AU2021100689A4 - GNSS (Global Navigation Satellite System) Dynamic Kalman Filter Method In Autonomous Cooperation - Google Patents
GNSS (Global Navigation Satellite System) Dynamic Kalman Filter Method In Autonomous Cooperation Download PDFInfo
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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
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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
- G01S19/03—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers
- G01S19/04—Cooperating elements; Interaction or communication between different cooperating elements or between cooperating elements and receivers providing carrier phase data
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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
- G01S19/393—Trajectory determination or predictive tracking, e.g. Kalman filtering
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Abstract
The invention discloses a GNSS dynamic Kalman filter method in autonomous
cooperation. The method comprises the following steps: calculating a double-difference
observation value, calculating an observation equation, calculating a double-difference pseudo
range observation value, calculating double-difference pseudo-range observation equations,
calculating double-difference observation equations based on a pseudo-range and a carrier
phase, listing the double-difference observation equations and performing Kalman filter
calculation. According to the invention, receiver clock errors and satellite clock errors are
eliminated by calculating double-difference observation values. Satellites with high elevation
angles are called as the first choice of reference satellites, so that the accuracy of each double
difference observation value is ensured. Pseudo-range measurement values corresponding to
different stations and between satellites form a double-difference pseudo-range, and the
corresponding double-difference pseudo-range is smoothed by utilizing a double-difference
carrier phase, so that measurement noises of a double-difference pseudo-range observation
value are reduced, and the smoothed or filtered double-difference pseudo-range observation
value has the advantages of relatively low measurement noises and no integer ambiguity.
1 / 1
Calculate a double-difference
observation value
Calculate an observation
[eequation
Calculate a double-difference
pseudorange observation value
Calculate double-difference
pseudorange observation
LCalculate double-difference
observation equations based on
a pseudor eand a carrier
List the double-difference
observation equations
perform Kalman filter calculation J
Fig. 1
Description
1 /1
Calculate a double-difference observation value
Calculate an observation
[eequation
Calculate a double-difference pseudorange observation value
Calculate double-difference pseudorange observation
LCalculate double-difference observation equations based on a pseudor eand a carrier
List the double-difference observation equations
perform Kalman filter calculation J
Fig. 1
GNSS (Global Navigation Satellite System) Dynamic Kalman Filter Method In
Autonomous Cooperation
[01] The invention relates to the technical field of cluster autonomous coordination, and in particular to a GNSS dynamic Kalman filter method in autonomous coordination.
[02] On the future informatized battlefield, UAVs (Unmanned Aerial Vehicle) will be used more and more widely to perform various lethal combat missions. On highly informatized battlefields, a combat mode of the UAVs will be changed to a combat mode of fleet to fleet and fleet to ground/surface targets from an autonomous combat mode. This cluster cooperation of the UAVs has scale advantages, and excellent battlefield survivability and mission completion capabilities, and can be used to complete tasks such as cooperative search, cooperative interference, cooperative attack, cooperative observation/attack, and cluster confrontation in a complex confrontation environment.
[03] The key problems that need to be solved include large-scale UAV management and control, multi-UAV autonomous formation flying, cluster awareness and situation sharing, cluster defense penetration and attack, cluster combat mission control stations, etc., which require satellite navigation systems. With the successive completion of various satellite navigation systems, more and more satellite signals are available in the sky. In recent years, the receivers on the market have the characteristics of multiple systems and multiple frequency points, and can usually receive more than 200 channels at the same time. A satellite signal, in practical application, passes through a carrier when a multi-antenna receiver receives it. The signal strength changes drastically or even disappears as the carrier often needs to pass through a complex road section. RTK positioning cannot be performed as the receivers have clock and satellite clock errors, so it is necessary to perform double-difference observation calculation with noises, and it is difficult to ensure the accuracy of each double-difference observation value. Therefore, the present invention discloses a GNSS dynamic Kalman filter method in autonomous cooperation to solve the problems in the prior art.
[04] To solve the problems, the invention discloses a GNSS dynamic Kalman filter method in autonomous cooperation, where receiver clock errors and satellite clock errors are eliminated by calculating double-difference observation value. Satellites with high elevation angles are called as the first choice of reference satellites, so that the accuracy of each double-difference observation value is ensured. Pseudo-range measurement values corresponding to different stations and between satellites form a double-difference pseudo-range, and the corresponding double-difference pseudo range is smoothed by utilizing a double-difference carrier phase, so that measurement noises of a double-difference pseudo-range observation value are reduced.
[05] To achieve the above objectives, the invention provides the following technical solution: the GNSS dynamic Kalman filter method in autonomous cooperation includes the following steps:
[06] I: Calculate a double-difference observation value.
