Adaptive step length adjustment method for predicting LMS power inversion based on neural network

Abstract

The invention discloses a neural network prediction-based LMS (Least Mean Square) power inversion adaptive step length adjustment method, which relates to the technical field of satellite navigation and signal processing, and comprises the following steps of: constructing and training a neural network model, inputting a current frame input signal power and a maximum characteristic value, and outputting a current frame prediction step length; compared with an LMS power inversion algorithm with a fixed step length, the method introduces a neural network to dynamically predict the optimal step length, solves the problem that traditional empirical step length adjustment is not adaptive, reflects interference intensity in combination with a covariance matrix and a maximum characteristic value of an input signal, realizes interference sensing adjustment, can increase the step length under the condition of relatively strong interference, and improves the accuracy of interference sensing adjustment. Convergence is accelerated and the tracking capability is enhanced; and under the condition of weak interference, the step length is reduced, so that steady state imbalance is reduced, and the anti-interference performance is improved. The method can solve the problem that in an existing LMS power inversion algorithm, step length parameters are difficult to adjust in a self-adaptive mode, and especially the problem that convergence is slow or system divergence is caused by improper step length setting in a multi-interference channel or dynamic environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of satellite navigation and signal processing, and particularly relates to a neural network-based LMS power inversion adaptive step size adjustment method. BACKGROUND

[0002] As a typical adaptive filtering algorithm, the least mean squares (LMS) algorithm is widely used in communication systems, radar signal processing, GNSS anti-jamming and other fields. To improve its robustness in strong interference environment, the LMS power inversion (Power Inverse) algorithm is proposed, and its step size is a function of the input signal power. However, the power estimation has problems such as time delay and nonlinear response, which leads to a decline in convergence performance in a variable interference scenario.

[0003] In practical applications, especially in strong interference or interference burst conditions, the performance of the LMS power inversion algorithm with fixed step size is severely restricted. On the one hand, a too small step size will result in slow convergence of the algorithm, which cannot adapt to sudden changes in channel conditions in time; on the other hand, a too large step size will cause weight oscillation and even algorithm divergence, which will damage the stability and robustness of the system.

[0004] Existing variable step size methods mainly update the step size parameter based on the error signal size, gradient change trend or signal autocorrelation characteristics. However, the algorithm still shows slow response and poor suppression when it faces strong interference bursts. In high-precision positioning and high-speed communication scenarios, the system's anti-interference ability is required to be higher, so there is an urgent need for a technology that can sense the intensity of interference in real time and dynamically adjust the step size of the LMS power inversion algorithm to improve the robustness and adaptive ability of the algorithm in strong interference conditions. SUMMARY

[0005] In order to overcome the defects in the prior art, the present application provides a neural network-based LMS power inversion adaptive step size adjustment method, which constructs and trains a neural network model, the input is the current frame input signal power P x and the maximum eigenvalue λ max , and the output is the current frame predicted step size μ, solving the problem of non-adaptive traditional empirical step size adjustment.

[0006] To achieve the above purpose, the present application adopts the following technical solutions, comprising:

[0007] A neural network-based LMS power inversion adaptive step size adjustment method comprises the following steps:

[0008] S1, input signal X(n)=[x1(n), x2(n),...] is a signal vector received by array antenna of multi-element linear array, fix the first input signal x1(n) as desired signal d(n)=x1(n); wherein, n represents sampling time;

[0009] S2, the rest of the input signal, that is, [x2(n),...] constitutes a vector X a (n), calculate the covariance matrix of vector X a (n) E[·] represents mathematical expectation, is the conjugate transpose of vector X a (n)

[0010] S3, calculate the input signal power P x (n) and the maximum eigenvalue λ max (n) of the current sampling time, that is, the current frame:

[0011] Input signal power P x (n) = E[||X a (n) || 2 ] = tr(R aa (n))

[0012] Wherein, ||·|| 2 represents the square of norm; E[·] represents mathematical expectation; tr(·) represents the trace of matrix;

[0013] Initialize random vector (||v (0) ||2 = 1);

[0014] Iterative calculation Wherein, superscript t = 1, 2,..., T, represents the number of iterations; norm(·) represents the normalization function;

[0015] Maximum eigenvalue λ max (n) = (v (T) ) H R aa (n)v (T) ;

[0016] S4, construct and train a neural network, the network input is the current frame input signal power P x (n) and the maximum eigenvalue λ max (n), the output is the predicted step size μ pred (n) of the current frame in LMS power inversion algorithm.

