CN112526569B - Multi-epoch step-by-step ambiguity solving method for inertial navigation auxiliary navigation relative positioning - Google Patents

Multi-epoch step-by-step ambiguity solving method for inertial navigation auxiliary navigation relative positioning Download PDF

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CN112526569B
CN112526569B CN202110186956.5A CN202110186956A CN112526569B CN 112526569 B CN112526569 B CN 112526569B CN 202110186956 A CN202110186956 A CN 202110186956A CN 112526569 B CN112526569 B CN 112526569B
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ambiguity
inertial navigation
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CN112526569A (en
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董毅
吴杰
王鼎杰
李青松
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National University of Defense Technology
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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
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • 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
    • G01S19/42—Determining position
    • G01S19/43—Determining position using carrier phase measurements, e.g. kinematic positioning; using long or short baseline interferometry
    • G01S19/44—Carrier phase ambiguity resolution; Floating ambiguity; LAMBDA [Least-squares AMBiguity Decorrelation Adjustment] method
    • 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
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • 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
    • G01S19/42—Determining position
    • G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
    • G01S19/47—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement the supplementary measurement being an inertial measurement, e.g. tightly coupled inertial

Abstract

The application relates to a multi-epoch step-by-step ambiguity solving method for inertial navigation auxiliary navigation relative positioning. The method comprises the following steps: obtaining position increment between reference station inertial navigation epochs and position increment between mobile station inertial navigation epochs, constructing an inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model according to the position increment between the reference station inertial navigation epochs and the position increment between the mobile station inertial navigation epochs, obtaining a baseline vector floating point solution and an ambiguity floating point solution at the k +1 moment by adopting a least square method, solving the integer ambiguity step by adopting a wide lane and a single frequency after the wide lane according to the baseline vector floating point solution and the ambiguity floating point solution to obtain a single-frequency ambiguity fixed solution, updating a baseline vector according to the single-frequency ambiguity fixed solution and the inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model, and obtaining a baseline vector fixed solution. The method can provide continuous and accurate positioning calculation.

Description

Multi-epoch step-by-step ambiguity solving method for inertial navigation auxiliary navigation relative positioning
Technical Field
The application relates to the technical field of satellite navigation precise relative positioning, in particular to a multi-epoch step-by-step ambiguity solving method for inertial navigation auxiliary satellite navigation relative positioning.
Background
The defense and guide relative positioning technology is widely applied to space rendezvous and docking of spacecrafts, air refueling of airplanes, intelligent vehicle transportation and carrier-based aircraft landing. Efficient and reliable integer ambiguity resolution is a key technology for precise relative positioning of satellite navigation. The multi-system multi-frequency signals of the satellite and navigation system can provide more observation information, and although the strength of a relative positioning model can be enhanced, the whole-cycle ambiguity solving success rate is improved, the problems of low efficiency and long time consumption of high-dimensional whole-cycle ambiguity solving are brought. At present, a commonly used three-frequency ambiguity solving algorithm based on multi-frequency observation information has a low widelane ambiguity solving success rate under the condition of high noise, and influences the overall success rate and the initialization performance of a step-by-step algorithm. In addition, the satellite signal is fragile, and in dynamic navigation, the satellite signal is easily interrupted due to the obstruction of adverse observation environments such as high buildings, overhead frames, tunnels and forests, and the reinitialization of the whole-cycle ambiguity is difficult to realize by simple satellite navigation. The two points enable the pure guide to have low success rate of a step-by-step solving algorithm based on multi-frequency observation information, the required initialization time is long, and a continuous and reliable precise relative positioning solution cannot be provided for a user.
Disclosure of Invention
Therefore, in order to solve the above technical problem, it is necessary to provide a multi-epoch step-by-step ambiguity resolution method for inertial navigation assistance guidance relative positioning, which can solve the problem that continuous positioning cannot be provided.
A multi-epoch step-by-step ambiguity solving method for inertial navigation auxiliary navigation relative positioning comprises the following steps:
acquiring position increment between reference station inertial navigation epochs and position increment between mobile station inertial navigation epochs;
constructing an inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model according to the position increment between the reference station inertial navigation epochs and the position increment between the mobile station inertial navigation epochs; the inertial navigation auxiliary satellite navigation multi-epoch floating solution filtering model determines the relationship between a k-moment ambiguity floating solution and a baseline vector forecast floating solution and a k + 1-moment ambiguity and a baseline vector;
obtaining a baseline vector floating solution and an ambiguity floating solution at the moment k +1 by adopting a least square method;
according to the baseline vector floating solution and the ambiguity floating solution, solving the integer ambiguity step by adopting a wide lane first and a single frequency later to obtain a single-frequency ambiguity fixed solution;
and updating a baseline vector according to the single-frequency ambiguity fixed solution and the inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model to obtain a baseline vector fixed solution.
