CN112799110B - Doppler-considered Beidou corrected pseudo-range single-point positioning method, system and equipment - Google Patents
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- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
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Abstract
The invention discloses a Doppler-considered Beidou corrected pseudo-range single-point positioning method, a Doppler-considered Beidou corrected pseudo-range single-point positioning system and Doppler-considered single-point positioning equipment, wherein the method specifically comprises the following steps of: first, a smoothed pseudorange observation expression is constructed that accounts for Doppler: wherein ω is a smoothing factor; lambda is the carrier wavelength; p and PThe unit is meter, and the subscript is epoch identifier; then introducing a weight factor into the smoothed pseudo-range observation expression to adjust the weights of the original pseudo-range observation and the smoothed pseudo-range observation, and thenWherein η is a weight factor;to correct the pseudo-range; the Doppler function of the independent observed value is fully exerted, the error of the Beidou original pseudo-range observed value is weakened, the influence of Doppler integral accumulated error is restrained, and the weight factor eta is not infinitely close to 0 and the pseudo-range is smoothed because the sampling interval is generally not more than 30 secondsThe correction function can be exerted to ensure the precision and reliability of the Beidou pseudo-range single-point positioning.
Description
Technical Field
The invention belongs to the technical field of data preprocessing of Beidou satellite navigation systems, and particularly relates to a Doppler-considered Beidou correction pseudo-range single-point positioning method, system and equipment.
Background
At present, because a pseudo-range single-point positioning module of a global navigation satellite system (GNSS, global Navigation Satellite System) has the advantages of all-weather, small size, portability and the like, the pseudo-range single-point positioning technology is widely applied to various fields.
The Beidou satellite navigation system (BDS, beiDou Navigation Satellite System) is formally opened in 31 days of 7 months in 2020, marks the new era of global service by Beidou, and also means that the Beidou pseudo-range single-point positioning technology has wider application prospect
However, because the pseudo-range observation value is influenced by various error sources, the positioning accuracy is difficult to ensure, and the individual positioning error is more than hundred meters, which becomes the bottleneck for restricting the popularization and application of the Beidou pseudo-range positioning technology.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a Doppler-considered Beidou correction pseudo-range single-point positioning method, a Doppler-considered Beidou correction pseudo-range single-point positioning system and Doppler-considered Beidou correction single-point positioning equipment, which are used for calculating Beidou pseudo-range single-point positioning based on improving precision of Beidou pseudo-range observation values and improving precision and reliability of Beidou pseudo-range single-point positioning.
In order to achieve the above purpose, the present invention adopts the following technical scheme: a Doppler-considered Beidou corrected pseudo-range single-point positioning method specifically comprises the following steps:
acquiring Doppler observation values and original pseudo-range observation values;
constructing a smoothed pseudorange observation expression taking into account Doppler:
wherein ω is a smoothing factor; lambda is the carrier wavelength; p is the original pseudorange observations and,to smooth outPseudo-range observation values are measured in meters, and subscripts are epoch marks; d is Doppler observation, k is a smoothing window, and dt is Doppler observation integration interval t k-1 ,t k ]；
Introducing a weight factor eta into the smoothed pseudo-range observation expression to adjust the weights of the original pseudo-range observation and the smoothed pseudo-range observation, and correcting the pseudo-rangeThe method comprises the following steps:
wherein η is a weight factor;
and carrying out single-point positioning calculation based on the corrected pseudo-range observation value to obtain a space three-dimensional coordinate value of the ground receiver, namely a single-point positioning value of the ground receiver.
Setting the smoothing factor in the smoothed pseudo-range observation expression to be the reciprocal ω=1/k of the smoothing window, the smoothed pseudo-range observation expression is:
wherein t=t k -t k-1 Representing the sampling interval.
Introducing the influence of the satellite altitude angle into a smooth pseudo-range observation value expression, wherein the smooth pseudo-range observation value expression is as follows:
wherein θ is the satellite altitude.
