CN114465630B - WF-NF filtering algorithm and device for eLORAN signal in-band interference - Google Patents
WF-NF filtering algorithm and device for eLORAN signal in-band interference Download PDFInfo
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Abstract
The invention provides a WF-NF filtering algorithm aiming at eLORAN signal in-band interference, which inputs an expected signal and generates a reference signal; initializing variables such as phase weight vector, frequency difference weight coefficient, frequency difference weight function, phase learning step length, frequency difference learning step length, reference signal time number, frequency difference function time number and the like; calculating and outputting a difference signal, a phase gradient term and a frequency difference gradient term, and then updating a phase weight coefficient and a frequency difference weight coefficient; calculating the average value of a plurality of continuous points at intervals of a certain sampling interval, and judging the difference value of the two continuous average values according to a set convergence threshold value; updating the filtering cycle times, the reference signal time number and the frequency difference function time number, and entering the next iterative learning process; if the updated filtering sampling points enter the signal section, the learning step length is reduced, otherwise, the original learning step length is recovered. The invention solves the problem caused by interference detection deviation, avoids signal distortion and improves the convergence speed of the frequency difference weight coefficient.
Description
Technical Field
The invention belongs to the technical field of communication, and relates to a filtering algorithm of a long wave signal WF-NF (Weight Function Notch Filter), in particular to a filtering method based on frequency difference, amplitude tracking and reconstruction technology of in-band point frequency interference.
Background
In view of the vulnerability of GNSS, a new eLORAN system is being developed in multiple countries in recent years, and is intended to be an important backup of the GNSS satellite-based system. The implementation of eLORAN system positioning, navigation, time service (PNT) functions can be affected by various interferences, including point frequency interference, sky wave interference, cross interference, various noises, and the like. Where the mid-frequency continuous wave interference is also known as narrowband interference, it can seriously affect the phase tracking accuracy of the received signal.
Considering the characteristics of continuous wave interference, the most fundamental solution is fitting and cancellation. The most common means in each field is NF (Notch Filter). In the past, the principle research on NF wave traps in the anti-narrow-band interference of the Rowland system is also carried out, but the defect that signals are easy to distort can occur when the power of a plurality of interference signals is slightly strong; in addition, interference detection errors are unavoidable, and the same assumption as the detection frequency point also seriously affects the practicability of the NF algorithm in the eLORAN system.
The above problems can be summarized in the following two points:
(1) eLORAN signal distortion caused by weight coefficient learning;
(2) The weight coefficient caused by the detection frequency difference cannot be converged, namely the notch fails.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a WF-NF filtering algorithm aiming at eLORAN signal in-band interference, which is upgraded, firstly, signal distortion is overcome by a variable step design aiming at the characteristics of eLORAN signals, secondly, a frequency difference weight function is increased according to theoretical deduction, the influence of frequency difference on notch is fundamentally solved, and convergence speed is improved by a self-adaptive adjustment design.
The technical scheme adopted for solving the technical problems is as follows: a WF-NF filtering algorithm for eLORAN signal in-band interference, comprising the steps of:
Step1, inputting a desired signal And generates a reference signal/>, according to the interference detection frequency of the front-end flow；
Step 2, initializing phase weight vectorFrequency difference weight coefficient/>Frequency difference weight function/>Reference signal time number/>Sum frequency difference function time number/>Wherein/>，/>，/>，/>，，/>，/>The update amount of the time parameter is/>，/>For the receiver sampling rate, ω 1 is a first dimension parameter in the phase weight vector W, ω 2 is a second dimension parameter in the phase weight vector W;
Step 3, calculating an error signal Wherein/>N is the number of filter cycles,/>，/>Reference signal/>To detect frequency/>, based on interferenceThe generated sine and cosine signals, namely/>, are，/>First signal parameter of reference signal x,/>A second signal parameter being a reference signal x;
Step 4, calculating a phase gradient term Sum frequency difference gradient term/>；
Step 5, updating the phase weight vectorSum frequency difference weight coefficient/>，/>，Wherein/>、/>Respectively setting a phase and a frequency difference learning step length;
Step 6, starting to calculate continuously at regular sampling intervals Mean value of points,/>For the difference value of two continuous average values, q is judged according to a set convergence threshold K, and/>Performing secondary adjustment;
wherein old and new respectively represent before and after adjustment;
step 7, updating the value of n to n+1 and t 0 to T v updates to/>Returning to the step 3 to enter the next iterative learning process; if/>After updating, the corresponding filtering sampling points enter the signal section, and the learning step length/>, is adjusted，If/>And after updating, entering a non-signal section, and recovering the original learning step length.
