CN117289323A

CN117289323A - Course angle constraint whole-cycle ambiguity searching method

Info

Publication number: CN117289323A
Application number: CN202311244681.1A
Authority: CN
Inventors: 张成龙; 陈雯; 董大南; 彭宇
Original assignee: East China Normal University
Current assignee: East China Normal University
Priority date: 2023-09-26
Filing date: 2023-09-26
Publication date: 2023-12-26

Abstract

The invention discloses a course angle constraint whole-cycle ambiguity searching method, which is characterized in that an inertial navigation component is adopted to obtain a carrier attitude observation value, a priori course angle is calculated through a GNSS/INS tight combination or integration method, then an objective function of course angle constraint is constructed in the searching process of the GNSS whole-cycle ambiguity, the searching and fixing of the whole-cycle ambiguity are constrained, and the precision of GNSS carrier attitude measurement is improved. Compared with the prior art, the invention has the advantages of improving the fuzzy fixing accuracy and the GNSS gesture heading angle accuracy, can be applied to a mobile baseline mode and a base station differential mode, and has good application prospect.

Description

Course angle constraint whole-cycle ambiguity searching method

Technical Field

The invention relates to the technical field of GNSS high-precision positioning, in particular to a course angle constraint integer ambiguity searching method.

Background

INS (Inertial Navigation Systems) has the advantages of no interference from external environment and high precision in observing the posture of the carrier, but has higher cost and cannot keep high precision for a long time. The long term stability of GNSS (Global Navigation Satellite System) can complement the INS system to help the measurement of carrier attitude. GNSS carrier attitude measurements solve for a baseline vector by means of a number of antennas placed on the carrier and obtain attitude information of the carrier in a corresponding coordinate system by conversion of the baseline vector. Because the distance between the antennas is fixed, the distance can be obtained by measurement in advance before observation, and therefore the baseline length can be used as an observation auxiliary LAMBDA (class-squares AMBiguity Decorrelation Adjustment) ambiguity search, and the solution of the baseline vector is constrained from the angle of the baseline length. However, the baseline length constraint LAMBDA has a limitation, and the premise of using the constraint is that the length of the baseline needs to be known, the baseline length can be conveniently measured in a mobile baseline measurement mode, but the baseline length in a differential mode of the reference station cannot be measured in advance. More importantly, the base line length is a scale unit, and the constraint condition can ensure that the settled base line length keeps high precision, but cannot ensure the posture of the carrier in the three-dimensional space.

The cost of the combined GNSS/INS navigation is reduced due to the large-scale use of the low cost IMU (Inertial Messurement Unit). And the accuracy of the short-time course angle provided by the IMU is also superior to the course angle calculated by the GNSS gesture measurement technology. Thus, heading angle may be considered for aiding in searching of GNSS ambiguities, constraining heading angle accuracy of the carrier in three-dimensional space.

The carrier course angle calculated by the prior art has low accuracy, and the application field is greatly limited.

Disclosure of Invention

The invention aims to provide a course angle constraint integer ambiguity searching method aiming at the defects of the prior art, which adopts an inertial navigation component to obtain a carrier attitude observation value, calculates a priori course angle through a GNSS/INS tight combination or integration method, then constructs a course angle constraint objective function in the GNSS integer ambiguity searching process, constrains the integer ambiguity searching and fixing, and improves the precision of GNSS carrier attitude measurement. The method adopts a low-cost IMU to observe carrier attitude change, calculates a priori carrier course angle for constraint by using a loose combination navigation and integration method, determines an ambiguity search space by using initial ambiguity, enumerates all ambiguity candidate vectors in the search space, linearizes conditional baseline vectors and course angles obtained by calculating each set of ambiguity candidate vectors according to covariance propagation rate, iteratively estimates a baseline vector constraint solution, evaluates each set of baseline vector constraint solution based on a course angle and ambiguity search objective function, selects a baseline vector constraint solution with the minimum quadratic residue as a final baseline vector, and constructs a test condition to test the final baseline vector in order to ensure the accuracy of the solution, if the test condition is met, the epoch is a fixed solution, otherwise, the epoch is a floating point solution. The method is characterized in that an inertial navigation component is adopted to obtain a carrier attitude observation value, a priori course angle is calculated through a GNSS/INS tight combination or integration method, then an objective function of course angle constraint is constructed in the searching process of GNSS whole-cycle ambiguity, and the searching and fixing of the whole-cycle ambiguity are constrained, so that the accuracy of fuzzy fixing is greatly improved, the accuracy of GNSS attitude measurement course angle is effectively improved, and the method can be applied to a mobile baseline mode and a base station differential mode and has good application prospects.