[07] In a process of receiving satellite signals by a multi-antenna receiver, each double-difference observation involves measurement values of two receivers on two satellites at the same moment. A difference between single differences of two different satellites is made, i.e., the difference between the stations and the satellites is calculated once. Assuming that a user receiver u and a base station receiver r track a satellite i and a satellite j at the same time, a single-difference carrier phase observation value of the two receivers to the satellite i is as follows:
[08] AA,= ±(1) (fA~tu,+A
[09] a single-difference carrier phase observation value of the two receivers to the satellite j is as follows:
Aq =1- Ar. + fAt, + AN,, +cI
[010] ur A, (2)
[011] a double-difference carrier phase observation value consisting of the two is defined as follows:
[012] -Acpu'r (3)
[013] an observation equation of the double-difference observation values is obtained as follows:
[014] VAp9 = A VAr +VAN,,, +(4)
[015] where, VAr = Ar' - Ar VAN" = AN, - AN seA,, = i,,1 - CAs9 , the formula (4) indicates that the double-difference observation values can completely eliminate receiver clock errors and satellite clock errors;
[016] the double-difference carrier phase observation value is a key measurement I
value to determine a baseline vector r, for the satellite j,
Ar'=-b -l'
[017] u' u' ' (5)
[018] get
[019] VAr,= burl'+b r,- - r,' bur (6)
[020] therefore, a relationship between the double-difference observation values and the baseline vector is as follows:
VA pr = J) -!)b +IVANJ +
[021] "' 'r±Ar ur (7)
[022] In the formula, - at the left side of the equal sign is the double difference carrier phase observation value calculated by four carrier phase measurement I
values of the same epoch, and is a known quantity; and ur at the left side of the equal sign is a three-dimensional baseline vector to be determined, and double-difference
integer ambiguity VAN.ur is an unknown integer.
[023] II: Calculate an observation equation
[024] The carrier phase measurement values of two different satellites can be linearly combined by the user and the base station receiver to form a double-difference measurement value. Therefore, if the two receivers have measurement values for M satellites at the same time, M(M-1) double-difference observation values can be generated between every two pairs of the M pairs of carrier phase measurement values, but only the (M-1) double-difference values are independent of each other. Assuming that the (M-1) mutually independent double-difference carrier phase measurement
values are expressed asV , u,. r , each double-difference value has an observation equation similar to (7), and the (M-1) double-difference observation equations are integrated together to form the following matrix equation:
VAp VAP _ r-2 r _ rr 1r] - VAN 2 1 A1 2~p31 3 r- /rl)T r VA3 V r _'r bur + Au
V~cp Milr r )V M
[025] - - r r -ANj' (8)
[026] Where, double-difference observation noises are omitted; if the VN receivers can determine each double-difference integer ambiguity value VANUr in the I
matrix equation, the baseline vector br can be solved from the equation, and thus, baseline solution can be realized; the formula (8) selects the satellite 1 as a reference
satellite for double-difference calculation, so its single-difference value r enters all the above (M-1) double-interpolation values.
[027] III: Calculate a double-difference pseudo-range observation value
[028] Similar to a combination mechanism of the double-difference carrier phase measurement values, the pseudo-range measurement values corresponding to different stations and between satellites constitute a double-difference pseudo-range. In the case of a short baseline, a single-difference pseudo-range observation equation of the user receiver u and the reference station receiver r to the satellite i is follows:
[029] Ap = ArT+CAStU + Ep, (9)
[030] a single-difference pseudo-range to the satellite j can be written as follows:
[031] Ap, ArC,+ (10)
[032] the definition of a double-difference pseudo-range observation value of the receivers u and r to the satellites i and j, and an observation equation thereof are as follows:
(11).
[033] VAPr rAPr- APu = Ar
[034] IV: Calculate double-difference pseudo-range observation equations
[035] If the two receivers have pseudo-range observation values for M satellites, (M-1) mutually independent double-difference pseudo-range observation equations constitute a matrix equation as follows:
21 _(- _ OT r r ur _ r - r
V Ap 1 M -(r| ,) r
[036] - p jr r )T] (12)
[037] given enough double-difference pseudo-range measurement values, the I
receiver solves the baseline vector bur from the matrix equation, and the double
difference carrier phase is used to smooth the corresponding double-difference
pseudo-range Pr, so that measurement noises of the double-difference pseudo
range observation value are reduced.
[038] V: Calculate double-difference pseudo-range observation equations based on a pseudo-range and a carrier phase
[039] In accordance with the step IV, carrier phase and pseudo-range observation equations are separately as follows:
A~p = r + c(t, - t') + -Ir, AN + e ,o+ (3
p = r +c(t, - t')+ Tro + Io±2+NC((13
[040] in the formula, P is a pseudo-range observation value, ' is a carrier phase
observation value, r is a station-satellite distance, tu is receiver clock errors, t" is a
satellite clock errors, trop is tropospheric delay, iono is ionospheric delay,L is carrier wavelength, and N is carrier integer ambiguity.
