Normalized navigation signal self-adaptive filtering method based on variable step size dustpan-like line

Abstract

The invention provides a normalized navigation signal adaptive filtering method based on a variable-step-size dustpan-like line, and relates to the field of satellite navigation signal processing. The method comprises the following steps: firstly, obtaining an output weight vector at the current moment based on an initial weight vector of a minimum mean square filter and a received mixed signal, and generating an initial weight matrix; a step length factor vector is obtained based on the dustpan-like line function, the step length factor vector passes through a curve obtained after a reciprocal of a standard dustpan-like line independent variable is obtained, three parameters are introduced, and the curve is adjusted into an autocorrelation estimation step length factor; taking an updating equation of the proportional step size control matrix as a condition for updating a real-time weight vector at a next moment, and continuously updating the real-time weight vector in an iterative filtering process; multiplying the real-time weight vector by the received mixed signal to realize front-end filtering; the method can effectively solve the contradiction between the steady-state error and the convergence speed in the least mean square adaptive filtering algorithm, and improves the anti-interference capability of the navigation system.

Description

Technical Field

[0001] The invention belongs to the field of satellite navigation and signal processing, and in particular relates to a normalized navigation signal adaptive filtering method based on a variable step-length quasi-curve. Background Art

[0002] In the networked battlefield, the implementation of ammunition precision guidance often adopts the combination of inertial guidance + satellite navigation assisted guidance. However, in the process of satellite navigation positioning, high-power environmental noise makes it impossible for the navigation signal to achieve accurate target positioning. Adaptive filtering is one of the main branches of navigation front-end filtering processing. Its advantage lies in its ability to combine observation data and decision rules to achieve the purpose of updating during the observation process while avoiding the extraction of prior statistical knowledge, thereby achieving noise suppression.

[0003] At present, the Least Mean Square (LMS) algorithm is the most common front-end filtering algorithm. In the LMS algorithm, the filter parameters are updated according to the convolution of the error signal and the input signal and a parameter called the step size. It is widely used because of its simple algorithm, fast convergence speed, model independence and high noise reduction performance. However, as a fixed-step algorithm, LMS has a contradiction between convergence speed and steady-state error, which makes the anti-interference ability of the dynamic system poor, and thus cannot achieve accurate positioning of satellite navigation. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a normalized navigation signal adaptive filtering method based on a variable step-size sprawl-like curve in view of the deficiencies in the above-mentioned prior art. The method is based on a sprawl-like curve function and combines parameters α, β and γ to establish a nonlinear relationship between the correlation error and the step-size factor to achieve the purpose of dynamic adjustment of the step-size. By testing the influence of α, β and γ on the algorithm performance, the corresponding optimal parameters are selected.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: a normalized navigation signal adaptive filtering method based on a variable step-size spur-type line, comprising the following steps:

[0006] Step 1: Based on the initial weight vector of the least mean square filter and the mixed signal received by the least mean square filter, the output weight vector of the least mean square filter at the current moment is obtained, and then the initial weight matrix is ​​generated, and the corresponding step size factor is assigned to each weight component;

[0007] The initial weight vector of the least mean square filter is multiplied by the mixed signal received by the least mean square filter to obtain the output weight vector of the least mean square filter at the current moment, and the output weight vector at the current moment is multiplied by the mixed signal received by the least mean square filter at the next moment to obtain the output weight vector at the next moment, thereby generating an initial weight matrix;

[0008] The mixed signal includes a navigation signal received by a minimum mean square filter and an interference signal obtained after channel interference;

[0009] Assume the minimum mean square filter order L, the mixed signal sequence X(n) = [x(n), x(n-1), ···, x(n-L+1)], where x(n) is the mixed signal at time n, X(n) = S(n)+I(n), S(n) is the navigation signal, and I(n) is the interference signal; the weight vector W(n) of the minimum mean square filter at time n = [w(n), w(n-1), ···w(n-L+1)], then the output weight vector at time n after adaptive filtering is

[0010] Based on the existing variable step size least mean square adaptive algorithm, a proportional step size control matrix is ​​used to assign a corresponding step size factor to each weight component of the output real-time weight vector;