When there are multiple interferences, 2k paths of reference signals are generated according to the number k of the interferences and the frequency thereof, and thenAnd/>Corresponding modification is to diagonal block matrix, each block is/>Is a matrix of the (c) in the matrix,
，/>。
The phase learning step length of the step 5Frequency offset learning step size/>。
And 1e-4 is taken as K.
The sampling intervalFor 10000 sampling points,/>Taking 500-1000.
The signal section is the length extension of eLORAN main station pulse group, and the length ensures that the ground wave signal front edge is contained.
The beneficial effects of the invention are as follows:
Firstly, the invention deduces a WF-NF Notch algorithm aiming at the frequency difference problem based on the Notch Filter theory, thereby fundamentally solving the problem caused by interference detection deviation; secondly, the invention designs a variable step length mode of the signal section and the non-signal section aiming at the processing mode of eLORAN pulse group signal characteristics, thereby avoiding the signal distortion problem caused by the error learning of the useful signals in the signal section by the learning factors and providing a guarantee for the application of the invention; finally, a self-adaptive convergence value adjusting mode is designed, so that the convergence speed of the frequency difference weight coefficient is greatly improved, and finally successful notch of a plurality of interferences is realized.
The prior eLORAN systems have few in-band interference related researches, and the prior interference removing mode using the NF filter has fatal defects and cannot be well applied to the signal processing flow of a receiver. The method is used for processing the signal distortion problem of the signal section of the GRI pulse group and solving the problem of deviation between the interference frequency and the detection frequency. If the first problem is not considered, the filtering weight coefficient can remove the interference with frequency difference to a certain extent under a pseudo convergence state, but the distortion of the signal is caused, and the filtering weight coefficient can have a certain effect under the condition of low interference power, so that the second problem does not need to pay special attention. Aiming at the two core problems, the invention performs strict mathematical deduction from the theoretical essence and provides a complete notch scheme, so that the problem of multiple point frequency interference in the signal bandwidth is solved.
A large number of experiments prove that the WF-NF notch algorithm provided by the invention can simultaneously fit and remove a plurality of in-band point frequency interferences under a noise environment, does not influence signal characteristics, has extremely high practical value in the design of eLORAN receivers, provides reliable guarantee for each subsequent signal processing flow, and also can provide theoretical reference for the design of other related filters.
Drawings
FIG. 1 is an overall block diagram of an algorithm of the present invention;
FIG. 2 is a graph of the notch effect of a multi-interference lower WF-NF trap, wherein (a) the notch effect of WF-NF and (b) the notch effect details are compared;
FIG. 3 is a graph of a plurality of interference down-frequency difference weight learning coefficients;
FIG. 4 is a graph of the frequency offset tracking effect of a multi-interference plus noise environment WF-NF trap, wherein (a) the notch effect of the noise environment WF-NF, (b) the frequency offset weight coefficient learning curve;
fig. 5 is a graph of the frequency difference weight learning number in a 6 interference +10dB white noise environment.
Detailed Description
The invention will be further illustrated with reference to the following figures and examples, which include but are not limited to the following examples.
The invention is a popularization of an LMS self-adaptive filter, and realizes weight adjustment based on a random gradient descent algorithm, so that the error is reduced as much as possible. The basic steps include filtering, error calculation, gradient calculation, weight coefficient updating, etc., which will be deduced and explained in detail below.
Take 1 interference as an example, whereinIs interference frequency point,/>Is the interference phase, B is the interference amplitude,/>For interference detection frequency,/>For the frequency difference,/>Is the sampling rate.
Step1, inputting a desired signalAnd according to/>A reference signal is generated.
Wherein,For input signal,/>To detect frequency/>, based on interferenceAnd the generated sine and cosine signals.
Step 2, initializing phase weight vectorFrequency difference weight coefficient/>Frequency difference weight function/>Phase learning step size/>Frequency offset learning step size/>Reference signal time number/>Frequency difference function time number/>Isovaries.
Wherein the method comprises the steps of=0，/>=0, Update amount is/>；/>；/>；/>；/>Initialized to 1/2≡14,/>Initialized to 1/2^5.
Step 3, calculating，/>Calculating and outputting an error signal/> according to the formulas (1) and (2)。
(1)
(2)
With respect to: The interference signal can be written as
If the filtering converges, it can be seen that there is、/>And/>Three time-invariant parameters, so the trap can be designed and two sets of weight parameters (phase weight vector/>Frequency difference weight coefficient/>) To approximate the above three parameters and to obtain/>, according to the form of the above formula。
Step 4, calculating a phase gradient term according to the formulas (3) and (4)Sum frequency difference gradient term/>。
(3)
(4)
In the method, in the process of the invention,，/>For the matrix generated by the reference signal, respectively adapted to the phase gradient and the frequency difference gradient,/>Is a phase weight vector,/>Is a frequency difference weight vector,/>Is a frequency difference weight function vector; /(I)The time number of the frequency difference function is optimized in the follow-up derivation; /(I)、/>Respectively a phase gradient and a frequency difference gradient; /(I)、For/>, by reference signalThe generated matrix is respectively applicable to the phase gradient and the frequency difference gradient; in addition, in the formula (4), a product/>, should be obtained after differentiationIs a phase parameter, has periodic property and is less than a fixed value/>Therefore, the method is not written in the formula and can be embodied in the setting of the subsequent learning step length.