The specific technical scheme for realizing the aim of the invention is as follows: the course angle constraint integer ambiguity searching method is characterized in that the course angle constraint ambiguity searching obtained by low-cost IMU calculation is utilized, so that the accuracy of GNSS attitude measurement is ensured, and the course angle constraint ambiguity fixing specifically comprises the following steps:

and step 1, carrying out Kalman filtering parameter calculation on GNSS multi-system combined observation data to obtain a baseline vector, a ambiguity floating solution and a variance covariance matrix.

Step 2, calculating the prior course angle by using GNSS Doppler observation value and INS pine combination, if the carrier speed is less than 3m/s, directly calculating the prior course angle by using an integral method, and giving the variance of the prior course angle

And 3, carrying out orthogonal decomposition and decorrelation on the floating ambiguity vectors, fixing a group of initial ambiguity vectors by using a Bootstrapping algorithm, and calculating the size of a search space according to an ambiguity search objective function containing prior course angle constraint.

Step 4, enumerating all ambiguity candidate vectors in the search space, calculating a conditional baseline vector corresponding to each ambiguity candidate vector according to covariance propagation rate, linearizing the prior course angle and the conditional baseline vector, and using the baseline vector parameter estimation value under the constraint condition of Gaussian Newton iteration estimation

Step 5, constraint baseline vector calculated based on Gaussian Newton iterationAnd calculating quadratic residues under the objective function with the corresponding ambiguity candidate vectors, and selecting the set of ambiguity candidate vectors with the minimum quadratic residues and constraint baseline vector parameters.

Step 6, utilizing the set prior course angle varianceConstructing a test condition, namely, a constraint baseline vector with minimum quadratic residue>And (5) checking, wherein if the checking is passed, the current moment is a fixed solution, and otherwise, the current moment is a floating solution.

In the step 1, an observation equation is constructed for the GNSS multi-system observation values, and a baseline vector and an ambiguity floating solution are directly solved by using Kalman filtering.

In the step 2, a priori course angle is calculated in a self-adaptive mode, and when the carrier speed is less than 3m/s, the course angle is calculated by integration directly adopting an original observation value of an INS system; when the carrier speed is greater than 3m/s, the carrier course angle is calculated by using the loose combination of GNSS/INS, so that each epoch is ensured to have the prior course angle available for constraint.

In the step 3, a Bootstrapping algorithm is used to obtain an initial ambiguity vector, and then an ambiguity search space is calculated by using an ambiguity fixed objective function F (a) containing a priori heading angle, wherein the ambiguity fixed objective function F (a) is obtained by the following formula (1):

wherein,fixing the initial ambiguity vector for Bootstrapping, a is the unknown ambiguity vector, is an ambiguity covariance matrix +.>Conditional baseline vector solution calculated for covariance propagation rate,/->Obtained by the following formula (2):

wherein argmin represents a minimum function parametrization operator, b is an actual baseline vector, R represents a real number, b _E Representing the baseline component in the E direction, b _N Representing the baseline component in the N direction, and γ represents the heading angle for the constraint.