[0011] Step 2: Based on the quasi-spike function, the step size factor vector is obtained, and the proportional step size control matrix is ​​updated to obtain the update equation of the proportional step size control matrix, which is used as the new proportional step size control matrix, and the proportional step size control matrix is ​​iteratively updated in each filtering process;

[0012] The quasi-spike function is a function that adjusts the step size factor by combining the quasi-spike function and the autocorrelation estimation of the error;

[0013] The specific method for obtaining the step factor vector based on the quasi-spike function is as follows: the step factor vector is adjusted to an autocorrelation estimated step factor through a curve obtained by taking the inverse of the standard quasi-spike function independent variable, and parameters α, β and γ are introduced to control the direction and change trend of the quasi-spike function to obtain the step factor vector μ(n). The specific formula is:

[0014]

[0015] Among them, α>0 and β>0 are used to coordinately control the value range of the step factor vector μ(n), γ>0 is used to control the direction of the quasi-spike function, e(n) is the error signal at the current moment, e(n-1) is the error signal at the previous moment, e(n)e(n-1) is the autocorrelation estimate of the error signal at the current moment and the error signal at the previous moment, and E() is the expected function;

[0016] The error signal e(n) is the difference between the expected output signal d(n) and the actual output weight vector y(n) after filtering;

[0017] The step size of the autocorrelation estimate e(n)e(n-1) is adjusted in combination with the number of iterations to keep the fluctuation value of the step size factor vector μ(n) within a controllable range. The update equation of the proportional step size control matrix is ​​obtained by updating the proportional step size control matrix. The updated proportional step size control matrix is ​​used as the condition for updating the real-time weight vector at the next moment, and the real-time weight vector is continuously updated during the iterative filtering process. The values ​​of α, β and γ need to be selected by comprehensively considering the convergence speed, steady-state error and steady-state misalignment.

[0018] The specific method for iteratively updating the proportional step control matrix in each filtering process is as follows: the least mean square filter filters the output weight vector at different times once, then the proportional step control matrix is ​​updated once, and the updated proportional step control matrix is ​​used as the condition for updating the real-time weight vector output at the next moment, and the real-time weight vector is continuously updated during the iterative filtering process;

[0019] Step 3: Obtain a weight update function based on the error signal, the proportional step control matrix and the real-time weight vector, and update the real-time weight vector;

[0020] The real-time weight vector is the weight vector used when filtering the mixed signal, and the next moment weight vector is the sum of the current moment weight vector, the current step length, and twice the received mixed signal;

[0021] The update equation of the real-time weight vector is used as the new real-time weight vector of the filter, and the real-time weight vector is iteratively updated in each filtering process;

[0022] The update of the real-time weight vector combines the gradient factor, and the new real-time weight vector is expressed as: Where μ is the step size factor, W(n) is the gradient estimate of i = [e(n), W(n)], is the gradient factor. Combining the above two equations, we get the weight update function W(n+1)=W(n)+2μ(n)e(n)X(n);

[0023] To ensure the convergence of the algorithm, let the maximum eigenvalue of the autocorrelation matrix of the mixed signal X(n) be λ max , then the step factor

[0024] Step 4: Multiply the real-time weight vector with the received mixed signal to achieve front-end filtering;

[0025] The currently received mixed signal is corrected by a new real-time weight vector to obtain a real-time output weight vector, and the value of the real-time output weight vector is close to or equal to the value of the expected output signal of the received mixed signal, thereby realizing front-end filtering of the navigation signal.