Step 5, updating the phase weight vector according to the formulas (5) and (6)Sum frequency difference weight coefficient/>；
(5)
(6)
In the method, in the process of the invention,、/>The learning steps are respectively the phase and the frequency difference.
The learning step size is typically an empirical value in the adaptive filter, and the two learning parameters are selected differently because they are related to the amplitude and the frequency difference, respectively. Recommending initial according to the signal amplitude 1 set by simulationThe method can be adjusted according to the quantization proportion of hardware in practical application; according to the measurement frequency difference magnitude which is not more than 2e2Hz, the initial/> isrecommended(Example test 400Hz, multiple disturbances are effective).
Step 6, according to the convergence threshold value K pairAnd (3) judging, carrying out secondary adjustment in the modes of formulas (7) - (9) according to requirements, counting +1, and judging whether the signal section exists or not to adjust the learning step length.
(7)
(8)
(9)
Wherein at regular intervalsCalculation/>Mean value of individual points,/>Is the deviation of two consecutive means. /(I)To pair(s)Is used for adjusting the adjustment amount of the (a). /(I)To be according to the before adjustment/>Phase/>Updating the obtained time parameter.
The convergence of the frequency difference weight coefficient is the key of the convergence speed of the whole wave trap, the convergence curve is similar to a log function curve, the earlier stage is faster, and the two gradient terms are smaller and smaller at the tail part due to smaller error, so that the convergence speed is extremely slow. Even a frequency difference of 1Hz will cause a small filtering error. Therefore, the invention designs a method for accelerating convergence by utilizing the curve characteristics, shortens the convergence time while not changing the convergence stability of the original convergence curve, and adds protective measures to limit the upper limit of the modification quantity.
Wherein, correspondingly adjustThe step (2) is important that the deviation is adjusted only without the processing shown in the formula (9), and corresponds to the weight function/>Phase jump occurs, and gradient, error, etc. are changed, so/>Re-convergence is performed according to the new intermediate quantity and the error value, and the trend of the original convergence curve is not changed; and pair/>The adjustment of (a) is intended to not change/>I.e. without changing any other intermediate variables and the steady trend of the output and convergence, but simply by forcibly pumping the convergence curve out of the middle part.
For N, M, considering factors such as GRI size and cross interference, and according to the design of the novel eLORAN receiver 2MHz sampling rate, it is recommended that N is not more than 10000 points, and M is not more than 1000 points.
Regarding the threshold K, considering fluctuation caused by factors such as noise and the like and experimental results, the recommended value is not too small so as not to influence the convergence of the tail, and the recommended value is not less than 1e-4Hz.
In the step 7 of the method, the step of,，/>，/>Then, the next iterative learning process is entered from step 3.
If n is updated and enters the signal section, the step-variable processing is carried out, and selection is carried out，/>22000 Points (slightly more than 10 ms) in length, and if n is updated and enters a non-signal segment, restoring the original learning step size.
The signal section is the length extension of eLORAN main station pulse groups (10 ms), 22000 points (11 ms) can be taken, so that the front edge of the ground wave signal is ensured to be contained, and filtering distortion caused by false capturing of the ground wave is prevented. If gri=60000 us, the non-signal segment is 50ms long.
In this example, 2 cases were taken as examples to respectively prove the correctness and practicality of the method. The design conditions are as follows:
the number of the interference is 6, =(97/106/93/112.3/87.2/102.5)KHz，B=（0.5/0.42/1.1/0.73/0.57/1.35），/>=(97.1/105.95/92.808/112.7/87.232/102.435)KHz，φ=（-100/50/192/-400/-32/ 65）Hz，/>Randomly generated, and has no noise. 6 interference,/>=(97/106/93/112.3/87.2/102.5)KHz，B=（0.5/0.42/1.1/0.73/0.57/1.35），/>=(97.1/105.95/92.808/112.7/87.232/102.435)KHz，φ=（-100/50/192/-400/-32/ 65）Hz，/>Randomly generating 10dB white noise. According to the above settings, the specific flow and result of the algorithm are as follows:
1) Results under condition a:
According to NF principle, output signal Error Signal/>, as a fitted interference SignalThen it is a notched signal. Fig. 2 shows the powerful notch capability of WF-NF in multi-interference situations, where the SIR = -20dB (simulation verification can be much smaller than-20 dB), a stable signal can be output substantially at the 3 rd GRI (120 ms), and the error signal also substantially coincides with the standard signal. The frequency difference weight coefficient in fig. 3 reaches a convergence state quickly.