[0017] Preferably, in step S4, the training process of the neural network is:

[0018] S41, generate simulation signals containing different interference intensities, noise powers and mutation frequencies, and construct a simulation data set;

[0019] Set the step size range [μ min ,μ max ], iterate a series of step sizes μ∈[μ min ,μ max ] for each scene, execute the LMS power inversion algorithm, compare the performance indicators J(μ) corresponding to all step sizes μ, and select the step size that minimizes J(μ) as the optimal step size μ opt for the current scene; wherein μ min ,μ max are the minimum and maximum values of the step size, respectively;

[0020] The calculation formula of the performance indicator J(μ) is:

[0021]

[0022] Wherein, T is the number of iterations to reach steady state; N s is the number of sampling points; α and β are weight coefficients; N0 is the starting time of steady state evaluation; J(μ) is the performance indicator; e(n) is the error signal between the expected signal and the output signal of the LMS power inversion algorithm;

[0023] The calculation formula of the optimal step size μ opt is as follows:

[0024]

[0025] S42, train the neural network using the simulation data set, and the loss function is:

[0026]

[0027] Wherein, N is the total number of samples; represents the predicted step size output by the neural network for the i-th sample; represents the optimal step size corresponding to the i-th sample.

[0028] Preferably, the LMS power inversion algorithm is as follows:

[0029] W a (n+1)=W a (n)+μ(n)X a (n)e H (n);

[0030] e(n)=d(n)-Y a (n);

[0031]

[0032] wherein W a (n) is the weight vector of X a (n) is the error signal between d(n) and Y a (n) is the error signal between d(n) and Y H (n) is the conjugate transpose of e(n); is the conjugate transpose of weight vector W a (n) is the conjugate transpose of e(n); μ is the iteration step size; and n is the sampling time.

[0033] Preferably, in the subsequent iterations, the covariance matrix is recursively updated according to the following formula:

[0034]

[0035] wherein α is a forgetting factor, 0 < α < 1.

[0036] Preferably, until the error signal e(n) converges, the output signal is obtained.

[0037] The application further provides a computer program product comprising computer programs / instructions which, when executed by a processor, implement the neural network-based prediction LMS power inversion adaptive step size adjustment method.

[0038] The application further provides a readable storage medium having a computer program stored thereon, which, when executed, implements the neural network-based prediction LMS power inversion adaptive step size adjustment method.

[0039] The application further provides an electronic device comprising a processor, a memory, and a computer program stored on the memory and executable on the processor, wherein the processor, when executing the computer program, implements the neural network-based prediction LMS power inversion adaptive step size adjustment method.

[0040] The application has the following advantages:

[0041] (1) The application constructs and trains a neural network model, the input being the current frame input signal power P x and the maximum eigenvalue λ max , and the output being the current frame predicted step size μ. Compared with the fixed step size LMS power inversion algorithm, the application introduces a neural network to dynamically predict the optimal step size, solves the problem of non-adaptive step size adjustment in the traditional experience formula, and combines the covariance matrix and the maximum eigenvalue of the input signal to reflect the interference intensity, realizes interference-aware adjustment, can increase the step size in the case of strong interference to accelerate convergence and enhance tracking ability, and can reduce the step size in the case of weak interference to reduce the steady-state error and improve the anti-interference performance.

[0042] (2) The application can solve the problem that the step size parameter in the existing LMS power inversion algorithm is difficult to adaptively adjust, especially the problem of slow convergence or system divergence caused by improper step size setting in a multi-interference channel or a dynamic environment. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 is a schematic diagram of the LMS power inversion array;

[0044] Figure 2 is a schematic diagram of the four-element linear array;

[0045] Figure 3 is a flowchart of the method of the application;

[0046] Figure 4 is a structural diagram of the neural network;

[0047] Figure 5 is a three-dimensional beam pattern of the embodiment of the method of the application. DETAILED DESCRIPTION

[0048] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the application. Obviously, the described embodiments are only some of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the application.

