阅读说明：本技术 一种用于改善卫星双差伪距定位精度的方法 (Method for improving satellite double-difference pseudo range positioning accuracy ) 是由 曲春凯 周胜洪 陈晓智 王雪松 王翀 张玉国 姜陶然 高航 林治浩 曹睿 李振 于 2021-10-15 设计创作，主要内容包括：本发明公开了一种用于改善卫星双差伪距定位精度的方法包含以下步骤：建立伪距观测方程,建立单差伪距观测方程,建立双差伪距观测方程,计算双差伪距测量值,计算双差伪距测量值残差,对残差进行零相位Kaiser窗滤波,利用滤波后的双差伪距测量值求解基线向量。本方法利用双差伪距测量值来消除卫星钟差、大气时延和接收机钟差,又利用零相位Kaiser窗滤波压制热噪声,从而提高双差伪距定位精度。零相位Kaiser窗滤波器能够灵活设置滤波器参数,包括滤波器的截断频率、滤波器节数、滤波器衰减,可以有效滤除噪声成分,而且不会引入相位误差。(The invention discloses a method for improving satellite double-difference pseudorange positioning accuracy, which comprises the following steps: establishing a pseudo-range observation equation, establishing a single-difference pseudo-range observation equation, establishing a double-difference pseudo-range observation equation, calculating double-difference pseudo-range measurement values, calculating double-difference pseudo-range measurement value residual errors, performing zero-phase Kaiser window filtering on the residual errors, and solving a baseline vector by using the filtered double-difference pseudo-range measurement values. The method utilizes the double-difference pseudorange measurement value to eliminate the satellite clock error, the atmospheric time delay and the receiver clock error, and utilizes the zero-phase Kaiser window to filter and suppress the thermal noise, thereby improving the double-difference pseudorange positioning accuracy. The zero-phase Kaiser window filter can flexibly set filter parameters including the cut-off frequency of the filter, the pitch number of the filter and the attenuation of the filter, can effectively filter noise components, and can not introduce phase errors.)

1. A method for improving satellite double-differenced pseudorange positioning accuracy, comprising the steps of:

s1, establishing a pseudo-range observation equation:

wherein the content of the first and second substances,

: satellite i to base stationPseudorange measurement for receiver r, unit: rice;

: pseudorange calculation for satellite i to base station receiver r, in units: rice;

c: speed of light, unit: m/s;

: clock error of base station receiver r, unit: second;

: clock error of satellite i, unit: second;

: ionospheric delay from satellite i to base station receiver r, unit: rice;

: tropospheric delay from satellite i to base station receiver r, unit: rice;

: pseudorange measurement noise from satellite i to base station receiver r, in units: rice;

s2, establishing a single difference observation equation:

wherein the content of the first and second substances,

: single differenced pseudorange measurements for satellite i by base station receiver r and user receiver u, in units: rice;

: pseudorange measurements from satellite i to user receiver u, in units: rice;

: the unit of the difference between the single difference pseudo range calculation value of the base station receiver r to the satellite i and the single difference pseudo range calculation value of the user receiver u to the satellite i is: rice;

: the difference between the clock difference of the base station receiver r and the clock difference of the user receiver u, unit: second;

: difference between pseudorange measurement noise from satellite i to base receiver r and pseudorange measurement noise from satellite i to user receiver u, in units: rice;

s3, establishing a double-difference pseudorange observation equation:

wherein the content of the first and second substances,

: double difference pseudorange measurements for satellites i and j by base station receiver r and user receiver u, in units: rice;

: single differenced pseudorange measurements for satellite j by base station receiver r and user receiver u, in units: rice;

：anda difference of (d);the unit of the difference between the single difference pseudo range calculation value of the base station receiver r to the satellite j and the single difference pseudo range calculation value of the user receiver u to the satellite i is: rice;

：andthe difference value of (a) to (b),the difference between the pseudorange measurement noise from satellite j to the base receiver r and the pseudorange measurement noise from satellite j to the user receiver u is given by: rice;

