CN110646815A - GNSS signal multipath parameter estimation method based on moving average FFT - Google Patents
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Abstract
The invention discloses a GNSS signal multipath parameter estimation method based on a moving average FFT, which comprises the following steps: splitting the baseband digital signal into M signals with the length of L and windowing the M signals; step two: calculating the cross-spectral density CPSD between each segment of the signal and the local replica signaliObtaining the CPSD of the M-segment signali(ii) a Step three: CPSD of M-segment signaliAveraging to obtain the cross-spectral density CPSD of the received signal; step four: dividing the CPSD of the received signal by the power spectral density of the local signal of the receiver, and then carrying out IFFT on the CPSD to obtain a channel impulse response function; step five: and carrying out time offset and amplitude search on each pulse in the signal impulse response function to obtain a multipath parameter estimation value. Compared with the existing multipath suppression algorithm, the method has stronger universality, higher robustness and lower calculation complexity compared with other parameter algorithms, thereby showing wider applicability and stronger practicability.
Description
Technical Field
The invention relates to a GNSS signal multipath parameter estimation method based on an averaging-FFT (aFFT) technology. Particularly aiming at the problems of operation amount and noise performance, the method for estimating the multipath signal parameters of the classical GNSS is improved by utilizing aFFT. The method provided by the invention belongs to the technical field of signal processing.
Background
Multipath error is one of the main error sources of GNSS positioning, and seriously affects positioning accuracy and integrity of GNSS applications. The GNSS new system signal adopts a BOC modulation mode, and has a narrower correlation peak, so that the GNSS new system signal has better multipath performance. However, the application of BOC modulation signals in urban and mountain areas still suffers from a large degree of multipath influence, and a multipath suppression technology adapted to the BOC modulation scheme needs to be provided.
For BOC modulation signals, there are two multipath mitigation methods, parametric and nonparametric ones. The nonparametric multipath inhibiting method adopts an improved code delay discriminator and a specially designed local reference code waveform to avoid the error locking of a correlator to a secondary peak of a BOC signal, thereby reducing the influence of multipath. However, such methods are generally not applicable to all BOC modulated signals and are less versatile. Meanwhile, the method has poor performance under the condition of low signal-to-noise ratio and is easily influenced by the dynamic state of a tracking loop; the parameter algorithm achieves the effect of thoroughly eliminating the multipath influence by estimating the characteristics of the direct signal and the reflected signal, such as time delay, amplitude, relative carrier phase and the like; compared with nonparametric algorithms, the method has the advantage of representing more excellent BOC signal multipath elimination capability. The time-frequency processing is used as a new parameter-like multipath suppression algorithm, and multipath estimation is carried out by adopting a mode of carrying out parameter estimation in a frequency domain. A method for multipath parameter estimation by means of direct FFT has been proposed so far, which performs multipath parameter estimation based on the fact that multipath signals overlapping in the time domain are equal to the product of the LOS spectrum and the multipath channel transfer function in the frequency domain. The method can be suitable for any signal modulation mode, does not need prior information, and has excellent adaptability and universality. However, the method has a large calculation amount, which is not beneficial to practical application, and the method is sensitive to noise and cannot be applied to scenes with large noise.
In order to further improve the practicability of the parameter-based method, the anti-noise performance needs to be improved to be suitable for more application scenes, and meanwhile, the operation amount needs to be reduced to be easy to realize.
Disclosure of Invention
The invention aims to provide a GNSS signal multipath parameter estimation method based on moving average FFT, which is applied to the estimation of FFT multipath parameters for multipath suppression, so that the method can embody better anti-noise performance while having reasonable calculation complexity, and can estimate and eliminate multipath parameters of any BOC signal and different multipath numbers.