The variance of the smoothed pseudorange is:
wherein,noise is the original pseudo-range observation value; />Noise is Doppler observations; the sampling interval determines the variance value of the smooth pseudo-range, the size of the smooth window and the noise level of the original pseudo-range and Doppler; as the smoothing window increases, the variance value of the smoothed pseudorange decreases; obtaining an optimal smooth window value F 1 Deriving k:
is a cubic equation about k, namely 3 k values, including 1 real number solution and 2 conjugate complex number solutions; the smoothing window value should be a valid positive integer, rounding the 1 real solution, the number of epoch data that participate in smoothing is
The minimum of (2) is guaranteed that at least 2 epoch data participates in smoothing.
Calculating a corrected pseudo-range according to the error propagation lawVariance value of (c):
F 2 deriving k to obtain a calculated value of the weight factor:
wherein τ and μ are both substitution characters, nonsensical, and the weight factor calculation value is introduced into the corrected pseudo rangeThe modified pseudo-range is obtained from the expression of (2)>
The invention also provides a Doppler-considered Beidou modified pseudo-range single-point positioning system, which comprises a data acquisition module, a data processing module and a positioning module, wherein the data acquisition module is used for acquiring Doppler observed values and original pseudo-range observed values, and the data processing module is used for correcting the original pseudo-range observed values based on the Doppler observed values and the original pseudo-range observed values, and specifically comprises the following steps:
acquiring Doppler observation values and original pseudo-range observation values;
constructing a smoothed pseudorange observation expression taking into account Doppler:
wherein ω is a smoothing factor; lambda is the carrier wavelength; p is the original pseudorange observations and,the unit is meter, and the subscript is epoch identifier; d is Doppler observation, k is a smoothing window, and dt is Doppler observation integration interval t k-1 ,t k ]；
Introducing a weight factor eta into the smoothed pseudo-range observation expression to adjust the weights of the original pseudo-range observation and the smoothed pseudo-range observation, and correcting the pseudo-rangeThe method comprises the following steps:
wherein η is a weight factor;
and the positioning module performs single-point positioning calculation based on the corrected pseudo-range observation value to obtain a space three-dimensional coordinate value of the ground receiver, namely a single-point positioning value of the ground receiver.
In order to solve the technical problems, the invention also provides computer equipment, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor realizes the steps of the Doppler-considered Beidou correction pseudo-range single-point positioning method when executing the computer program.
The invention also provides a computer readable storage medium storing a computer program which when executed by a processor implements the steps of the Doppler-considered beidou correction pseudo-range single-point positioning method of the invention.
Compared with the prior art, the invention has at least the following beneficial effects: fully playing the role of an independent observation value Doppler, weakening the error of the Beidou original pseudo-range observation value, correcting the precision of the pseudo-range observation value, and enabling the value of a weight factor to depend on a satellite altitude angle, a smooth window k and a sampling interval T; when the satellite altitude angle and the smoothing window k are determined, the size of the weight factor is mainly determined by the sampling interval T, i.e. the larger the sampling interval T is, the larger the tau value is, the smaller the weight factor eta is, and the pseudo range is smoothedThe smaller the weight of the original observations P κ The greater the weight of (a), the trend is in accordance with the initial setting of the weight factor, i.e. suppressing the effect of Doppler integral accumulated error, since the sampling interval is typically not more than 30 seconds, the weight factor η will not be nullThe limit is close to 0, i.e. smooth pseudo-range +.>The precision and reliability of the single-point positioning of the Beidou pseudo-range can be guaranteed by always playing the correction function, and because the precision of the corrected pseudo-range observation value is superior to that of the original pseudo-range observation value, the coordinate precision of the single-point positioning based on the corrected pseudo-range is superior to that of the original pseudo-range single-point positioning, thereby laying a foundation for popularization and application of the single-point positioning technology of the Beidou pseudo-range.
Drawings
Fig. 1a is a graph of the noise level of the original pseudo-range according to the sampling interval, in which different colors (blue, green and red) respectively represent the observed values of the frequency points of the beidou B1, B2 and B3.
Fig. 1B is a graph of smoothed pseudo-range noise level as a function of sampling interval, where different colors (blue, green, red) respectively represent the observed values of the frequency points of the beidou B1, B2 and B3.
