CN111580137B - Fitting method for high-precision navigation receiver radio frequency channel group delay characteristics - Google Patents
Fitting method for high-precision navigation receiver radio frequency channel group delay characteristics Download PDFInfo
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Abstract
The invention provides a fitting method for the group delay characteristic of a radio frequency channel of a high-precision navigation receiver. The measured group delay characteristic of the radio frequency channel of the receiver is segmented according to the segment length by utilizing the characteristics of resolvability of approximate fitting of Fourier decomposition and small operation amount of segmented decomposition, the first sampling point of each segment is superposed with the last sampling point of the previous segment, the approximate fitting of Fourier decomposition is respectively carried out on each segment data, and finally the group delay characteristic can be accurately fitted by obtaining a segmented function. The method can effectively fit the time delay characteristic of the radio frequency channel group of the high-precision navigation receiver, and has the advantages of high fitting precision, low complexity and small calculated amount.
Description
Technical Field
The invention belongs to the technical field of satellite navigation, and particularly relates to a high-precision navigation receiver radio frequency channel group delay characteristic fitting method and a fitting effect evaluation method thereof.
Background
The high-precision navigation receiver is widely distributed and applied to a ground section, a space section and a control section of a satellite navigation system, is a core measuring device for the satellite navigation system to finish important system services such as satellite-ground time synchronization, satellite precision orbit determination and the like, and is a basis for guaranteeing the service performance of the navigation system. The group delay and amplitude characteristics of the receiver signal channel are mainly determined by the radio frequency front end, and the amplitude-phase characteristics of the receiver signal channel can be similar to a band-pass filter with a nonlinear phase. Wherein the group delay characteristic has a large influence on the high-precision navigation and positioning system. In an actual navigation receiver, the group delay characteristic is generally difficult to guarantee to be an ideal condition of constant (linear phase), and at this time, a signal correlation peak is distorted, so that a ranging deviation is generated. Therefore, in order to analyze the influence of the group delay on the high-precision ranging and study the measurement and calibration technology thereof, it is necessary to have a high-precision fit of the group delay characteristics.
The common fitting methods in engineering are linear fitting and nonlinear fitting based on the least square method. Due to the non-linearity of the group delay characteristic, it is clear that the linear fitting method is not suitable for the group delay characteristic. For nonlinear fitting, least squares based polynomial fitting is the most common fitting method, but the fitted analytical expression has no practical physical significance. Although the Fourier decomposition approximate fitting has physical significance, the fitting order required for achieving high-precision fitting is high, and the calculation amount is large. The disadvantage of the piecewise fitting based on the least square method is the same as the polynomial fitting based on the least square method.
Therefore, how to reduce the complexity of the fitting process of the group delay characteristics of the radio frequency channels of the high-precision navigation receiver and make the calculation amount in the fitting process small under the condition of ensuring the fitting precision is a technical problem to be solved urgently in the field, and the solution of the problem is necessary for analyzing the influence of the group delay on the high-precision distance measurement and researching the measurement and calibration technology thereof.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a fitting method for the group delay characteristic of a radio frequency channel of a high-precision navigation receiver. The method can effectively fit the time delay characteristic of the radio frequency channel group of the high-precision navigation receiver, and has the advantages of high fitting precision, low complexity and small calculated amount.
In order to achieve the technical purpose, the invention adopts the following specific technical scheme:
the method for fitting the group delay characteristics of the radio frequency channels of the high-precision navigation receiver comprises the steps of utilizing the characteristics of resolvability of approximate fitting of Fourier decomposition and small operation amount of segmentation decomposition to segment the measured group delay characteristics of the radio frequency channels of the receiver according to the segment length, enabling a first sampling point of each segment to coincide with a last sampling point of the previous segment, respectively carrying out approximate fitting of Fourier decomposition on each segment, and finally obtaining a segment function to accurately fit the group delay characteristics.
A fitting method for the time delay characteristics of a radio frequency channel group of a high-precision navigation receiver comprises 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 receiveri，yi) 1,2, n, wherein fiIndicating the measured frequency, y, of the ith sample pointiAnd expressing the measured group delay value of the ith sampling point, and measuring the bandwidth of the group delay characteristic.
And 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.