[041] Double-difference pseudo-range observation equations based on pseudo range and carrier phase are separately obtained from formulas (13) and (14) as follows:
AVAp =VAr+VAT",,, -VA' +AVANI (15)
VAp"r = VAr" r +VAT" + VATLno,ur + trop,,r + -VAp (16)
[042] when RTK positioning is performed, the correction of VA"Pu" is generally accomplished by a tropospheric model and a value of a baseline is solved by a Kalman filter method; and observation equations are linearized before Kalman filter for separately linearizing the formulas (15) and (16) to obtain:
AVAp -VAR =- [e. ej ef'][dXy dY dZ] T +AVANy +e V~q(17)
AVApY-VAR1,.=-[el ur ejy efl][dX dY dZ]+ ^ (18) (18)
[043] in the formula, VAR is a double-difference value of a station-satellite
distance, [ e,'xel e,' e,'] is a single difference value of a satellite direction vector,
[dX dY dZ]T is coordinate difference between the user receiver u and the reference
station receiver r in the geocentric ground-fixed coordinate system, where X.-X Y.-Y Zi-Z e, = "e_ = e = " | " | "R' e'e-e' e"=e' -e e-=eke
(XjYj,Zj) are coordinates of the satellite j, and (X,YZu) are approximate coordinates of the user receiver.
[044] VI: List double-difference observation equations
[045] Assuming that and ,I M satellites are observed, and the combination of (1, -1,0) and (1,0,0) for the carrier phase combination observations is selected for single navigation system. From the double difference pseudo-range and the carrier, 4(M-1) double-difference observation equations can be listed as follows:
LV e. ey ez' - -A, s LA e eYe dZf) 0 AN e" eM1 2 -2 ANM1 L , em' EIII e 1dY + 0, -2,+V2
9, ex eY ez 0 AN f2 VAp
41I~ eli ' emej 0 AN7'j ICVA 0 0
0J (19)
[046] A matrix equation can be shown as follows:
[047] L=AX+BF+ E (20)
[048] where, L is a carrier phase and pseudo-range double-difference residual vector, A is a double-difference direction cosine matrix, B is an integer ambiguity coefficient matrix, X is a baseline vector to be estimated, F is a single-difference ambiguity vector, and e is a double-difference noise vector, the observation equations are established when the Kalman filter is solved.
[049] VII: Perform Kalman filter calculation
[050] Kalman filter can be divided into six steps, and a predicted value k~k-I
of a state vector X is firstly calculated as follows:
[051] k~k-1- kjk-I k-i (21)
[052] where, Mk- is a state transition matrix, and a state vector in the
geocentric ground-fixed coordinate system is as follows:
AN' AN,' . . . A M AN AN ... AN ] X=[dX dY dZ ji IlIl 12 12 1 (22)
[053] a covariance matrix of k-is then calculated as follows:
[054] klk-I kk-I k-i kk- -Qkl (23)
[055] in the formula, *-I is a process noise matrix, then, a filter gain matrix K, is calculated, and a gain condition of the original observation and the predicted value is compared as follows:
T p T K - kk-1A +
[056] kk Ak Rk (24)
[057] in the formula, Rk is a measurement noise matrix;
[058] after the gain matrix is calculated, the state vector is filtered according to
the gain matrix to obtain a filtered value ofX as follows:
[059] kkL-k (25)
[060] a covariance matrix * of the Xk is calculated as follows:
[061] P =(I-KAkEk- (26)
[062] Xkcalculated by the Kalman filter algorithm includes the single-difference
integer ambiguity values of the baseline vector and each frequency point, where kis a
floating point solution; the floating point solution -kand its corresponding variance covariance matrix are transformed for calculating a fixed solution, where a single difference integer ambiguity value is transformed into double-difference integer ambiguity, and a transformation matrix is as follows:
1 0 0 0 1 0 0 0 0 1 1 -1 -1 1 1 -1 -1 1 D =... ... ... ... ... ......... 1 -1 -1 1 1 1 -1 0 0 1 -1 0 1 .0
[063] 1 -1 0] (27)
[064] a double-difference floating point solution is as follows:
[065] 3X4=D-X4 (28)
[066] the variance-covariance matrix corresponding to the double-difference floating point solution is as follows:
[067] 5_=D-P-D (29)
[068] the integer ambiguity double-difference floating point solution and its corresponding variance-covariance matrix are substituted into the LAMBDA algorithm to solve the fixed solution of the integrity ambiguity.
[069] A further improvement is that: in the step I, the formula (4) shows that the double-difference observation values can completely eliminate the receiver clock errors and the satellite clock errors at the cost of increasing mean square errors of the noises
V^-with the double-difference observation values to be N times of mean square errors of the original single-difference observation noises.
[070] A further improvement is that: in the step II, in order to ensure the accuracy of each double-difference observation value, single-difference values of the reference satellites must be precise, and the satellites with high elevation angles are called as the first choice of reference satellites.
[071] A further improvement is that: in the step III, the advantages of the double difference pseudo-range are that it does not include integer ambiguity compared with
the formulas (11) and (14), and mean square errors of its measurement noises 4^A,- are
much higher than those of double-difference carrier phase measurement noisesA^o_
[072] A further improvement is that: in the step IV, the smoothed and filtered double-difference pseudo-range observation values not only have lower measurement noises, but also maintain the advantage of no ambiguity.
