CN116794688A - Robust filtering method based on satellite quality evaluation - Google Patents
Robust filtering method based on satellite quality evaluation Download PDFInfo
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/23—Testing, monitoring, correcting or calibrating of receiver elements
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/13—Receivers
- G01S19/35—Constructional details or hardware or software details of the signal processing chain
- G01S19/37—Hardware or software details of the signal processing chain
Abstract
The application relates to the technical field of satellite positioning, in particular to a robust filtering method based on satellite quality evaluation, which comprises the following steps: the receiver collects navigation messages in real time; step 2: single-point positioning obtains the position of a receiver and signal quality evaluation parameters; step 3: carrying out satellite signal quality evaluation and judging whether the observation matrix is full of rank; step 4: calculating an anti-difference factor and calculating a Kalman gain; step 5: multi-epoch joint observation is carried out, and a full-rank complete geometric constraint solving new predicted value is established; step 6: and reserving the current epoch parameters and entering the next epoch calculation. The scheme of the application has the advantages of being capable of reducing the influence of weak satellite signal strength, multipath effect and the like on positioning accuracy and improving continuous positioning resolving power.
Description
Technical Field
The application relates to the technical field of satellite positioning, in particular to a relative positioning method based on robust filtering and multi-epoch combined observation interpolation of satellite quality evaluation.
Background
Thanks to global networking of the Beidou satellite navigation system, the positioning scheme about satellites is widely applied. The method is developed from pseudo-range single-point positioning to carrier phase differential positioning (RTK) and then to network RTK, and the positioning precision can reach millimeter level optimally. However, the satellite signal carrier frequency is ultimately selected to be in the ultra high frequency range (UHF) subject to the specific requirements of the satellite signal. In complex environments such as the wild or urban canyon, satellite signals can face the problems of crown or high building shielding, reduced signal strength, uneven satellite geometric distribution, multipath effect and the like, and the satellite positioning precision can be rapidly deteriorated and even can not be positioned.
In the satellite positioning process, a Kalman filter is an indispensable link, and is generally improved in relation to the satellite positioning characteristics, so as to solve the problem that an Extended Kalman (EKF) is derived from a nonlinear system, and to solve the problem of precision reduction of a high-dimensional state space, a volume Kalman (CKF) method is proposed by Haykin, and the like. Aiming at the problem of outlier errors and multipath, the concept of robust Kalman filtering is proposed. Yang Yuanxi it is proposed that the IGGIII model can construct an equivalent weight matrix of the observed variance with a weight-reducing factor for different residual values. For the research of robust filtering, most of the research is focused on different calculation schemes of the weight reduction factors, and in the actual working condition, due to the correlation of signals among epochs, for the situation that the number of visible satellites is insufficient for relative positioning and resolving, part of rough differences can influence other observed values, so that abnormal weight reduction phenomenon is caused.
Disclosure of Invention
The application aims to provide a robust filtering method based on satellite quality evaluation, which aims to enhance the robustness of Kalman filtering, reduce the occurrence probability of outliers and provide a scheme for continuously outputting a settlement result under the condition of insufficient resolution of visible satellites.
In order to achieve the above object, the present application provides a robust filtering method based on satellite quality assessment, comprising the steps of:
step 1: the receiver collects navigation messages in real time;
step 2: single-point positioning obtains the position of a receiver and signal quality evaluation parameters;
step 3: carrying out satellite signal quality evaluation and judging whether the observation matrix is full of rank;
step 4: calculating an anti-difference factor and calculating a Kalman gain;
step 5: multi-epoch joint observation is carried out, and a full-rank complete geometric constraint solving new predicted value is established;
step 6: and reserving the current epoch parameters and entering the next epoch calculation.
In the process of acquiring the navigation message in real time by the receiver, the multimode single-frequency receiver is used for receiving the Beidou satellite single-frequency signal and the GPS satellite single-frequency signal, decoding the signals to obtain the observation data and the navigation message, and converting the data format into an RTCM3 format.
In the process of acquiring the receiver position and the signal quality evaluation parameters by single-point positioning, the pseudo-range and carrier phase observation values are extracted from the observation data, the receiver position is acquired by single-point positioning of the pseudo-range, satellite-to-ground vectors of all satellites are acquired, and therefore precision factors and satellite elevation angles are calculated, and iteration initial values are provided for Kalman filtering.
