CN109459778B - Code pseudo range/Doppler joint velocity measurement method based on robust variance component estimation and application thereof - Google Patents
Code pseudo range/Doppler joint velocity measurement method based on robust variance component estimation and application thereof Download PDFInfo
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Abstract
The invention discloses a code pseudo range/Doppler combined velocity measurement method based on robust variance component estimation. The method provided by the invention can break through the limitation that the single-frequency satellite receiver only uses single information for speed measurement at present, can inhibit the influence of observation gross error, and obviously improves the robustness, unbiased property and stability of the combined speed measurement method.
Description
Technical Field
The invention belongs to the technical field of GNSS (global navigation satellite system) positioning and navigation, and particularly relates to a code pseudorange/Doppler joint measurement receiver movement speed based on robust variance component estimation.
Background
The speed is one of important motion parameters in the fields of aviation flight, intelligent navigation, unmanned driving, marine traffic and the like, and the GNSS speed measurement has wide application in the fields due to the characteristics of high precision, real time, low price and the like. Foreign scholars obtain the direct proportional relation between the speed measurement error and the movement speed and the acceleration rate of the carrier through differential data simulation test, and the error range is from submillimeter per second to several meters per second. The scholars in China also carry out system analysis and evaluation on the velocity measurement model and velocity measurement precision of pseudo range, carrier wave, doppler and differential observation values thereof. Specifically, the pseudorange, the carrier wave, and the doppler observed value can all measure the receiver velocity, and the average velocity can be obtained by performing position differentiation directly using the GNSS positioning result, but this is very dependent on the accuracy of the positioning result, and is not practical. In addition, the average speed in the differential time can be obtained through pseudo-range difference between epochs, but the speed measurement error is large due to the influence of code pseudo-range precision; the average speed in the differential time can be obtained by utilizing the phase difference between epochs, the precision is high, but the carrier phase is easy to be interfered, the cycle slip is frequent, even no output exists, and the reliability is low; the Doppler observed value can obtain high-precision instantaneous speed, is insensitive to orbit error, receiver clock error and atmospheric error, has no cycle slip, and is a practical and reliable observed value because the influence of pseudo-range single-point positioning error on speed measurement precision is also in the millimeter level.
Various observation information or speed measurement methods exist in longitudinal observation, but how to fuse different types of observation information and realize high-precision stable speed measurement to the maximum is an urgent problem in engineering application.
Disclosure of Invention
The technical problem is as follows: aiming at the prior art, by using the thought of multi-source information fusion for reference, a method for jointly resolving the speed of the receiver by adopting two types of observed values with different accuracies, namely single-frequency code pseudorange and Doppler is provided, and a more reasonable and effective random model is explored and established based on a mode of combining robust estimation and variance component estimation so as to maximally exert the effect of the combined model.
The technical scheme is as follows: firstly, respectively establishing a function model and a random model for speed measurement by adopting observation information of code pseudorange, doppler, carrier-to-noise ratio and satellite elevation angle; then obtaining an robust random model capable of inhibiting the coarse error influence by adopting a least square robust estimation method; and finally, forming a combined velocity measurement model by a code pseudorange and Doppler velocity measurement function model and an robust random model, and iteratively solving the motion velocity of the satellite receiver by adopting a variance component estimation method.
Further, the code pseudorange/Doppler joint velocity measurement method based on robust variance component estimation comprises the following specific steps:
step 1), respectively establishing a function model and a random model for speed measurement by adopting code pseudorange, doppler, carrier-to-noise ratio and satellite altitude observation information, and comprising the following specific steps:
a) And calculating the code pseudorange and the change rate of the carrier wave by means of difference between epochs, wherein the formula (1) is as follows:
wherein ρ and
respectively the code pseudorange and its rate of change,
and
respectively a carrier phase and a change rate thereof, D is a Doppler observed value, delta t is differential time, and subscripts k and k +1 of each item are respectively a kth moment and a kth +1 moment;
b) A function model of velocity measurement is established by using the code pseudorange and the doppler observation value, and generally, the GNSS observation equation is shown as formula (2):
where ρ is the receiver code pseudorange observation,
for receiver carrier observations, N 0 Lambda is the carrier wavelength, R is the true geometric distance between the receiver and the satellite, c is the speed of light, δ t is the clock error, δ ρ ion For ionospheric delay, δ ρ trop For tropospheric delay, epsilon ρ And
other error terms including orbital error, multipath effects, and observation noise are used, where the superscript s and subscript r of each term represent the satellite and receiver, respectively.
