CN110646815A - A GNSS Signal Multipath Parameter Estimation Method Based on Moving Average FFT - Google Patents

Abstract

The invention discloses a method for estimating multipath parameters of GNSS signals based on moving average FFT. The steps are as follows: step 1: splitting a baseband digital signal into M segments of signals with length L and adding windows; step 2: calculating the sum of each segment of the signal and the The cross-spectral density CPSD _i between the local copy signals obtains the CPSD _{i of the M-segment signal; Step 3: the CPSD i of} the M-segment signal is averaged to obtain the cross-spectral density CPSD of the received signal; Step 4: Use the CPSD of the received signal to divide Taking the power spectral density of the local signal of the receiver, and then performing IFFT on it to obtain the channel impulse response function; Step 5: For each pulse in the signal impulse response function, perform time offset and amplitude search to obtain the estimated value of multipath parameters . Compared with the existing multipath suppression algorithms, the invention has stronger versatility, higher robustness and lower computational complexity compared with other parameter-based algorithms, thus showing wider applicability flexibility and greater usability.

Description

A GNSS Signal Multipath Parameter Estimation Method Based on Moving Average FFT

technical field

The present invention relates to a GNSS signal multipath parameter estimation method based on moving average FFT (averaging-FFT, aFFT) technology. Especially for the problems of computational complexity and noise performance, aFFT is used to improve the classical GNSS multipath signal parameter estimation method. The method provided by the present invention belongs to the technical field of signal processing.

Background technique

Multipath error is one of the main error sources of GNSS positioning, which seriously affects the positioning accuracy and integrity of GNSS applications. The signal of the new GNSS system adopts BOC modulation, which has better multipath performance because of its narrower correlation peak. However, the application of BOC modulated signals in urban, mountainous and other environments is still affected by multipath to a large extent, and it is necessary to propose a multipath suppression technology suitable for BOC modulation.

For BOC modulated signals, there are generally two multipath suppression methods, parametric and nonparametric. The non-parametric multipath suppression method uses an improved code delay discriminator and a specially designed local reference code waveform to avoid the correlator erroneously locking on the secondary peak of the BOC signal, thereby reducing the influence of multipath. However, such methods are usually not applicable to all BOC modulated signals and have poor generality. At the same time, such methods have poor performance under low signal-to-noise ratio conditions and are easily affected by the dynamics of the tracking loop; parametric algorithms estimate the characteristics of the direct signal and the reflected signal, such as time delay, amplitude and relative carrier phase, so as to achieve It completely eliminates the effect of multipath effects; compared with non-parametric algorithms, it reflects better BOC signal multipath cancellation capabilities. As a new parametric multipath suppression algorithm, time-frequency processing adopts the method of parameter estimation in frequency domain to estimate multipath. A method for multipath parameter estimation by direct FFT has been proposed, which is based on the fact that the overlapping multipath signals 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 applied to any signal modulation method without prior information, and has excellent adaptability and versatility. However, this method requires a large amount of calculation, which is not conducive to practical application, and this method is sensitive to noise, so it cannot be applied to scenes with large noise.

In order to further improve the practicability of the parametric method, it is necessary to improve its anti-noise performance to make it suitable for more application scenarios, and at the same time, it is necessary to reduce its computational load to make it easy to implement.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a GNSS signal multipath parameter estimation method based on moving average FFT, and apply the moving average method to FFT multipath parameter estimation for multipath suppression, so that it can reflect the reasonable computational complexity at the same time. It can achieve better anti-noise performance, and can estimate and eliminate multipath parameters of any BOC signal and different multipath numbers.

To achieve the above object, the present invention proposes a method for estimating GNSS signal multipath parameters based on moving average FFT, the steps of which are as follows:

Step 1: split the baseband digital signal into M-segment length L signals and add windows;

Step 2: Calculate the cross-spectral density CPSD _i between each segment of the signal and the local replicated signal to obtain the CPSD _i of the M segment signal;

Step 3: Averaging the CPSD _i of the M-segment signal to obtain the cross-spectral density CPSD of the received signal;

Step 4: Divide the CPSD of the received signal by the power spectral density of the local signal of the receiver, and then perform IFFT on it to obtain the channel impulse response function;

Step 5: For each pulse in the signal impulse response function, time offset and amplitude search are performed to obtain the estimated value of the multipath parameter.