In order to achieve the above object, the present invention provides a GNSS signal multipath parameter estimation method based on moving average FFT, which comprises the following steps:
the method comprises the following steps: splitting the baseband digital signal into M signals with the length of L and windowing the M signals;
step two: calculating the cross-spectral density CPSD between each segment of the signal and the local replica signaliObtaining the CPSD of the M-segment signali；
Step three: CPSD of M-segment signaliAveraging to obtain the cross-spectral density CPSD of the received signal;
step four: dividing the CPSD of the received signal by the power spectral density of the local signal of the receiver, and then carrying out IFFT on the CPSD to obtain a channel impulse response function;
step five: and carrying out time offset and amplitude search on each pulse in the signal impulse response function to obtain a multipath parameter estimation value.
In step one, "splitting the baseband digital signal into M segments of length L and windowing" is performed as follows:
and passing the sampled and down-converted data through an interleaver, and splitting the baseband digital signal by the interleaver. The total received signal is divided into M sections, the length of each section is L sampling points, and the distance between the starting points of each section is D sampling points. The overlap ratio (1-D/L). times.100% was 50%.
Thereafter, in order to reduce the effect of spectral leakage, each segmented sample is windowed and weighted by a window function w (n). And obtaining the signal with the length of L which is split into M sections after weighting processing.
Wherein, in the step two, the cross-spectral density CPSD between each section of signal and the local copy signal is calculatedi", the procedure is as follows:
for the ith segment signal in the M segments, the cross-spectral density between the signal and the local replica signal is calculated. The ith section of signals of the received signals are subjected to discrete Fourier transform to obtain
Simultaneously, the local copy signal is subjected to discrete Fourier transform to obtain Snom(k) In that respect It is thus obtained that the cross-spectral density between the i-th signal and the Fourier transform of the local replica signal is
Wherein,for compensating for the effect of the window function on the signal power.
Wherein, in step three, the CPSD of the M-segment signaliAveraging is performed to obtain the cross-spectral density CPSD "of the received signal, as follows:
for the M CPSDs calculated in the step twoiAnd carrying out averaging processing to obtain the final CPSD of the received signal:
the noise in the received signal can be significantly reduced by the averaged cross-spectral density. This provides greater robustness for subsequent multipath parameter estimation.
In step four, the method for obtaining the channel impulse response function by dividing the CPSD of the received signal by the power spectral density of the local signal of the receiver and performing IFFT thereon is as follows:
dividing the CPSD calculated in step three by the power spectral density of the local signal, taking into account the presence of noise in each segment of the received signal, the expression:
wherein alpha isi,
And τiAmplitude, phase and chip delay distortion caused by multipath signals in a relevant domain respectively; f. ofsIs the sampling rate; p is the number of multipath signals;
representing the power spectral density of the noise corresponding to the ith section of the signal; g0,L(k) Representing the ideal power spectral density of an L-point length BOC signal.
It is readily seen that the first term in the above equation is related only to the multipath model, while the second term is related only to noise and is the average of the noise power spectrum. Then IFFT is carried out on the formula to obtain:
it can be seen that the first two terms in the equation after IFFT are impulse response functions, the amplitude of the impulse is the normalized amplitude of the multipath, the time offset of the impulse is the code phase offset of the multipath correlation function, and the multipath parameters can be estimated through the first two terms. The third term of the equation is the noise term, which is significantly reduced by the moving average processing of the present invention.
In step five, time offset and amplitude search is performed on each pulse in the signal impulse response function to obtain the multipath parameter estimation value. ", the procedure is as follows:
for the impulse response function obtained in step four, in order to determine whether all the multi-paths exist, a threshold needs to be determined according to the false alarm rate and the detection rate to detect the multi-path signals corresponding to the pulses. The method adopted by the invention is to analyze the noise of the direct signal without multipath, and to take IFFT to analyze the probability distribution of the noise after IFFT. And then carrying out Bayesian detection according to the probability distribution function of the noise, and finding out a threshold value which accords with the false alarm rate and the detection rate.
After the threshold is determined, for all pulses greater than the threshold, the pulse with the largest amplitude represents the LOS signal, and the other pulses represent multi-path signals. The amplitude and time delay of the pulse corresponding to the LOS signal and other signals are calculated, and the signal power and code phase delay of the multipath signal can be correspondingly estimated according to the impulse response function formula in the step four.