Fig. 1c is a graph of the noise level of the corrected pseudo range according to the sampling interval, in which different colors (blue, green and red) respectively represent the observed values of the frequency points of the beidou B1, B2 and B3.
Detailed Description
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application. However, it will be understood by those skilled in the art that the claimed invention may be practiced without these specific details and with various changes and modifications from the embodiments that follow.
To make the objects, technical solutions and advantages of the present application more apparent, embodiments of the present application will be described in further detail below with reference to the accompanying drawings, in which Doppler observations and raw pseudorange observations are obtained
Step 1: constructing a smoothed pseudorange observation expression taking into account Doppler:
it should be noted that equation (1) recursively acquires smoothing artifactsDistance from each otherWherein ω is a smoothing factor; lambda is the carrier wavelength; p and->The unit is meter, and the subscript is epoch identifier; d is Doppler observation, k is a smoothing window, and dt is Doppler observation integration interval t k-1 ,t k ]。
Further, the smoothing factor may be set to be the inverse of the smoothing window (ω=1/k), and the smoothed pseudorange observations are expressed as:
it is noted that as the smoothing window increases, the smoothing factor decreases, the specific gravity of the original pseudorange observation decreases, and the specific gravity of the Doppler observation increases, which increases in the effect of smoothing the pseudorange.
The satellite altitude is used to characterize the observed data quality, and the influence of the satellite altitude is introduced into a smoothed pseudorange observation expression, which may be expressed as
Wherein θ is the satellite altitude, and since the correlation between the Doppler observed value and time is negligible, the variance value of the smoothed pseudo-range is calculated using the error propagation law:
it should be noted that where the sampling interval is fixed and the noise level of the original pseudorange and the Doppler observed value is fixed, the variance value of the smoothed pseudorange depends primarily on the size of the smoothing window. Since k is both a numerator term and a denominator term, the smoothed pseudorange variance value decreases with increasing smoothing window, but the two are not linearly inversely related.
Further, to determine the smooth window size, F 1 To derive k, there is
Note that equation (5) is a cubic equation for k, i.e., k has 3 roots. Considering that the function theoretically has only one intersection with the X-axis, the root of the equation includes 1 real solution and 2 complex conjugate solutions. Since the smoothing window is a positive integer, the real solution is rounded up and rounded down, there are
It should be noted that, in order to ensure that the smoothing effect is effective,the minimum of (2), i.e., at least 2 epoch data participate in the smoothing.
Step 2: introducing weight factors to construct a modified pseudo-range observation expression:
equation (7) aims at adjusting the original pseudo-range observations P by introducing a weight factor η κ And smoothing pseudorange observationsThe purpose of which is to suppress the integrated accumulated error of the Doppler observations. With the increase of the sampling interval, the Doppler integral accumulated error is obviously increased, the weight of the smoothed pseudo-range value needs to be reduced through a weight factor, and the accuracy of the corrected pseudo-range observed value is ensured.
Further, according to the error propagation law, the variance value of the corrected pseudo-range can be expressed as:
further, equation (8) derives and assigns k asThe calculated value of the weight factor can be obtained:
in equation (9), the weighting factor is mainly determined by the satellite altitude, the smoothing window k, and the sampling interval T. When the satellite altitude is fixed with the smoothing window k, the size of the weighting factor is mainly determined by the sampling interval T, i.e. the larger the sampling interval T is, the smaller the weighting factor eta is, and the smoothed pseudo-range isThe smaller the weight of the original observations P κ The greater the weight of (2). From this, it is clear that the larger the sampling interval, the smaller the effect exerted by the smoothed pseudorange observations, and the smaller the effect of the Doppler integration accumulated error; τ and μ are both substitution characters, nonsense, and κ is Kelvin.