In one embodiment, the method further comprises the following steps: obtaining the position increment between the reference station inertial navigation epochs and the position increment between the mobile station inertial navigation epochs as follows:
Figure 652398DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 501405DEST_PATH_IMAGE002
and
Figure 141334DEST_PATH_IMAGE003
respectively the sampling time of the leading epoch and the trailing epoch of the guard,
Figure 392187DEST_PATH_IMAGE004
representing the position increment among the inertial navigation epochs of the reference station,
Figure 967525DEST_PATH_IMAGE005
representing reference station inertial navigation
Figure 303828DEST_PATH_IMAGE006
The position of the epoch is determined by the location of the epoch,
Figure 763759DEST_PATH_IMAGE007
representing reference station inertial navigation
Figure 603539DEST_PATH_IMAGE008
The position of the epoch is determined by the location of the epoch,
Figure 349779DEST_PATH_IMAGE009
representing the position increment between the inertial navigation epochs of the mobile station,
Figure 907799DEST_PATH_IMAGE010
representing mobile station inertial navigation
Figure 656574DEST_PATH_IMAGE011
The position of the epoch is determined by the location of the epoch,
Figure 616440DEST_PATH_IMAGE012
representing mobile station inertial navigation
Figure 533580DEST_PATH_IMAGE013
Location of epoch.
In one embodiment, the method further comprises the following steps: according to the baseline vector floating solution at the previous moment, the baseline vector fixed solution at the previous moment, the position increment between the base station inertial navigation epochs and the position increment between the mobile station inertial navigation epochs, calculating to obtain a baseline vector forecast floating solution at the current moment and a baseline vector forecast fixed solution:
Figure 844476DEST_PATH_IMAGE014
wherein the content of the first and second substances,
Figure 380631DEST_PATH_IMAGE015
representing the baseline vector forecast floating solution at the current time,
Figure 195003DEST_PATH_IMAGE016
representing a baseline vector forecast fixed solution at the current moment;
Figure 548624DEST_PATH_IMAGE017
and
Figure 81236DEST_PATH_IMAGE018
respectively a previous-time baseline vector floating solution and a previous-time baseline vector fixed solution,
Figure 670350DEST_PATH_IMAGE019
and
Figure 339228DEST_PATH_IMAGE020
respectively obtaining position increment between reference station inertial navigation epochs and position increment between mobile station inertial navigation epochs;
to be provided with
Figure 863751DEST_PATH_IMAGE021
Time of day ambiguity float solution
Figure 883659DEST_PATH_IMAGE022
Baseline vector forecast floating point solution at current time
Figure 761616DEST_PATH_IMAGE023
And forecast fixed solutions
Figure 550581DEST_PATH_IMAGE024
For observed quantity, according to pseudo range and carrier phase double-difference observed quantity of current time
Figure 246004DEST_PATH_IMAGE025
Obtaining an inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model as follows:
Figure 487630DEST_PATH_IMAGE026
wherein the content of the first and second substances,
Figure 914151DEST_PATH_IMAGE027
and
Figure 823201DEST_PATH_IMAGE028
are respectively as
Figure 423947DEST_PATH_IMAGE029
The time-of-day ambiguity and the baseline vector,
Figure 418448DEST_PATH_IMAGE030
is composed of
Figure 638208DEST_PATH_IMAGE031
A covariance matrix of the time ambiguity floating solution,
Figure 401764DEST_PATH_IMAGE032
is composed of
Figure 173411DEST_PATH_IMAGE029
A covariance matrix of the floating solution is forecast at all times,
Figure 655208DEST_PATH_IMAGE033
is composed of
Figure 927927DEST_PATH_IMAGE029
The covariance matrix of the fixed solution is forecast at any moment,
Figure 545990DEST_PATH_IMAGE034
is composed of
Figure 754117DEST_PATH_IMAGE029
A covariance matrix of double-differenced pseudoranges at time and carrier-phase observations,
Figure 457631DEST_PATH_IMAGE035
is a unit matrix which is formed by the following steps,
Figure 19193DEST_PATH_IMAGE036
is a zero matrix.