The time t is derived and linearized according to a GNSS observation equation, as shown in equation (3):
in the formula (I)
Represents the rate of change with time t, and
in the formula, r s 、
Is a satellite position and velocity column vector in an ECEF (Earth-Centered, earth-Fixed) coordinate system, r r 、
Is a receiver position and velocity column vector R under an ECEF coordinate system 0 To be approximated by a receiver r0 The geometric distance between the receiver and the satellite is obtained,
for the receiver approximate velocity, x, y and z are the projections of the position vector in the ECEF coordinate system, v x 、v y And v z Is the projection of the velocity vector in the ECEF coordinate system. Corresponding speed measuring function models can be obtained by combining the formulas (1), (3) and (4);
c) And establishing a random model for speed measurement by utilizing observation information such as carrier-to-noise ratio, satellite altitude angle and the like, as shown in formula (5):
where σ is covariance, E is satellite altitude, subscript i is satellite number, S is scaling factor, and constant term a 0 、a 1 And E 0 Defined by Table A:
TABLE A
Wherein the scaling factor S is defined by the satellite carrier-to-noise ratio, as shown in equation (6):
in the formula, C/N 0 Represents the satellite carrier-to-noise ratio, and int (—) is an integer function. The prior random model of velocity measurement can be determined by equations (5), (6) and table a.
Step 2), obtaining an robust random model capable of inhibiting the effect of gross errors by adopting a least square robust estimation method, and comprising the following specific steps:
a) And obtaining a residual vector and a corresponding co-factor through least square estimation, wherein the formula (7) is as follows:
wherein B is a design matrix, P is a prior weight, l is an observed value vector, Q is an observed value co-factor,
the parameter to be estimated, V is the residual vector, Q vv Is the residual co-factor.
b) An robust random model capable of suppressing gross influence is obtained through an IGG III equivalent weight scheme proposed by Zhoujiang, as shown in formula (8):
in the formula (I), the compound is shown in the specification,
to normalize the residual, k 0 And k 1 Is a constant value, typically k 0 ∈[1.0～1.5]，k 1 ∈[2.5～8.0]，
For robust equivalence, the index i represents the ith observation.
Step 3), a combined velocity measurement model is formed by a code pseudorange and Doppler velocity measurement function model and an anti-difference random model, and the motion velocity of the satellite receiver is iteratively solved by adopting a variance component estimation method, wherein the method comprises the following specific steps:
a) And combining a code pseudorange and Doppler velocity measurement function model and an robust random model into a combined velocity measurement model, wherein the formula (9) is as follows:
in the formula, subscripts 1 and 2 represent code pseudorange and doppler, respectively, and N and W represent corresponding combination terms, respectively;
b) Iteratively adjusting the weight of each type of observed value by adopting a variance component estimation method, wherein the formula (10) is as follows:
in the formula, tr (x) represents matrix tracing, E (x) represents expectation, n is the number of observed values,
is an estimate of the variance of the unit weight, V is the residual vector,
for robust equivalence, subscripts 1 and 2 of each term represent code pseudorange and doppler, respectively. The unit weight variance is obtained by solving the equation (10)
Evaluation of
Obtaining the weight of each type of observation value after adjustment by substitution formula (11):
in the formula (I), the compound is shown in the specification,
represents the weight obtained by single iteration adjustment, C is constant and can be fixedly selected
Subscripts 1 and 2 of each term represent code pseudorange and doppler, respectively.
c) And solving the motion speed of the satellite receiver by using the combined velocity measurement model after the estimation and adjustment of the power difference component, as shown in formula (12):
in the formula (I), the compound is shown in the specification,
for the estimated velocity vector, superscript-1 represents the matrix inversion operation;
and repeating the steps a), b) and c) until the estimated values of the unit weight variances of all types are equal or are verified to be equal by hypothesis, and then obtaining the final motion speed of the receiver.
Further, when the step 3) is carried out, if the unit weight variance estimation value is not equal after 4-5 loop iterations or the hypothesis test is passed, the loop is skipped, and the robust solution is directly adopted as the final solution result.