[0049] Referring to Figure 1 the power inversion array shown in FIG. 1 and Figure 2 the four-element linear array shown in FIG. 2, the principle of the LMS power inversion algorithm is as follows:

[0050] The input signal X(n) = [x1(n), x2(n),...] is a signal vector received by the array antenna of the four-element linear array, and the received signal x1(n) of the first input signal is the expected signal d(n) = x1(n); the received signal vector X a (n) = [x2(n), x3(n), x4(n)] of the remaining array elements is taken as the input signal of the filter (i.e., the input signal of the LMS power inversion algorithm) to estimate d(n), and the difference is taken to achieve the purpose of interference cancellation.

[0051] W a (n+1) = W a (n) + μ(n)X a (n)e H (n);

[0052]

[0053] e(n) = d(n) - Ya (n);

[0054] wherein, X a (n) is a vector composed of the received signals of the 2nd, 3rd and 4th array elements, i.e. a vector composed of the 2nd, 3rd and 4th input signals, X a (n) = [x2(n), x3(n), x4(n)] ; W a (n) is a weight vector of the vector X a (n) ; n is a sampling time; is a conjugate transpose of the weight vector W a (n) ; μ is an iteration step size; e(n) is an error signal between d(n) and Y a (n) ; e H (n) is a conjugate transpose of e(n) ; Y a (n) is a filter output signal (i.e. an output signal of the LMS power inversion algorithm).

[0055] As Figure 3 shown in the figure, the neural network-based LMS power inversion adaptive step size adjustment method of the application comprises the following specific steps:

[0056] Step 1, the input signal X(n) = [x1(n), x2(n), x3(n), x4(n)] is a signal vector received by a four-element linear array antenna, and the first input signal x1(n) is fixed as the expected signal d(n) = x1(n).

[0057] Step 2, the remaining input signals, i.e. the 2nd, 3rd and 4th input signals, constitute a vector X a (n), and the covariance matrix of the vector X a (n) is calculated. E[·] represents mathematical expectation, is a conjugate transpose of the vector X a (n).

[0058] In the subsequent iterations, the covariance matrix can be recursively updated, and the formula is as follows:

[0059]

[0060] wherein, α is a forgetting factor, 0 < α < 1.

[0061] Step 3, the input signal power P x (n) of the current frame and the maximum eigenvalue λ max (n) are calculated, and the specific manner is as follows:

[0062] The input signal power P x (n) = E[||X a (n) || 2] = tr(R aa (n));

[0063] where ||·||2 2 denotes the square of the norm; E[·] denotes the mathematical expectation; tr(·) denotes the trace of a matrix;

[0064] the maximum eigenvalue λ max characterizes the projection power of the received signal on the interference subspace, and the power iteration method can be used to approximate λ max , and the specific process is as follows:

[0065] Initialize a random vector v (||v (0) ||2=1);

[0066] Iterative calculation where the superscript t = 1, 2,..., T represents the number of iterations; norm(·) represents a normalization function;

[0067] Estimate the maximum eigenvalue λ max (n)≈(v (T) ) H R aa (n)v (T) .

[0068] Step 4, construct and train a neural network, the network input is the current frame input signal power P x (n) and the maximum eigenvalue λ max (n), and the output is the current frame prediction step size μ pred (n) used to update the weight vector in the LMS power inversion algorithm.

[0069] The neural network sets the output activation function as the Sigmoid function, first maps the output to [0, 1], and then linearly scales it to [μ min ,μ max ], to ensure that the prediction step size is within a reasonable range. μ min ,μ max are the minimum and maximum values of the step size, respectively.

[0070] The neural network training process is as follows:

[0071] S41, use an offline simulation data set to generate simulation signals containing different interference intensities, noise powers, and mutation frequencies, set the step size range [μ min ,μ max ], and traverse the step size μ∈[μ min ,μ maxS41, try a series of different step values, execute the LMS power inversion algorithm, compare the performance indicators J(μ) corresponding to all steps μ, and select the step that minimizes J(μ) as the optimal step μ under the current scenario opt ;

[0072] The calculation formula of the performance indicator J(μ) is:

[0073]

[0074] Wherein, T is the number of iterations to reach steady state; N s is the number of sampling points; α, β are weight coefficients; N0 is the starting time of steady state evaluation, N0>T; J(μ) is the performance indicator; e(n) is the error signal between the expected signal and the output signal of the LMS power inversion algorithm;

[0075] The calculation formula of the optimal step μ opt is as follows:

[0076]

[0077] S42, train the neural network using the simulation data set, and the loss function is:

[0078]

[0079] Wherein, N is the total number of samples; represents the predicted step output by the neural network for the i-th sample; represents the optimal step corresponding to the i-th sample (obtained by offline simulation).