[0026] The beneficial effects of adopting the above technical scheme are as follows: a normalized navigation signal adaptive filtering method based on a variable-step-size dustpan-like line proposed in the present invention is based on the dustpan-like line deformation function, introduces a step-size adjustment parameter, and combines the autocorrelation estimation of the error to realize the dynamic adjustment of the step-size factor; the optimal step-size adjustment parameter is selected through simulation analysis, the contradiction between the convergence speed, steady-state error and algorithm tracking ability is balanced, and a relatively excellent performance is achieved in terms of steady-state offset and anti-noise performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A flow chart of a method for adaptive filtering of normalized navigation signals based on variable step-size spur-type lines provided by an embodiment of the present invention;

[0028] Figure 2 Principle diagram of the minimum mean square filter provided by an embodiment of the present invention;

[0029] Figure 3 A comparison diagram of MSE learning curves of different algorithms in a time-invariant system provided by an embodiment of the present invention;

[0030] Figure 4 A comparison diagram of MSE learning curves of different algorithms in a time-varying system provided by an embodiment of the present invention;

[0031] Figure 5 The signal time domain comparison waveform diagram under 1000 interference noise points provided by the embodiment of the present invention, where (a) is the Beidou signal waveform SigSig BD (n); (b) is the Beidou expected signal waveform d(n); (c) is the environmental noise waveform I(n); (d) is the filtered output waveform y(n);

[0032] Figure 6 A time domain comparison waveform diagram of a signal under 200-point interference noise provided by an embodiment of the present invention;

[0033] Figure 7 A standard dustpan-like line function adjustment process curve diagram provided by an embodiment of the present invention;

[0034] Figure 8 The adjustment curve diagram of μ(n) and e(n) provided in this embodiment, wherein (a) and (b) are respectively α>0 and β>0 for collaboratively controlling the value range of μ(n); (c) is γ>0 for controlling the shape of the function;

[0035] Fig. 9The algorithm convergence speed diagram when α is different provided by the embodiment of the present invention;

[0036] Fig.10 The algorithm convergence speed diagram when β is different provided by the embodiment of the present invention;

[0037] Fig.11 The algorithm convergence speed diagram when γ is different provided by the embodiment of the present invention;

[0038] Fig.12 A comparison chart of the noise resistance capabilities of different algorithms provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0040] In this embodiment, the normalized navigation signal adaptive filtering method based on the variable step-size spur line is as follows: Figure 1 As shown, the following steps are included:

[0041] Step 1: Based on the initial weight vector of the least mean square filter and the mixed signal received by the least mean square filter, the output weight vector of the least mean square filter at the current moment is obtained, and then the initial weight matrix is ​​generated, and the corresponding step size factor is assigned to each weight component;

[0042] The initial weight vector of the least mean square filter is multiplied by the mixed signal received by the least mean square filter to obtain the output weight vector of the least mean square filter at the current moment, and the output weight vector at the current moment is multiplied by the mixed signal received by the least mean square filter at the next moment to obtain the output weight vector at the next moment, thereby generating an initial weight matrix;

[0043] The mixed signal includes a navigation signal received by a minimum mean square filter and an interference signal obtained after channel interference;

[0044] Set the minimum mean square filter order L, the mixed signal sequence X(n) = [x(n), x(n-1), ···, x(n-L+1)], where x(n) is the mixed signal at time n, X(n) = S(n)+I(n), S(n) is the navigation signal, and I(n) is the interference signal; the weight vector W(n) of the minimum mean square adaptive filter at time n = [w(n), w(n-1), ···w(n-L+1)], then the output weight vector at time n after adaptive filtering is

[0045] In this embodiment, the received mixed signal is input into the minimum mean square filter. In the process of receiving the mixed signal, common suppression interference and deceptive interference are added as interference items. The initial weight vector is multiplied by the mixed signal to obtain the output weight vector of the minimum mean square filter at the current moment. The output weight vector at the current moment is multiplied by the mixed signal received by the minimum mean square filter at the next moment to obtain the weight vector at the next moment. And so on, an initial weight matrix is ​​generated.

[0046] In this embodiment, in order to verify the influence of the algorithm on the convergence speed, steady-state error and tracking performance, the following simulation environments and conditions are selected in the time-varying system and the time-invariant system respectively: Figure 2 The minimum mean square filter order shown is 2, the sampling rate is 8KHz, and the minimum mean square filter initial weight vector is set to W = [0.8, 0.5] Τ ; The navigation signal in the mixed signal received by the minimum mean square filter is the B1I signal, and the interference signal after channel interference is a Gaussian white noise with a mean of 0 and a variance of 0.001, which can be selected according to the actual situation; the sampled mixed signal is input into the adaptive filter and multiplied with the initial weight vector as the output weight vector at the current moment;