VA T" ""p,"
[073] A further improvement is that: in the step V, atmospheric errors(
VAI" 4 vg""""') between the two antennas can be regarded as the same and can be eliminated directly in case of an ultra-short baseline.
[074] A further improvement is that: in the step VII, the double-difference ambiguity searched by the LAMBDA algorithm is the ambiguity value corresponding to the wide lane combination (1,-1,0) and (1,0,0), and the double-difference integer ambiguity value corresponding to each frequency point is obtained through further linear transformation.
[075] The beneficial effects of the present are that: receiver clock errors and satellite clock errors are eliminated by calculating double-difference observation values, and satellites with high elevation angles are called as the first choice of reference satellites, so that the accuracy of each double-difference observation value is ensured. Pseudo-range measurement values corresponding to different stations and between satellites form a double-difference pseudo-range, and the corresponding double difference pseudo-range is smoothed by utilizing a double-difference carrier phase, so that measurement noises of a double-difference pseudo-range observation value are reduced, and the smoothed or filtered double-difference pseudo-range observation value has the advantages of relatively low measurement noises and no integer ambiguity. At the same time, when RTK positioning is performed, the Kalman filter method is used to calculate the single-difference integer ambiguity value vector including the baseline vector and each frequency point. After the single-difference integer ambiguity value is transformed into double-difference integer ambiguity, the double-difference integer ambiguity value corresponding to each frequency point can be obtained more precisely through further linear transformation via the LAMBDA algorithm.
[076] Fig. 1 is a flow chart of the invention.
[077] In order to understand the invention more deeply, the invention will be described in further detail below in conjunction with the embodiments. This embodiment is only used to explain the invention and does not limit the protection scope of the invention.
[078] As shown in Fig. 1, the embodiment provided a GNSS dynamic Kalman filter method in autonomous cooperation, including the following steps:
[079] I: Double-difference observation value was calculated.
[080] In a process of receiving satellite signals by a multi-antenna receiver, each double-difference observation involved measurement values of two receivers on two satellites at the same moment. A difference between single differences of two different satellites was made, i.e., the difference between the stations and the satellites was calculated once. Assuming that a user receiver u and a base station receiver r tracked a satellite i and a satellite j at the same time, a single-difference carrier phase observation value of the two receivers to the satellite i was as follows:
[081] Ar,=ri(r+fA1tu,+AN +1)
[082] a single-difference carrier phase observation value of the two receivers to the satellite j was as follows:
[083] A = i + fA5t,+ AN,+,' .c (2)
[084] a double-difference carrier phase observation value consisting of the two was defined as follows:
[085] VAp2" - (3)
[086] an observation equation of the double-difference observation values was obtained as follows:
[087] VApI = A VAr +VAN+ jCA, (4)
[088] where, VAr = Ar'- Ar VAN. = AN., - AN 8 eVA = , - e the formula (4) indicated that the double-difference observation values could completely eliminate receiver clock errors and satellite clock errors at the cost of increasing mean
square errors of the noises4A 0^with the double-difference observation values to be
NF2times of mean square errors of the original single-difference observation noises.
[089] The double-difference carrier phase observation value was a key 1
measurement value to determine a baseline vector bar , for the satellite j,
[090]
Ar'=-b -l'
[091] u' u' ' (5)
[092] Got
[093] V r,=bUr lr'±bur ,- r, r' bur (6)
[094] Therefore, a relationship between the double-difference observation values and the baseline vector was as follows:
[095] N, (7) b(r
[096] In the formula, at the left side of the equal sign was the double difference carrier phase observation value calculated by four carrier phase measurement I
values of the same epoch, and was a known quantity; and br at the left side of the equal sign was a three-dimensional baseline vector to be determined, and double-difference VAY integer ambiguity VAnU was an unknown integer.
[097] II: An observation equation was calculated.
[098] The carrier phase measurement values of two different satellites could be linearly combined by the user and the base station receiver to form a double-difference measurement value. Therefore, if the two receivers had measurement values for M satellites at the same time, M(M-1) double-difference observation values could be generated between every two pairs of the M pairs of carrier phase measurement values, but only the (M-1) double-difference values were independent of each other. Assuming that the (M-1) mutually independent double-difference carrier phase measurement VA 'IVAqp" VA ml values were expressed as , , ... , each double-difference value had an observation equation similar to (7), and the (M-1) double-difference observation equations were integrated together to form the following matrix equation:
- I VA 21 7 I2 _ 1)T v 21 r r VA_1 ( - rI)T r VAN 3 1 =r r bur+
T V M VApM1 Mr r
[099] - - rl -' r (8)
[0100] Where, double-difference observation noises were omitted; if the
receivers could determine each double-difference integer ambiguity valueVA u in
the matrix equation, the baseline vector bir could be solved from the equation, and thus, baseline solution could be realized; the formula (8) selected the satellite 1 as a reference
satellite for double-difference calculation, so its single-difference valueA~pr entered all the above (M-1) double-interpolation values. In order to ensure the accuracy of each double-difference observation value, single-difference values of the reference satellites must be precise, and the satellites with high elevation angles were called as the first choice of reference satellites.