Wherein, the method of "splitting the baseband digital signal into M-segment signals of length L and adding windows" described in step 1 is as follows:

The sampled and down-converted data is passed through an interleaver, which splits the baseband digital signal. The total received signal is divided into M segments, each segment is L sampling points in length, and the starting point of each segment is D sampling points away. Let the overlap ratio (1-D/L)×100% be 50%.

Afterwards, in order to reduce the influence of spectral leakage, each segmented sample is windowed and weighted with a window function w(n). After weighting processing, a signal of length L divided into M segments is obtained.

Wherein, the method of "calculating the cross-spectral density CPSD _i between each segment of the signal and the local replicated signal" described in step 2 is as follows:

同时将本地复制信号进行离散傅里叶变换得到S_nom(k)。由此可以得到第i段信号和本地复制信号的傅里叶变换之间的互谱密度为For the i-th segment signal in M segments, calculate the cross-spectral density between the signal and the local replica signal. The i-th segment of the received signal is subjected to discrete Fourier transform to obtain

At the same time, the local replica signal is subjected to discrete Fourier transform to obtain S _nom (k). From this, the cross-spectral density between the Fourier transform of the i-th signal and the local replica signal can be obtained as

in, It is used to compensate for the influence of the window function on the signal power.

Wherein, the method of "averaging the CPSD _i of the M-segment signal to obtain the cross-spectral density CPSD of the received signal" described in step 3 is as follows:

The M CPSD _i calculated in step 2 are averaged 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 stronger robustness for subsequent multipath parameter estimation.

Among them, in step 4, the method of "dividing the CPSD of the received signal by the power spectral density of the receiver's local signal, and then performing IFFT on it to obtain the channel impulse response function" is as follows:

Divide the CPSD calculated in step 3 and the power spectral density of the local signal, considering that there is noise in each segment of the received signal, the expression will be obtained:

和τ_i分别为多径信号在相关域引起的幅度、相位和码片延迟畸变；f_s为采样率；P为多径信号个数；

表示第i段信号对应噪声的功率谱密度；G_0,L(k)表示一个L点长度BOC信号的理想功率谱密度。Among them, α _i ,

and τ _i are the amplitude, phase and chip delay distortion caused by the multipath signal in the correlation domain, respectively; f _s is the sampling rate; P is the number of multipath signals;

represents the power spectral density of the noise corresponding to the i-th signal; G _0,L (k) represents the ideal power spectral density of a BOC signal with a length of L point.

It is not difficult to see that the first term in the above formula is only related to the multipath model, while the second term is only related to the noise and is the average of the noise power spectrum. Then perform IFFT on the above formula to get:

It can be seen that the first two items in the formula after IFFT are the impulse response function, the amplitude of the pulse is the normalized amplitude of the multipath, and the time offset of the pulse is the code phase offset of the multipath correlation function. An estimation of multipath parameters can be performed. The third term of the formula is the noise term, which is obviously reduced by the moving average processing of the present invention.

Among them, in step 5, "for each pulse in the signal impulse response function, perform time offset and amplitude search to obtain the estimated value of multipath parameters.", the method is as follows:

For the impulse response function obtained in step 4, in order to determine whether all multipaths exist, a threshold needs to be determined according to the false alarm rate and the detection rate to detect pulses corresponding to different multipath signals. The method adopted in the present invention is to first analyze the noise of the direct signal when there is no multipath, and take the IFFT to analyze the probability distribution of the noise after the IFFT for the noise. Afterwards, Bayesian detection is performed according to the probability distribution function of noise, and the thresholds that meet the false alarm rate and detection rate are found.