Figure 757342DEST_PATH_IMAGE037
And
Figure 870792DEST_PATH_IMAGE038
the design matrices for the corresponding ambiguity and unknown parameters of the baseline vector are provided.
In one embodiment, the method further comprises the following steps: and obtaining a baseline vector floating solution and an ambiguity floating solution at the moment k +1 by adopting a least square method:
Figure 61602DEST_PATH_IMAGE039
wherein the content of the first and second substances,
Figure 177588DEST_PATH_IMAGE040
and
Figure 770243DEST_PATH_IMAGE041
to obtain
Figure 320173DEST_PATH_IMAGE042
An ambiguity float solution at the time and a baseline vector float solution.
In one embodiment, the method further comprises the following steps: obtaining a single-frequency ambiguity floating solution of each frequency point, and converting the single-frequency ambiguity floating solution according to a wide lane operator to obtain a wide lane ambiguity floating solution;
obtaining a wide lane ambiguity floating-point solution variance matrix of the wide lane ambiguity floating-point solution according to a covariance propagation law;
and searching the wide lane ambiguity floating solution variance matrix by adopting an LAMBDA algorithm to obtain an ultra-wide lane ambiguity fixed solution and a wide lane ambiguity fixed solution, establishing a single-frequency ambiguity observation equation according to the ultra-wide lane ambiguity fixed solution and the wide lane ambiguity fixed solution, and updating the single-frequency ambiguity floating solution according to the single-frequency ambiguity observation equation to obtain a single-frequency ambiguity fixed solution.
In one embodiment, the method further comprises the following steps: obtaining a carrier phase observation equation according to the single-frequency ambiguity fixed solution and the inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model;
and obtaining a baseline vector fixed solution through a least square algorithm according to the carrier phase observation equation.
According to the method for solving the multi-epoch step-by-step ambiguity of the inertial navigation auxiliary navigation relative positioning, the more accurate baseline vector and ambiguity floating solution are obtained, the success rate of solving the widelane ambiguity in the step-by-step algorithm is improved, and the initialization time of single-frequency ambiguity is shortened.
Drawings
FIG. 1 is a schematic flow chart illustrating a multi-epoch step-by-step ambiguity resolution method for inertial navigation assistance guidance relative positioning in one embodiment;
FIG. 2 is a schematic diagram of position increments between inertial navigation epochs in one embodiment;
FIG. 3 is a diagram of a baseline vector in one embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
The inertial navigation auxiliary navigation relative positioning multi-epoch step-by-step ambiguity solving method can be applied to a navigation and inertial navigation tight combination, namely the navigation and inertial navigation tight combination is arranged on a reference station or a mobile station, and the reference station or the mobile station can obtain navigation observation data and inertial navigation observation data. Satellite navigation devices, such as GPS receivers, GNSS devices, beidou receivers, etc., are referred to herein as satellite navigation devices, and inertial navigation devices, such as IMUs, are referred to as inertial navigation devices.
In one embodiment, as shown in fig. 1, a multi-epoch step-by-step ambiguity resolution method for inertial navigation assistance guided relative positioning is provided, which includes the following steps:
and 102, acquiring position increment between the reference station inertial navigation epochs and position increment between the mobile station inertial navigation epochs.
And 104, constructing an inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model according to the position increment between the reference station inertial navigation epochs and the position increment between the mobile station inertial navigation epochs.
And step 106, acquiring a baseline vector floating solution and an ambiguity floating solution at the moment k +1 by adopting a least square method.
And step 108, solving the integer ambiguity step by adopting a wide lane first and a single frequency later according to the baseline vector floating solution and the ambiguity floating solution to obtain a single-frequency ambiguity fixed solution.
And step 110, updating the baseline vector according to the single-frequency ambiguity fixed solution and the inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model to obtain a baseline vector fixed solution.
According to the method for solving the multi-epoch step-by-step ambiguity of the inertial navigation auxiliary navigation relative positioning, the more accurate baseline vector and ambiguity floating solution are obtained, the success rate of solving the widelane ambiguity in the step-by-step algorithm is improved, and the initialization time of single-frequency ambiguity is shortened.