In the 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, a fitting order N of the group delay fourier decomposition approximate fitting is set, and a unit segment length l is 2N +1, that is, each segment of segment data includes 2N +1 group delay characteristic sampling points, so as to ensure that each segment of sampling points can be covered by the fitted segment function. In order to ensure the consistency of the fitting function, the first sampling point of each segment of data obtained by segmentation is coincided with the last sampling point of the previous segment of data, namely the last sampling point of the previous segment is taken as the starting point of the next segment of data. And if the total segment number of the segmented data after the segmentation is P, intercepting effective sampling points as the first L group delay characteristic sampling points of the group delay characteristic sampling points obtained in the whole sampling process, wherein L is 2PN + 1. Wherein the total number of segments of the segmented data is P is given by:
P＝(n-(n％(2N+1)))/(2N+1)。
in S3 of the present invention, for 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 f2jN-2N+1≤fi≤f2jN+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 isji，bjiJ 1.. P; n is a fourier fitting parameter for each segmented data. And inputting each piece of segmented data into the matlab fitting function to generate the Fourier fitting parameter corresponding to each piece of segmented data.
The invention also provides an evaluation method of the group delay characteristic fitting effect of the navigation receiver, which is used for evaluating the fitting effect through the contact ratio of sampling points after fitting the group delay characteristic of the real receiver measured by the vector network analyzer by adopting the fitting method of the group delay characteristic of the radio frequency channel of the high-precision navigation receiver, 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)-yi|≤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.
In practical application, the contact ratio of a single sampling point is not enough to indicate the goodness of the fitting, and the fitting is also very important for the gap between the sampling points. Therefore, the fitting effect is evaluated through the contact ratio of the sampling points and the fitting error of gaps among the sampling points. The fitting effect is evaluated through the fitting error of the gaps among the sampling points, and the method comprises the following steps:
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.f1Frequency step length, y, of the sampling point and the fitting point, respectivelyiIs the true group delay value, z, of the ith sample pointiAnd fitting 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.
The present invention also provides a storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the above-described method for fitting a group delay characteristic of radio frequency channels of a high precision navigation receiver.
The invention further provides a computer system, which comprises a machine body and an onboard circuit board arranged in the machine body, wherein a processor and a memory are arranged on the onboard circuit board, the memory stores a computer program, and the processor executes the computer program to realize the step of the fitting method of the group delay characteristic of the radio frequency channel of the high-precision navigation receiver.
The invention has the following technical effects:
the invention can fit sampling points with group delay characteristics without distortion, ensures that the gap fitting error of the sampling points is smaller, and the fitting parameters have practical physical significance. The method has the advantages of good fitting effect, simple realization, small calculation amount and convenient implementation, can be directly used for fitting the group delay characteristic of the radio frequency channel of the high-precision navigation receiver, and provides convenience for analyzing the influence of the group delay on high-precision distance measurement and researching the measurement and calibration technology of the high-precision navigation receiver.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a time delay characteristic of a radio frequency channel group of a navigation receiver with a certain type precision measured by a vector network analyzer;
fig. 3 is a diagram of the fitting effect of fitting the group delay characteristics shown in fig. 2 by using the fitting method provided by the present invention;
fig. 4 is a sampling point gap fitting effect graph obtained by the fitting method provided by the invention.
Detailed Description
In order to make the technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1:
referring to fig. 1, the present embodiment provides a method for fitting a group delay characteristic of a radio frequency channel of a high-precision navigation receiver, including:
s1, measuring the time delay characteristic of a radio frequency channel group of a high-precision navigation receiver by using a vector network analyzer, and measuring the bandwidth.
Group delay of receiver signal pathAnd the amplitude and phase characteristics of the radio frequency front end are mainly determined by the radio frequency front end, the amplitude and phase characteristics of the radio frequency front end can be similar to a band-pass filter with a nonlinear phase, and the group delay characteristics are similar to a parabola shape. Selecting a certain type of radio frequency front end module, adopting a vector network analyzer to sample the radio frequency channel group delay characteristic of the high-precision navigation receiver at equal time intervals, and obtaining n groups of high-precision navigation receiver radio frequency channel group delay characteristic sampling points (f)i，yi) I 1, 2.. times.n, and measuring the bandwidth of the group delay characteristic. Wherein f isiIndicating the measured frequency, y, of the ith sample pointiAnd the measured group delay value of the ith sampling point is shown, and n represents the number of the sampling points.
And 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.
The fitting order N of the group delay Fourier decomposition approximate fitting is set, the unit segment length l is 2N +1, namely each segment of segment data contains 2N +1 sampling points of the group delay characteristic, so that the sampling points of each segment can be covered by the fitted segment function. In order to ensure the consistency of the fitting function, the first sampling point of each segment of data obtained by segmentation is coincided with the last sampling point of the previous segment of data, namely the last sampling point of the previous segment is taken as the starting point of the next segment of data. And if the total segment number of the segmented data after the segmentation is P, intercepting effective sampling points as the first L group delay characteristic sampling points of the group delay characteristic sampling points obtained in the whole sampling process, wherein L is 2PN + 1. Wherein the total number of segments of the segmented data is P is given by:
P＝(n-(n％(2N+1)))/(2N+1)。
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.
