CN111580137B - A Fitting Method of RF Channel Group Delay Characteristics of High Precision Navigation Receiver - Google Patents

Abstract

The invention proposes a method for fitting the delay characteristic of radio frequency channel group of high precision navigation receiver. Taking advantage of the analyzability of the Fourier decomposition approximate fitting and the small computational complexity of the segment decomposition, the measured receiver RF channel group delay characteristics are segmented according to segment lengths. The first sample of each segment is The point coincides with the last sampling point of the previous segment, and each segmented data is approximately fitted by Fourier decomposition, and finally the segmented function is obtained, which can accurately fit the group delay characteristics. The invention can effectively fit the delay characteristics of the radio frequency channel group of the high-precision navigation receiver, has high fitting precision, low complexity and small calculation amount.

Description

A Fitting Method of RF Channel Group Delay Characteristics of High Precision Navigation Receiver

technical field

The invention belongs to the technical field of satellite navigation, and in particular relates to a method for fitting delay characteristics of radio frequency channels of a high-precision navigation receiver and a method for evaluating the fitting effect thereof.

Background technique

High-precision navigation receivers are widely used in the ground segment, space segment, and control segment of the satellite navigation system. The basis of performance. The group delay and amplitude characteristics of the receiver signal channel are mainly determined by the RF front-end, and its amplitude and phase characteristics can be approximated by a nonlinear phase bandpass filter. Among them, the group delay characteristic has a great influence on the high-precision navigation and positioning system. In practical navigation receivers, the group delay characteristic is generally difficult to guarantee an ideal condition of constant constant (linear phase), which will cause the signal correlation peak to be distorted, resulting in ranging deviation. Therefore, in order to easily analyze the influence of group delay on high-precision ranging and study its measurement and calibration techniques, it is necessary to perform high-precision fitting of group delay characteristics.

The common fitting methods in engineering are linear fitting and nonlinear fitting based on the least squares method. Due to the nonlinearity of the group delay characteristic, it is obvious that the linear fitting method is not suitable for the group delay characteristic. For nonlinear fitting, polynomial fitting based on the least squares method is the most commonly used fitting method, but the fitted analytical formula has no actual physical meaning. Although Fourier decomposition approximate fitting has physical meaning, in order to achieve high-precision fitting, the fitting order required is high, and the computational load is large. The disadvantage of the piecewise fitting based on the least squares method is the same as that of the polynomial fitting based on the least squares method.

Therefore, how to reduce the complexity of the fitting process of the radio frequency channel group delay characteristics of the high-precision navigation receiver under the condition of ensuring the fitting accuracy, and make the calculation amount small in the fitting process, is a technology that needs to be solved urgently in this field. It is necessary to analyze the influence of group delay on high-precision ranging and study its measurement and calibration techniques to solve this problem.

SUMMARY OF THE INVENTION

Aiming at the defects existing in the prior art, the present invention proposes a method for fitting the delay characteristics of radio frequency channels of a high-precision navigation receiver. The invention can effectively fit the delay characteristics of the radio frequency channel group of the high-precision navigation receiver, has high fitting precision, low complexity and small calculation amount.

For realizing the above-mentioned technical purpose, the concrete technical scheme that the present invention adopts is as follows:

The fitting method of the radio frequency channel group delay characteristic of the high-precision navigation receiver of the present invention utilizes the features of the analyticity of the Fourier decomposition approximate fitting and the small computation amount of the segmental decomposition to fit the measured receiver radio frequency channel. The group delay characteristic is segmented according to the segment length, the first sampling point of each segment coincides with the last sampling point of the previous segment, and the data of each segment is approximately fitted by Fourier decomposition, and finally the segment function can be obtained. Accurately fit group delay characteristics.

A method for fitting a radio frequency channel group delay characteristic of a high-precision navigation receiver, comprising:

S1. Sampling the delay characteristics of the radio frequency channel group of the high-precision navigation receiver at equal time intervals to obtain n groups of sampling points (f _i , y _i ) of the radio frequency channel group delay characteristics of the high-precision navigation receiver, i=1, 2, ..., n, where f _i represents the measured frequency of the ith sampling point, _yi represents the measured group delay value of the ith sampling point, and measures the bandwidth of the group delay characteristic.

S2. Segment the group delay characteristics obtained in the entire sampling process in S1, and intercept valid sampling points therein.