[0101] III: A double-difference pseudo-range observation value was calculated.
[0102] Similar to a combination mechanism of the double-difference carrier phase measurement values, the pseudo-range measurement values corresponding to different stations and between satellites constituted a double-difference pseudo-range. In the case of a short baseline, a single-difference pseudo-range observation equation of the user receiver u and the reference station receiver r to the satellite i was follows:
[0103] Ap = Ar + cASt.r ± E
[0104] a single-difference pseudo-range to the satellite j could be written as follows:
[0105] Ar tur+ +1cA (10)
[0106] the definition of a double-difference pseudo-range observation value of the receivers u and r to the satellites i and j, and an observation equation thereof were as follows:
[0107] VAPu' r APu'r - APu r + V^,u+ (11)
[0108] the advantages of the double-difference pseudo-range were that it did not include integer ambiguity compared with the formulas (11) and (14), and mean square
errors of its measurement noises4X Mwere much higher than those of double-difference
carrier phase measurement noises Mr .
[0109] IV: Double-difference pseudo-range observation equations were calculated.
[0110] If the two receivers had pseudo-range observation values for M satellites, (M-1) mutually independent double-difference pseudo-range observation equations constituted a matrix equation as follows:
L~ VAp1tj] VApM1 _1 r r M l)T]r (lr- 1 T r
[0111] - Lpm] i r -rMlrl)T] r (12)
[0112] Given enough double-difference pseudo-range measurement values, the I
receiver solved the baseline vector bir from the matrix equation, and the double
difference carrier phase VAcpoiur was used to smooth the corresponding double
difference pseudo-range r, so that measurement noises of the double-difference pseudo-range observation value were reduced, and the smoothed and filtered double difference pseudo-range observation values not only had lower measurement noises, but also maintained the advantage of no ambiguity.
[0113] V: Double-difference pseudo-range observation equations based on a pseudo-range and a carrier phase were calculated.
[0114] In accordance with the step IV, carrier phase and pseudo-range observation equations were separately as follows:
A~p =r+c(t,-t")+T -I. +AN+c
[0115] " "trop boh" (13)
p=r+c(t -t")+T +I. +c
[0116] "ro 1"01'"" P (14)
[0117] In the formula, P was a pseudo-range observation value, q was a carrier
phase observation value, r was a station-satellite distance, t. was receiver clock
errors, t was a satellite clock errors, Trop was tropospheric delay, iono was
ionospheric delay, Awas carrier wavelength, and was carrier integer ambiguity.
[0118] Double-difference pseudo-range observation equations based on pseudo range and carrier phase were separately obtained from formulas (13) and (14) as follows:
[0119]
AVArp =VAr+VAT -VAI +AVAN +(15)
[0120]
VAp' r VAr +VAT" +VA'no,ur + s Ap urtrop~ Aonj u (16)
[0121] When RTK positioning was performed, the correction of ''"P,ur was generally accomplished by a tropospheric model and a value of a baseline was solved VAT" VAI" by a Kalman filter method; atmospheric errors ( 'rop,"r4 V '","') between the two antennas could be regarded as the same and could be eliminated directly in case of an ultra-short baseline, and observation equations were linearized before Kalman filter for separately linearizing the formulas (15) and (16) to obtain:
[0122]
AV Aypo -V ARy =-[e. es ef'][dX dY dZ] T +AVANU +e' y V~q(17)
[0123]
AVAp' -VARu=-[e ur es el'][dX dY dZ]+ ^ 1 (18)
[0124] In the formula,VAR was a double-difference value of a station-satellite
[e e' e"] distance, x y was a single difference value of a satellite direction vector,
[dX dY dZ]T was coordinate difference between the user receiver u and the
reference station receiver r in the geocentric ground-fixed coordinate system, where x.-x Y.1Y * Z. U X I -Y I -Z "e| " R=" R' e' k-e e"=e' -e ef =e'-
(i, YJZJ) were coordinates of the satellite j, and (X,,YZ ) were approximate coordinates of the user receiver.
[0125] VI: Double-difference observation equations were listed.
V ALU = WVA p, - V AR" VALJ = IVApJ - VAR"
[0126] Assuming thatL "' "'uand L I "'r', M satellites were observed, and the combination of (1, -1,0) and (1,0,0) for the carrier phase combination observations was selected for single navigation system. From the double-difference pseudo-range and the carrier, 4 (M-1) double-difference observation equations could be listed as follows:
[0127]
L e e e1 A - AN1 2 31 A1 e 1 e. A1 -A .f, .. .. ... .. -A.... .. I e e, e- 0 AN'
0 0
0j (19)
[0128] a matrix equation could be shown as follows:
[0129] L=AX+BN+e (20)
[0130] where, L was a carrier phase and pseudo-range double-difference residual vector, A was a double-difference direction cosine matrix, B was an integer ambiguity coefficient matrix, X was a baseline vector to be estimated, N was a single-difference ambiguity vector, and , was a double-difference noise vector, the observation equations were established when the Kalman filter was solved.