For P sections of 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 f2jN-2N+1≤fi≤f2jN+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 isji，bjiJ 1.. P; n is a fourier fitting parameter for each segmented data. And inputting each piece of segmented data into the matlab fitting function to generate the Fourier fitting parameter corresponding to each piece of segmented data.
And obtaining a group delay characteristic fitting value under the same frequency with the actual sampling point through the piecewise function.
Example 2:
the embodiment provides an evaluation method for a group delay characteristic fitting effect of a navigation receiver. After the group delay characteristic of the real receiver measured by the vector network analyzer is fitted by using the fitting method of the group delay characteristic of the radio frequency channel of the high-precision navigation receiver provided in embodiment 1, the fitting effect is evaluated by the contact ratio of the sampling points and the fitting error of the gaps between the sampling points.
The fitting effect is evaluated through the contact ratio of the 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)-yi|≤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.
In practical application, the contact ratio of a single sampling point is not enough to indicate the goodness of the fitting, and the fitting is also very important for the gap between the sampling points. For the piecewise fitting method, although it is possible to fit accurately for the sampling points, the gaps of the fitting function between the sampling points are generally expressed as a fluctuating curve, and thus linear estimation cannot be performed. Therefore, the fitting effect is evaluated through the contact ratio of the sampling points and the fitting error of gaps among the sampling points. The fitting effect is evaluated through the fitting error of the gaps among the sampling points, and the method comprises the following steps:
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.f1Frequency step length, y, of the sampling point and the fitting point, respectivelyiIs the true group delay value, z, of the ith sample pointiAnd fitting 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.
Example 3:
s1, in the embodiment, the group delay characteristic of the radio frequency channel of the navigation receiver with certain model precision measured by using a vector network analyzer is shown in fig. 2, and it can be seen that the shape of the group delay characteristic is similar to a parabola and is accompanied with certain fluctuation. Sampling is carried out on the sampling points, and the number of the sampling points is used for obtaining the number of the segments and effective sampling points according to the length of the segments. The number of sampling points n obtained in this example is 201, and B is 80 MHz.
S2, for fourier decomposition approximate fitting, the fourier decomposition coefficients may predict the echo amplitude of the receiver autocorrelation function, and generally, the fourier coefficients of more than four orders have little influence on the main peak, so that in this embodiment, if the fourier fitting order of each segment is N ═ 3, the segment length L is 7, the total number of segments P is 33, the number of effective sampling points is L ═ 199, and the first 199 sampling points are taken as effective sampling points.
S3, for 33 pieces of segmented data, 33 Fourier fitting equations of 3 orders can be sought, as follows:
the final piecewise fourier fit equation, i.e., the piecewise function, is:
wherein a isjiJ 1.., 33; i is 1,2 and 3 are fitting parameters.
And obtaining a group delay characteristic fitting value under the same frequency with the actual sampling point through the piecewise function.
Fig. 3 is a diagram of the fitting effect of fitting the group delay characteristics shown in fig. 2 by using the fitting method provided by the present invention; the group delay characteristics are shifted to be symmetric about zero frequency prior to fitting to facilitate fourier decomposition. It can be seen that the piecewise fourier decomposition fit can fit the sample points without distortion. The contact ratio of the sampling points was 100.00%.
Fig. 4 is a sampling point gap fitting effect graph obtained by the fitting method provided by the invention. To make n be1> n, the fitted piecewise function is taken 18 fitting points from two sampling points, in order to better observe the difference between the two sampling points, 2 sampling points are enlarged locally, it can be seen that the sampling point gap is not linear fitting, but has oneThe fixed fluctuation is that 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 common fitting method in the prior art, and the performance of the segmented Fourier decomposition fitting method provided by the invention is excellent.
In summary, although the present invention has been described with reference to the preferred embodiments, it should be understood that various changes and modifications can be made by those skilled in the art without departing from the spirit and scope of the invention.
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 receiveri,yi) I is 1,2, …, n, wherein fiIndicating the measured frequency, y, of the ith sample pointiRepresenting 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 f2jN-2N+1≤fi≤f2jN+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 isji,bji,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)-yi|≤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, yiIs the true group delay value, z, of the ith sample pointiFitting 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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| CN113253310B (en) * | 2021-06-28 | 2021-10-08 | 中国人民解放军国防科技大学 | Method and system for measuring group delay of high-precision GNSS receiver of carrier phase |
| CN113447962B (en) * | 2021-09-01 | 2021-11-12 | 中国人民解放军国防科技大学 | Method and system for analyzing influence of time delay characteristics of navigation channel group on ranging performance |
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