In the step 4, the course angle and the conditional baseline vector are linearized, and the estimated value of the baseline vector parameter under the constraint condition is calculated by using gaussian newton iteration, wherein the linearization process of the course angle and the conditional baseline vector is shown in the formulas (3), (4), (5), (6) and (7):

Δb ⁱ ＝b ⁱ -b ^i-1 (7)。

wherein E (-) is a mathematical desired operator, D (-) is a variance operator, Q _H As a matrix of variances which is to be found,andb in the course angle observation equation respectively at the ith iteration _E 、b _N And b _U Coefficient of Deltab ⁱ Baseline vector b representing the ith iteration estimate ⁱ And b ^i-1 Delta of when deltab ⁱ When the I is smaller than the set threshold, the iteration is considered to be converged, and then the final estimated value of the baseline vector under the constraint condition is calculated by the following formula (8)>

In the step 5, the quadratic residuals of all the base line vector constraint solutions are compared directly based on the ambiguity objective function, and the smallest base line vector is selected as the final base line vector.

In the step 6, the selected baseline vector is checked by using a checking condition, if the checking condition is met, the epoch is a fixed solution, otherwise, the epoch is a floating solution, and the checking condition is obtained by the following formula (9):

wherein, gamma is the prior course angle; sigma (sigma) _γ Is the prior course angle standard deviation; arctan is an arctangent function;a baseline vector E direction component selected under the course angle constraint; />A baseline vector N direction component selected under heading angle constraints.

Compared with the prior art, the method has the advantages of improving the fuzzy fixing accuracy, greatly improving the precision of the GNSS gesture-measuring course angle, further widening the application field, being applicable to a mobile baseline mode and a base station differential mode, having higher calculated carrier course angle precision, providing more reliable course angle information for navigation of the carrier in urban environment and having good application prospect.

Drawings

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a schematic diagram of a vehicle-mounted dynamic experimental route;

FIG. 3 is a visible satellite throughout an observation period;

FIG. 4 is a schematic diagram of PDOP (Position Dilution of Precision);

FIG. 5 is a graph of deviation of vector heading angle from true value for combined solution of loose combination and integral method;

FIG. 6 is a diagram of the initial search space size for each epoch;

FIG. 7 is a graph of the number of ambiguities enumerated in each epoch search space;

FIG. 8 is a quadratic residue size corresponding to the ambiguity candidate vector ultimately selected for each epoch;

fig. 9 is a plot of the heading angle deviation for the LAMBDA with the baseline length constraint and the LAMBDA algorithm with the heading angle constraint.

Detailed Description

Referring to fig. 1, the present invention specifically includes the following steps:

step 1: and carrying out Kalman filtering parameter calculation on the GNSS multi-system combined carrier and the pseudo-range observation value to obtain a baseline vector, a ambiguity floating solution and a variance covariance matrix.

Step 2: calculating the course angle by using GNSS Doppler observation value and INS pine combination, and directly calculating the course angle by using an integral method and giving the course angle variance if the carrier speed is less than 3m/s

Step 3: and carrying out orthogonal decomposition and decorrelation on the ambiguity floating solution, fixing a group of initial ambiguity vectors by using a Bootstrapping algorithm, and calculating the size of a search space according to an ambiguity search objective function containing course angle constraint.

Step 4: enumerating all ambiguity candidate vectors in a search space, calculating a conditional baseline vector corresponding to each ambiguity candidate vector according to covariance propagation rate, linearizing the prior course angle and the conditional baseline vector, and calculating a baseline vector parameter estimation value under a constraint condition by using Gaussian Newton iteration.

Step 5: based on the estimated baseline vector parameters and the corresponding ambiguity candidate vectors calculated by Gaussian Newton iteration, the quadratic residual of each group of ambiguity candidate vectors is calculated, and the group of ambiguity candidate vectors with the smallest quadratic residual and the estimated baseline vector parameters are selected.

Step 6: and (3) carrying out reliability test on the baseline vector selected in the step (6) by using a test condition, wherein if the test condition is met, the epoch is a fixed solution, otherwise, the epoch is a floating solution.

The invention is further illustrated by the following specific examples of vehicle experiments on day 53 of the year product day 2023.

Example 1

Referring to fig. 2 to 4, taking a vehicle-mounted mobile baseline mode as an example, two antennas are disposed on a roof parallel to a vehicle advancing direction, and a distance between the two antennas is about 1.2m. There is a lot of shielding on both sides of the vehicle driving route, challenges to the receiving of GNSS signals, to ensure enough GNSS satellites to participate in the solution, signals of GPS, BDS, GLONASS and GALIEO systems are received, the cut-off altitude is set to 10 degrees, and the sampling frequency is 5HZ. The whole dynamic data acquisition process lasts for about 30 minutes, and single epoch solution is carried out on experimental data by using Kalman filtering to obtain a baseline vector, a ambiguity floating solution and a variance covariance matrix.