[0131] VII: Kalman filter calculation was performed.
[0132] Kalman filter could be divided into six steps, and a predicted value kjk-1
of a state vector X was firstly calculated as follows:
[0133] kjk-1- kjk-1Xk-i (21)
[0134] where, k~k-1 was a state transition matrix, and a state vector in the
geocentric ground-fixed coordinate system was as follows:
AN' AN,' . . . A M AN AN ... AN ] X=[dX dY dZ ji IlIl 12 12 1 (22)
[0135] a covariance matrix of kk-1 was then calculated as follows:
[0136] klk-1 kk-1 k-i kk-1 -Qk (23)
[0137] In the formula, *-1 was a process noise matrix, then, a filter gain matrix Kk was calculated, and a gain condition of the original observation and the predicted value was compared as follows:
T p T K - kk-1A +
[0138] k kk Rk (24)
[0139] in the formula, Rk was a measurement noise matrix.
[0140] After the gain matrix was calculated, the state vector was filtered according
to the gain matrix to obtain a filtered value ofX as follows:
X=X+Kk-L
[0141] X = lk-l K (25)
[0142] a covariance matrix k of the Xk was calculated as follows:
[0143] Pk ( KkAW*k-1 (26)
[0144] Xkcalculated by the Kalman filter algorithm included the single-difference
integer ambiguity values of the baseline vector and each frequency point, where k was
a floating point solution; the floating point solution -kand its corresponding variance covariance matrix were transformed for calculating a fixed solution, where a single difference integer ambiguity value was transformed into double-difference integer ambiguity, and a transformation matrix was as follows:
1 0 0 0 1 0 0 0 0 1 1 -1 -1 1 1 -1 -1 1 D= ... ... ... ... ... ... ... ... 1 -1 -1 1 1 1 -1 0 0 1 -1 0 1 .0
[0145] 1 -1 0] (27)
[0146] a double-difference floating point solution was as follows:
[0147] X4 = D- X4 (28)
[0148] the variance-covariance matrix corresponding to the double-difference floating point solution was as follows:
[0149] 5*=D-P-D (29)
[0150] the integer ambiguity double-difference floating point solution and its corresponding variance-covariance matrix were substituted into the LAMBDA algorithm to solve the fixed solution of the integrity ambiguity. The double-difference ambiguity searched by the LAMBDA algorithm was the ambiguity value corresponding to the wide lane combination (1, -1, 0) and (1, 0, 0), and the double-difference integer ambiguity value corresponding to each frequency point was obtained through further linear transformation. Receiver clock errors and satellite clock errors were eliminated by calculating double-difference observation values through GNSS dynamic Kalman filter method in cluster autonomous cooperation. Satellites with high elevation angles were called as the first choice of reference satellites, so that the accuracy of each double difference observation value was ensured. Pseudo-range measurement values corresponding to different stations and between satellites formed a double-difference pseudo-range, and the corresponding double-difference pseudo-range was smoothed by utilizing a double-difference carrier phase, so that measurement noises of a double difference pseudo-range observation value were reduced, and the smoothed or filtered double-difference pseudo-range observation value had the advantages of relatively low measurement noises and no integer ambiguity. At the same time, when RTK positioning was performed, the single-difference integer ambiguity values including the baseline vector and each frequency point were calculated through the Kalman filter method; and after the single-difference integer ambiguity values were transformed into double difference integer ambiguity, the double-difference integer ambiguity value corresponding to each frequency point was obtained more precisely through further linear transformation via the LAMBDA algorithm.
[0151] Although the invention has been described with reference to specific examples, it will be appreciated by those skilled in the art that the invention may be embodied in many other forms, in keeping with the broad principles and the spirit of the invention described herein.
