediction model is screened to ensure the reliability of the training data used in the training model and prevent the influence of useless noise data. In one embodiment, the correlation between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is determined by using the approximate linear correlation criterion. in, is the i-th eigenvector in the feature matrix Φ(n), and m is the total number of eigenvectors in the feature matrix Φ(n).

[0063] If δ(n) is greater than the correlation threshold, it is determined that the historical sample sequence at sampling time l+n is linearly independent of the feature matrix Φ(n), and the historical sample sequence at sampling time l+n is mapped to the feature space to obtain the corresponding feature vector And add it to the feature matrix Φ(n), and update the feature matrix Φ(n+1);

[0064] If δ(n) is less than or equal to the correlation threshold, it is determined that the historical sample sequence at sampling time l+n is linearly correlated with the feature matrix Φ(n), and the updated feature matrix Φ(n+1)=Φ(n) is determined, where the correlation threshold can be customized according to the actual application situation.

[0065] Then, the kernel matrix K(n+1) of the n+1th iteration is updated based on the historical sample sequence at sampling time l+n, combined with the updated feature matrix Φ(n+1) and the updated forgetting factor λ(n+1). Since the kernel recursive least squares method with the introduction of the forgetting factor is used to construct the prediction model, the calculation of the recursive formula of the kernel matrix K(n+1) must also take into account the influence of the forgetting factor.

[0066] In one embodiment, when the correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is greater than the correlation threshold, it is determined The inner product of the historical sample sequence x(l+n) at sampling time l+n and the historical sample sequence from sampling time l to sampling time l+n-1 mapped to the feature space is h(n+1)=[k(x(l+n),x(l)),k(x(l+n),x(l+1)),...,k(x(l+n),x(l+n-1))] T , K(n)=Φ(n) T Φ(n),[] T represents matrix transpose, [] -1 represents matrix inversion;

[0067] When the correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is less than or equal to the correlation threshold, it is determined that K(n+1)=K(n).

[0068] Finally, according to the updated kernel matrix K(n+1), combined with the calculation formula of the inner product h(n+1), the intermediate quantities including the adaptive control quantity z(n+1), the adaptive control quantity γ(n+1) and the incremental vector q(n+1) can be calculated, and then the coefficient vector α(n+1) of the n+1th iteration can be updated.

[0069] In one embodiment, when the correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is greater than the correlation threshold, the coefficient vector of the n+1th iteration is updated according to the updated kernel matrix K(n+1)

[0070] Among them, the adaptive control amount z(n+1)=K(n) -1 h(n+1), adaptive control quantity The inner product of the historical sample sequence x(l+n) at sampling time l+n and the historical sample sequence from sampling time l to sampling time l+n-1 mapped to the feature space is h(n+1)=[k(x(l+n),x(l)),k(x(l+n),x(l+1)),...,k(x(l+n),x(l+n-1))] T , K(n)=Φ(n) T Φ(n), y(l+n) is the measured signal data at sampling time l+n, ε(n) is the prediction error, and c is the regularization parameter;

[0071] When the correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is less than or equal to the correlation threshold, the coefficient vector α(n+1) = α(n) + K(n+1) for the n+1th iteration is updated according to the updated kernel matrix K(n+1) -1 q(n+1)ε(n);

[0072] Among them, the increment vector Adaptive control amount γ(n+1)=(λ(n+1)) n+1 +z(n+1) T P(n)z(n+1), the inverse autocorrelation matrix of the coefficient vector α(n+1) At the initial iteration n=1, P(1)=I, where I is the identity matrix.

[0073] Let n=n+1 and execute (2) again until the iteration condition is met to obtain the trained prediction model. The iteration condition can be a specified number of iterations or the iteration condition of updating the last training sample.

[0074] Step 3: Use the trained multipath gain prediction model of path p to obtain the multipath gain prediction value of path p at prediction time T according to the multipath gain sequence of several consecutive times before prediction time T. The multipath delay prediction value of path p at prediction time T is obtained by using the multipath delay sequence of several consecutive times before prediction time T using the trained multipath delay prediction model of path p.