Referring to fig. 1a, 1B and 1c, where three columns from left to right are illustrated to represent the observed values of the beidou B1, B2 and B3, respectively, the original pseudo-range noise level varies with the sampling interval, fig. 1B, the smoothed pseudo-range noise level varies with the sampling interval, and fig. 1c is a corrected pseudo-range noise level varies with the sampling interval, it can be seen that the pseudo-range noise level increases with the increase of the sampling interval, and the B1 frequency point pseudo-range noise level is greater than the B2 and B3 frequency points. When the sampling interval is not greater than 2 seconds, the smoothed pseudorange noise level is better than the original pseudorange observations due to the small Doppler observations integration error. As the sampling interval continues to increase, the Doppler observation integration error increases significantly, and the smoothed pseudorange noise level is greater than the original pseudorange observation. Due to the adjustment of the weight factors, the noise level of the corrected pseudo range is better than that of the original pseudo range and the smooth pseudo range observation value, and the correction effect is better when the sampling interval is smaller.
As known from the prior literature, the Doppler integral accumulated error is generally not more than 2cm/s. When the data sampling interval does not exceed 1s, the Doppler integral accumulated error level is better than the noise level of the original pseudo-range observation value, so that the accuracy of the smoothed pseudo-range observation value is better than the original pseudo-range observation value, and the weight of the smoothed pseudo-range observation value is increased. As the sampling interval increases, the Doppler accumulated integration error increases and the smoothed pseudorange observations weight will decrease. Since the sampling interval is typically no more than 30 seconds, the weighting factor η is not infinitely close to 0, i.e. a smoothed pseudorangeThe correction function is always exerted.
The invention provides a Doppler-considered Beidou modified pseudo-range single-point positioning system, which comprises a data acquisition module, a data processing module and a positioning module, wherein the data acquisition module is used for acquiring Doppler observed values and original pseudo-range observed values, and the data processing module is used for correcting the original pseudo-range observed values based on the Doppler observed values and the original pseudo-range observed values, and specifically comprises the following steps:
acquiring Doppler observation values and original pseudo-range observation values;
constructing a smoothed pseudorange observation expression taking into account Doppler:
wherein ω is a smoothing factor; lambda is the carrier wavelength; p is the original pseudorange observations and,the unit is meter, and the subscript is epoch identifier; d is Doppler observation, k is a smoothing window, and dt is Doppler observation integration interval t k-1 ,t k ]；
To the houseIntroducing a weight factor eta into the smoothed pseudo-range observation expression to adjust the weights of the original pseudo-range observation and the smoothed pseudo-range observation, and correcting the pseudo-rangeThe method comprises the following steps:
wherein η is a weight factor;
and the positioning module performs single-point positioning calculation based on the corrected pseudo-range observation value to obtain a space three-dimensional coordinate value of the ground receiver, namely a single-point positioning value of the ground receiver.
The Doppler Beidou pseudo-range observation value correction method can take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein. The Doppler's Beidou pseudorange observation correction method is considered to be stored in a computer readable storage medium if the method is realized in a form of a software functional unit and sold or used as an independent product.
Based on such understanding, in an exemplary embodiment, a computer readable storage medium is also provided, where the present invention implements all or part of the flow of the method of the above embodiment, and may also be implemented by a computer program to instruct related hardware, where the computer program may be stored in the computer readable storage medium, where the computer program, when executed by a processor, may implement the steps of each of the method embodiments described above. Wherein the computer program comprises computer program code which may be in source code form, object code form, executable file or some intermediate form etc. Computer-readable storage media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. It should be noted that the computer readable medium contains content that can be appropriately scaled according to the requirements of jurisdictions in which such content is subject to legislation and patent practice, such as in certain jurisdictions in which such content is subject to legislation and patent practice, the computer readable medium does not include electrical carrier signals and telecommunication signals. The computer storage media may be any available media or data storage device that can be accessed by a computer, including, but not limited to, magnetic storage (e.g., floppy disks, hard disks, magnetic tape, magneto-optical disks (MOs), etc.), optical storage (e.g., CD, DVD, BD, HVD, etc.), and semiconductor storage (e.g., ROM, EPROM, EEPROM, nonvolatile storage (NANDFLASH), solid State Disk (SSD)), etc.
In an exemplary embodiment, a computer device is also provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor implementing the steps of the Doppler-considered beidou pseudorange observation value correction method when executing the computer program. The processor may be a central processing unit (Central Processing Unit, CPU), but may also be other general purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), off-the-shelf programmable gate arrays (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.