[0152] The present invention and the described embodiments specifically include the best method known to the applicant of performing the invention. The present invention and the described preferred embodiments specifically include at least one feature that is industrially applicable
Claims (4)
1. A GNSS dynamic Kalman filter method in autonomous cooperation,
characterized by comprising the following steps:
I. calculating a double-difference observation value,
wherein in a process of receiving satellite signals by a multi-antenna receiver, each
double-difference observation involves measurement values of two receivers on two
satellites at the same moment, a difference between single differences of two different
satellites is made, i.e., the difference between the stations and the satellites is calculated
once; assuming that a user receiver u and a base station receiver r track a satellite i and
a satellite j at the same time, a single-difference carrier phase observation value of the
two receivers to the satellite i is as follows:
, +fAt,+ANur+ (1)
a single-difference carrier phase observation value of the two receivers to the
satellite j is as follows:
A r i +fAtur,+ ANr + c1 (2)
a double-difference carrier phase observation value consisting of the two is defined
as follows:
VAp =Ap'- Apj (3) an observation equation of the double-difference observation values is obtained as follows:
VArp=VVAr"+VAN" +ur A9 (4)
whereinVAr" = Ar' - Ar' VANur =AN ur -ANu 8 VAq = - e , the ween ur ur ur ur, VpC th
formula (4) indicates that the double-difference observation values can completely
eliminate receiver clock errors and satellite clock errors;
the double-difference carrier phase observation value is a key measurement value I
to determine a baseline vector bur for the satellite j,
ArJ=-b ur - u(5) '
Get
Vr, b.,ir'+bu,- | (l,'- |- ir bur (6)
therefore, a relationship between the double-difference observation values and the
baseline vector is as follows:
VA~p = -'z -V - l J|)- bur± ,+ VANY r (7)
VAp in the formula, -r at the left side of the equal sign is the double-difference
carrier phase observation value calculated by four carrier phase measurement values of the same epoch, and is a known quantity; and ur at the left side of the equal sign is a three-dimensional baseline vector to be determined, and double-difference integer ambiguity V -is an unknown integer;
II. calculating an observation equation,
wherein the carrier phase measurement values of two different satellites can be
linearly combined by the user and the base station receiver to form a double-difference
measurement value, therefore, if the two receivers have measurement values for M
satellites at the same time, M(M-1) double-difference observation values can be
generated between every two pairs of the M pairs of carrier phase measurement values,
but only the (M-1) double-difference values are independent of each other; assuming
that the (M-1) mutually independent double-difference carrier phase measurement
values are expressed asV , u,. r , each double-difference value has
an observation equation similar to (7), and the (M-1) double-difference observation
equations are integrated together to form the following matrix equation:
- I I VAe -(/2 _1)T - VAN 2 1
rr VAeoY'r , _ -1 -(/3- "r r r)T r r VAN b' ,+r
VAqrpM rM r Mi - - ('rM 'r) AN (8)
wherein double-difference observation noises ^Amare omitted; if the receivers
VN can determine each double-difference integer ambiguity value VANUr in the matrix I
equation, the baseline vector bir can be solved from the equation, and thus, baseline solution can be realized; the formula (8) selects the satellite 1 as a reference satellite for double-difference calculation, so its single-difference value r enters all the above
(M-1) double-interpolation values;
III. calculating a double-difference pseudo-range observation value,
wherein similar to a combination mechanism of the double-difference carrier
phase measurement values, the pseudo-range measurement values corresponding to
different stations and between satellites constitute a double-difference pseudo-range;
and in the case of a short baseline, a single-difference pseudo-range observation
equation of the user receiver u and the reference station receiver r to the satellite i is
follows:
(9)
a single-difference pseudo-range to the satellite j can be written as follows
Ag ' Air±CA'tur (10)
the definition of a double-difference pseudo-range observation value of the
receivers u and r to the satellites i and j, and an observation equation thereof are as
follows:
V Ap' =Ap - Apj = i± (C)
IV. calculating double-difference pseudo-range observation equations,
wherein if the two receivers have pseudo-range observation values for M satellites,
(M-1) mutually independent double-difference pseudo-range observation equations
constitute a matrix equation as follows:
Ar 2 r2 r1)T r r V" 3 _O -(r -11 )T r =r r bu
VApM] M /1)T( -r (12)
given enough double-difference pseudo-range measurement values, the receiver I
solves the baseline vector bur from the matrix equation, and the double-difference
carrier phase VAcpoiur is used to smooth the corresponding double-difference pseudo
VApy range ur , so that measurement noises of the double-difference pseudo-range
observation value are reduced;
V. calculating double-difference pseudo-range observation equations based on a
pseudo-range and a carrier phase,
wherein in accordance with the step IV, carrier phase and pseudo-range
observation equations are separately as follows:
ALp = r +c(t, -t )+ T -I ± + AN+e (1 p =r+c(t,-t')+Tro,+I,,o+
(14)
in the formula, P is a pseudo-range observation value, 'P is a carrier phase
observation value, r is a station-satellite distance, tu is receiver clock errors, t" is a