In the process of evaluating satellite signal quality and judging whether an observation matrix is full of rank, performing rough evaluation on satellite signals according to PDOP and elevation angle, wherein the PDOP threshold is set to 4, the satellite elevation angle is set to 20 degrees, and judging whether the observation matrix is full of rank for screened satellites; if the signal quality evaluation is passed, the method proceeds to step 4 of claim 1, and if the signal quality evaluation is not passed, the current epoch observation value is considered to be unable to complete the resolving process, and step 4 is skipped.
Wherein, for calculating the robust factor, the process of calculating the Kalman gain comprises the following steps:
1) Obtaining pseudo-range residual errors and carrier phase residual errors through the observation values and the one-step predicted values, calculating the mahalanobis distance of residual error vectors obeying Gaussian distribution, and carrying out chi-square test on the residual error vectors;
2) Setting the chi-square test quantity threshold as the hyper-parameter of the Huber loss function, normalizing the Mahalanobis distance of the residual vector, and calculating the Huber loss function after comparing with the hyper-parameter to obtain a more robust measurement error covariance matrix;
3) And calculating a Kalman filtering gain by using the new error covariance matrix, updating the state estimation value and the state mean square error matrix, and skipping step 5.
For multi-epoch joint observation, a process of establishing a full-rank complete geometric constraint to solve a new predicted value includes the following steps:
1) Exiting the calculation of the filtering gain, and respectively stacking the predicted values and residual values of the first N epoch observation data to obtain a new measurement matrix so as to obtain a satellite observation equation set with complete geometric constraint;
2) And respectively interpolating the predicted value and the residual error by using a Lagrange interpolation method to obtain a new fitting value. Assuming that the first N epochs share N satellite observations, constructing an N-1 degree basic polynomial;
3) Obtaining a fitting polynomial curve p (X) of residual errors and predicted values, and further obtaining predicted values X of all satellites in the current epoch k The state estimation value and the state mean square error matrix are updated.
And the calculation filter gain part for updating Kalman filter measurement is completed, and the subsequent calculation is continued.
The application has the beneficial effects that:
the method is used for reducing the influence of weak satellite signal strength, multipath effect and the like on positioning accuracy and improving continuous positioning resolving power. The improved filtering scheme aiming at the complex environment is provided, satellite quality evaluation is carried out before Kalman gain is calculated, and multi-epoch combined observation is adopted for the observation value with poor signal quality so as to avoid pollution to subsequent epoch solution; in the weighted part of the measurement covariance matrix, firstly calculating the mahalanobis distance of the residual vector, and tuning the hyper-parameters of the Huber loss function according to the mahalanobis distance, so that the faster loss speed can be obtained in the part with larger residual; the application enhances the robustness of Kalman filtering and reduces the occurrence probability of wild values; and under the condition of solving the insufficient visible star, multi-epoch joint observation is adopted, so that the continuous output of a solving result is ensured, and the influence on the filtering gain is reduced.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings that are required to be used in the description of the embodiments of the present application will be briefly described below.
Fig. 1 is a flow chart of a robust filtering method based on satellite quality assessment.
Fig. 2 is a block diagram of a specific robust filtering algorithm.
Detailed Description
The application provides a robust filtering method based on satellite quality evaluation, which enhances the robustness of Kalman filtering, prevents the divergence of the filtering and reduces the occurrence probability of wild values; the positioning result can be continuously output and the influence on the Kalman filtering system is reduced under the condition of insufficient number of visible satellites.
Embodiments of the present application are described below with reference to the drawings in the present application. It should be understood that the embodiments described below with reference to the drawings are exemplary descriptions for explaining the technical solutions of the embodiments of the present application, and the technical solutions of the embodiments of the present application are not limited.
The embodiment of the application aims to solve the problem of Kalman filtering divergence in a positioning process caused by insufficient visible satellites, concentrated satellite distribution, overlarge residual errors and the like in complex environments such as urban canyons and tree shadows, and solves the problem that a complete resolving process cannot be completed due to poor satellite quality.