In one embodiment, as shown in fig. 2, the position increment between the reference station inertial navigation epochs and the position increment between the mobile station inertial navigation epochs are obtained as follows:
Figure 998279DEST_PATH_IMAGE043
wherein the content of the first and second substances,
Figure 901644DEST_PATH_IMAGE044
and
Figure 348806DEST_PATH_IMAGE045
respectively the sampling time of the leading epoch and the trailing epoch of the guard,
Figure 69637DEST_PATH_IMAGE046
representing the position increment among the inertial navigation epochs of the reference station,
Figure 235039DEST_PATH_IMAGE047
representing reference station inertial navigation
Figure 191363DEST_PATH_IMAGE048
The position of the epoch is determined by the location of the epoch,
Figure 493031DEST_PATH_IMAGE049
representing reference station inertial navigation
Figure 384764DEST_PATH_IMAGE050
The position of the epoch is determined by the location of the epoch,
Figure 37462DEST_PATH_IMAGE051
representing the position increment between the inertial navigation epochs of the mobile station,
Figure 282630DEST_PATH_IMAGE052
representing mobile station inertial navigation
Figure 704384DEST_PATH_IMAGE053
The position of the epoch is determined by the location of the epoch,
Figure 767018DEST_PATH_IMAGE054
representing mobile station inertial navigation
Figure 641433DEST_PATH_IMAGE055
Location of epoch. + denotes the filtered data.
In another embodiment, as shown in fig. 3, the baseline vector forecast floating solution and the baseline vector forecast fixed solution at the current time are calculated according to the baseline vector floating solution at the previous time, the baseline vector fixed solution at the previous time, the position increment between the base station inertial navigation epochs and the position increment between the mobile station inertial navigation epochs as follows:
Figure 706603DEST_PATH_IMAGE056
wherein the content of the first and second substances,
Figure 982864DEST_PATH_IMAGE057
representing the baseline vector forecast floating solution at the current time,
Figure 216399DEST_PATH_IMAGE058
representing a baseline vector forecast fixed solution at the current moment;
Figure 578110DEST_PATH_IMAGE059
and
Figure 165080DEST_PATH_IMAGE060
respectively a previous-time baseline vector floating solution and a previous-time baseline vector fixed solution,
Figure 561427DEST_PATH_IMAGE061
and
Figure 965863DEST_PATH_IMAGE062
respectively obtaining position increment between reference station inertial navigation epochs and position increment between mobile station inertial navigation epochs;
to be provided with
Figure 814870DEST_PATH_IMAGE063
Time of day ambiguity float solution
Figure 454799DEST_PATH_IMAGE064
Baseline vector forecast floating point solution at current time
Figure 705652DEST_PATH_IMAGE065
And forecast fixed solutions
Figure 280990DEST_PATH_IMAGE066
For observed quantity, according to pseudo range and carrier phase double-difference observed quantity of current time
Figure 617293DEST_PATH_IMAGE067
Obtaining an inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model as follows:
Figure 811645DEST_PATH_IMAGE068
wherein the content of the first and second substances,
Figure 917005DEST_PATH_IMAGE069
and
Figure 663244DEST_PATH_IMAGE070
are respectively as
Figure 221264DEST_PATH_IMAGE071
The time-of-day ambiguity and the baseline vector,
Figure 970039DEST_PATH_IMAGE072
is composed of
Figure 929905DEST_PATH_IMAGE073
A covariance matrix of the time ambiguity floating solution,
Figure 581466DEST_PATH_IMAGE074
is composed of
Figure 892362DEST_PATH_IMAGE075
A covariance matrix of the floating solution is forecast at all times,
Figure 553150DEST_PATH_IMAGE076
is composed of
Figure 242889DEST_PATH_IMAGE075
The covariance matrix of the fixed solution is forecast at any moment,
Figure 862089DEST_PATH_IMAGE077
is composed of
Figure 129122DEST_PATH_IMAGE075
A covariance matrix of double-differenced pseudoranges at time and carrier-phase observations,
Figure 328022DEST_PATH_IMAGE035
is a unit matrix which is formed by the following steps,
Figure 387114DEST_PATH_IMAGE078
is a zero matrix.
Figure 911636DEST_PATH_IMAGE079
And
Figure 665966DEST_PATH_IMAGE080
the design matrices for the corresponding ambiguity and unknown parameters of the baseline vector are provided.
In particular, the method comprises the following steps of,
Figure 934136DEST_PATH_IMAGE081
is composed of
Figure 598467DEST_PATH_IMAGE082
The unit matrix of (a) is obtained,
Figure 28311DEST_PATH_IMAGE083
is composed of
Figure 535516DEST_PATH_IMAGE082
The zero matrix of (2).