[0047] In this embodiment, the mixed signal X(n) is the sum of the standard Gaussian white noise that obeys the N(0, 1) distribution and the environmental interference noise that obeys the N(0, 0.001) distribution. The two are unrelated vectors. The total number of iterations is 1000, and the number of simulations for each curve is 200. In the time-varying system, the adaptive filter weights suddenly change to W = [0.4, 0.2] when the number of iterations is 500. T , thus obtaining the comparison chart of MSE learning curves under different dynamic systems;

[0048] In this embodiment, the MSE learning curve comparison diagram of different algorithms under the time-invariant system is as follows: Figure 3 As shown, it can be seen that after the system has been iterated for many times, the MSE steady value of the I-Sigmoid algorithm is about 0.15, and the MSE steady values ​​of other algorithms are basically the same as the algorithm in this paper, which is about 0.026; from the perspective of initial convergence speed, the method of the present invention tends to a stable state when the number of iterations is about 40, and the number of iterations for K-Versoria, I-Sigmoid, SVS, IVIS and M-arctan to reach a stable state are 50, 240, 300, 100 and 75 respectively. It can be seen that the method can further improve the convergence speed under the condition of lower steady-state error;

[0049] Figure 4This is a comparison diagram of the MSE learning curves of the time-varying system. It can be seen that after the system iterates 500 times and the time-varying occurs, the steady-state error is the largest and the tracking ability is the worst. The steady-state error of the method of the present invention is the lowest and the tracking ability is the best.

[0050] In this embodiment, in order to further evaluate the anti-noise ability of the algorithm, the received sample signal is Sig BD (n) = AC (n) D (n) cos (2πf1n + φ), where Sig BD (n) is the Beidou B1I signal, A is the amplitude factor; C(n) is the signal pseudo code; D(n) is the data code used for phase modulation; f1 is the carrier frequency used to modulate the signal to a high frequency; is the initial carrier phase; the first 500 points of the interference noise I(n) are band-limited white noise with an amplitude of 1, and the last 500 points are band-limited white noise with an amplitude of 0.5, and anti-noise processing is performed on them. The experimental results are as follows Figure 5 As shown;

[0051] Let the mixed signal x(n) be the sum of the Beidou B1I signal and the interference noise of which the first 100 points are band-limited white noise with an amplitude of 1 and the last 100 points are band-limited white noise I(n) with an amplitude of 0.5. After anti-noise processing, the experimental results are as follows: Figure 6 shown; observed Figure 5 , and compare the signal x(n), the filtering result y and the expected signal d. It is found that the method of the present invention has obvious anti-noise ability when the transmitted signal is Beidou B1I. Further, according to Figure 6 , it can be clearly seen that as the noise amplitude decreases, the filtering residual value becomes smaller, that is, the anti-noise ability is better;

[0052] The adaptive algorithm based on the existing variable step size least mean square adopts a proportional step size control matrix to allocate a corresponding step size factor to each weight component of the output real-time weight vector; however, there is still a problem that too large a proportional step factor is allocated to a larger weight component, and too small a proportional step factor is allocated to a smaller weight component, resulting in unsatisfactory overall convergence speed and convergence accuracy of the adaptive filtering algorithm;

[0053] Step 2: Based on the quasi-spike function, the step size factor vector is obtained, and the proportional step size control matrix is ​​updated to obtain the update equation of the proportional step size control matrix, which is used as the new proportional step size control matrix, and the proportional step size control matrix is ​​iteratively updated in each filtering process;

[0054] The quasi-spike function is a function that adjusts the step size factor by combining the quasi-spike function and the autocorrelation estimation of the error;

[0055] The specific method for obtaining the step factor vector based on the quasi-spike function is as follows: the step factor vector is adjusted to an autocorrelation estimated step factor through a curve obtained by taking the inverse of the standard quasi-spike function independent variable, and parameters α, β and γ are introduced to control the direction and change trend of the quasi-spike function to obtain the step factor vector μ(n). The specific formula is:

[0056]