[0080] The loss function aims to make the predicted step of each sample output by the neural network as close as possible to the optimal step

[0081] Step 5, use the predicted step μ pred (n) output by the neural network to update the weight vector of the LMS power inversion algorithm, and the update formula is:

[0082] W a (n)=W a (n-1)+μ pred (n)X a (n-1)e H (n-1).

[0083] Step 6, subtract the expected signal d(n) from the output signal Y a (n) of the filter to obtain the error signal:

[0084] e(n)=d(n)-Y a (n).

[0085]

[0086] Step 7, according to steps 2 to 6, the loop calculation is performed, and the subsequent loop does not need to be iteratively trained on the neural network, but only needs to be updated and iterated on the weight vector of the LMS power inversion algorithm until the error e(n) converges, and finally the output signal Y(n) of the entire array, i.e. the error signal, is as follows:

[0087] Y(n) = e(n) = x1(n) - Y a (n).

[0088] Embodiment 1

[0089] In this embodiment, the antenna array in the simulation is a four-element linear array as shown in Figure 2 , the signal-to-noise ratio SNR is -35dB, the interference-to-noise ratio INR is 20dB, the inter-element spacing is set to half a wavelength, the angle of incidence of a narrowband interference signal is (60°, 30°), the signal direction is (0°, 30°), c is the speed of light, which is 3x10 8 m / s, and the carrier frequency f0 of the satellite signal is 1575.42MHz. As shown in Figure 5 , the interference angle direction null based on the neural network prediction LMS power inversion adaptive step size adjustment method can reach a depth of about 50dB, and the null position is also relatively accurate, with a narrow width and reduced suppression of useful signals.

[0090] Embodiment 2

[0091] An electronic device includes a processor, a memory, and a computer program stored on the memory and executable on the processor, and the processor implements the method of embodiment 1 when executing the computer program.

[0092] The electronic device of the embodiments of the present application can be a mobile device itself or a single device independent of the mobile device, which can communicate with the mobile device to receive the collected input signals therefrom and send the selected target decision behavior thereto.

[0093] The electronic device includes one or more processors and a memory. The processor can be a central processing unit (CPU) or other form of processing unit that has data processing and / or instruction execution capabilities, and can control other components in the electronic device to perform desired functions. The memory can include one or more computer program products that can include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory, for example, can include random access memory (RAM), cache memory, and / or the like. The non-volatile memory, for example, can include read-only memory (ROM), hard disk, flash memory, and / or the like. One or more computer program instructions can be stored on the computer-readable storage media, and the processor can execute the program instructions to implement the decision-making method of the various embodiments of the present application described above and / or other desired functions.

[0094] The electronic device can further include an input device and an output device.

[0095] Embodiment 3

[0096] In addition to the above method and device, an embodiment of the present application can also be a computer program product, which includes computer program instructions, which, when executed by a processor, cause the processor to perform the steps in the decision-making method according to various embodiments of the present application described in Embodiment 1 above.

[0097] The computer program product can be written in any combination of one or more programming languages, including an object-oriented programming language such as Java, C++, and the like, and conventional procedural programming languages, such as the "C" programming language, or the like. The program code can execute entirely on the user's computing device, partly on the user's device, as a stand-alone software package, partly on the user's computing device and partly on a remote computing device, or entirely on the remote computing device or server.

[0098] Embodiment 4

[0099] An embodiment of the present application can also be a computer-readable storage medium, which stores computer program instructions, which, when executed by a processor, cause the processor to perform the steps in the decision-making method according to various embodiments of the present application described in Embodiment 1 above.

[0100] The computer readable storage medium can be any combination of one or more computer readable media. The computer readable medium can be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium include the following: an electrical connection having one or more wires, a portable disc, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0101] The above merely provides the preferred embodiments of the present application, and is not intended to limit the present application. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present application shall fall within the scope of the present application.