Referring to fig. 1, the present application provides a robust filtering method based on satellite quality evaluation, which includes the following steps:
step 1: the receiver collects navigation messages in real time, and the method is characterized in that a multimode single-frequency receiver is used for receiving Beidou satellite single-frequency signals and GPS satellite single-frequency signals, decoding is carried out to obtain observation data and navigation messages, and the data format is converted into an RTCM3 format;
step 2: single-point positioning is used for obtaining a receiver position and signal quality evaluation parameters, a pseudo range and a carrier phase observation value are extracted from observation data, the receiver position is obtained by using the pseudo range single-point positioning, satellite-to-earth vectors of all satellites are obtained, and therefore precision factors and satellite elevation angles are calculated, and iteration initial values are provided for Kalman filtering;
step 3: carrying out satellite signal quality evaluation, judging whether an observation matrix is full of rank, and carrying out coarse evaluation on satellite signals according to PDOP and elevation angle, wherein the PDOP threshold is set to 4, the satellite elevation angle is set to 20 degrees, judging whether the observation matrix is full of rank for the screened satellites, if the satellite signal quality evaluation is passed, entering step 4, and if the satellite signal quality evaluation is not passed, judging that the current epoch observation value cannot complete a resolving process per se, and skipping step 4;
step 4: calculating an robust factor, and calculating a Kalman gain, comprising the steps of:
obtaining pseudo-range residual errors and carrier phase residual errors through the observation values and the one-step predicted values, calculating the mahalanobis distance of residual error vectors obeying Gaussian distribution, and carrying out chi-square test on the residual error vectors;
setting the chi-square test quantity threshold as the hyper-parameter of the Huber loss function, normalizing the Mahalanobis distance of the residual vector, and calculating the Huber loss function after comparing with the hyper-parameter to obtain a more robust measurement error covariance matrix;
calculating Kalman filtering gain by using the new error covariance matrix, updating the state estimation value and the state mean square error matrix, and skipping step 5;
step 5: the multi-epoch joint observation establishes a full-rank complete geometric constraint to solve a new predicted value, and comprises the following steps:
exiting the calculation of the filtering gain, and respectively stacking the predicted values and residual values of the first N epoch observation data to obtain a new measurement matrix so as to obtain a satellite observation equation set with complete geometric constraint;
and respectively interpolating the predicted value and the residual error by using a Lagrange interpolation method to obtain a new fitting value. Assuming that the first N epochs share N satellite observations, constructing an N-1 degree basic polynomial;
obtaining a fitting polynomial curve p (x) of residual errors and predicted values, thereby obtaining each current epochPredicted value X of satellite k Updating the state estimation value and the state mean square error matrix;
step 6: the current epoch parameters are reserved, next epoch resolving is carried out, specifically, the predicted value and the residual vector are reserved for providing measurement data when the subsequent epoch joint observation is carried out, the calculation filtering gain part of Kalman filtering measurement updating is completed, and the subsequent resolving is continued.
Before Kalman filtering calculates the filtering gain, the embodiment of the application evaluates coarse screening according to satellite signal quality, excludes observation values with poor signal quality, combines multiple epochs to form an observation value augmentation matrix, combines residual values of all satellites and one-step prediction values, and generates a new prediction value of a current epoch through a Lagrange interpolation method so as to avoid polluting other observation values and a Kalman filtering system. Furthermore, it is proposed to use the Huber loss function to weight down the covariance matrix, use the mahalanobis distance based on the residual as a reference for the super parameter, so that the tuning function is associated with the residual, and obtain a faster loss speed in case the residual is much larger than the super parameter, please refer to fig. 2, and the following will describe from the specific steps:
step 1: the application uses the receiver to receive GNSS satellite signals in real time, and in order to make the scheme have larger universality, the application selects to use a multimode single-frequency receiver to receive Beidou and GPS single-frequency signals, and decodes the Beidou and GPS single-frequency signals to obtain observation data and navigation messages. Firstly, single-point positioning is carried out to obtain the position of a receiver, and taking an nth satellite as an example, a pseudo-range observation equation of a receiver R is expressed as follows:
the carrier phase observation equation is:
wherein ρ is (n) Is the pseudo-range observation value phi (n) R is the carrier phase observation (n) ＝||x (n) -x||For the geometrical distance between the receiver R and the satellite n δt R And δt (n) The clock error and satellite clock error of the receiver are respectively, I and T are atmospheric delays, N is integer ambiguity, and ζ is random noise. In determining the receiver position, equation (1) may be rewritten as:
wherein, the liquid crystal display device comprises a liquid crystal display device,for the pseudo-range observation value after error correction, if N satellites form a nonlinear equation set, the following matrix equation can be obtained by linearizing the pseudo-range observation value:
wherein the method comprises the steps of
Represents r (n) Bias to x at x k-1 Values at, namely:
then h= (G T G) -1 The trace of the weight matrix H is expressed as a geometric precision factor (PDOP), where the PDOP may reflect the geometric distribution of the satellite relative to the receiver, the more dispersed the geometric distribution, the stronger the correlation between the PDOP and the positioning error, and the smaller the PDOP value may make the positioning error smaller. Errors caused by atmospheric delays and multipath effects of satellites with too low elevation angles are difficult to eliminate, and the elevation parameters are obtained from the satellite-to-ground vectors when calculating the receiver position. A time update initial value is provided for the kalman filter.