In one embodiment, the baseline vector float solution and the ambiguity float solution at time k +1 are obtained by using a least squares method:
Figure 341798DEST_PATH_IMAGE084
wherein the content of the first and second substances,
Figure 605508DEST_PATH_IMAGE085
and
Figure 471833DEST_PATH_IMAGE086
to obtain
Figure 200754DEST_PATH_IMAGE087
The ambiguity float solution and the baseline vector float solution at the time,
Figure 810727DEST_PATH_IMAGE088
to represent
Figure 449650DEST_PATH_IMAGE087
A covariance matrix of the ambiguity float solution at that moment.
In one of the embodiments, according to
Figure 221297DEST_PATH_IMAGE087
And obtaining a single-frequency ambiguity floating solution of each frequency point by using the ambiguity floating solution at the moment, and converting the single-frequency ambiguity floating solution according to a wide lane operator to obtain a wide lane ambiguity floating solution. Obtaining a wide lane ambiguity floating-point solution variance matrix of a wide lane ambiguity floating-point solution according to a covariance propagation law; the method comprises the steps of searching a wide lane ambiguity floating solution variance matrix by adopting an LAMBDA algorithm to obtain an ultra-wide lane ambiguity fixed solution and a wide lane ambiguity fixed solution, establishing a single-frequency ambiguity observation equation according to the ultra-wide lane ambiguity fixed solution and the wide lane ambiguity fixed solution, and updating the single-frequency ambiguity floating solution according to the single-frequency ambiguity observation equation to obtain the single-frequency ambiguity fixed solution.
Specifically, taking a BDS three-frequency signal as an example for explanation, the wide lane ambiguity floating solution is:
Figure 703094DEST_PATH_IMAGE089
wherein the content of the first and second substances,
Figure 851179DEST_PATH_IMAGE090
、
Figure 593876DEST_PATH_IMAGE091
and
Figure 536424DEST_PATH_IMAGE092
single frequency ambiguities for the B1, B2, and B3 bins, respectively, i.e., in the previous embodiment
Figure 239938DEST_PATH_IMAGE093
The ambiguity float solution at a time is,
Figure 191713DEST_PATH_IMAGE094
and
Figure 539649DEST_PATH_IMAGE095
for the ambiguities of the respective two independent linear combinations,
Figure 918678DEST_PATH_IMAGE096
called widelane ambiguity conversion operator.
Figure 109488DEST_PATH_IMAGE097
The super-wide lane ambiguity of B3-B2 is formed by ambiguities of two close frequency points in three frequencies.
Figure 599375DEST_PATH_IMAGE098
Then the widelane ambiguities are comprised of B1-B3 ambiguities. The corresponding wide-lane ambiguity floating-point solution variance matrix can be obtained by the covariance propagation law:
Figure 818129DEST_PATH_IMAGE099
obtaining ultra-wide lane ambiguity fixing solution by using LAMBDA algorithm search
Figure 368059DEST_PATH_IMAGE100
Ambiguity fixed solution for sum-width lane
Figure 780586DEST_PATH_IMAGE101
Then, a single-frequency ambiguity observation equation under the constraint of the fixed solution can be established, and the single-frequency ambiguity floating solution is updated. Taking the BDS B3 frequency point as an example, single-frequency ambiguity observationThe equation is
Figure 74164DEST_PATH_IMAGE102
Wherein the content of the first and second substances,
Figure 396692DEST_PATH_IMAGE103
an array of variances for a single-frequency ambiguity float solution for all bins, i.e.
Figure 117523DEST_PATH_IMAGE104
A covariance matrix of the ambiguity float solution at that moment. The single-frequency ambiguity floating solution and the variance matrix of the B3 frequency point can be obtained by adopting a least square algorithm, and then the single-frequency ambiguity floating solution and the variance matrix are substituted into an LAMBDA algorithm to search and obtain a fixed solution of the B3 frequency point
Figure 282925DEST_PATH_IMAGE105
. Further combining the fixed solution of the ambiguity of the ultra-wide lane
Figure 114615DEST_PATH_IMAGE106
Fixed solution of ambiguity of sum-width lane
Figure 540917DEST_PATH_IMAGE107
Single-frequency ambiguity fixed solution of B1 and B2 frequency points can be obtained through recovery
Figure 432650DEST_PATH_IMAGE108
In one embodiment, a carrier phase observation equation is obtained according to the single-frequency ambiguity fixed solution and the inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model;
and obtaining a baseline vector fixed solution through a least square algorithm according to the carrier phase observation equation.
In particular, the last fixed single frequency ambiguity is recorded as
Figure 819769DEST_PATH_IMAGE109
Observation of corresponding carrier phaseThe equation is
Figure 455149DEST_PATH_IMAGE110
Then the baseline vector fixation solution can be found by the least square algorithm
Figure 752270DEST_PATH_IMAGE111
The following is a more clear description of the embodiments of the present invention in a specific calculation case.