: a unit vector of a base station receiver r to the observation direction of a satellite i;

: a unit vector of a base station receiver r to a satellite j observation direction;

for baseline vectors from user receiver u to base receiver r；

S4, calculating the residual error of the double-difference pseudorange measurement value:

: a double-difference pseudo range fitting value is obtained by performing high-order fitting on a double-difference pseudo range measured value;

s5, designing a Kaiser window low-pass filter:

the low pass filter designed using the Kaiser window as the window function is:

wherein the content of the first and second substances,is the impulse response of an ideal digital low-pass filter;is a Kaiser window function;

s6, performing zero-phase filtering on the residual error given in the S4 to obtain a filtered double-difference pseudorange measurement value:

wherein the content of the first and second substances,

: filtering the double difference pseudorange measurement;

: filtering out the double-difference pseudorange measurement residual errors after noise filtering;

s7, constructing a double-difference observation equation set by using the filtered double-difference pseudo-range measured values and solving a baseline vector。

2. The method for improving satellite double-differenced pseudorange positioning accuracy of claim 1, wherein impulse response of ideal digital low pass filterThe following formula is satisfied:

wherein the content of the first and second substances,is the normalized cut-off frequency of the filter,is the filter window length.

3. The method of claim 1, wherein said Kaiser window function is a function of a single pseudorange to a single pseudorangeThe following formula is satisfied:

wherein the content of the first and second substances,a first type of modified zero order Bessel function;is an adjustable parameter.

4. The method of claim 1, wherein the zero-phase filtering in step S6 is performed by FRR method.

5. The method of claim 4, wherein the FRR-method-filtered time-domain description is represented by:

wherein, N is the sequence length,；representing input sequences, i.e. double-differenced pseudorange measurement residuals；Representing the result after filtering or sequence inversion,for double-differenced pseudorange measurement residuals after filtering noise, i.e.。

6. The method of claim 1, wherein the constructing of the double-difference observation equation set in step S7 comprises:

if the base station receiver r and the user receiver u have pseudo-range measurements for M satellites, then M-1 mutually independent double-differenced pseudo-range observation equations may form a matrix equation as follows:

=

in the formula (I), the compound is shown in the specification,the remaining residual is.

7. The method of claim 1, wherein the baseline vector is used to improve accuracy of double-differenced pseudorange positioningThe solution is performed by the least square method.

Technical Field

The invention relates to the field of communication satellite navigation and testing, in particular to a method for improving satellite double-difference pseudorange positioning accuracy.

Background

During differential positioning, there are three types of errors in the pseudorange measurements. The first is satellite-related errors, such as satellite clock error, ephemeris error. The second is propagation-related delay errors that are difficult to correct by the model, such as ionospheric delay, tropospheric delay. The third is the error inherent to various devices, such as thermal noise of satellite transmitters and receivers, etc. The first error can be completely eliminated by differential positioning, the second error can be eliminated by most of the differential positioning, the second error is mainly determined by the positions of a user receiver and a base station, and the third error is difficult to eliminate by the differential positioning and can only be weakened by a filtering noise reduction technology.

Noise is a random signal whose spectrum is spread over the radio frequency range and is one of the main factors affecting the performance of various types of receivers. The noise may be classified into thermal noise, shot noise, and flicker noise. Thermal noise is white noise that is very common in electronic devices and is also a noise component that the present technique considers to cancel. Thermal noise in satellite communication equipment originates mainly from the receiver and the satellite transmitter.

Double-differenced pseudorange location algorithms may remove most of the error but have no effect on thermal noise. The double-difference pseudo range observation quantity containing thermal noise can influence the precision of differential positioning, and simple filtering can introduce phase errors and can also influence the precision of differential positioning.

In summary, it is necessary to design a method for improving the double-differenced pseudorange positioning accuracy of a satellite to solve the problem of poor thermal noise cancellation effect in the prior art.