Step 3: and (3) carrying out satellite quality evaluation, firstly excluding satellites with the elevation angle smaller than 20 degrees, checking whether an observation matrix is full of rank or not by the residual satellites, and judging whether PDOP is smaller than 4 or not. By entering the subsequent step, step 4 is not entered by passing.
Step 3.1: and calculating pseudo-range residual errors and carrier phase residual errors, and endowing the current epoch observation values with robust factors according to the chi-square test results of the residual errors.
Wherein the residual error v k Is the difference between the observed value and the one-step predicted value. And carrying out chi-square test on the residual vector according to the square compliance chi-square distribution of the mahalanobis distance of the residual vector subjected to Gaussian distribution. The calculation formula of the mahalanobis distance is as follows:
where μ is the residual mean of the first N epochs, Σ -1 Is a covariance matrix. D (D) mk Square compliance chi-square distribution of (c):
according to the method of the substation hypothesis test, the residual vector is considered to completely exclude the influence of observation errors and system noise, namely the probability that the residual vector obeys normal distribution is alpha
In the method, in the process of the application,for chi-square distribution with significant level α, T is the detection threshold. The choice of the threshold determines the robustness of the filtering.
Step 3.2: the detection amount threshold of step 3 is set as the super-parameter of the Huber loss function. The normalized residual can be directly involved in tuning the robust factor. The Huber function expression is:
the Huber function is a tuning function that integrates MAE (linear error) and MSE (square error), the speed of MSE loss is faster, and the robustness of MAE is better, and the gradient drop is more gradual. The emphasis of functions on MAE and MSE is determined by the parameter adjustment of the super-parameter delta, in the generation of the robust factor, the smoothness of filtering iteration is ensured, the sensitivity problem to outliers is reduced, and the variance matrix with overlarge residual error is properly expanded to reduce the weight of the variance matrix in the calculation of filtering gain.
Step 3.3: and calculating a filter Gain, updating the state estimation value and the state mean square error matrix, and performing subsequent calculation.
Wherein, the liquid crystal display device comprises a liquid crystal display device,and R is an observation covariance matrix for the estimated value mean square error matrix.
Step 4: for the observation values which do not pass through the satellite data coarse screen in the step 3, if the number of satellites is too small, the equation set cannot be solved due to the fact that the rank of the observation equation is insufficient, and if the geometric precision factor of the satellite is too large, the satellite is considered to be difficult to fix the whole-cycle ambiguity due to too large residual value after the double-difference equation is established. The first 5 epoch observations are selected to be fitted to obtain a new predicted value, the Kalman filtering gain is skipped, and the subsequent calculation is continued.
Step 4.1: obtaining predicted values in the first 5 epoch observation data by adopting a multi-epoch combined observation interpolation methodAnd residual value v k The augmented matrices are stacked separately to obtain satellite observations with complete geometric constraints.
Step 4.2: and respectively interpolating the predicted value and the residual error by using a Lagrange interpolation method to obtain a new fitting value. Assuming that the first 5 epochs have N satellite observations in total, constructing N-1 base polynomials such that they satisfy the following conditions: l (L) i (x) At x i The function value at 1, at x j Where the function value is equal to 0, i.e
Wherein x is j To divide by x i Residual values of other satellites than L i (x) Constructing an n-1 degree polynomial for the predicted value of the current satellite as follows:
step 4.3: obtaining a fitting polynomial curve p (X) of residual errors and predicted values, and further obtaining predicted values X of all satellites in the current epoch k And skipping the calculation of the filter gain, and continuing the subsequent calculation step.