Taking observation data with an epoch of 134740.9s before and after a certain dynamic test as an example, processing BDS single-system three-frequency B1+ B2+ B3 data, wherein the sampling rate of the observation data is 10 Hz. The satellite cut-off angle is set to 15deg, and the Ratio check threshold value is set to 3.0.
1) And calculating position increment between inertial navigation epochs of the reference station and the mobile station.
Previous epoch
Figure 814904DEST_PATH_IMAGE112
Mobile station filtered inertial navigation position
Figure 689319DEST_PATH_IMAGE113
Current epoch
Figure 862811DEST_PATH_IMAGE114
Moving inertial navigation position of
Figure 765170DEST_PATH_IMAGE115
Then the position increment between the inertial navigation epochs of the mobile station is
Figure 998706DEST_PATH_IMAGE116
。
For the reference station, the position increment between epochs is obtained by adopting the same algorithm
Figure 360417DEST_PATH_IMAGE117
。
2) And establishing an inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model.
The baseline vector of the previous epoch 134740.8s is fixed solved as
Figure 337600DEST_PATH_IMAGE118
The baseline vector floating point solution is
Figure 609312DEST_PATH_IMAGE119
The extrapolated 134740.9s baseline vector prediction solution has a floating solution and a prediction fixed solution of
Figure 13749DEST_PATH_IMAGE120
And
Figure 597177DEST_PATH_IMAGE121
the corresponding covariance matrices are respectively
Figure 378051DEST_PATH_IMAGE122
And
Figure 753538DEST_PATH_IMAGE123
。
the BDS of the current time 134740.9s has 6 common view satellites, the pseudo-range and the carrier phase of three frequency points have 36 observed values, the unknown ambiguity and the baseline vector parameter have 21, and only the observation vector corresponding to the PRN2 satellite is given for shortening the space
Figure 328876DEST_PATH_IMAGE124
Design matrix
Figure 399600DEST_PATH_IMAGE125
And
Figure 718586DEST_PATH_IMAGE126
：
Figure 699311DEST_PATH_IMAGE127
，
Figure 445550DEST_PATH_IMAGE128
，
Figure 269150DEST_PATH_IMAGE129
the corresponding weighting matrix is
Figure 126247DEST_PATH_IMAGE130
。
The PRN2 satellite ambiguity floating solution inherited from the previous time 134740.8s is
Figure 977791DEST_PATH_IMAGE131
Corresponding variance matrix is
Figure 894931DEST_PATH_IMAGE132
。
3) A least squares algorithm is used to obtain a baseline vector and ambiguity float solution.
Unknown baseline vector floating point solution
Figure 940248DEST_PATH_IMAGE133
And PRN2 ambiguity float solution
Figure 601036DEST_PATH_IMAGE134
Is composed of
Figure 556354DEST_PATH_IMAGE135
，
Figure 378816DEST_PATH_IMAGE136
The corresponding PRN2 ambiguity floating point solution covariance matrix is
Figure 177008DEST_PATH_IMAGE137
4) Step-by-step solving integer ambiguity by adopting first (ultra) wide lane and then single frequency
The ambiguity of a wide lane and an ultra-wide lane formed by PRN2 satellites B1-B3 and B3-B2 is as follows:
Figure 641488DEST_PATH_IMAGE138
the variance matrix corresponding to the formula is
Figure 700579DEST_PATH_IMAGE139
. Ambiguity of wide lane
Figure 959522DEST_PATH_IMAGE140
Sum and variance matrix
Figure 713852DEST_PATH_IMAGE141
Substituting LAMBDA algorithm for searching to obtain (ultra) wide lane ambiguity fixing solution:
Figure 982022DEST_PATH_IMAGE142
establishing a B3 frequency point ambiguity observation equation under the constraint of the wide-lane ambiguity fixed solution, and obtaining an observation vector as follows:
Figure 770986DEST_PATH_IMAGE143
the ambiguity floating solution of the frequency point of the PRN satellite B3 can be obtained according to the least square solution
Figure 76197DEST_PATH_IMAGE144
Variance is
Figure 583402DEST_PATH_IMAGE145
Then, a standard LAMBDA algorithm is adopted to search and obtain a fixed solution
Figure 389684DEST_PATH_IMAGE146
。
According to B3 frequency point ambiguity fixed solution and (ultra) wide lane ambiguity fixed solution
Figure 33155DEST_PATH_IMAGE147
And
Figure 808735DEST_PATH_IMAGE148
and recovering to obtain integer ambiguity of B1 and B2 frequency points as follows:
Figure 537657DEST_PATH_IMAGE149
finally, a single-frequency ambiguity fixed solution of three frequency points of B1, B2 and B3 of the PRN2 satellite is obtained as follows:
Figure 147630DEST_PATH_IMAGE150
6) and updating the baseline vector by using the single-frequency ambiguity fixed solution of all the frequency points.