Disclosure of Invention

In order to solve the problems in the prior art, the invention provides a method for improving the satellite double-difference pseudorange positioning accuracy, which can flexibly set filter parameters including the cutoff frequency of a filter, the number of filter nodes and the attenuation of the filter, can effectively filter noise components and does not introduce a phase error.

In order to achieve the purpose, the invention adopts the following technical scheme:

a method for improving satellite double-differenced pseudorange positioning accuracy, comprising the steps of:

s1, establishing a pseudo-range observation equation:

wherein the content of the first and second substances,

: pseudorange measurements from satellite i to base station receiver r, in units: rice;

: pseudorange calculation for satellite i to base station receiver r, in units: rice;

c: speed of light, unit: m/s;

: clock error of base station receiver r, unit: second;

: clock error of satellite i, unit: second;

: ionospheric delay from satellite i to base station receiver r, unit: rice;

: tropospheric delay from satellite i to base station receiver r, unit: rice;

: pseudorange measurement noise from satellite i to base station receiver r, in units: rice;

s2, establishing a single difference observation equation:

wherein the content of the first and second substances,

: single differenced pseudorange measurements for satellite i by base station receiver r and user receiver u, in units: rice;

: pseudorange measurements from satellite i to user receiver uBit: rice;

: the unit of the difference between the single difference pseudo range calculation value of the base station receiver r to the satellite i and the single difference pseudo range calculation value of the user receiver u to the satellite i is: rice;

: the difference between the clock difference of the base station receiver r and the clock difference of the user receiver u, unit: second;

: difference between pseudorange measurement noise from satellite i to base receiver r and pseudorange measurement noise from satellite i to user receiver u, in units: rice;

s3, establishing a double-difference pseudorange observation equation:

wherein the content of the first and second substances,

: double difference pseudorange measurements for satellites i and j by base station receiver r and user receiver u, in units: rice;

: single differenced pseudorange measurements for satellite j by base station receiver r and user receiver u, in units: rice;

：anda difference of (d);the unit of the difference between the single difference pseudo range calculation value of the base station receiver r to the satellite j and the single difference pseudo range calculation value of the user receiver u to the satellite i is: rice;

：andthe difference value of (a) to (b),the difference between the pseudorange measurement noise from satellite j to the base receiver r and the pseudorange measurement noise from satellite j to the user receiver u is given by: rice;

: a unit vector of a base station receiver r to the observation direction of a satellite i;

: a unit vector of a base station receiver r to a satellite j observation direction;

for baseline vectors from user receiver u to base receiver r；

S4, calculating the residual error of the double-difference pseudorange measurement value:

: a double-difference pseudo range fitting value is obtained by performing high-order fitting on a double-difference pseudo range measured value;

s5, designing a Kaiser window low-pass filter:

the low pass filter designed using the Kaiser window as the window function is:

wherein the content of the first and second substances,is the impulse response of an ideal digital low-pass filter;is a Kaiser window function;

s6, performing zero-phase filtering on the residual error given in the S4 to obtain a filtered double-difference pseudorange measurement value:

wherein the content of the first and second substances,

: filtering the double difference pseudorange measurement;

: filtering out the double-difference pseudorange measurement residual errors after noise filtering;

s7, constructing a double-difference observation equation set by using the filtered double-difference pseudo-range measured values and solving a baseline vector。

In some embodiments of the invention, the impulse response of the ideal digital low-pass filterThe following formula is satisfied:

wherein the content of the first and second substances,is the normalized cut-off frequency of the filter,is the filter window length.

In some embodiments of the invention, the Kaiser window functionThe following formula is satisfied:

wherein the content of the first and second substances,a first type of modified zero order Bessel function;is an adjustable parameter.

In some embodiments of the present invention, the zero-phase filtering in step S6 is performed by using an FRR method.