In addition, the above cites the context of the Zhoujiang province, the man-made geodesic scientist, IGG III project, the 3 rd set of robust estimation method proposed by the Weujiang province in 1989 according to the bounded nature of the measurement error, namely the equivalent weight of the robust
Obtained from equation (8). The robust estimation method is a robust estimation method which is generally adopted in the robust estimation field and has a good robust effect, is widely applied and advocated by the industry, and becomes a known practical robust method. Equation (8) is the core equation in the most widely used method among the proposed robust methods. The invention also adopts the anti-difference method to carry out coarse inhibition.
Has the advantages that: according to the code pseudo range/Doppler joint velocity measurement method based on robust variance component estimation, the velocity of the receiver is solved by using the code pseudo range and Doppler observation information in a joint mode, and the limitation that the single-frequency satellite receiver only uses a single observation value to measure the velocity at present is broken through; aiming at the problem that a combined speed measurement model is susceptible to poor observed values such as gross errors, the influence of the gross errors in the similar observed values on the model is inhibited by adopting an equivalent weight robust estimation principle; for the problems of incompatibility and inconsistent precision of various information when multi-source information is fused for carrying out combined speed measurement, a variance component estimation method is adopted to balance weight proportion among different types of observed values, and a random model for the combined speed measurement is adaptively adjusted. By using the method provided by the invention, the full and effective utilization of single-frequency observation information can be realized, and the robustness, unbiased property and stability of the combined velocity measurement method are obviously improved.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
FIG. 1 is a flowchart illustrating a code pseudorange/Doppler joint velocity measurement method based on robust variance component estimation according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating true errors in velocity measurement for each solution in an embodiment of the present invention;
FIG. 3 illustrates a true error in the N and E directions for single point positioning according to an embodiment of the present invention;
FIG. 4 shows the true X-axis error of each solution in one embodiment of the present invention;
FIG. 5 illustrates the composite velocity error for each solution in one embodiment of the present invention;
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating the present invention, are given by way of illustration and explanation only, not limitation.
A code pseudo-range/Doppler joint velocity measurement method based on robust variance component estimation is characterized in that a function model and a random model for velocity measurement are respectively established by using observation information such as code pseudo-range, doppler, carrier-to-noise ratio and satellite altitude, a robust random model capable of inhibiting the effect of gross errors is obtained by adopting a least square robust estimation method, the code pseudo-range and Doppler velocity measurement function model and the robust random model form a joint velocity measurement model, and the motion velocity of a satellite receiver is iteratively solved based on a variance component estimation method.
In GNSS velocity solution, position or velocity information is obtained by establishing an observation equation and solving (estimating) unknown parameters (such as position and velocity) in the equation. The observation equation can be divided into two parts: a functional model of the observed values and a stochastic model. The function model describes a mathematical relation between the observed value and the to-be-estimated value (namely, the natural physical law is expressed by a mathematical equation, such as displacement = speed x time, and the like, wherein the displacement is the observed value of each time node, and the speed is the to-be-estimated parameter); the stochastic model describes the magnitude of the noise (i.e., error) of the observed values and the correlation between the observed values. To obtain accurate and effective solution (estimation) of the parameters to be estimated, an accurate function model and a random model matched with the function model need to be established. In the actual calculation, the function model can be accurately obtained from the determined physical meaning, and due to the random or non-random comprehensive influence of the observation equipment and the environment, the accurate error of the obtained observation value is often difficult to ensure, that is, the random model is difficult to accurately obtain and establish. Therefore, in order to establish an accurate random model, the invention jointly establishes a prior random model by using the main characteristic information (namely signal-to-noise ratio, satellite altitude angle and the like) of an observed value, and then finely adjusts the random model and the functional model by using a robust variance component estimation method, so that the random model and the functional model are matched as much as possible, and the actual measurement condition can be accurately reflected. The invention is mainly characterized in that the observed value not only adopts a single conventional code pseudo-range observed value, but also fuses a Doppler observed value, which are two different types of observed values, and the physical meaning and the observation error level of the observed value are inconsistent. Therefore, not only a function model of the combined velocity measurement needs to be established, but also an accurate random model needs to be established, so that the estimation precision of the velocity information is improved, and the method is a variance component estimation method with the robust capability.