[0075] In one embodiment, for any prediction time T, the inner product h of the historical sample sequence at the prediction time T and the historical sample sequence from the initial time T0 to the prediction time T-1 mapped to the feature space is calculated. p (T)=[k(x(T),x(T0)),k(x(T),x(T0+1)),...,k(x(T),x(T-1))] T When calculating the multipath gain prediction value, the inner product is calculated using the multipath gain sequence in the historical sample sequence, and x(T) corresponds to the multipath gain sequence; when calculating the multipath delay prediction value, the inner product is calculated using the multipath delay sequence in the historical sample sequence, and x(T) corresponds to the multipath delay sequence.

[0076] Get the multipath gain prediction value of path p at the prediction time T Among them, α pA is the coefficient vector of the multipath gain prediction model of the trained path p; the multipath delay prediction value of path p at the prediction time T is obtained Among them, α pτ is the coefficient vector of the trained multipath delay prediction model for path p.

[0077] Step 4: Combining the multipath gain prediction value and multipath delay prediction value of all paths at the prediction time T, the channel prediction value of the underwater acoustic time-varying channel at the prediction time T is obtained. τ is the time delay.

[0078] Since the iterative update process of the prediction model usually requires a large amount of computation and complexity, frequent updates of the prediction model require a lot of time, which will cause each prediction process to take a long time, thus seriously reducing the prediction efficiency. In addition, due to the time-varying characteristics of the underwater acoustic time-varying channel, the prediction performance of the trained prediction model may decline after a period of time. Therefore, in order to solve these problems, this application proposes a method that combines offline training and online prediction, please refer to Figure 3 As shown in the framework diagram, the model is trained offline using the acquired channel sample data, and then the trained model is directly used for channel prediction over a period of time.

[0079] The online prediction part is responsible for obtaining channel sample data. Specifically, in the process of channel prediction using the trained multipath gain prediction model and multipath delay prediction model of each path, the channel sample data of each continuous prediction moment of the underwater acoustic time-varying channel is obtained.

[0080] The offline training part is responsible for storing channel sample data and training the prediction model. Specifically, the channel sample data at each continuous prediction moment is used to update the model parameters of each multipath gain prediction model and multipath delay prediction model obtained by training at every predetermined time interval.

[0081] The above is only a preferred embodiment of the present application, and the present application is not limited to the above embodiments. It is understood that other improvements and changes directly derived or associated by those skilled in the art without departing from the spirit and concept of the present application should be considered to be included in the protection scope of the present application.

Claims

1. A method for predicting underwater acoustic time-varying channels based on kernel recursive least squares, characterized in that: The underwater acoustic time-varying channel prediction method comprises: The kernel recursive least squares method is used to respectively construct a multipath gain prediction model of any path p and a multipath delay prediction model of any path p in an underwater acoustic time-varying channel, wherein the underwater acoustic time-varying channel includes N p Multipath, N p is an integer parameter; Acquire channel sample data of an underwater acoustic time-varying channel at multiple consecutive sampling moments, and construct multiple gain training samples and multiple delay training samples for any path p, wherein the channel sample data of the underwater acoustic time-varying channel at any sampling moment includes the multipath gain and multipath delay of any path p in the underwater acoustic time-varying channel at the current sampling moment; any t-th training sample constructed for path p includes the signal measured data y(t) of path p at sampling moment t and the historical sample sequence x(t) at sampling moment t, wherein the historical sample sequence x(t) at sampling moment t includes a sequence composed of the signal measured data at all sampling moments before sampling moment t; the signal measured data y(t) in the gain training sample is the multipath gain, the signal measured data y(t) in the delay training sample is the multipath delay, and the initial value of the integer parameter t is l; The multipath gain prediction model of path p is trained using the gain training samples of path p, and the multipath delay prediction model of path p is trained using the delay training samples of path p. When the corresponding prediction model is trained using the training samples of path p: (1) using the lth training sample to initialize the model parameters of the prediction model at the iteration number n=1; (2) Determine the characteristic matrix Φ(1) when the iteration number n=1 based on the historical sample sequence at sampling time l, and combine the characteristic matrix Φ(n) and use the prediction model of the nth iteration to obtain the channel prediction data at sampling time l+n-1 The channel prediction data when training the multipath gain prediction model is the multipath gain, and the channel prediction data when training the multipath delay prediction model is the multipath delay; (3) Update the feature matrix Φ(n+1) based on the historical sample sequence at sampling time l+n, and combine the l+n-1th training sample and the channel prediction data at sampling time l+n-1 Update the model parameters of the prediction model at the n+1th iteration to obtain the prediction model at the n+1th iteration, and set n=n+1 and execute (2) again until the iteration condition is met to obtain the trained prediction model; The multipath gain prediction value of path p at prediction time T is obtained by using the trained multipath gain prediction model of path p according to the multipath gain sequence of several consecutive times before prediction time T. The multipath delay prediction value of path p at prediction time T is obtained by using the multipath delay sequence of several consecutive times before prediction time T using the trained multipath delay prediction model of path p. The channel prediction value of the underwater acoustic time-varying channel at the prediction time T is obtained by combining the multipath gain prediction value and multipath delay prediction value of all paths at the prediction time T. τ is the time delay.

