CN118112498B - A fast time difference estimation method based on data segmentation - Google Patents

Abstract

The present invention belongs to the field of radio positioning technology, and specifically relates to a time difference fast estimation method based on data segmentation. The present invention proposes to extract data to the maximum extent, reduce the sampling rate, reduce the data length, use a segmentation method to calculate the correlation function, and then use an efficient interpolation method to obtain the time difference. The method of the present invention can significantly reduce the amount of calculation, and has a fast speed and high accuracy.

Description

A fast time difference estimation method based on data segmentation

Technical Field

The invention belongs to the technical field of radio positioning, and in particular relates to a time difference fast estimation method based on data segmentation.

Background Art

The basis for the realization of multi-station time difference positioning system is to obtain TDOA/FDOA parameters. Since the two parameters are generated simultaneously during the signal propagation and forwarding process, time-frequency analysis method is usually used to realize joint estimation of parameters. There are many methods for time-frequency analysis at present, which can be summarized into the following three categories: TDOA/FDOA joint estimation algorithm based on second-order statistics, TDOA/FDOA joint estimation algorithm based on high-order statistics, and TDOA/FDOA joint estimation algorithm based on signal cyclostationary characteristics.

In practical applications, signals are received by sensors at different spatial locations, so the noise is often independent. In this case, the high-order cumulant algorithm has no obvious advantage over the second-order statistics algorithm, but the calculation is too complicated; the parameter estimation method based on cyclostationary characteristics is also a parameter estimation method based on second-order statistics, which only increases the ability to resist interference and correlated noise, so it has no obvious advantage in the application scenario where the noise is independent. Through simulation and actual data application analysis, it is found that the cross-correlation function is one of the most effective time-frequency difference estimation methods based on second-order statistics in the application.

The time-frequency difference estimation method based on mutual fuzzy function is a two-dimensional search method with huge computational complexity, resulting in poor timeliness of time-frequency difference estimation. In practical applications, the frequency difference is often estimated first, and then the time difference is estimated by correlation method after compensation. This reduces the two-dimensional search to two one-dimensional calculations, greatly reducing the amount of calculation. However, when performing long-term accumulation correlation calculations on communication signals, the data length increases linearly with the time length. When performing correlation calculations, the amount of calculation increases exponentially according to the data length. Limited by the resources of the computing platform, the timeliness of the calculation is still low.

Summary of the invention

In view of the above problems, the present invention proposes to extract data to the maximum extent, reduce the sampling rate, shorten the data length, adopt a segmented method to calculate the correlation function, and then use an efficient interpolation method to obtain the time difference.

For the fast time difference estimation method in the multi-station time difference positioning system, taking the signals received by two receiving stations as an example, the signal model is described as follows:

The communication signals received in the multi-station time difference positioning system are generally narrowband signals, so the received signal can be written as:

x(t)＝s(t)+ _n1 (t)

Where r is the relative attenuation coefficient, t is the relative time delay TDOA, f _d is the relative Doppler frequency shift, and after compensating for the frequency difference, the signal model is:

x(t)＝s(t)+ _n1 (t)

y(t)＝rs(tt)+ _n2 (t)

At this time, the time difference between the two signals is obtained by using the correlation of the two signals. In the positioning system, the data acquisition time is often hundreds of milliseconds or even seconds, and the time difference is in the order of microseconds. Therefore, when estimating the time difference using the correlation function, only the value near the zero value of the correlation function can be calculated. In view of this, the present invention adopts the method of data segmentation to realize the time difference estimation.

The technical solution of the present invention is:

A time difference fast estimation method based on data segmentation, using two receiving stations to receive signals, includes the following steps:

S1. Define the two signals received by the two receiving stations as x(n) and y(n), respectively, and the signal length is L. Divide the signal into M segments, and the length of each segment is N, that is, N×M＝L. Calculate the segmented spectrum of the two signals:

S2. The discrete spectrum of the correlation function with a resolution of 2π/L is obtained by conjugating and multiplying the discrete spectra X(k) and Y(k) of the two signals:

For the sake of simplicity, Replacing the corresponding parts of X(K) and Y(k) in S1, the discrete spectrum of the correlation function with a resolution of 2π/L is expressed as follows

is the mth order term;

S3. In order to improve the calculation efficiency, the discrete spectrum Xf(k)·Yf ^* (k) of the above two signals is calculated by fast Fourier transform:

Because the data has been segmented into M segments, the length of each segment is only N. In order to meet the requirements of fast Fourier transform calculation, the resolution of the discrete spectrum of the correlation function needs to be reduced to 2π/N, and the discrete spectrum of x(n) and y(n) needs to be rewritten as:

make W＝e ^-jπk ，

The discrete spectrum of the correlation function with a resolution of 2π/N is expressed as follows

S4. Perform inverse Fourier transform on the fast-calculated discrete spectrum X(k)·Y ^* (k), obtain the correlation function R(n) of the two signals, and search for n, max(R(n), 0≤n≤N-1). The n corresponding to the maximum value is the rough time difference estimation value _R0 of the two signals.