S3. Perform Fourier decomposition and fitting on the segmented data respectively to obtain a segment function, and obtain a group delay characteristic fitting value through the segment function.

In the present invention S1, the sampling vector network analyzer samples the group delay characteristic of the radio frequency channel of the high-precision navigation receiver, and measures the bandwidth of the group delay characteristic.

In S2 of the present invention, the fitting order N of the approximate fitting of the group delay Fourier decomposition is set, and the unit segment length l=2N+1, that is, each segment of segmented data includes 2N+1 group delay characteristic sampling points , to ensure that the sampling points of each segment can be covered by the fitted piecewise function. In order to ensure the coherence of the fitting function, the first sampling point of each segment of segmented data obtained by segmenting at the same time coincides with the last sampling point of the previous segment of segmented data, that is, the last sampling point of the previous segment is taken as the next segment. The starting point of the data. Assuming that the total number of segments of segmented data is P, the intercepted effective sampling points are the first L group delay characteristic sampling points of the group delay characteristic sampling points obtained in the whole sampling process, L=2PN+1. The total number of segments of segmented data is P, which is obtained by the following formula:

P=(n-(n%(2N+1)))/(2N+1).

In the present invention S3, for the segmented data of P segments, each point in each segmented data satisfies the following N-order Fourier fitting equation:

The sampling data of the j-th segment data is taken to satisfy the above equation, wherein the frequency of the sampling data of the j-th segment data is f _2jN-2N+1 ≤f _i ≤f _2jN+1 .

Then the fitting value of the radio frequency channel group delay characteristic of the high-precision navigation receiver is obtained by the following piecewise function:

where a _ji , b _ji , j=1,...,P; i=1, 2,...,N are Fourier fitting parameters of each segmented data. Inputting each segment data into the matlab fitting function can generate the Fourier fitting parameters corresponding to each segment data.

The present invention also provides a method for evaluating the fitting effect of the group delay characteristic of the navigation receiver. The group delay characteristic of the real receiver measured by the vector network analyzer adopts the group delay characteristic of the radio frequency channel of the high-precision navigation receiver. After the fitting method is fitted, the fitting effect is evaluated by the coincidence of the sampling points. The method is as follows:

Let the instrumental measurement accuracy of the vector network analyzer be t ₀ , the coincidence of the sampling points is defined as the absolute value of the difference between the actual sampling point and the fitting value at the same frequency is less than the instrumental measurement accuracy of the vector network analyzer, namely |g (f _i )-y _i |≤t ₀ points n ₀ proportion of the total sampling points:

The higher the q value, the higher the fitting accuracy of the sampling points, and the better the fitting effect.

In practical applications, the coincidence of the sampling points alone is not enough to indicate the quality of the fitting, and it is also very important for the gap fitting between the sampling points. Therefore, the present invention evaluates the fitting effect by the degree of coincidence of the sampling points and the fitting error for the gap between the sampling points. The fitting effect is evaluated by the fitting error of the gap between the sampling points, as follows:

The sampling is represented by the difference between the piecewise trapezoidal area enclosed by the sampling points of the real receiver's group delay characteristic and the piecewise trapezoidal area enclosed by the fitting points of the group delay characteristic fitting by the piecewise function. The fitting error of the gap between the points, i.e.

where n is the number of sampling points, n ₁ is the number of fitting points, Δf and Δf ₁ are the frequency step size of the sampling point and fitting point, respectively, _yi is the true group delay value of the ith sampling point, and _zi is the ith sampling point. The group delay value obtained by fitting the fitting points.

If n ₁ =n, for the piecewise function, ΔS=0, it is necessary to interpolate the fitting function between the sampling points, so that n ₁ >>n, so that the fitting error of the sampling point gap is obtained; The smaller the fitting error of the point gap, the higher the fitting accuracy of the sampling points and the better the fitting effect.

The present invention also provides a storage medium on which a computer program is stored, and when the computer program is run by a processor, the computer program executes the steps of the above-mentioned method for fitting the radio frequency channel group delay characteristic of a high-precision navigation receiver.

Further, the present invention also provides a computer system, comprising a body and an onboard circuit board arranged in the body, the onboard circuit board is provided with a processor and a memory, the memory stores a computer program, the processing When the computer executes the computer program, the above-mentioned method for fitting the radio frequency channel group delay characteristic of the high-precision navigation receiver is realized.