The PRN2 satellite has carrier double-difference observed values, sight line vector matrix and variance matrix
Figure 380028DEST_PATH_IMAGE151
，
Figure 292621DEST_PATH_IMAGE152
，
Figure 508838DEST_PATH_IMAGE153
。
The current 6 satellites are simultaneously connected, and the total number of 3 frequency points is 18 observation equations, so that the fixed solution of the baseline vector can be obtained as follows:
Figure 656923DEST_PATH_IMAGE154
the technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (4)

1. A multi-epoch step-by-step ambiguity solving method for inertial navigation auxiliary navigation relative positioning is characterized by comprising the following steps:
acquiring position increment between reference station inertial navigation epochs and position increment between mobile station inertial navigation epochs;
constructing an inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model according to the position increment between the reference station inertial navigation epochs and the position increment between the mobile station inertial navigation epochs; the inertial navigation auxiliary satellite navigation multi-epoch floating solution filtering model determines the relationship between a k-moment ambiguity floating solution and a baseline vector forecast floating solution and a k + 1-moment ambiguity and a baseline vector;
obtaining a baseline vector floating solution at the moment k +1 and a ambiguity floating solution at the moment k +1 by adopting a least square method;
according to the baseline vector floating solution at the moment k +1 and the ambiguity floating solution at the moment k +1, solving the integer ambiguity step by adopting a wide lane first and a single frequency later to obtain a single-frequency ambiguity fixed solution;
updating a baseline vector according to the single-frequency ambiguity fixed solution and the inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model to obtain a baseline vector fixed solution;
the acquiring of the position increment between the reference station inertial navigation epochs and the position increment between the mobile station inertial navigation epochs comprises:
obtaining the position increment between the reference station inertial navigation epochs and the position increment between the mobile station inertial navigation epochs as follows:
Figure 895447DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 853039DEST_PATH_IMAGE002
and
Figure 324471DEST_PATH_IMAGE003
respectively the sampling time of the leading epoch and the trailing epoch of the guard,
Figure 113436DEST_PATH_IMAGE004
representing the position increment among the inertial navigation epochs of the reference station,
Figure 995810DEST_PATH_IMAGE005
representing reference station inertial navigation
Figure 440698DEST_PATH_IMAGE003
The position of the epoch is determined by the location of the epoch,
Figure 246980DEST_PATH_IMAGE006
representing reference station inertial navigation
Figure 93713DEST_PATH_IMAGE007
The position of the epoch is determined by the location of the epoch,
Figure 897721DEST_PATH_IMAGE008
representing the position increment between the inertial navigation epochs of the mobile station,
Figure 626643DEST_PATH_IMAGE009
representing mobile station inertiaGuide tube
Figure 187680DEST_PATH_IMAGE010
The position of the epoch is determined by the location of the epoch,
Figure 154499DEST_PATH_IMAGE011
representing mobile station inertial navigation
Figure 863829DEST_PATH_IMAGE012
The location of the epoch;
according to the position increment between the reference station inertial navigation epochs and the position increment between the mobile station inertial navigation epochs, an inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model is constructed, and the method comprises the following steps:
according to the baseline vector floating solution at the previous moment, the baseline vector fixed solution at the previous moment, the position increment between the base station inertial navigation epochs and the position increment between the mobile station inertial navigation epochs, calculating to obtain a baseline vector forecast floating solution at the current moment and a baseline vector forecast fixed solution:
Figure 345626DEST_PATH_IMAGE013
wherein the content of the first and second substances,
Figure 696973DEST_PATH_IMAGE014
representing the baseline vector forecast floating solution at the current time,
Figure 501987DEST_PATH_IMAGE015
representing a baseline vector forecast fixed solution at the current moment;
Figure 444535DEST_PATH_IMAGE016
and
Figure 351312DEST_PATH_IMAGE017
respectively a previous-time baseline vector floating solution and a previous-time baseline vector fixed solution,