In some embodiments of the present invention, the time-domain description filtered by the FRR method may be expressed as:

wherein, N is the sequence length,；representing input sequences, i.e. double-differenced pseudorange measurement residuals；Representing the result after filtering or sequence inversion,for double-differenced pseudorange measurement residuals after filtering noise, i.e.。

In some embodiments of the present invention, the step of constructing the double-difference observation equation set in step S7 is:

if the base station receiver r and the user receiver u have pseudo-range measurements for M satellites, then M-1 mutually independent double-differenced pseudo-range observation equations may form a matrix equation as follows:

=

in the formula (I), the compound is shown in the specification,the remaining residual is.

In some embodiments of the invention, the baseline vectorThe solution is performed by the least square method.

Compared with the prior art, the technical scheme of the invention has the following technical effects:

the method utilizes the double-difference pseudorange measurement value to eliminate the satellite clock error, the atmospheric time delay and the receiver clock error, and utilizes the zero-phase Kaiser window to filter and suppress the thermal noise, thereby improving the double-difference pseudorange positioning accuracy. The zero-phase Kaiser window filter can flexibly set filter parameters including the cut-off frequency of the filter, the pitch number of the filter and the attenuation of the filter, can effectively filter noise components, and can not introduce phase errors.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.

Fig. 1 is a diagram illustrating calculation of the double-differenced pseudorange measurements.

Fig. 2 is a diagram showing the actual amplitude characteristic of the low-pass filter.

FIG. 3 is a schematic view of the shape of the Kaiser window for different values of α.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

In the description of the present invention, it should be noted that the terms "mounted," "connected," and "connected" are to be construed broadly and may be, for example, fixedly connected, detachably connected, or integrally connected unless otherwise explicitly stated or limited. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art. In the foregoing description of embodiments, the particular features, structures, materials, or characteristics may be combined in any suitable manner in any one or more embodiments or examples.

In the process of propagation, Beidou satellite signals are affected by factors such as an ionosphere, a troposphere, a broadcast ephemeris error, a satellite clock error, tides and a relativistic effect, so that the positioning accuracy errors are larger, but the errors are closely related to 2 geographically adjacent Beidou receivers, so that most of the errors can be cancelled out by establishing a differential equation to obtain a relatively accurate baseline azimuth solution, but the cost is that the double-difference pseudorange measurement value noise is increased. The invention can effectively eliminate the noise of the double-difference pseudo-range measured value by a zero-phase Kaiser window filtering mode.

The method specifically comprises the following steps:

a method for improving satellite double-differenced pseudorange positioning accuracy, comprising the steps of:

s1, establishing a pseudo-range observation equation:

wherein the content of the first and second substances,

: pseudorange measurements from satellite i to base station receiver r, in units: rice;

: pseudorange calculation for satellite i to base station receiver r, in units: rice;

c: speed of light, unit: m/s;

: clock error of base station receiver r, unit: second;

: clock error of satellite i, unit: second;

: ionospheric delay from satellite i to base station receiver r, unit: rice;

: tropospheric delay from satellite i to base station receiver r, unit: rice;

: pseudorange measurement noise from satellite i to base station receiver r, in units: rice;

s2, establishing a single difference observation equation:

single differencing is the first difference between the receivers to the same satellite measurement, and single differencing pseudo-range measurements of the base receiver r and the user receiver u to the satellite iThe definition and observation equation of (a) is as follows:

wherein the content of the first and second substances,

: single differenced pseudorange measurements for satellite i by base station receiver r and user receiver u, in units: rice;

: pseudorange measurements from satellite i to user receiver u, in units: rice;

: the unit of the difference between the single difference pseudo range calculation value of the base station receiver r to the satellite i and the single difference pseudo range calculation value of the user receiver u to the satellite i is: rice;

: the difference between the clock difference of the base station receiver r and the clock difference of the user receiver u, unit: second;

: difference between pseudorange measurement noise from satellite i to base receiver r and pseudorange measurement noise from satellite i to user receiver u, in units: rice;

s3, establishing a double-difference pseudorange observation equation:

the double difference is the difference between the single differences of two different satellites, i.e. the difference is obtained between the stations and between the satellites. Double differenced pseudorange measurements to satellites i and j by base receiver r and user receiver uThe definition and observation equation of (1) are:

wherein the content of the first and second substances,

: double difference pseudorange measurements for satellites i and j by base station receiver r and user receiver u, in units: rice;