The present invention has the following technical effects:

The invention can fit the sampling points of the group delay characteristic without distortion, and ensures that the fitting error of the gap between the sampling points is small, and the fitting parameters have actual physical meaning. The present invention has good fitting effect, simple implementation, small computation amount and convenient implementation, and can be directly used for fitting of group delay characteristics of radio frequency channels of high-precision navigation receivers, in order to analyze the influence of group delay on high-precision ranging and study Its measurement and calibration technology provides convenience.

Description of drawings

Fig. 1 is the flow chart of the present invention;

Figure 2 shows the radio frequency channel group delay characteristics of a certain type of precision navigation receiver measured by a vector network analyzer;

Fig. 3 is the fitting effect diagram that utilizes the fitting method provided by the present invention to fit the group delay characteristic shown in Fig. 2;

FIG. 4 is a fitting effect diagram of sampling point gap obtained by the fitting method provided by the present invention.

Detailed ways

In order to make the technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

Example 1:

Referring to FIG. 1 , this embodiment provides a method for fitting a radio frequency channel group delay characteristic of a high-precision navigation receiver, including:

S1. Use a vector network analyzer to measure the radio frequency channel group delay characteristics of a high-precision navigation receiver, and measure the bandwidth.

The group delay and amplitude characteristics of the receiver signal channel are mainly determined by the RF front-end, and its amplitude and phase characteristics can be approximated to a non-linear phase band-pass filter, where the group delay characteristics are similar to a parabolic shape. Select a certain type of RF front-end module, use a vector network analyzer to sample the RF channel group delay characteristics of high-precision navigation receivers at equal time intervals, and obtain n groups of high-precision navigation receiver RF channel group delay characteristics sampling points (f _i , y _i ), i=1, 2, . . . , n, and measure the bandwidth of the group delay characteristic. Where f _i represents the measured frequency of the ith sampling point, _yi represents the measured group delay value of the ith sampling point, and n represents the number of sampling points.

S2. Segment the group delay characteristics obtained in the entire sampling process in S1, and intercept valid sampling points therein.

Set the fitting order N of the approximate fitting of the group delay Fourier decomposition, and the unit segment length l=2N+1, that is, each segment of segmented data contains 2N+1 group delay characteristic sampling points to ensure that each segment The sampling points of can be covered by the fitted piecewise function. In order to ensure the coherence of the fitting function, the first sampling point of each segment of segmented data obtained by segmenting at the same time coincides with the last sampling point of the previous segment of segmented data, that is, the last sampling point of the previous segment is taken as the next segment. The starting point of the data. Assuming that the total number of segments of segmented data is P, the intercepted effective sampling points are the first L group delay characteristic sampling points of the group delay characteristic sampling points obtained in the whole sampling process, L=2PN+1. The total number of segments of segmented data is P, which is obtained by the following formula:

P=(n-(n%(2N+1)))/(2N+1).

S3. Perform Fourier decomposition and fitting on the segmented data respectively to obtain a segment function, and obtain a group delay characteristic fitting value through the segment function.

For the segmented data of P segments, each point in each segmented data satisfies the following Nth-order Fourier fitting equation:

The sampling data of the j-th segment data is taken to satisfy the above equation, wherein the frequency of the sampling data of the j-th segment data is f _2jN-2N+1 ≤f _i ≤f _2jN+1 .

Then the fitting value of the radio frequency channel group delay characteristic of the high-precision navigation receiver is obtained by the following piecewise function:

where a _ji , b _ji , j=1,...,P; i=1, 2,...,N are Fourier fitting parameters of each segmented data. Inputting each segment data into the matlab fitting function can generate the Fourier fitting parameters corresponding to each segment data.

The fitting value of the group delay characteristic at the same frequency as the actual sampling point can be obtained through the above piecewise function.

Example 2:

This embodiment provides a method for evaluating the fitting effect of a group delay characteristic of a navigation receiver. After fitting the group delay characteristic of the real receiver measured by the vector network analyzer using the fitting method of the radio frequency channel group delay characteristic of the high-precision navigation receiver provided in Embodiment 1, the coincidence degree of the sampling points is obtained. and the fitting error of the gap between sampling points to evaluate the fitting effect.

Among them, the fitting effect is evaluated by the coincidence of the sampling points, and the method is as follows:

Let the instrumental measurement accuracy of the vector network analyzer be t ₀ , the coincidence of the sampling points is defined as the absolute value of the difference between the actual sampling point and the fitting value at the same frequency is less than the instrumental measurement accuracy of the vector network analyzer, namely |g (f _i )-y _i |≤t ₀ points n ₀ proportion of the total sampling points:

The higher the q value, the higher the fitting accuracy of the sampling points, and the better the fitting effect.