Claims

1. A neural network-based prediction LMS power inverse adaptive step size adjustment method, characterized in that, The method comprises the following steps: S1, an input signal X(n)=[x1(n), x2(n),...] is a signal vector received by an array antenna of a multi-element linear array, and a first input signal x1(n) is fixed as a desired signal d(n)=x1(n); wherein n represents a sampling time; S2, the remaining input signal, i.e. [x2(n),...], forms the vector X a (n), the covariance matrix of the vector X a (n), the covariance matrix of the vector X E[·] denotes the mathematical expectation, is the vector X a (n) the conjugate transpose of the vector X S3, calculate the input signal power P of the current frame at the current sampling moment x (n) and the maximum eigenvalue λ max (n): Input signal power P x (n) = E[||X a (n)| 2 ] = tr(R aa (n)); Among them, ||·|| 2 E[·] represents the square of the norm; E[·] represents the mathematical expectation; tr(·) represents the trace of the matrix; Initializing a random vector (||v (0) ||2=1) Iterative computation where the superscript t = 1, 2,..., T denotes the iteration number; norm(·) denotes a normalization function; Maximum eigenvalue λ max (n) = (v (T) ) H R aa (n)v (T) ; S4, construct and train a neural network with input being the current frame input signal power P x (n) and the maximum eigenvalue λ max (n), and output being the predicted step size μ pred (n) for the current frame in the LMS power inversion algorithm.

2. The neural network-based method for predicting LMS power inverse adaptive step size adjustment according to claim 1, wherein, In step S4, the training process of the neural network is as follows: S41, a simulation signal containing different interference intensities, noise powers and mutation frequencies is generated to construct a simulation data set; Setting step size range [μ min ,μ max ], for each scene, a series of step sizes μ∈[μ min ,μ max ] are traversed, the LMS power inversion algorithm is executed, the performance indicators J(μ) corresponding to all step sizes μ are compared, and the step size that makes J(μ) minimum is selected as the optimal step size μ opt under the current scene; where μ min , μ max are the minimum and maximum values of the step size, respectively. The performance index J(μ) is calculated according to the following formula: Wherein, T is the number of iterations to reach steady state; N s is the number of sampling points; a, b are weight coefficients; N0 is the starting time of steady state evaluation; J(μ) is the performance index; e(n) is the error signal between the expected signal and the output signal of the LMS power inversion algorithm; optimal step size μ opt The formula for calculating is as follows: S42, the neural network is trained using the simulation data set, and the loss function is as follows: Wherein, N is the total number of samples; represents the predicted step length output by the neural network for the i th sample; represents the optimal step length corresponding to the i th sample.

3. The neural network-based method of claim 1 or 2, wherein the step size is adjusted according to the following equation: ###0001### where μ is the step size, μ0 is the initial step size, and ###0002### is the step size adjustment factor. The LMS power inversion algorithm is as follows: W a (n+1) = W a (n) + μ(n)X a (n)e H (n); e(n) = d(n) - Y a (n); where W a (n) is the weight vector of X a (n); e(n) is the error signal between d(n) and Y a (n); e H (n) is the conjugate transpose of e(n); is the conjugate transpose of the weight vector W a (n); μ is the iteration step size; and n is the sampling time.

4. The neural network-based method of claim 1, wherein, In subsequent iterations, the covariance matrix is recursively updated according to the following formula: Wherein, α is a forgetting factor, 0<α<1.

5. The neural network-based method of claim 3, wherein the step size is adjusted according to the following equation: ###0001### where μ is the step size, μ0 is the initial step size, and ###0002### is the step size adjustment factor. Until the error signal e(n) converges, the output signal is obtained.

6. A computer program product, characterised in that, The computer program / instructions are executed by the processor to implement the neural network prediction-based LMS power inversion adaptive step size adjustment method according to any one of claims 1-5.

7. A readable storage medium, characterized by, The computer program is stored on the computer program, and the computer program is executed to implement the neural network prediction-based LMS power inversion adaptive step size adjustment method according to any one of claims 1-5.

8. An electronic device, comprising: The computer program is stored on the computer program, and the computer program is executed to implement the neural network prediction-based LMS power inversion adaptive step size adjustment method according to any one of claims 1-5.

Images