Claims (5)
1. The Doppler-considered Beidou corrected pseudo-range single-point positioning method is characterized by comprising the following steps of:
acquiring Doppler observation values and original pseudo-range observation values;
constructing a smoothed pseudorange observation expression taking into account Doppler:
wherein ω is a smoothing factor; lambda is the carrier wavelength; p is the original pseudorange observations and,the unit is meter, and the subscript is epoch identifier; d is Doppler observation, k is a smoothing window, and dt is Doppler observation integration interval t k-1 ,t k ]；
Introducing a weight factor eta into the smoothed pseudo-range observation expression to adjust the weights of the original pseudo-range observation and the smoothed pseudo-range observation, and correcting the pseudo-rangeThe method comprises the following steps:
wherein η is a weight factor;
performing single-point positioning calculation based on the corrected pseudo-range observation value to obtain a space three-dimensional coordinate value of the ground receiver, namely a single-point positioning value of the ground receiver; introducing the influence of the satellite altitude angle into a smooth pseudo-range observation value expression, wherein the smooth pseudo-range observation value expression is as follows:
wherein θ is the satellite altitude, T represents the sampling interval, and is not more than 30s;
calculating a corrected pseudo-range according to the error propagation lawVariance value of (c):
F 2 deriving k to obtain a calculated value of the weight factor:
wherein τ and μ are both substitution characters, nonsensical, and the weight factor calculation value is introduced into the corrected pseudo rangeThe modified pseudo-range is obtained from the expression of (2)>The variance of the smoothed pseudorange is:
wherein,noise is the original pseudo-range observation value; />Noise is Doppler observations; the sampling interval determines the variance value of the smooth pseudo-range, the size of the smooth window and the noise level of the original pseudo-range and Doppler; as the smoothing window increases, the variance value of the smoothed pseudorange decreases; obtaining an optimal smooth window value F 1 Deriving k:
is a cubic equation about k, namely 3 k values, including 1 real number solution and 2 conjugate complex number solutions; the smoothing window value should be a valid positive integer, rounding the 1 real solution, the number of epoch data that participate in smoothing is
The minimum of (2) is guaranteed that at least 2 epoch data participates in smoothing.
2. The Doppler-taking-into-account Beidou modified pseudo-range single-point positioning method of claim 1, wherein,
setting the smoothing factor in the smoothed pseudo-range observation expression to be the reciprocal ω=1/k of the smoothing window, the smoothed pseudo-range observation expression is:
wherein t=t k -t k-1 Representing the sampling interval.
3. A Doppler-considered single point positioning system for correcting a pseudo range, which is characterized by being configured to implement the method of any one of claims 1-2, and comprising a data acquisition module, a data processing module and a positioning module, wherein the data acquisition module is configured to acquire a Doppler observed value and an original pseudo range observed value, and the data processing module corrects the original pseudo range observed value based on the Doppler observed value and the original pseudo range observed value, specifically as follows:
acquiring Doppler observation values and original pseudo-range observation values;
constructing a smoothed pseudorange observation expression taking into account Doppler:
wherein ω is a smoothing factor; lambda is the carrier wavelength; p is the original pseudorange observations and,the unit is meter, and the subscript is epoch identifier; d is Doppler observation, k is a smoothing window, and dt is Doppler observation integration interval t k-1 ,t k ]；
Introducing a weight factor eta into the smoothed pseudo-range observation expression to adjust the weights of the original pseudo-range observation and the smoothed pseudo-range observation, and correcting the pseudo-rangeThe method comprises the following steps:
wherein η is a weight factor;
and the positioning module performs single-point positioning calculation based on the corrected pseudo-range observation value to obtain a space three-dimensional coordinate value of the ground receiver, namely a single-point positioning value of the ground receiver.
4. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor, when executing the computer program, carries out the steps of the Doppler-considered beidou corrected pseudo-range single-point positioning method according to any one of claims 1 to 2.
5. A computer readable storage medium storing a computer program, wherein the computer program when executed by a processor implements the steps of the Doppler-considered beidou corrected pseudorange single point positioning method of any one of claims 1 to 2.
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