In practical applications, the coincidence of the sampling points alone is not enough to indicate the quality of the fitting, and it is also very important for the gap fitting between the sampling points. For the piecewise fitting method, although the sampling points can be accurately fitted, the gap between the sampling points of the fitting function is generally expressed as a fluctuating curve, so linear estimation cannot be performed. Therefore, the present invention evaluates the fitting effect by the degree of coincidence of the sampling points and the fitting error for the gap between the sampling points. The fitting effect is evaluated by the fitting error of the gap between the sampling points, as follows:

The sampling is represented by the difference between the piecewise trapezoidal area enclosed by the sampling points of the real receiver's group delay characteristic and the piecewise trapezoidal area enclosed by the fitting points of the group delay characteristic fitting by the piecewise function. The fitting error of the gap between the points, i.e.

where n is the number of sampling points, n ₁ is the number of fitting points, Δf and Δf ₁ are the frequency step size of the sampling point and fitting point, respectively, _yi is the true group delay value of the ith sampling point, and _zi is the ith sampling point. The group delay value obtained by fitting the fitting points.

If n ₁ =n, for the piecewise function, ΔS=0, it is necessary to interpolate the fitting function between the sampling points, so that n ₁ >>n, so that the fitting error of the sampling point gap is obtained; The smaller the fitting error of the point gap, the higher the fitting accuracy of the sampling points and the better the fitting effect.

Example 3:

S1. In this embodiment, the group delay characteristics of the radio frequency channel of a certain type of precision navigation receiver measured by a vector network analyzer are shown in Figure 2. It can be seen that the shape of the group delay characteristics is similar to a parabola, accompanied by certain fluctuations . It is sampled, and the number of sampling points is to match the length of the segment to obtain the number of segments and effective sampling points. The number of sampling points obtained in this embodiment is n=201, and B=80MHz.

S2. For the approximate fitting of Fourier decomposition, the Fourier decomposition coefficient can predict the echo amplitude of the autocorrelation function of the receiver. Generally speaking, the Fourier coefficient above the fourth order has little effect on the main peak, so In this embodiment, the Fourier fitting order of each segment is taken as N=3, then the segment length is l=7, the total number of segments is P=33, the number of valid sampling points is L=199, and the first 199 sampling points are taken. is a valid sampling point.

S3. For 33 segmented data, 33 3rd-order Fourier fitting equations can be sought, as follows:

Then the final piecewise Fourier fitting equation, that is, the piecewise function, is:

where a _ji , j=1,...,33; i=1, 2, 3 are fitting parameters.

The fitting value of the group delay characteristic at the same frequency as the actual sampling point can be obtained through the above piecewise function.

Fig. 3 is a fitting effect diagram of using the fitting method provided by the present invention to fit the group delay characteristic shown in Fig. 2; Leaf decomposition. It can be seen that the piecewise Fourier decomposition fitting can fit the sampling points without distortion. The coincidence of the sampling points is 100.00%.

FIG. 4 is a fitting effect diagram of sampling point gap obtained by the fitting method provided by the present invention. In order to make n ₁ >>n, 18 fitting points are taken from the two sampling points for the fitted piecewise function. The sampling point gap is not linearly fitted, but fluctuates to a certain extent. The sampling point gap fitting error in the example is 0.029, which is far smaller than the sampling point gap fitting error of the commonly used fitting methods in the prior art. The piecewise Fourier decomposition fitting method provided by the invention has excellent performance.

In summary, although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person of ordinary skill in the art, without departing from the spirit and scope of the present invention, can make various modifications. Therefore, the protection scope of the present invention shall be subject to the scope defined by the claims.

Claims (10)

1. A method for fitting the time delay characteristic of a radio frequency channel group of a high-precision navigation receiver is characterized by comprising the following steps:

s1, sampling the time delay characteristics of the radio frequency channel group of the high-precision navigation receiver at equal time intervals to obtain n groups of sampling points (f) of the time delay characteristics of the radio frequency channel group of the high-precision navigation receiver_i,y_i) I is 1,2, …, n, wherein f_iIndicating the measured frequency, y, of the ith sample point_iRepresenting the measured group delay value of the ith sampling point, and measuring the bandwidth of the group delay characteristic;

s2, segmenting the group delay characteristics obtained in the whole sampling process in the S1, and intercepting effective sampling points in the segmented group delay characteristics;

and S3, performing Fourier decomposition fitting on each segmented data to obtain a segmented function, and obtaining a group delay characteristic fitting value through the segmented function.