Example 1
A code pseudo-range/Doppler joint velocity measurement method based on robust variance component estimation comprises the following specific steps:
step 1), a function model and a random model for speed measurement are respectively established by adopting observation information such as code pseudorange, doppler, carrier-to-noise ratio, satellite altitude angle and the like, and the method comprises the following specific steps:
a) And calculating the code pseudorange and the change rate of the carrier wave by means of difference between epochs, wherein the formula (1) is as follows:
wherein ρ and
respectively the code pseudorange and its rate of change,
and
respectively, a carrier phase and a change rate thereof, D is a doppler observation value, Δ t is a differential time, and subscripts k and k +1 of each item are respectively a kth time and a kth + 1 time.
b) A function model of velocity measurement is established by using the code pseudorange and the doppler observation value, and generally, the GNSS observation equation is shown as formula (2):
where ρ is the receiver code pseudorange observation,
for receiver carrier phase observations, N 0 Lambda is the carrier wavelength, R is the true geometric distance between the receiver and the satellite, c is the speed of light, δ t is the clock error, δ ρ ion For ionospheric delay, δ ρ trop For tropospheric delay, epsilon ρ And
other error terms including orbital error, multipath effects, and observation noise are included, where the superscript s and subscript r of each term represent the satellite and receiver, respectively.
The time t is derived and linearized according to a GNSS observation equation, as shown in equation (3):
in the formula (I)
Represents the rate of change with time t, and
in the formula, r s 、
Is a satellite position and velocity column vector in an ECEF (Earth-Centered, earth-Fixed) coordinate system, r r 、
Is a receiver position and velocity column vector R under an ECEF coordinate system 0 To be approximated by a receiver r0 The geometric distance between the receiver and the satellite is obtained,
for the receiver approximate velocity, x, y and z are the projections of the position vector in the ECEF coordinate system, v x 、v y And v z Is the projection of the velocity vector in the ECEF coordinate system. Corresponding speed measuring function models can be obtained by combining the formulas (1), (3) and (4);
c) And establishing a random model for speed measurement by utilizing observation information such as carrier-to-noise ratio, satellite altitude angle and the like, as shown in formula (5):
where σ is covariance, E is satellite altitude, subscript i is satellite number, S is scaling factor, and constant term a 0 、a 1 And E 0 Defined by Table A:
TABLE A
Wherein the scaling factor S is defined by the satellite carrier-to-noise ratio, as shown in equation (6):
in the formula, C/N 0 Represents the satellite carrier-to-noise ratio, and int (—) is an integer function. The prior random model of velocity measurement can be determined from equations (5), (6) and table a.
Step 2), obtaining an robust random model capable of inhibiting the effect of gross errors by adopting a least square robust estimation method, and comprising the following specific steps:
a) And obtaining a residual vector and a corresponding co-factor through least square estimation, as shown in formula (7):
wherein B is a design matrix, P is a prior weight, l is an observed value vector, Q is an observed value co-factor,
the parameter to be estimated, V is the residual vector, Q vv Is the residual co-factor.
b) An robust random model capable of suppressing gross errors is obtained through an IGG III equivalent weight scheme proposed in Zhoujiang, as shown in formula (8):
in the formula (I), the compound is shown in the specification,
to normalize residual error, k 0 And k 1 Is a constant, generally k 0 ∈[1.0～1.5]，k 1 ∈[2.5～8.0]，
For robust equivalence, the index i represents the ith observation.
Step 3), a combined velocity measurement model is formed by a code pseudorange and Doppler velocity measurement function model and an anti-difference random model, and the motion velocity of the satellite receiver is iteratively solved by adopting a variance component estimation method, wherein the method comprises the following specific steps:
a) And combining a code pseudorange and Doppler velocity measurement function model and an robust random model to form a combined velocity measurement model, as shown in formula (9):
in the equation, subscripts 1 and 2 represent code pseudorange and doppler, respectively.
b) Iteratively adjusting the weight of each type of observed value by adopting a variance component estimation method, wherein the formula (10) is as follows:
in the formula, tr (x) represents matrix tracing, E (x) represents expectation, n is the number of observed values,
is an estimate of the unit weight variance, V is the residual vector,
for robust equivalence, subscripts 1 and 2 of each term represent code pseudorange and doppler, respectively. The unit weight variance is obtained by solving the equation (10)
Evaluation of
Obtaining the weight of each type of observation value after adjustment by substituting formula (11):
in the formula (I), the compound is shown in the specification,
represents the weight obtained by single iteration adjustment, C is constant and can be fixedly selected
The subscripts 1 and 2 of each term represent code pseudorange and doppler, respectively.
c) And solving the motion speed of the satellite receiver by using the combined velocity measurement model after the estimation and adjustment of the power difference component, as shown in formula (12):
in the formula (I), the compound is shown in the specification,
for the estimated velocity vector, superscript-1 represents the matrix inversion operation;
repeating the steps a), b) and c) until the estimates of the unit weight variances of all types are equal or are verified to be equal by hypothesis, and then obtaining the final movement speed of the receiver. When the step 3) is carried out, if the unit weight variance estimation value is not equal after 4-5 times of loop iteration or hypothesis test is passed, the loop is skipped, and the robust solution is directly adopted as the final resolving result.