: single differenced pseudorange measurements for satellite j by base station receiver r and user receiver u, in units: rice;

：anda difference of (d);the unit of the difference between the single difference pseudo range calculation value of the base station receiver r to the satellite j and the single difference pseudo range calculation value of the user receiver u to the satellite i is: rice;

：andthe difference value of (a) to (b),the difference between the pseudorange measurement noise from satellite j to the base receiver r and the pseudorange measurement noise from satellite j to the user receiver u is given by: rice and its production process；

: a unit vector of a base station receiver r to the observation direction of a satellite i;

: a unit vector of a base station receiver r to a satellite j observation direction;

for baseline vectors from user receiver u to base receiver r；

Fig. 1 is a schematic diagram of double-difference pseudorange measurement values, in which a user receiver u and a base station receiver r observe a satellite i and a satellite j respectively, and the pseudoranges thereof are used to form double-difference pseudorange observations.Where is the baseline vector of user receiver u to base receiver r,is the pseudorange measurement from satellite i to receiver r,is a unit vector of the direction of observation of satellite i by the base station receiver,the pseudoranges are computed for the base receiver r and the user receiver u for satellite i.

S4, calculating the residual error of the double-difference pseudorange measurement value:

performing high-order fitting on the double-difference pseudo range measured value to obtain a double-difference pseudo range fitted valueAnd with double differenced pseudorange measurementsAnd (3) carrying out difference to obtain a double-difference pseudorange measurement value residual error:

s5, designing a Kaiser window low-pass filter:

the low pass filter designed using the Kaiser window as the window function is:

wherein the content of the first and second substances,is the impulse response of an ideal digital low-pass filter;is a Kaiser window function;

with respect to filters, transfer functions of filtersCan be expressed in polar coordinates as:

in the formula (I), the compound is shown in the specification,、referred to as the amplitude response and the phase response of the filter, respectively, expressed as:

where Re () is the real part of the function, Im () is the imaginary part of the function, j is the imaginary unit, and ω is the digital frequency.

According to the amplitude response of the filter, the filter can be divided into four types of filters, namely a low-pass filter, a high-pass filter, a pass band filter and a stop band filter, when the filter is actually designed, the filter is allowed to have certain deviation from an ideal state in the pass band and the stop band filter according to actual filtering requirements, and a transition band is allowed between the pass band and the stop band filter. Taking a low-pass filter as an example, the actual amplitude-frequency characteristic of the filter is shown in fig. 2. The abscissa is angular frequency and the ordinate is amplitude.、Referred to as passband ripple and stopband ripple, respectively;、referred to as passband cutoff frequency and stopband cutoff frequency, respectively;referred to as the transition zone. The frequency components in the stop band are regarded as harmful components, the amplitude of the frequency components after filtering is obviously suppressed, the frequency components in the pass band are regarded as useful components, and the amplitude of the frequency components after filtering is not influenced, so that the aim of filtering the harmful components is fulfilled.

When designing a filter, the amplitude characteristics are generally determined by the attenuation given to the pass band and stop band, and the attenuation a (ω) is generally determined by the magnitude square function or modulo square function reflecting the power gainTo define, namely:

so pass band attenuationAnd stopband attenuationCan be expressed as:

the invention needs a low-pass filter to filter out the high-frequency thermal noise in the original signal, and improves the signal-to-noise ratio of the signal, so as to improve the double-difference positioning resolving precision. Considering that the FIR digital filter can have strict linear phase and can adopt fast Fourier transform when realizing filtering, the invention designs a low-pass FIR digital filter by using a window function method. The Kaiser window has adjustability.

The Kaiser window functionThe following formula is satisfied:

wherein the content of the first and second substances,a first type of modified zero order Bessel function;the following number of stages can be used for calculation:

is a tunable parameter, and is related to the main lobe width and the side lobe attenuation. In general terms, the amount of the solvent to be used,the larger the transition band, the wider the stop band, and the greater the attenuation.