[0057] Among them, α>0 and β>0 are used to coordinately control the value range of the step factor vector μ(n), γ>0 is used to control the direction of the quasi-spike function, e(n) is the error signal at the current moment, e(n-1) is the error signal at the previous moment, e(n)e(n-1) is the autocorrelation estimate of the error signal at the current moment and the error signal at the previous moment, and E() is the expected function;

[0058] The error signal e(n) is the difference between the expected output signal d(n) and the actual output weight vector y(n) after filtering;

[0059] The step size of the autocorrelation estimate e(n)e(n-1) is adjusted in combination with the number of iterations, so that the fluctuation value of the step size factor vector μ(n) is maintained within a controllable range. The update equation of the proportional step size control matrix is ​​obtained by updating the proportional step size control matrix. The updated proportional step size control matrix is ​​used as the condition for updating the real-time weight vector at the next moment, and the real-time weight vector is continuously updated during the iterative filtering process.

[0060] The adjustment process curve of the standard quasi-spike function in this embodiment is as follows: Figure 7 As shown, curve 1 is a standard quasi-spike function, and the function expression is: Draw a tangent circle with a radius of 1 / 2 on curve 1 and name it curve 2. Its function expression is: Let the interval of the independent variable x be 0.1, draw the standard quasi-spike function, and name the curve after taking the inverse of the independent variable as curve 3. The function curve after adjusting to the autocorrelation estimation step factor is named curve 4. The function expression of curve 4 is: like Figure 7 As shown, curve 4 meets the dynamic adjustment requirements of the step factor; the parameters α, β and γ are introduced to control the direction and change trend of the function, and the step factor vector is obtained. Among them, α, β and γ are all greater than 0, the value range of μ(n) is jointly regulated by parameters α and β, and the shape of μ(n) is regulated by γ;

[0061] Based on the above analysis, in order to obtain a better denoising effect, it is necessary to analyze the α, β and γ parameters in the step function. Since different parameter values ​​have different effects on the function convergence speed, steady-state error and steady-state misalignment, α>0 and β>0 are used to coordinately control the value range of μ(n), and γ>0 is used to control the shape of the function. Under the conditions of β=0.1 and γ=0.1, with parameter α as the independent variable, the relationship curve between μ(n) and e(n) is as follows: Figure 8 (a), where the values ​​of α are 0.3, 0.5, 1 and 2 respectively; Figure 8 (a) It can be seen that α has a great influence on the value of μ(n). When e(n) is the same, the larger the value of α, the faster the curve converges in the initial stage, resulting in a larger mutation value of the step size factor, which affects the steady-state performance of the system. Therefore, the value of α cannot be too large; the trend of the steady-state offset is the same as the trend of the steady-state step size, so the smaller the value of the parameter α, the lower the steady-state offset; however, when the value of the α parameter is less than a certain threshold, it will lead to a sudden drop in the convergence speed, and the reduction of the step size span will also increase the steady-state error and steady-state offset at the same time;

[0062] Under the conditions of α=1,γ=0.1, taking parameter β as the independent variable, the relationship curve between μ(n) and e(n) and the algorithm convergence speed curve are as follows: Figure 8 (b), where the values ​​of β are 0.01, 0.05, 0.1 and 0.2 respectively; Figure 8 (b) It can be seen that β has the same changing trend as α, so the value of β cannot be too large. However, when the value of β is less than a certain threshold, the convergence speed will drop sharply. The reduction of step span will also increase the steady-state error and steady-state misalignment.

[0063] Under the conditions of α=1,β=0.1, taking parameter γ as the independent variable, the relationship curve between μ(n) and e(n) is as follows: Figure 8 (c), where the values ​​of γ are 0.05, 0.1, 0.2 and 0.4 respectively; Figure 8 (c) It can be seen that γ has a great influence on the function shape of μ(n). When e(n) is the same, the smaller the value of γ, the greater the slope of the tangent line of the curve, that is, the faster the convergence speed. When e(n) is close to zero, the step increment is relatively small; however, too small γ leads to a large mutation value of the step factor, which affects the steady-state performance of the system. Therefore, the value of γ cannot be too large. However, as γ increases, the steady-state misalignment decreases; however, if γ is too large, the convergence speed will be significantly reduced, the step span will be small, and the steady-state error and steady-state misalignment will increase.