In the present embodiment, the gross error determination threshold k is set 0 Is 1.2, k 1 5.5, and a maximum cycle threshold of 4.
Example 2
The following exemplifies an application scenario of the code pseudorange/doppler joint velocity measurement method based on robust variance component estimation:
in order to comprehensively compare the actual resolving effect of the method provided by the invention, three testing modes such as static state, static simulation dynamic state and vehicle-mounted dynamic state are designed, and the comparison is carried out according to 4 resolving schemes:
scheme a: and least square estimation, namely, directly adopting a prior random model and a function model of joint speed measurement to carry out least square adjustment calculation.
Scheme B: and (4) estimating a variance component, namely adjusting a prior random model of pseudorange and Doppler by directly adopting a conventional method component estimation method on the basis of the scheme A.
Scheme C: and (3) least square robust estimation, namely, adjusting the weight of a bad observation value by respectively aiming at the prior weight arrays of pseudo range and Doppler in a robust least square estimation mode, and then combining the weight of the bad observation value into a combined velocity measurement model to carry out least square adjustment calculation.
Scheme D: and (4) robust variance component estimation, namely adding variance component estimation on the basis of the scheme C, thereby forming an estimation method combining robust and variance components to carry out adjustment calculation on the pseudo range and Doppler combined velocity measurement model.
1) Static test
FIG. 2 is a chart of true errors in velocity measurements for each solution. The method comprises the steps of selecting static observation data with annual accumulation date of 148d all days of the Australia Curtin University CUT0 station, and specifically resolving pseudo range and Doppler observation information on GPS L1 and BDS B1 acquired by a TrimbleNet R9 receiver. The speed true error of the conventional least square estimation has obvious fluctuation, and the speed true error has certain jitter due to the influence of poor observation values such as a lifting satellite and the like. After robust estimation, the fluctuation and jump are restrained to a certain degree, and in addition, the conventional variance component estimation can also achieve similar effect, but the estimation method based on the combination of robust estimation and variance component has the best effect.
Table 1 below is a true error statistical table for each solution. In the mean value of each solution scheme, the velocity mean value of the robust variance component estimation is closest to the velocity true value zero, the variance component estimation and the robust estimation are sequentially carried out, and the least square estimation is worst. According to the unbiased estimation of the parameters, the velocity estimation value of the robust variance component has the best unbiased property, so that the robust variance component estimation method can effectively balance the weights among observed values with different accuracies and correct the influence of systematic deviation, and the point is verified by the basic consistency of the statistics of internal and external coincidence. In addition, the inner and outer coincidence precision of the robust variance component estimation is smaller than that of other schemes, and the robust variance component estimation is the optimal of the four schemes according to the effectiveness of parameter estimation.
TABLE 1
2) Static simulation dynamic test
Fig. 3 shows true errors in the N and E directions of single-point positioning. Static simulation dynamic test is carried out on GPS and BDS single-frequency observation data with the year integration date of a certain CORS station in Jiangsu being 152d, the time duration being 12h and the frequency being 1 Hz. Except that the spike and the jump are caused by poor observed values such as a small amount of gross errors, the positioning error of the single-point positioning in each direction is within 5 m.
Fig. 4 shows the true X-direction velocity error of each solution. It can be seen from the figure that the variance component estimation is affected by the poor observation, and a speed estimation significantly deviating from the true value occurs, which can be suppressed to a greater extent by the robust estimation, so that the estimation of the robust variance component is improved. Therefore, variance component estimation is sensitive to poor observation values, and robustness performance is improved by combining robust estimation with robust estimation.
Table 2 below is a table of true error statistics for each scenario. The performance of the statistics of each solution is basically consistent with that of table 1, and the robust variance component estimation is still the optimal estimation in the four parameter estimation methods. Except that the amount of velocity error is increased compared to table 1, which indicates that the speed measurement accuracy is closely related to the quality of the original observed value, so it is necessary to add robust estimation to the variance component estimation.