2. The underwater acoustic time-varying channel prediction method according to claim 1, characterized in that: The cost function of each prediction model at the nth iteration is x(i) is the historical sample sequence at sampling time i, the integer parameter is 1≤i≤n, the model parameters of each prediction model at the nth iteration include the kernel matrix K(n), the coefficient vector α(n) and the forgetting factor λ(n), and the model parameters of the prediction model initialized with the lth training sample at the iteration number n=1 include: Initialize the coefficient vector α(1)=K(1) using the measured signal data y(l) at sampling time l -1 y(l), the historical sample sequence x(l) at sampling time l to initialize the kernel matrix Kernel Function σ is the kernel function width parameter, and λ(1) is initialized to a value in the range of (0,1); Among them, the forgetting factor λ(n) of the nth iteration indicates the weight of the historical sample sequence at the sampling time l+n-1 in the prediction model. The larger the value of the forgetting factor λ(n), the greater the weight of the historical sample sequence at the sampling time l+n-1.

3. The underwater acoustic time-varying channel prediction method according to claim 2, characterized in that: The updating of the model parameters of the prediction model at the n+1th iteration includes: Calculate the channel sample data at sampling time l+n-1 and the channel prediction data at sampling time l+n-1 The prediction error ε(n) between the nth iteration and the forgetting factor λ(n+1) of the n+1th iteration are updated according to the prediction error ε(n) of the nth iteration; According to the historical sample sequence at sampling time l+n, the updated feature matrix Φ(n+1) and the updated forgetting factor λ(n+1) are combined to update the kernel matrix K(n+1) of the n+1th iteration; The coefficient vector α(n+1) of the n+1th iteration is updated according to the updated kernel matrix K(n+1).

4. The underwater acoustic time-varying channel prediction method according to claim 3, characterized in that: Update the forgetting factor of the n+1th iteration λ(n+1)=λ min +(λ max -λ min ) -βE(n) , where λ min is the minimum value of the forgetting factor, λ max is the maximum value of the forgetting factor, β is the decay constant that controls the convergence rate, and the error feedback function ε0 is the benchmark error, parameter k>

0.

5. The underwater acoustic time-varying channel prediction method according to claim 3, characterized in that: Determining the characteristic matrix Φ(1) and updating the characteristic matrix Φ(n+1) includes: Map the historical sample sequence at sampling time l to the feature space to obtain the corresponding feature vector And initialize the feature matrix Φ(1) containing the feature vector The correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is determined using the approximate linear correlation criterion; If δ(n) is greater than the correlation threshold, it is determined that the historical sample sequence at sampling time l+n is linearly independent of the feature matrix Φ(n), and the historical sample sequence at sampling time l+n is mapped to the feature space to obtain the corresponding feature vector And add it to the feature matrix Φ(n), and update the feature matrix Φ(n+1); If δ(n) is less than or equal to the correlation threshold, it is determined that the historical sample sequence at sampling time l+n is linearly correlated with the feature matrix Φ(n), and the updated feature matrix Φ(n+1)=Φ(n) is determined.