2. The method for fitting the group delay characteristics of the radio frequency channels of the high-precision navigation receiver according to claim 1, wherein the sampling vector network analyzer samples the group delay characteristics of the radio frequency channels of the high-precision navigation receiver in S1, and measures the bandwidth of the group delay characteristics.

3. The method as claimed in claim 1, wherein in S2, the fitting order N of the group delay fourier decomposition approximate fitting is set, and the unit segment length l is 2N +1, that is, each segment of data includes 2N +1 group delay characteristic sampling points, and the first sampling point of each segment of data obtained by segmentation coincides with the last sampling point of the previous segment of data.

4. The method according to claim 3, wherein in step S2, the total number of segments of segmented data is P, and the effective sampling points are obtained as the first L group delay characteristic sampling points of the group delay characteristic sampling points obtained in the whole sampling process, where L is 2PN + 1.

5. The method for fitting the group delay characteristics of the radio frequency channels of the high-precision navigation receiver according to claim 4, wherein in S2, the total number of segments of the segmented data is P, which is obtained by:

P＝(n-(n％(2N+1)))/(2N+1)。

6. the method for fitting the group delay characteristics of the radio frequency channels of the high-precision navigation receiver according to claim 5, wherein in S3, for the P-segment segmented data, each point in each segmented data satisfies the following N-th order Fourier fitting equation:

the sampling data of the j section data satisfies the equation, wherein the frequency of the sampling data of the j section data is f_2jN-2N+1≤f_i≤f_2jN+1；

Then, the fitting value of the group delay characteristic of the radio frequency channel of the high-precision navigation receiver is obtained by the following piecewise function:

wherein a is_ji,b_ji,j＝1, 1.. P; n is a fourier fitting parameter for each segmented data.

7. A method for evaluating the fitting effect of the group delay characteristic of a navigation receiver is characterized in that the group delay characteristic of a real receiver measured by a vector network analyzer is fitted by the fitting method of the group delay characteristic of the radio frequency channel of the high-precision navigation receiver as claimed in any one of claims 1 to 6, and the fitting effect is evaluated by the contact ratio of sampling points, and the method comprises the following steps:

let the instrument measurement accuracy of the vector network analyzer be t₀The contact ratio of the sampling points is defined as the absolute value of the difference between the actual sampling points and the fitting value under the same frequency is less than the instrument measurement accuracy of the vector network analyzer, namely | g (f)_i)-y_i|≤t₀Number of points n₀Ratio of total sampling points:

the higher the q value, the higher the fitting accuracy of the sampling point, and the better the fitting effect.

8. The method of claim 7, wherein the fitting effect is further evaluated by a fitting error of gaps between sampling points, and the method comprises:

the fitting error of the gap between sampling points is expressed by the difference between the sectional trapezoidal area surrounded by the sampling points of the real receiver group delay characteristic and the sectional trapezoidal area surrounded by the fitting points for performing group delay characteristic fitting through the sectional function, that is to say

Where n is the number of sampling points, n₁To fit the number of points,. DELTA.f₁Respectively, at a sampling point andfrequency step of fitting point, y_iIs the true group delay value, z, of the ith sample point_iFitting the ith fitting point to obtain a group delay value;

if n is₁For a piecewise function, Δ S is 0, the fitting function interpolation needs to be done at frequencies between sample points so that n is₁> n, thus obtaining the fitting error of the sampling point gap; the smaller the fitting error of the sampling point gap is, the higher the fitting accuracy of the sampling point is, and the better the fitting effect is.

9. A storage medium having a computer program stored thereon, characterized in that: the computer program, when executed by a processor, performs the steps of the method for fitting a group delay characteristic of a radio frequency channel of a high precision navigation receiver as claimed in any one of claims 1 to 6.

10. A computer system comprises a machine body and an airborne circuit board arranged in the machine body, wherein a processor and a memory are arranged on the airborne circuit board, and a computer program is stored in the memory, and the computer system is characterized in that: the processor, when executing the computer program, implements the steps of the method for fitting a group delay characteristic of a radio frequency channel of a high precision navigation receiver as claimed in any one of claims 1 to 6.

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