TABLE 2
3) Exercise testing
Fig. 5 shows the resultant velocity measurement error for each solution. A SPAN series high-precision optical fiber closed-loop inertial navigation integrated navigation system and an Ublox NEO-M8T single-frequency receiver module of NovAtel, canada are installed on a motor vehicle, the two modules share the same satellite antenna, and dynamic data acquisition and test are carried out in Nanjing urban areas. And resolving the speed of the integrated navigation by adopting high-precision post-processing interferometric Explorer software as a reference value to make a difference with the speed of calculating single-frequency data acquired by the Ublob by each resolving scheme. As can be seen from the speed measurement error diagram of fig. 5, except for the tunnel of 553-581 epochs and the initial parking period, the satellite signal is interfered by the shielding, and the speed estimation errors obtained from other road sections can be guaranteed to be within 1.
Table 3 below is a statistical table of the errors of the respective solutions. As can be seen from Table 3, the statistics performed substantially in accordance with tables 1 and 2, and the general regularity thereof was further verified.
TABLE 3
Example 3
A global navigation satellite system comprising a receiver characterized by: the system comprises a code pseudo range/Doppler joint velocity measurement method based on robust variance component estimation. The satellite data is collected through the receiver, and when the speed is resolved, the observation data output by the receiver is resolved on a computing platform (such as a computer, a mobile phone and the like) and speed information is output or displayed.
It will be understood that the above embodiments are merely exemplary embodiments taken to illustrate the principles of the present invention, which is not limited thereto. It will be apparent to those skilled in the art that various modifications and improvements can be made without departing from the spirit and scope of the invention, and such modifications and improvements are also considered to be within the scope of the invention.
Claims (7)
1. A code pseudo range/Doppler joint velocity measurement method based on robust variance component estimation is characterized in that: the method comprises the following steps:
(1) Establishing a speed measuring function model and a random model;
(2) Obtaining an robust random model capable of inhibiting gross errors;
(3) Forming a combined velocity measurement model by a code pseudorange and Doppler velocity measurement function model and an robust random model;
(4) Solving the motion speed of the satellite receiver;
the method comprises the following specific steps of forming a combined velocity measurement model by a code pseudorange and Doppler velocity measurement function model and an robust random model, and iteratively solving the motion velocity of the satellite receiver by adopting a variance component estimation method: a) And combining a code pseudorange and Doppler velocity measurement function model and an robust random model into a combined velocity measurement model, wherein the formula (9) is as follows:
in the formula, subscripts 1 and 2 represent code pseudorange and doppler, respectively, and N and W represent corresponding combination terms, respectively; b) Iteratively adjusting the weight of each type of observed value by adopting a variance component estimation method, wherein the formula (10) is as follows:
in the formula, tr (x) represents matrix tracing, E (x) represents expectation, n is the number of observed values,
is an estimate of the unit weight variance, V is the residual vector,
subscripts 1 and 2 of each item represent code pseudorange and doppler, respectively, for robust equivalence weights;
the unit weight variance is obtained by solving the equation (10)
Evaluation of
Obtaining the weight of each type of observation value after adjustment by substituting formula (11):
in the formula (I), the compound is shown in the specification,
represents the weight obtained by single iteration adjustment, C is constant and can be fixedly selected
Subscripts 1 and 2 of each item represent code pseudorange and doppler, respectively;
c) And solving the motion speed of the satellite receiver by using the combined velocity measurement model after the estimation and adjustment of the component of the power difference, wherein the formula (12) is as follows:
in the formula (I), the compound is shown in the specification,
for the estimated velocity vector, superscript-1 represents the matrix inversion operation;
repeating the steps a), b) and c) until the estimated values of the unit weight variances of all types are equal or are verified to be equal by hypothesis, and then obtaining the final movement speed of the receiver;
when the step of iteratively solving the motion speed of the satellite receiver by adopting a variance component estimation method is carried out, if the equal unit weight variance estimation value can not be met or hypothesis test is passed through 4-5 times of loop iteration, a loop is skipped, and the robust solution is directly adopted as a final solving result.
2. The robust variance component estimation-based code pseudorange/doppler joint velocity measurement method according to claim 1, characterized in that: the velocity measurement function model and the random model are established according to observation information of code pseudo range, doppler, carrier-to-noise ratio and satellite altitude.