6. The underwater acoustic time-varying channel prediction method according to claim 5, characterized in that: Determine the correlation between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) in, is the i-th eigenvector in the feature matrix Φ(n), and m is the total number of eigenvectors in the feature matrix Φ(n).

7. The underwater acoustic time-varying channel prediction method according to claim 3, characterized in that: The kernel matrix K(n+1) of the n+1th iteration is updated to include: When the correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is greater than the correlation threshold, it is determined Among them, the inner product of the historical sample sequence x(l+n) at sampling time l+n and the historical sample sequence from sampling time l to sampling time l+n-1 mapped to the feature space is h(n+1)=[k(x(l+n),x(l)),k(x(l+n),x(l+1)),...,k(x(l+n),x(l+n-1))] T , K(n)=Φ(n) T Φ(n); When the correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is less than or equal to the correlation threshold, it is determined that K(n+1)=K(n).

8. The underwater acoustic time-varying channel prediction method according to claim 3, characterized in that: The coefficient vector α(n+1) of the n+1th iteration is updated to include: When the correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is greater than the correlation threshold, the coefficient vector of the n+1th iteration is updated according to the updated kernel matrix K(n+1) Among them, the adaptive control amount z(n+1)=K(n) -1 h(n+1), adaptive control quantity The inner product of the historical sample sequence x(l+n) at sampling time l+n and the historical sample sequence from sampling time l to sampling time l+n-1 mapped to the feature space is h(n+1)=[k(x(l+n),x(l)),k(x(l+n),x(l+1)),...,k(x(l+n),x(l+n-1))] T , K(n)=Φ(n) T Φ(n), y(l+n) is the measured signal data at sampling time l+n, ε(n) is the prediction error, c is the regularization parameter, [] T Represents matrix transpose; When the correlation δ(n) between the historical sample sequence at sampling time l+n and the feature matrix Φ(n) is less than or equal to the correlation threshold, the coefficient vector α(n+1) = α(n) + K(n+1) for the n+1th iteration is updated according to the updated kernel matrix K(n+1) -1 q(n+1)ε(n); Among them, the increment vector Adaptive control amount γ(n+1)=(λ(n+1)) n+1 +z(n+1) T P(n)z(n+1), the inverse autocorrelation matrix of the coefficient vector α(n+1) 9. The underwater acoustic time-varying channel prediction method according to claim 1, characterized in that: Get the multipath gain prediction value of path p at the prediction time T and multipath delay prediction value include: For any prediction time T, calculate the inner product h of the historical sample sequence at the prediction time T and the historical sample sequence from the initial time T0 to the prediction time T-1 mapped to the feature space p (T)=[k(x(T),x(T0)),k(x(T),x(T0+1)),...,k(x(T),x(T-1))] T ; Get the multipath gain prediction value of path p at the prediction time T Among them, α pA is the coefficient vector of the multipath gain prediction model of the trained path p; the multipath delay prediction value of path p at the prediction time T is obtained Among them, α pτ is the coefficient vector of the trained multipath delay prediction model for path p.

10. The underwater acoustic time-varying channel prediction method according to claim 9, characterized in that: The underwater acoustic time-varying channel prediction method further includes: In the process of performing channel prediction using the multipath gain prediction model and the multipath delay prediction model of each path obtained through training, channel sample data at each continuous prediction moment of the underwater acoustic time-varying channel is obtained; The model parameters of each multipath gain prediction model and multipath delay prediction model obtained by training are updated respectively by using the channel sample data at each continuous prediction moment at every predetermined time interval.

Images