[0064] In this embodiment, the convergence speed curves of different algorithms are as follows: Figure 9-11 as shown; Fig. 9As shown in FIG. 1 , under the conditions of β=0.1 and γ=0.1, with parameter α as the independent variable, as α increases, the convergence speed is faster when the MSE value is the same. However, when α is 1 and 2, the convergence speed is basically the same. Therefore, in this embodiment, α=1 is taken; Fig.10 As shown in FIG. 1 , under the conditions of α=1 and γ=0.1, with parameter β as the independent variable, as β increases, the convergence speed is faster when the MSE value is the same. However, when β is 0.1 and 0.2, the convergence speed is basically the same. Therefore, in this embodiment, β=0.1 is taken; Fig.11 As shown, under the conditions of α=1, β=0.1, with parameter γ as the independent variable, as γ decreases, the convergence speed is faster under the same MSE value. However, when γ is 0.1 and 0.05, the convergence speed is basically the same. Therefore, in this embodiment, γ=0.1;

[0065] Verification is used to select the optimal index parameters. When the error is the same, the larger the values ​​of α and β, the faster the curve 4 converges in the initial stage, resulting in a larger mutation value of the step factor vector, which affects the steady-state performance of the system. Therefore, the values ​​of α and β cannot be too large; since the trend of the steady-state offset is the same as the trend of the steady-state step, the smaller the values ​​of the parameters α and β, the lower the steady-state offset. However, when the values ​​of the α and β parameters are less than a certain threshold, the convergence speed will drop sharply, and the reduction of the step factor vector span will also increase the steady-state error and steady-state offset at the same time; as α and As β increases, the convergence speed is faster and gradually tends to be stable when the mean square error value is the same; when the error is the same, as γ decreases, the greater the slope of the tangent of curve 4, that is, the faster the convergence speed, when the error is close to zero, the increment of the step factor vector is relatively small, and the convergence speed is faster when the mean square error value is the same; however, too small γ leads to a large mutation value of the step factor vector, affecting the steady-state performance of the system, so the value of γ cannot be too large; therefore, it is necessary to comprehensively consider the convergence speed, steady-state error and steady-state misalignment to select the values ​​of α, β and γ;

[0066] In this embodiment, under the prerequisite of algorithm convergence, the smaller the MSE value, the better the algorithm's anti-noise performance. To verify the anti-noise ability of the algorithm in this paper, based on the original simulation conditions, background noises with signal-to-noise ratios (SNR) of 5dB and 15dB were added to the received signal, and the comparison of the MSE mean after iteration was used as the basis for anti-noise evaluation. Fig.12 As shown;

[0067] Depend on Fig.12It can be seen that as the signal-to-noise ratio increases, the MSE mean decreases, and the noise resistance of each algorithm is relatively improved, which is in line with communication theory; the I-Sigmoid algorithm has a high MSE mean due to its slow convergence speed, which makes the algorithm's noise resistance performance poor. Since the received signal X(n) and the environmental interference noise signal I(n) in the algorithm are unrelated, the MSE mean of the algorithm is the smallest under the conditions of SNR=5 and SNR=15. The simulation results show that the algorithm has a strong noise resistance ability;

[0068] The specific method for iteratively updating the proportional step control matrix in each filtering process is as follows: the least mean square filter filters the output weight vector at different times once, then the proportional step control matrix is ​​updated once, and the updated proportional step control matrix is ​​used as the condition for updating the real-time weight vector output at the next moment, and the real-time weight vector is continuously updated during the iterative filtering process;

[0069] Step 3: Obtain a weight update function based on the error signal, the proportional step control matrix and the real-time weight vector, and update the real-time weight vector;

[0070] The real-time weight vector is the weight vector used when filtering the mixed signal, and the next moment weight vector is the sum of the current moment weight vector, the current step length, and twice the received mixed signal;

[0071] The update equation of the real-time weight vector is used as the new real-time weight vector of the filter, and the real-time weight vector is iteratively updated in each filtering process;