FIG. 3 is the shape of a Kaiser window; if the stopband minimum attenuation is expressed asThen, thenThe following empirical formula may be used for the determination of (c):

if the filter passband and stopband ripple are equal, i.e.Then the number of filter sections N can be determined by:

the most basic parameter of the Kaiser low-pass filter is the cut-off frequencyFilter number N and Kaiser window parameter alpha. But in the actual design of the filter,the Kaiser window parameter alpha is not intuitive enough and filter attenuation is usually chosen，And α can be converted by a formula.

And the double-difference pseudo-range measurement value is filtered by using a zero-phase Kaiser window low-pass filter and then subjected to double-difference positioning calculation, so that the settlement precision of the baseline vector from the user receiver to the base station receiver can be greatly improved.

Impulse response of the ideal digital low-pass filterThe following formula is satisfied:

wherein the content of the first and second substances,is the normalized cut-off frequency of the filter,is the filter window length.

S6, performing zero-phase filtering on the residual error given in the S4 to obtain a filtered double-difference pseudorange measurement value:

wherein the content of the first and second substances,

: filtering the double difference pseudorange measurement;: filtering out the double-difference pseudorange measurement residual errors after noise filtering;

regarding zero phase filtering, after a signal passes through a filter system, the amplitude of each frequency component of the signal is multiplied by the mode of the amplitude response of the system, so that the effect of changing the energy of different frequency components of the signal is achieved, and the effect of filtering noise is achieved. The filter system adds a phase to the original signal phase while changing the amplitude-frequency property of the signal, which is called the phase shift of the system. If such a change in phase is not desired, it can cause phase distortion and affect data quality.

When double difference pseudo-range measurement data are filtered, the phase is not expected to change, and the zero-phase filter has the characteristic of a zero-phase system, so that accurate zero-phase distortion signals can be obtained. The FRR method can be adopted for realizing the zero-phase filtering, firstly, the input sequence is filtered in sequence (forward filter), then, the obtained result is reversed and then passes through a filter (reverse filter), and then, the obtained result is reversed and output (reverse output), and the output sequence with accurate zero-phase distortion is obtained.

The time-domain description of the FRR method filtering can be expressed as:

wherein, N is the sequence length,；representing input sequences, i.e. double-differenced pseudorange measurement residuals；Representing the result after filtering or sequence inversion,for double-differenced pseudorange measurement residuals after filtering noise, i.e.。

The frequency descriptions of FRR filtering are:

this gives:

from the above equation, outputAnd inputThere is no additional phase between, FRR achieves accurate zero phase distortion filtering. The invention adopts the method to carry out zero phase filtering, and in order to reduce the boundary effect problem which is encountered by digital filtering, the prolongation which is the same as the node number of the filter is respectively carried out in the head and tail directions of the data before the filtering. Let the original data beThe data amount is N, the filter number is M, and the expanded data can be expressed as:

s7, constructing a double-difference observation equation set by using the filtered double-difference pseudo-range measured values and solving a baseline vector：

The double-difference observation equation set is constructed by the following steps:

if the base station receiver r and the user receiver u have pseudo-range measurements for M satellites, then M-1 mutually independent double-differenced pseudo-range observation equations may form a matrix equation as follows:

=

in the formula (I), the compound is shown in the specification,the remaining residual is.

Ignoring pseudorange measurement noiseGiven a sufficient number of double-differenced pseudorange measurementsUnder the condition (2), the receiver can theoretically solve the baseline vector from the above matrix equation(ii) a The baseline vectorThe solution is performed by the least square method.

But double differenced pseudorange measurement noiseThe existence of the pseudo-range can obviously influence the solution of the baseline vector, so that the invention effectively eliminates the influence of double-difference pseudo-range measurement noise through zero-phase kaiser window filtering.

In the foregoing description of embodiments, the particular features, structures, materials, or characteristics may be combined in any suitable manner in any one or more embodiments or examples.

The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.