After the threshold is determined, for all pulses larger than the threshold, the pulse with the largest amplitude represents the LOS signal, and the other pulses represent the multipath signal. The amplitude and time delay of the pulses corresponding to the LOS signal and other signals are calculated, and corresponding to the formula of the impulse response function in step 4, the signal power and code phase delay of the multipath signal can be estimated accordingly.

Through the above steps, the present invention realizes multipath parameter estimation suitable for BOC modulated signals. The method of piecewise moving average FFT can reduce the amount of calculation and reduce the influence of noise on estimation performance. A more robust multipath suppression function is achieved.

Based on the above steps, a method for estimating multipath parameters of GNSS signals based on moving average FFT provided by the present invention can achieve the following effects:

One: Realize the multipath parameter estimation and suppression effect suitable for any BOC modulated signal under multiple multipath conditions.

Two: The improved moving average FFT algorithm can smooth the noise in the process of segment averaging, and has a more robust multipath suppression capability.

Three: Using the method of segmented moving average FFT, the long-segment FFT can be replaced by a multi-segment short FFT, which can greatly reduce the computational complexity.

In conclusion, the present invention can solve the problem of estimation and suppression of multipath parameters of GNSS signals by means of frequency domain estimation. Compared with the existing multipath suppression algorithms, the invention has stronger versatility, higher robustness and lower computational complexity compared with other parameter-based algorithms, thus showing wider applicability flexibility and greater usability.

Description of drawings

FIG. 1 is a block diagram of the implementation of the method of the present invention.

FIG. 2 is a schematic truncation diagram of truncation of an input signal.

3a and b are performance simulation comparison diagrams of the method of the present invention and the existing frequency domain processing method

Detailed ways

A method for suppressing GNSS signal multipath based on frequency domain processing of the present invention will be further introduced below with reference to the accompanying drawings and specific embodiments.

As shown in FIG. 1 , a method for suppressing GNSS signal multipath based on frequency domain processing of the present invention, the specific implementation steps are as follows:

Step 1: Split the signal and add window

Using the interleaver to split the signal, the method of signal splitting is shown in Figure 2. For the unsplit input signal, assuming that its total input length is N, and the baseband signal sample set is written as s _r (0),...,s _r (N-1), its mathematical expression can be expressed as:

s _r (n)=s(n)+noise(n)

Among them, s(n) represents an ideal signal without noise, and noise(n) represents the thermal noise of the system, which obeys a Gaussian distribution, that is, noise(n)～N(0,σ ² ).

The signal is segmented by the method of Fig. 2, the total received signal is divided into M segments, and the starting point of each segment is D points away, so there is (M-1) D+L=N, and the intersection can be obtained at the same time. The stacking ratio r is (1-D/L)×100%. In the present invention, the overlap ratio is set to a reasonable value, that is, 50%. For the separated i-th segment signal (i=1,2,...M; n=0,1,...L-1), there are

After segmentation processing, in order to reduce the influence of spectral leakage, a Hamming window is added to each segmented sample in the time domain, and the window function is set as w(n), and the segmented samples are weighted by w(n).

Step 2: Calculate the cross-spectral density between each segment of the signal and the local replicated signal

For the i-th signal, its discrete Fourier transform coefficient can be obtained as follows:

Including:

Meanwhile, where j is an imaginary unit.

For the cross-spectral density of the i-th piece of data and the local replica signal, it is necessary to perform L-point Fourier transform on the local replica signal s _nom (n) to obtain the Fourier transform coefficient of the local replica signal S _nom (k ). Afterwards, the cross-spectral density between the i-th segment data and the local replicated signal can be obtained as:

Among them, * represents the conjugate operation. In order to reduce the influence of the window function on the total signal power, the coefficient U related to the window function is introduced, and its expression is written as the following formula:

Step 3: Take the average of the cross-spectral density of the M-segment

For a total of M segments of the cross-spectral density of the split signal and the local replicated signal, average it to obtain the final average cross-spectral density CPSD of the entire segment of the signal and the local replicated signal, which is expressed as:

Finally, the CPSD noise calculated by this formula will be significantly reduced, which can effectively improve the robustness of multipath parameter estimation in subsequent steps.