[0072] The update of the real-time weight vector combines the gradient factor, and the new real-time weight vector is expressed as: Where μ is the step size factor, W(n) is the gradient estimate of i = [e(n), W(n)], is the gradient factor. Combining the above two equations, we get the weight update function W(n+1)=W(n)+2μ(n)e(n)X(n);

[0073] To ensure the convergence of the algorithm, let the maximum eigenvalue of the autocorrelation matrix of the mixed signal X(n) be λ max , then the step factor

[0074] Step 4: Multiply the real-time weight vector with the received mixed signal to achieve front-end filtering;

[0075] The currently received mixed signal is corrected by a new real-time weight vector to obtain a real-time output weight vector, and the value of the real-time output weight vector is close to or equal to the value of the expected output signal of the received mixed signal, thereby realizing the front-end filtering of the navigation signal and improving the convergence speed and accuracy of the adaptive filtering algorithm;

[0076] In order to evaluate the performance of the algorithm in this paper, this embodiment uses MATLAB tool simulation. First, it compares the convergence speed, steady-state error and tracking ability in the dynamic system with the variable step-size algorithm. Then, the anti-noise ability of the algorithm in this paper and the variable step-size algorithm under different noise backgrounds is compared, and the time domain signal recovery in the anti-noise process is simulated and verified. Finally, the Beidou B1I signal is used as the received sample signal to evaluate the anti-noise ability of the algorithm in the satellite navigation positioning process. Table 2 shows the variable step-size algorithms and their corresponding parameter values;

[0077] Table 2 Function expressions and corresponding values ​​of different variable step size algorithms

[0078]

[0079] The method of the present invention analyzes the existing step-size adjustment algorithms of different ideas and proposes a variable step-size LMS adaptive filtering algorithm based on the sieve function; the idea of ​​the algorithm is to deform the traditional sieve, introduce the step-size adjustment parameter and combine the autocorrelation estimation of the error to realize the dynamic adjustment of the step-size factor, so as to ensure that a low steady-state error can be quickly achieved in the early stage of convergence. The optimal step-size adjustment parameter is selected through simulation analysis. The simulation results show that the algorithm in this paper can effectively improve the convergence speed of the algorithm under dynamic systems, has strong tracking ability, low steady-state error, and has excellent performance in terms of steady-state misalignment and anti-noise performance. Furthermore, compared with the existing technology, the algorithm in this paper can converge quickly and fluctuate slightly at a low steady-state error, and has better anti-noise performance. It also has obvious anti-noise ability when the Beidou B1I signal is the receiving signal.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A normalized navigation signal adaptive filtering method based on variable step-size spur-type line, characterized in that: The following steps are involved: Step 1: Based on the initial weight vector of the least mean square filter and the mixed signal received by the least mean square filter, the output weight vector of the least mean square filter at the current moment is obtained, and then the initial weight matrix is ​​generated, and the corresponding step size factor is assigned to each weight component; Step 2: Based on the quasi-spike function, the step size factor vector is obtained, and the proportional step size control matrix is ​​updated to obtain the update equation of the proportional step size control matrix, which is used as the new proportional step size control matrix, and the proportional step size control matrix is ​​iteratively updated in each filtering process; The quasi-spike function is a function that adjusts the step size factor by combining the quasi-spike function and the autocorrelation estimation of the error; Step 3: Obtain a weight update function based on the error signal, the proportional step control matrix and the real-time weight vector, and update the real-time weight vector; Step 4: Multiply the real-time weight vector with the received mixed signal to achieve front-end filtering; The currently received mixed signal is corrected by a new real-time weight vector to obtain a real-time output weight vector, and the value of the real-time output weight vector is close to or equal to the value of the expected output signal of the received mixed signal, thereby realizing front-end filtering of the navigation signal.