Through the steps, the multipath parameter estimation method is suitable for the BOC modulation signal. The method of the segmented moving average FFT can be utilized to reduce the influence of noise on the estimation performance while reducing the calculation amount. A more robust multipath mitigation function is achieved.
Based on the steps, the GNSS signal multipath parameter estimation method based on the moving average FFT can achieve the following effects:
firstly, the method comprises the following steps: the multipath parameter estimation and suppression effects suitable for any BOC modulation signal and under multiple multipath conditions are achieved.
II, secondly: the improved moving average FFT algorithm can smooth noise in the process of sectional averaging and has more robust multipath suppression capability.
Thirdly, the method comprises the following steps: by using the segmented sliding average FFT mode, a long-segment FFT mode can be replaced by a multi-segment short FFT mode, and the calculation complexity can be reduced to a greater extent.
In conclusion, the invention can solve the problems of GNSS signal multipath parameter estimation and suppression in a frequency domain estimation mode. Compared with the existing multipath suppression algorithm, the method has stronger universality, higher robustness and lower calculation complexity compared with other parameter algorithms, thereby showing wider applicability and stronger practicability.
Drawings
FIG. 1 is a block diagram of an implementation of the method of the present invention.
Fig. 2 is a schematic diagram of truncation of an input signal.
FIGS. 3a and b are graphs comparing performance simulation of the method of the present invention and the existing frequency domain processing method
Detailed Description
The GNSS signal multipath mitigation method based on frequency domain processing according to the present invention is further described with reference to the accompanying drawings and the specific embodiments.
As shown in fig. 1, the GNSS signal multipath mitigation method based on frequency domain processing of the present invention includes the following specific steps:
the first step is as follows: splitting signals and windowing
The signal is split by the interleaver in the manner shown in fig. 2. For an input signal that is not split, assuming its total input length is N, the set of baseband signal samples is written as sr(0),...,sr(N-1), the mathematical expression of which can be expressed as:
sr(n)＝s(n)+noise(n)
where s (N) represents the ideal signal without noise, noise (N) represents the thermal noise of the system, and follows a Gaussian distribution, i.e., noise (N) N (0, σ)2)。
The signal is segmented in the manner shown in fig. 2, the total received signal is divided into M segments, the starting point of each segment is D points apart, and thus (M-1) D + L is equal to N, and the overlap ratio r is (1-D/L) × 100%. In the present invention, the overlapping ratio is set to a more reasonable value, i.e., 50%. For the separated ith segment signal(i-1, 2, … M; n-0, 1, … L-1) there are
After the segmentation process, in order to reduce the influence of spectral leakage, a hamming window is added to each segmented sample in the time domain, the window function is given by w (n), and the segmented samples are weighted by w (n).
The second step is that: calculating the cross-spectral density of each segment of signal and the local copy signal
For the ith signal, the discrete fourier transform coefficients can be obtained as shown in the following formula:
among them are:
and j is an imaginary unit.
For the ith segment of data, the cross-spectral density with the local copy signal is calculated, and the local copy signal s needs to be firstly processednom(n) performing an L-point Fourier transform to obtain a Fourier transform coefficient S of the local replica signalnom(k) In that respect The cross-spectral density between the i-th segment of data and the local replica signal can then be found as:
wherein, denotes a conjugate operation, in order to reduce the influence of the windowing function on the total power of the signal, a coefficient U related to the windowing function is introduced, and the expression is written as follows:
the third step: averaging M-segment cross spectral density
For the cross-spectrum density of a total M-segment split signal and a local copy signal, averaging the cross-spectrum density to obtain the final average cross-spectrum density CPSD of the whole segment signal and the local copy signal, which is expressed as:
the CPSD noise calculated by the formula is obviously reduced, and the robustness of multipath parameter estimation in the subsequent step can be effectively improved.