Figure 240770DEST_PATH_IMAGE018
and
Figure 916602DEST_PATH_IMAGE019
respectively obtaining position increment between reference station inertial navigation epochs and position increment between mobile station inertial navigation epochs;
to be provided with
Figure 295631DEST_PATH_IMAGE020
Time of day ambiguity float solution
Figure 174856DEST_PATH_IMAGE021
Baseline vector forecast floating point solution at current time
Figure 868006DEST_PATH_IMAGE022
And forecast fixed solutions
Figure 460661DEST_PATH_IMAGE023
For observed quantity, according to pseudo range and carrier phase double-difference observed quantity of current time
Figure 948274DEST_PATH_IMAGE024
Obtaining an inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model as follows:
Figure 564063DEST_PATH_IMAGE025
wherein the content of the first and second substances,
Figure 857641DEST_PATH_IMAGE026
and
Figure 757333DEST_PATH_IMAGE027
are respectively as
Figure 415848DEST_PATH_IMAGE028
Time of day ambiguity and baseThe vector of the line or lines is,
Figure 581250DEST_PATH_IMAGE029
is composed of
Figure 350623DEST_PATH_IMAGE028
A covariance matrix of the floating solution is forecast at all times,
Figure 855553DEST_PATH_IMAGE030
is composed of
Figure 747286DEST_PATH_IMAGE028
The covariance matrix of the fixed solution is forecast at any moment,
Figure 91329DEST_PATH_IMAGE031
is composed of
Figure 664393DEST_PATH_IMAGE028
A covariance matrix of double-differenced pseudoranges at time and carrier-phase observations,
Figure 289410DEST_PATH_IMAGE032
is a unit matrix which is formed by the following steps,
Figure 352044DEST_PATH_IMAGE033
is a matrix of zero values, and is,
Figure 164142DEST_PATH_IMAGE034
and
Figure 337634DEST_PATH_IMAGE035
a design matrix corresponding to the unknown parameters of the ambiguity and baseline vector,
Figure 66425DEST_PATH_IMAGE036
to represent
Figure 237643DEST_PATH_IMAGE028
Of temporal ambiguity float solutionsAnd (4) covariance matrix.
2. The method of claim 1, wherein obtaining the baseline vector float solution at the time k +1 and the ambiguity float solution at the time k +1 by using a least squares method comprises:
and obtaining a baseline vector floating solution and an ambiguity floating solution at the moment k +1 by adopting a least square method:
Figure 802616DEST_PATH_IMAGE037
wherein the content of the first and second substances,
Figure 779800DEST_PATH_IMAGE038
and
Figure 113829DEST_PATH_IMAGE039
to obtain
Figure 472260DEST_PATH_IMAGE040
The ambiguity float solution and the baseline vector float solution at the time,
Figure 55688DEST_PATH_IMAGE041
to represent
Figure 774246DEST_PATH_IMAGE040
A covariance matrix of the ambiguity float solution at that moment.
3. The method of claim 2, wherein the step of solving the integer ambiguity step by using a wide lane first and a single frequency second according to the baseline vector floating solution at the time k +1 and the ambiguity floating solution at the time k +1 to obtain a single-frequency ambiguity fixed solution comprises:
according to
Figure 228361DEST_PATH_IMAGE040
Obtaining single frequency mode of each frequency point by using ambiguity floating point solution of timeConverting the single-frequency ambiguity floating solution according to a wide lane operator to obtain a wide lane ambiguity floating solution;
obtaining a wide lane ambiguity floating-point solution variance matrix of the wide lane ambiguity floating-point solution according to a covariance propagation law;
and searching the wide lane ambiguity floating solution variance matrix by adopting an LAMBDA algorithm to obtain an ultra-wide lane ambiguity fixed solution and a wide lane ambiguity fixed solution, establishing a single-frequency ambiguity observation equation according to the ultra-wide lane ambiguity fixed solution and the wide lane ambiguity fixed solution, and updating the single-frequency ambiguity floating solution according to the single-frequency ambiguity observation equation to obtain a single-frequency ambiguity fixed solution.
4. The method of claim 3, wherein updating a baseline vector according to the single-frequency ambiguity fixed solution and the inertial navigation-assisted satellite navigation multi-epoch floating-point solution filtering model to obtain a baseline vector fixed solution comprises:
obtaining a carrier phase observation equation according to the single-frequency ambiguity fixed solution and the inertial navigation auxiliary satellite navigation multi-epoch floating point solution filtering model;
and obtaining a baseline vector fixed solution through a least square algorithm according to the carrier phase observation equation.
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