2. The method for adaptive filtering of normalized navigation signals based on variable step-size quasi-tangent line according to claim 1, characterized in that: The specific method of step 1 is: The initial weight vector of the least mean square filter is multiplied by the mixed signal received by the least mean square filter to obtain the output weight vector of the least mean square filter at the current moment, and the output weight vector at the current moment is multiplied by the mixed signal received by the least mean square filter at the next moment to obtain the output weight vector at the next moment, thereby generating an initial weight matrix; The adaptive algorithm based on the existing variable step-size least mean square adopts a proportional step-size control matrix to allocate a corresponding step-size factor to each weight component of the output real-time weight vector.

3. The method for adaptive filtering of normalized navigation signals based on variable step-size quasi-tangent line according to claim 2 is characterized in that: The mixed signal includes the navigation signal received by the minimum mean square filter and the interference signal obtained after channel interference; the minimum mean square filter order L is set, the mixed signal sequence X(n) = [x(n), x(n-1), ···, x(n-L+1)], wherein x(n) is the mixed signal at time n, X(n) = S(n)+I(n), S(n) is the navigation signal, and I(n) is the interference signal; the weight vector W(n) of the minimum mean square filter at time n = [w(n), w(n-1), ···w(n-L+1)], then there is an output weight vector at time n after adaptive filtering 4. The method for adaptive filtering of normalized navigation signals based on variable step-size quasi-tangent line according to claim 1, characterized in that: The specific method for obtaining the step size factor vector based on the quasi-spike function is: The step factor vector is adjusted to the autocorrelation estimation step factor through the curve of the reciprocal of the standard quasi-spike function independent variable, and the parameters α, β and γ are introduced to control the direction and change trend of the quasi-spike function to obtain the step factor vector μ(n). The specific formula is: Among them, α>0 and β>0 are used to coordinately control the value range of the step factor vector μ(n), γ>0 is used to control the direction of the quasi-spike function, e(n) is the error signal at the current moment, e(n-1) is the error signal at the previous moment, e(n)e(n-1) is the autocorrelation estimate of the error signal at the current moment and the error signal at the previous moment, and E() is the expected function.

5. The method for adaptive filtering of normalized navigation signals based on variable step-size quasi-tangent line according to claim 4 is characterized in that: The specific method of step 2 is: The step size of the autocorrelation estimate e(n)e(n-1) is adjusted in combination with the number of iterations to keep the fluctuation value of the step size factor vector μ(n) within a controllable range. The update equation of the proportional step size control matrix is ​​obtained by updating the proportional step size control matrix. The updated proportional step size control matrix is ​​used as the condition for updating the real-time weight vector at the next moment, and the real-time weight vector is continuously updated during the iterative filtering process. The values ​​of α, β and γ need to be selected by comprehensively considering the convergence speed, steady-state error and steady-state misalignment. The specific method for iteratively updating the proportional step control matrix in each filtering process is as follows: the least mean square filter filters the output weight vector at different times once, then the proportional step control matrix is ​​updated once, and the updated proportional step control matrix is ​​used as the condition for updating the real-time weight vector output at the next moment, and the real-time weight vector is continuously updated during the iterative filtering process.

6. The method for adaptive filtering of normalized navigation signals based on variable step-size quasi-tangent line according to claim 5, characterized in that: The error signal e(n) is the difference between the expected output signal d(n) and the actual output weight vector y(n) after filtering.

7. The method for adaptive filtering of normalized navigation signals based on variable step-size quasi-curve lines according to claim 1, characterized in that: The real-time weight vector is a weight vector used when filtering the mixed signal, and the next moment weight vector is the sum of the current moment weight vector, the current step length, and twice the received mixed signal.

8. The method for adaptive filtering of normalized navigation signals based on variable step-size quasi-tangent line according to claim 7, characterized in that: In step 3, the update equation of the real-time weight vector is used as the new real-time weight vector of the filter, and the real-time weight vector is iteratively updated in each filtering process; The update of the real-time weight vector combines the gradient factor, and the new real-time weight vector is expressed as: Where μ is the step size factor, W(n) is the gradient estimate of i = [e(n), W(n)], is the gradient factor. Combining the above two equations, we get the weight update function W(n+1)=W(n)+2μ(n)e(n)X(n); To ensure the convergence of the algorithm, let the maximum eigenvalue of the autocorrelation matrix of the mixed signal X(n) be λ max , then the step factor

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