The fourth step: impulse response parameter estimation function computation
Assuming that the signal distortion correlation function under multipath is written as:
without loss of generality, discussion a ═ 1 and
in this case, the CPSD of the i-th segment can be written as:
wherein
G0,L(k) Is the ideal power spectral density of a BOC signal of length L points. The average CPSD of the M-segment signals can thus be obtained as:
to eliminate the effect of the PRN code, the present invention divides the average CPSD obtained above by the PSD of the ideal BOC signal to obtain the following equation:
then, performing an IFFT operation on the result to obtain a time domain impulse response function as follows:
the above equation is the impulse response parameter estimation function.
The fifth step: pulse search and multipath parameter estimation
In order to determine the existence of the multipath signal, a threshold needs to be set to search all impulse response functions, if the amplitude of a certain impulse function is greater than the threshold, the multipath signal corresponding to the impulse function is considered to be detected, otherwise, the multipath signal is considered to be absent.
The invention utilizes a statistical method to determine the threshold, firstly analyzes the probability distribution of the IFFT transformation result of the received signal without multipath, and removes the LOS signal pulse before calculation, namely only analyzes the probability distribution of the noise signal after IFFT. Once the probability distribution after the IFFT of the noise signal is obtained, bayesian detection can be performed using the known probability distribution to find a threshold value that satisfies the false alarm rate and the detection probability.
After the threshold value is found, all the pulses larger than the threshold value are searched. Firstly, searching the pulse with the maximum amplitude, considering the signal corresponding to the pulse as an LOS signal, and making the pulse amplitude corresponding to the LOS signal as alphaLOS. All other pulses above the threshold are then searched. These pulses are considered to represent different multipath signals, assuming that the ith pulse has an amplitude αmultiAnd the time delay between LOS signal pulses is Δ tiThen the parameters in the multipath signal model are estimated
And τi＝Δti. So far, the multipath signal parameters are estimated, and multipath suppression can be performed through the parameters.
In order to verify the effectiveness, rationality and superiority of the algorithm provided by the patent, the method provided by the invention is used for estimating multipath parameters and suppressing multipath. FIGS. 3a and b show the respective advantagesThe impulse response parameter estimation function obtained by the existing frequency domain processing and the method provided by the invention. The parameters in the test were set as follows: the receiving signal is composed of an LOS signal and two multipath signals, the delay of the first multipath signal is 0.5 chip, and the power of the first multipath signal is the same as that of the LOS signal; the second path of multipath signal is delayed by 1 chip and attenuated to 0.5 times of the LOS signal. Window length is 256 and carrier to noise ratio is C/N0＝38dB-Hz。
The test result shows that the method provided by the invention can effectively estimate the multipath parameters to realize multipath inhibition; it can be seen from the comparison between fig. 3a and 3b that, under the condition of poor carrier-to-noise ratio, the method provided by the invention not only can complete multipath parameter estimation, but also has lower bottom noise of a parameter estimation function compared with the existing algorithm, shows stronger anti-noise performance, and can be suitable for the condition of poor noise condition. In addition, the invention adopts a segmented FFT mode, and the FFT of one long-segment signal is divided into the FFTs of a plurality of short-segment signals, so that the calculation amount can be reduced to a greater extent, and the method is more beneficial to practical realization.
Claims (6)
1. A GNSS signal multipath parameter estimation method based on moving average FFT is characterized in that: the method comprises the following steps:
the method comprises the following steps: splitting the baseband digital signal into M signals with the length of L and windowing the M signals;
step two: calculating the cross-spectral density CPSD between each segment of the signal and the local replica signaliObtaining the CPSD of the M-segment signali；
Step three: CPSD of M-segment signaliAveraging to obtain the cross-spectral density CPSD of the received signal;
step four: dividing the CPSD of the received signal by the power spectral density of the local signal of the receiver, and then carrying out IFFT on the CPSD to obtain a channel impulse response function;
step five: and carrying out time offset and amplitude search on each pulse in the signal impulse response function to obtain a multipath parameter estimation value.