3. The robust variance component estimation based code pseudorange/doppler joint velocity measurement method as claimed in claim 1, wherein: the robust random model is obtained by adopting a least square robust estimation method and can inhibit the influence of gross errors.
4. The robust variance component estimation-based code pseudorange/doppler joint velocity measurement method according to claim 1, characterized in that: and solving the motion speed of the satellite receiver by adopting a variance component estimation method to carry out iterative solution.
5. The code pseudorange/doppler joint velocity measurement method based on robust variance component estimation according to claim 2, characterized by comprising the following specific steps:
the method comprises the following steps of respectively establishing a function model and a random model for speed measurement by adopting code pseudorange, doppler, carrier-to-noise ratio and satellite altitude observation information:
a) And calculating the change rate of the code pseudo range and the carrier wave by a differential mode among epochs, wherein the formula (1) is as follows:
wherein ρ and
respectively the code pseudorange and its rate of change,
and
respectively a carrier phase and a change rate thereof, D is a Doppler observed value, delta t is differential time, and subscripts k and k +1 of each item are respectively a kth moment and a kth +1 moment;
b) Establishing a function model for speed measurement by using the code pseudo range and the Doppler observed value, wherein a GNSS observation equation is shown as a formula (2):
where ρ is the receiver code pseudorange observation,
for receiver carrier phase observations, N 0 Lambda is the carrier wavelength, R is the true geometric distance between the receiver and the satellite, c is the speed of light, δ t is the clock error, δ ρ ion To ionospheric delay, δ ρ trop For tropospheric delay, epsilon ρ And
the method comprises the following steps of (1) taking other error items including orbit errors, multipath effects and observation noise, wherein superscripts s and subscripts r of the items represent a satellite and a receiver respectively;
the time t is derived and linearized according to a GNSS observation equation, as shown in equation (3):
in the formula (I)
Represents the rate of change with time t, and
in the formula, r s 、
Is a satellite position and velocity column vector, r, in the ECEF coordinate system r 、
Is a receiver position and velocity column vector R in an ECEF coordinate system 0 To be approximated by a receiver r0 The geometric distance between the receiver and the satellite is obtained,
for the receiver approximate velocity, x, y and z are the projections of the position vector in the ECEF coordinate system, v x 、v y And v z The projection of the velocity vector under the ECEF coordinate system;
corresponding speed measurement function models can be obtained by combining the formulas (1), (3) and (4);
c) And establishing a random model for speed measurement by utilizing the carrier-to-noise ratio and the satellite altitude angle observation information, wherein the formula (5) is as follows:
where σ is covariance, E is satellite altitude, subscript i is satellite number, S is scaling factor, and constant term a 0 、a 1 And E 0 Defined by the following table:
wherein the scaling factor S is defined by the satellite carrier-to-noise ratio, as shown in equation (6):
in the formula, C/N 0 Representing the satellite carrier-to-noise ratio, and int (—) is an integer function; is composed of equations (5), (6) and constant term a 0 、a 1 And E 0 Can determine a prior random model of velocity measurement.
6. The robust variance component estimation based code pseudorange/doppler joint velocity measurement method as claimed in claim 3, wherein: the method for obtaining the robust random model capable of inhibiting the gross error influence by adopting the least square robust estimation method comprises the following specific steps:
a) And obtaining a residual vector and a corresponding co-factor through least square estimation, as shown in formula (7):
wherein B is a design matrix, P is a prior weight, l is an observed value vector, Q is an observed value co-factor,
the parameter to be estimated, V is the residual vector, Q vv Is a residual error co-factor;
b) And obtaining an robust random model capable of inhibiting gross error influence by an IGG III equivalent weight scheme, wherein the robust random model is shown as a formula (8):
in the formula (I), the compound is shown in the specification,
to normalize the residual, k 0 And k 1 Is a constant value of k 0 ∈[1.0～1.5]，k 1 ∈[2.5～8.0]，
For robust equivalence, subscript i represents the ith observation.
7. A global navigation satellite system comprising a receiver characterized by: the system adopts a code pseudo-range/Doppler joint velocity measurement method based on robust variance component estimation as claimed in any one of claims 1-6; the satellite data is collected through the receiver, and when the speed is resolved, the speed information is resolved and output or displayed on the computing platform through observation data output by the receiver.
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