Referring to FIG. 5, since the deviation of the heading angle is 0.01 radian, the heading angle variance is set

Referring to fig. 6, an initial search space size for each epoch.

Referring to fig. 7, since it would take time to enumerate all ambiguity candidate vectors, the upper limit for enumerating ambiguity candidate vectors is set to 100.

Referring to fig. 8, the secondary residual size corresponding to the ambiguity candidate vector finally selected for each epoch.

Referring to fig. 9, it is illustrated that the course angle constraint may effectively constrain the carrier course angle to near true values.

It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.

Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.

Claims

1. The course angle constraint whole-cycle ambiguity searching method is characterized by adopting course angle constraint GNSS ambiguity searching and fixing, and specifically comprises the following steps:

step 1, carrying out Kalman filtering parameter calculation on GNSS multi-system combined observation data to obtain a baseline vector, a ambiguity floating solution and a variance covariance matrix;

Step 3, carrying out orthogonal decomposition and decorrelation on floating point ambiguity vectors, utilizing a Bootstrapping algorithm to fix a group of initial ambiguity vectors, and calculating the size of a search space according to an ambiguity search objective function containing prior course angle constraint;

Step 5, constraint baseline vector calculated based on Gaussian Newton iterationCalculating quadratic residues under an objective function with the corresponding ambiguity candidate vectors, and selecting the set of ambiguity candidate vectors with the minimum quadratic residues and constraint baseline vector parameters;

2. The method for searching the whole-cycle ambiguity constraint on the course angle according to claim 1, wherein said step 2 calculates the course angle by using a self-adaptive method, and when the carrier speed is less than 3m/s, directly adopts the original observed value of the INS system to calculate the course angle by integration; when the carrier speed is greater than 3m/s, the prior course angle is calculated by using the loose combination of GNSS/INS, so that each epoch is ensured to have the prior course angle available for constraint.

3. The course angle-constrained integer ambiguity search method of claim 1, wherein said step 3 uses Bootstrapping algorithm to obtain an initial ambiguity vector, and then calculates an ambiguity search space using an ambiguity-fixed objective function F (a) containing the course angle, said ambiguity-fixed objective function F (a) being obtained by the following equation (1):

wherein,fixing an initial ambiguity vector for Bootstrapping; a is an unknown ambiguity vector; />For ambiguity covariance matrix，/> A conditional baseline vector calculated for the covariance propagation rate of (2) below;

wherein argmin represents a minimum function parametrization operator; b is the actual baseline vector; r represents a real number; b _E Is the baseline component of the E direction; b _N Is the baseline component in the N direction; gamma is the heading angle for the constraint.

4. The course angle-constrained integer ambiguity search method of claim 1, wherein said step 4 linearizes the course angle and the conditional baseline vector, and calculates the estimated value of the baseline vector parameter under constraint conditions using gaussian newton iteration, wherein the linearization process of the a priori course angle and the conditional baseline vector is as follows (3) to (7):

Δb ⁱ ＝b ⁱ -b ^i-1 (7)；

wherein E (·) is the mathematical desired operator; d (·) is the variance operator; q (Q) _H Is a variance matrix;and->B in the course angle observation equation respectively at the ith iteration _E 、b _N And b _U Coefficients of (2); Δb ⁱ Baseline vector b estimated for the ith iteration ⁱ And b ^i-1 When |Δb ⁱ When the I is smaller than the set threshold, the iteration is considered to be converged, and then the final estimated value of the baseline vector under the constraint condition is calculated by using the following (8)>

5. The course angle-constrained integer ambiguity search method of claim 1, wherein said step 6 uses a check condition to check the baseline vector selected in step 5, and if the check condition is satisfied, the epoch is a fixed solution, and otherwise is a floating solution, said check condition being obtained by the following expression (9):