Step 4: Calculation of impulse response parameter estimation function

Suppose the signal distortion correlation function under multipath is written as:

的情况，可以将第i段的CPSD写为：Without loss of generality, discuss A=1 and

, the CPSD of the i-th paragraph can be written as:

in

G _0,L (k) is the ideal power spectral density of a BOC signal with a length of L point. In this way, the average CPSD of the M-segment signal can be obtained as:

In order to eliminate the influence of the PRN code, the present invention divides the average CPSD obtained above by the PSD of the ideal BOC signal, and then obtains the following formula:

After that, the IFFT operation is performed on the result, and the time-domain impulse response function is obtained as follows:

The above formula is the impulse response parameter estimation function.

Step 5: Pulse Search and Multipath Parameter Estimation

In order to determine the existence of multipath signals, it is necessary to set a threshold to search all impulse response functions. If the amplitude of an impulse function is greater than the threshold, it is considered that the multipath signal corresponding to the impulse function has been detected, otherwise it is considered that it does not exist. the multipath signal.

The present invention uses a statistical method to determine the threshold, first analyzes the probability distribution of the IFFT transform result of the received signal when there is no multipath, and removes the LOS signal pulse before calculation, that is, only analyzes the probability distribution of the noise signal after IFFT. Once the probability distribution of the noise signal after IFFT is obtained, the Bayesian test can be performed using the known probability distribution to find the threshold value that satisfies the false alarm rate and the detection probability.

和τ_i＝Δt_i。至此多径信号参数得以估计，并能通过参数进行多径抑制。After finding the threshold value, search for all pulses greater than the threshold value. First, the pulse with the largest amplitude is searched, the signal corresponding to the pulse is considered to be the LOS signal, and the pulse amplitude corresponding to the LOS signal is α _LOS . All other pulses greater than the threshold value are then searched for. Considering that these pulses represent different multipath signals, assuming that the amplitude of the i-th pulse is α _multi , and the time delay between the LOS signal pulses is Δt _i , the parameters in the multipath signal model are estimated

and τ _i =Δt _i . So far, the multipath signal parameters have been estimated, and multipath suppression can be performed through the parameters.

In order to verify the validity, rationality and superiority of the algorithm proposed in this patent, the method proposed in the present invention is used to estimate the multipath parameters and suppress the multipath. Figures 3a and b respectively show the impulse response parameter estimation functions obtained by using the existing frequency domain processing and by using the method proposed in the present invention. The parameters in the experiment are set as follows: the received signal consists of one LOS signal plus two multipath signals, the delay of the first multipath signal is 0.5 chips, and the power is the same as the LOS signal; the delay of the second multipath signal is 1 chip, the amplitude is attenuated to 0.5 times the LOS signal. The window length is L=256, and the carrier-to-noise ratio is C/N ₀ =38dB-Hz.

It can be seen from the test results that the method proposed by the present invention can effectively perform multipath parameter estimation to realize multipath suppression; it can be seen from the comparison of Figures 3a and 3b that in the case of poor CNR, the method proposed by the present invention Not only can the multipath parameter estimation be completed, but the noise floor of the parameter estimation function is lower than that of the existing algorithms, showing stronger anti-noise performance, and can be applied to the situation with poor noise conditions. In addition, the present invention adopts the method of segmented FFT, and divides the FFT of a long-segment signal into FFTs of a plurality of short-segment signals, which can greatly reduce the amount of calculation and is more conducive to practical implementation.