TABLE 1 noise free Environment 6 interference and WF-NF filter statistics
As can be seen from the data statistics in Table 1, the frequency difference errors are all controlled to be 1e-5 orders of magnitude under the noiseless condition, even the frequency difference is still converged at 400 Hz, and the amplitude error is smaller than 1e-8. According to the adaptive filtering principle, the tracking accuracy of the two weight parameters can reach a higher level after a longer time. The above performance indicators also demonstrate the theoretical correctness and universality of WF-NF.
2) Results under condition b:
As can be seen from fig. 4 (a), in the presence of noise, the trap can still output the normal eLORAN signal, and although there is still an unconverged state at the 3 rd GRI (near 120 ms), the convergence speed is only slightly affected by noise; fig. 4 (b) shows a 1 st pulse waveform of the 6 th GRI, but the relatively complete eLORAN waveform is still clearly visible despite noise interference. The convergence state of the frequency difference weight coefficient and the phase weight vector at the tail part is more intuitively shown by the figure 5, and noise does not have excessive influence on the frequency difference weight coefficient and the phase weight vector except small fluctuation.
Table 26 interference+ dB white noise Environment WF-NF filter statistics
As can be seen from Table 2, although the respective errors are not comparable to the values of the noiseless environment in Table 1 (jitter effect of noise), the frequency offset error is not substantially more than 0.1Hz, and the amplitude error can be controlled to be 5e-3 order, and still excellent WF-NF performance can be exhibited. The above performance displays also demonstrate the utility of the WF-NF algorithm.
The invention carries out corresponding processing modes on 2 example conditions of the different conditions, and proves the correctness and the robustness of the invention and the practical value in eLORAN systems from different angles.
Claims (6)
1. A WF-NF filtering algorithm for eLORAN signal in-band interference, comprising the steps of:
Step1, inputting a desired signal And generates a reference signal/>, according to the interference detection frequency of the front-end flow；
Step 2, initializing phase weight vectorFrequency difference weight coefficient/>Frequency difference weight function/>Reference signal time number/>Sum frequency difference function time number/>Wherein/>，/>，/>，/>，/>，/>，/>The update amount of the time parameter is/>，/>For the receiver sampling rate, ω 1 is a first dimension parameter in the phase weight vector W, ω 2 is a second dimension parameter in the phase weight vector W;
Step 3, calculating an error signal Wherein/>N is the number of filtering cycles,，/>Reference signal/>To detect frequency/>, based on interferenceThe generated sine and cosine signals, namely/>, are，/>First signal parameter of reference signal x,/>A second signal parameter being a reference signal x;
Step 4, calculating a phase gradient term Sum frequency difference gradient term/>；
Step 5, updating the phase weight vectorSum frequency difference weight coefficient/>，/>，Wherein/>、/>Respectively setting a phase and a frequency difference learning step length;
Step 6, starting to calculate continuously at regular sampling intervals Mean value of points,/>For the difference value of two continuous average values, q is judged according to a set convergence threshold K, and/>Performing secondary adjustment;
wherein old and new respectively represent before and after adjustment;
step 7, updating the value of n to n+1 and t 0 to T v updates to/>Returning to the step 3 to enter the next iterative learning process; if/>After updating, the corresponding filtering sampling points enter the signal section, and the learning step length/>, is adjusted，/>If/>And after updating, entering a non-signal section, and recovering the original learning step length.
2. The filtering algorithm of claim 1, wherein when there are multiple interferers, generating 2k reference signals based on the number k of interferers and their frequencies, the filtering algorithm willAnd/>Corresponding modification is to diagonal block matrix, each block is/>Is a matrix of the (c) in the matrix,
，/>。
3. The WF-NF filtering algorithm of claim 1 for in-band interference of eLORAN signals, wherein said phase learning step size of step 5Frequency offset learning step size/>。
4. The WF-NF filtering algorithm of claim 1 for eLORAN signal in-band interference, wherein K is 1e-4.
5. The filtering algorithm of claim 1, wherein the sampling interval isFor 10000 sampling points,/>Taking 500-1000.
6. The WF-NF filtering algorithm of claim 1 for eLORAN signal in-band interference, wherein said signal segment is a length extension of the eLORAN main pulse train, the length of which ensures that the ground wave signal front is included.
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