The foregoing description is directed to the preferred embodiments of the present application, but the embodiments are not intended to limit the scope of the application, and all equivalent changes or modifications made under the technical spirit of the present application should be construed to fall within the scope of the present application.
Claims (7)
1. A robust filtering method based on satellite quality assessment, comprising the steps of:
step 1: the receiver collects navigation messages in real time;
step 2: single-point positioning obtains the position of a receiver and signal quality evaluation parameters;
step 3: carrying out satellite signal quality evaluation and judging whether the observation matrix is full of rank;
step 4: calculating an anti-difference factor and calculating a Kalman gain;
step 5: multi-epoch joint observation is carried out, and a full-rank complete geometric constraint solving new predicted value is established;
step 6: and reserving the current epoch parameters and entering the next epoch calculation.
2. The robust filtering method based on satellite quality assessment according to claim 1, wherein in step 1, in the process of the receiver collecting the navigation message in real time, the multimode single-frequency receiver is used to receive the Beidou satellite single-frequency signal and the GPS satellite single-frequency signal, and the data format is converted into the RTCM3 format after decoding to obtain the observation data and the navigation message.
3. The robust filtering method based on satellite quality assessment according to claim 1, wherein in step 2, in the process of obtaining the receiver position and the signal quality assessment parameter by single-point positioning, the pseudo-range and carrier phase observations are extracted from the observed data, the receiver position is obtained by single-point positioning using the pseudo-range, and the satellite-to-ground vector of each satellite is obtained, thereby calculating the precision factor and the satellite elevation angle, and providing iterative initial values for the kalman filtering.
4. The robust filtering method based on satellite quality assessment according to claim 1, wherein in step 3, in the process of performing satellite signal quality assessment and judging whether the observation matrix is full rank, coarse assessment is performed on satellite signals according to PDOP and elevation angle, wherein PDOP threshold is set to 4, satellite elevation angle is set to 20 °, and whether the observation matrix is full rank is judged for the screened satellites; if the signal quality evaluation is passed, the step 4 is entered, and if the signal quality evaluation is not passed, the current epoch observation value is considered to be unable to complete the resolving flow, and the step 4 is skipped.
5. The robust filtering method based on satellite quality assessment according to claim 1, wherein in step 4, said process of calculating kalman gain for calculating robust factors comprises the steps of:
1) Obtaining pseudo-range residual errors and carrier phase residual errors through the observation values and the one-step predicted values, calculating the mahalanobis distance of residual error vectors obeying Gaussian distribution, and carrying out chi-square test on the residual error vectors;
2) Setting the chi-square test quantity threshold as the hyper-parameter of the Huber loss function, normalizing the Mahalanobis distance of the residual vector, and calculating the Huber loss function after comparing with the hyper-parameter to obtain a more robust measurement error covariance matrix;
3) And calculating a Kalman filtering gain by using the new error covariance matrix, updating the state estimation value and the state mean square error matrix, and skipping step 5.
6. The robust filtering method based on satellite quality assessment according to claim 1, wherein in step 5, the process of establishing a full-rank full geometric constraint for multi-epoch joint observation to solve for new predictions comprises the steps of:
1) Exiting the calculation of the filtering gain, and respectively stacking the predicted values and residual values of the first N epoch observation data to obtain a new measurement matrix so as to obtain a satellite observation equation set with complete geometric constraint;
2) And respectively interpolating the predicted value and the residual error by using a Lagrange interpolation method to obtain a new fitting value. Assuming that the first N epochs share N satellite observations, constructing an N-1 degree basic polynomial;
3) Obtaining a fitting polynomial curve p (X) of residual errors and predicted values, and further obtaining predicted values X of all satellites in the current epoch k The state estimation value and the state mean square error matrix are updated.
7. The robust filtering method based on satellite quality assessment according to claim 1, wherein in step 6, the prediction value and the residual vector are reserved to provide measurement data when the next epoch is jointly observed in the process of reserving the current epoch parameter and entering the next epoch solution, so as to complete the calculation filtering gain part of the kalman filtering measurement update and continue the subsequent solution.
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