S5, calculating the local time domain interpolation according to the rough time difference estimation value R ₀ to obtain a high-precision time difference estimation value expression;

For the correlation function obtained by S4, let nk = [n ² + k ² - (kn) ² ]/2, and fill the spectrum with zeros so that the data length is L, then:

Since we only need to get the time domain value of a certain interval, Where 0≤P,P+M≤L-1, we can get:

P＝L/N×R ₀ -M/2

make

The related function expression after interpolation is as follows:

S6. Perform a convolution operation on Z(k) and H(k). This convolution operation can be implemented through FFT and IFFT algorithms to find n corresponding to the maximum value, which is the high-precision time difference estimation value.

The beneficial effect of the present invention is that the method of the present invention can significantly reduce the amount of calculation, and has a high speed and high precision.

DETAILED DESCRIPTION

The present invention is verified by simulation data below.

Taking the BPSK signal with a bandwidth of 25KHz as an example, the signal-to-noise ratio is set to 10dB, and the accumulated signal time is 1 second. As can be seen from Table 1, the accuracy of the parameter estimation results obtained by the data segmentation method and the non-segmented method is equivalent, so the algorithm is effective, but this method can decompose the super-long point FFT into short point FFT, which can significantly improve the calculation efficiency.

Table 1 Comparison of time difference estimation

Table 1 shows that the time difference estimated by each segmentation method has an estimation accuracy of about 59ns.

Assuming that the length of the data after segmentation is 1024 points, as the length of the original data increases exponentially, the amount of calculation changes as shown in Table 2.

Table 2 Comparison of calculation amount

Data length 2 ¹² 2 ¹³ 2 ¹⁴ 2 ¹⁵ 2 ¹⁶ 2 ¹⁷ 2 ¹⁸ Number of segments twenty ^two twenty ^three twenty ^four 2 ⁵ 2 ⁶ 2 ⁷ 2 ⁸ Num1/Num2 1.65 2.67 3.81 4.87 5.74 6.43 6.98 Data length 2 ¹⁹ 2 ²⁰ 2 ²¹ 2 ²² 2 ²³ 2 ²⁴ 2 ²⁵ Number of segments 2 ⁹ 2 ¹⁰ 2 ¹¹ 2 ¹² 2 ¹³ 2 ¹⁴ 2 ¹⁵ Num1/Num2 7.44 7.85 8.24 8.62 8.99 9.35 9.71

The superiority of segmented calculation is illustrated by the multiple of the amount of calculation. As can be seen from Table 2, the longest data is 33M. After segmentation, the calculation speed is increased by nearly 10 times.

Claims (1)

1. The fast time difference estimation method based on data segmentation adopts two receiving stations to receive signals, and is characterized by comprising the following steps:

s1, defining two paths of signals received by two receiving stations as x (N), y (N) and L, dividing the signals into M sections, and calculating the discrete frequency spectrum of the two paths of signals, wherein each section of data has the length of N, namely N multiplied by M=L:

S2, order The discrete frequency spectrum X (k) and Y (k) of the two paths of signals are utilized for conjugate multiplication to obtain a correlation function discrete frequency spectrum with the resolution of 2 pi/L:

is the m-th order item;

S3, calculating a correlation function discrete spectrum X (k). Y ^* (k) of the two paths of signals by adopting fast Fourier transform:

rewriting the discrete spectrum of x (n), y (n) as:

Order the W＝e^-jπk，

The discrete spectrum of the correlation function with the resolution of 2 pi/N is expressed as follows:

s4, performing inverse Fourier transform on the obtained correlation function discrete frequency spectrum to obtain a correlation function R (n) of two paths of signals:

Searching n corresponding to the maximum value of R (n) to obtain a time difference estimated coarse value R ₀ of two paths of signals;

S5, calculating local time domain interpolation according to the time difference estimated coarse value R ₀ to obtain a high-precision time difference estimated value expression, wherein the method comprises the following steps:

Based on the correlation function obtained in S4, let nk= [ n ²+k²-(k-n)² ]/2, and zero-padding the spectrum so that the data length is L, then:

since only the time domain value of a certain interval needs to be obtained, Wherein, P is more than or equal to 0 and P+M is more than or equal to L-1, and the method is that:

P＝L/N×R₀-M/2

Order the

The interpolated correlation function expression is as follows:

S6, performing convolution operation on Z (k) and H (k), and obtaining n corresponding to the maximum value to obtain the high-precision time difference estimated value.