2. The method according to claim 1, wherein the method for estimating the multipath parameters of the GNSS signal based on the moving average FFT comprises: splitting the baseband digital signal into M signals with length L and windowing, wherein the process comprises the following steps:
the data after sampling and down-conversion passes through an interleaver, and the interleaver splits the baseband digital signal; dividing the total received signal into M sections, wherein the length of each section is L sampling points, and the distance between the starting points of each section is D sampling points; make the overlapping rate
(1-D/L). times.100% is 50%;
then, each segmented sample is subjected to windowing processing, and is weighted by a window function w (n); and obtaining the signal with the length of L which is split into M sections after weighting processing.
3. The method according to claim 1, wherein the method for estimating the multipath parameters of the GNSS signal based on the moving average FFT comprises: calculating the cross-spectral density CPSD between each segment of signal and the local copy signal in the second stepiThe process is as follows:
for the ith segment signal in the M segments, calculating the cross-spectral density between the signal and the local copy signal; the ith section of signals of the received signals are subjected to discrete Fourier transform to obtain
Simultaneously, the local copy signal is subjected to discrete Fourier transform to obtain Snom(k) (ii) a It is thus obtained that the cross-spectral density between the i-th signal and the Fourier transform of the local replica signal is
Wherein,
for compensating for the effect of the window function on the signal power.
4. A slide based slide according to claim 1The GNSS signal multipath parameter estimation method of average FFT is characterized in that: CPSD for M-segment signals as described in step threeiAveraging is carried out to obtain the cross-spectrum density CPSD of the received signal, and the process is as follows:
for the M CPSDs calculated in the step twoiAnd carrying out averaging processing to obtain the final CPSD of the received signal:
5. the method according to claim 1, wherein the method for estimating the multipath parameters of the GNSS signal based on the moving average FFT comprises: in step four, the CPSD of the received signal is divided by the power spectral density of the local signal of the receiver, and then the CPSD is subjected to IFFT to obtain the channel impulse response function, and the process is as follows:
dividing the CPSD calculated in step three by the power spectral density of the local signal, taking into account the presence of noise in each segment of the received signal, the expression:
wherein alpha isi,
And τiAmplitude, phase and chip delay distortion caused by multipath signals in a relevant domain respectively; f. ofsIs the sampling rate; p is the number of multipath signals;representing the power spectral density of the noise corresponding to the ith section of the signal; g0,L(k) Representing the ideal power spectral density of an L-point length BOC signal;
then IFFT is carried out on the formula to obtain:
the first two terms in the formula after IFFT are impulse response functions, the amplitude of the impulse is the normalized amplitude of multipath, the time offset of the impulse is the code phase offset of the multipath correlation function, and the multipath parameters can be estimated through the first two terms; the third term of the equation is the noise term.
6. The method according to claim 1, wherein the method for estimating the multipath parameters of the GNSS signal based on the moving average FFT comprises: in step five, time offset and amplitude search is performed for each pulse in the signal impulse response function to obtain an estimated multipath parameter value, and the process is as follows:
determining whether all multipath exists for the impulse response function obtained in the fourth step, and determining a threshold value according to the false alarm rate and the detection rate so as to detect different multipath signals corresponding to the pulse; the method comprises the steps of firstly analyzing the noise of a direct signal without multipath, taking IFFT to analyze the probability distribution of the noise after IFFT, and then carrying out Bayesian detection according to the probability distribution function of the noise to find a threshold value according with a false alarm rate and a detection rate;
after the threshold is determined, for all the pulses larger than the threshold, the pulse with the maximum amplitude represents an LOS signal, and other pulses represent multi-path signals; the amplitude and time delay of the pulse corresponding to the LOS signal and other signals are calculated, and the signal power and code phase delay of the multipath signal can be correspondingly estimated according to the impulse response function formula in the step four.
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| CN116068593A (en) * | 2023-01-28 | 2023-05-05 | 中国铁建电气化局集团有限公司 | Satellite positioning weight calculation method, device, equipment and medium based on Bayes |
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Application publication date: 20200103 |