Claims (6)

1. a GNSS signal multipath parameter estimation method based on moving average FFT, is characterized in that: the method steps are as follows: Step 1: split the baseband digital signal into M-segment length L signals and add windows; Step 2: Calculate the cross-spectral density CPSD _i between each segment of the signal and the local replicated signal to obtain the CPSD _i of the M segment signal; Step 3: Averaging the CPSD _i of the M-segment signal to obtain the cross-spectral density CPSD of the received signal; Step 4: Divide the CPSD of the received signal by the power spectral density of the local signal of the receiver, and then perform IFFT on it to obtain the channel impulse response function; Step 5: For each pulse in the signal impulse response function, time offset and amplitude search are performed to obtain the estimated value of the multipath parameter. 2. a kind of GNSS signal multipath parameter estimation method based on moving average FFT according to claim 1, is characterized in that: described in step 1, the baseband digital signal is split into M segment lengths of L signals and add window, the process is as follows: Passing the data after sampling and down-conversion through an interleaver, the interleaver splits the baseband digital signal; the total received signal is divided into M sections, each section has a length of L sampling points, and the starting point of each section is separated by D sampling points; Let the overlap rate (1-D/L)×100% is 50%; After that, perform windowing processing on each segmented sample, and use the window function w(n) for weighting; after the weighting processing, a signal of length L divided into M segments is obtained. 3. a kind of GNSS signal multipath parameter estimation method based on moving average FFT according to claim 1, is characterized in that: the cross-spectral density CPSD _i between each section of signal and local replica signal of calculating described in step 2 , the process is as follows: For the i-th segment signal in the M segment, calculate the cross-spectral density between the signal and the local replica signal; perform discrete Fourier transform on the i-th segment signal of the received signal to obtain

At the same time, the local replica signal is subjected to discrete Fourier transform to obtain S _nom (k); from this, the cross-spectral density between the i-th signal and the Fourier transform of the local replica signal can be obtained as

in,

It is used to compensate for the influence of the window function on the signal power. 4. a kind of GNSS signal multipath parameter estimation method based on moving average FFT according to claim 1, is characterized in that: described in the step 3, the CPSD _i of M segment signal is averaged to obtain the cross-spectral density of the received signal CPSD, the process is as follows: The M CPSD _i calculated in step 2 are averaged to obtain the final CPSD of the received signal:

5. a kind of GNSS signal multipath parameter estimation method based on moving average FFT according to claim 1, is characterized in that: the CPSD of utilizing received signal described in the step 4 is divided by the power spectral density of receiver local signal, Then perform IFFT on it to obtain the channel impulse response function. The process is as follows: Divide the CPSD calculated in step 3 and the power spectral density of the local signal, considering that there is noise in each segment of the received signal, the expression will be obtained:

Among them, α _i ,

and τ _i are the amplitude, phase and chip delay distortion caused by the multipath signal in the correlation domain, respectively; f _s is the sampling rate; P is the number of multipath signals; represents the power spectral density of the noise corresponding to the i-th signal; G _0,L (k) represents the ideal power spectral density of a BOC signal with a length of L point; Then perform IFFT on the above formula to get:

In the formula after IFFT, the first two items are the impulse response function, the amplitude of the pulse is the normalized amplitude of the multipath, and the time offset of the pulse is the code phase offset of the multipath correlation function. Estimation of parameters; the third term of the formula is the noise term. 6. a kind of GNSS signal multipath parameter estimation method based on moving average FFT according to claim 1, is characterized in that: described in step 5 for each pulse in the signal impulse response function, carry out time offset and amplitude search to obtain the estimated value of multipath parameters, the process is as follows: For the impulse response function obtained in step 4, determine whether all multipaths exist, and determine a threshold according to the false alarm rate and detection rate to detect pulses corresponding to different multipath signals; Analyze the noise, take IFFT to analyze the probability distribution of the noise after IFFT, and then perform Bayesian detection according to the probability distribution function of the noise to find the thresholds that meet the false alarm rate and detection rate; After the threshold is determined, for all pulses larger than the threshold, the pulse with the largest amplitude represents the LOS signal, and the other pulses represent the multipath signal; The formula of the impulse response function can estimate the signal power and code phase delay of the multipath signal accordingly.

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