satellite clock errors, trop is tropospheric delay, 'ono is ionospheric delay,L is carrier
wavelength, and N is carrier integer ambiguity;
double-difference pseudo-range observation equations based on pseudo-range and
carrier phase are separately obtained from formulas (13) and (14) as follows:
AVArp,=VAr +VA7 -VAIo +{VA++AV^ (15)
VAp. VAr +VAPIp.r +VAFInor + Ap (16)
VAT" when RTK positioning is performed, the correction of ""oPu is generally
accomplished by a tropospheric model and a value of a baseline is solved by a Kalman
filter method; and observation equations are linearized before Kalman filter for
separately linearizing the formulas (15) and (16) to obtain:
{VAypi -VARy =-[el e e][dX dY dZ] T +AVAN+s(
AVApy -VAR = -[e e e ] [dX dY dZ]T +Vsq^ (18) in the formula,VAR is a double-difference value of a station-satellite distance, ei eie e'] eis a single difference value of a satellite direction vector,
[dX dY dZ]T is coordinate difference between the user receiver u and the reference
station receiver r in the geocentric ground-fixed coordinate system, wherein
Xj-X e, = Yj-Y " eij = Zi-Z "JZ eij = X ". R R '=e e, e"e' -e,ese
(X,Y/,Z) are coordinates of the satellite j, and are approximate
coordinates of the user receiver;
VI. listing double-difference observation equations,
VALP = AV Arpa' - V AR" VAL = AVAp'j -VAR", wherein assuming that "' "' and = "r , M
satellites are observed, and the combination of (1, -1,0) and (1,0,0) for the carrier phase
combination observations is selected for single navigation system. From the double
difference pseudo-range and the carrier, 4(M-1) double-difference observation
equations can be listed as follows:
L L~ e'1 e 1 -ee1 AN I e11 e'1 21 -21 ANJ. 8V L e e eM dY2+
LMI e ey e dZ 02AN M e L e' eZ- 2 d0 ANfm ANf V'A1 e e 0 __21 31 31 dZ[dZJ 2 31 S e e1 ez 0 AN2 eVA
L _2 1j e' eI e1j 0 A]f'j _-'§VA, 0 0
0 j (19)
a matrix equation can be shown as follows:
L = AX + BF + E(20)
wherein L is a carrier phase and pseudo-range double-difference residual vector,
A is a double-difference direction cosine matrix, B is an integer ambiguity coefficient
matrix, X is a baseline vector to be estimated, F is a single-difference ambiguity vector,
and E is a double-difference noise vector, and the observation equations are established
when the Kalman filter is solved;
and VII, performing Kalman filter calculation,
wherein Kalman filter can be divided into six steps, and a predicted value kIk-1
of a state vector X is firstly calculated as follows:
kk-1- klk-1 k-1 (21) kk-1 is a state transition matrix, and a state vector in the geocentric ground fixed coordinate system is as follows:
X=[dX dY dZ ANJ AN, ... AN Apj AN f2 . . . A ]2 .i I fI f2 ./12 (22)
a covariance matrix of k1is then calculated as follows:
Pkk-1- P~ P T 0 klk-1 k-i kk-1 k-1
(23)
in the formula, *-I is a process noise matrix, then, a filter gain matrix K, is
calculated, and a gain condition of the original observation and the predicted value is
compared as follows:
PKA T k k AkPk~k-1 R
(24)
in the formula, Rk is a measurement noise matrix;
after the gain matrix is calculated, the state vector is filtered according to the gain
matrix to obtain a filtered value of X as follows:
k = kk-1 + Kk - L
(25) a covariance matrix * of the kis calculated as follows:
P =(IKkAk)Fkl (26)
Xkcalculated by the Kalman filter algorithm includes the single-difference integer
ambiguity values of the baseline vector and each frequency point, wherein kis a I floating point solution; the floating point solution kand its corresponding variance
covariance matrix are transformed for calculating a fixed solution, wherein a single
difference integer ambiguity value is transformed into double-difference integer
ambiguity, and a transformation matrix is as follows:
1 0 0 0 1 0 0 0 0 1 1 -1 -1 1 1 -1 -1 1 D =... ... ... ... ... ......... 1 -1 -1 1 1 1 -1 0 0 1 -1 0 1 .0 1 -1 0] (27)
a double-difference floating point solution is as follows:
3X4 =D- X (28)
the variance-covariance matrix corresponding to the double-difference floating
point solution is as follows:
P =D-P-D (29)
and the integer ambiguity double-difference floating point solution and its
corresponding variance-covariance matrix are substituted into the LAMBDA algorithm
to solve the fixed solution of the integrity ambiguity.
2. The GNSS dynamic Kalman filter method in autonomous cooperation
according to claim 1, wherein in the step II, the reference satellites adopt satellites with
high elevation angles.
3. The GNSS dynamic Kalman filter method in autonomous cooperation
VAT" VAI" according to claim 1, wherein in the step V, atmospheric errors ( "rop"'4 l"""u")
between the two antennas can be regarded as the same and can be eliminated directly
in case of an ultra-short baseline.
4. The GNSS dynamic Kalman filter method in autonomous cooperation
according to claim 1, wherein in the step VII, double-difference ambiguity searched by
the LAMBDA algorithm is the ambiguity value corresponding to the wide lane
combination (1, -1, 0) and (1, 0, 0), and the double-difference integer ambiguity value
corresponding to each frequency point is obtained through further linear transformation.
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| CN113466903A (en) * | 2021-08-16 | 2021-10-01 | 电子科技大学 | Partial ambiguity fixing algorithm considering observed value system error |
| CN113759407A (en) * | 2021-09-08 | 2021-12-07 | 广东汇天航空航天科技有限公司 | GNSS integer ambiguity fixing method, positioning device and mobile station |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113466903A (en) * | 2021-08-16 | 2021-10-01 | 电子科技大学 | Partial ambiguity fixing algorithm considering observed value system error |
| CN113759407A (en) * | 2021-09-08 | 2021-12-07 | 广东汇天航空航天科技有限公司 | GNSS integer ambiguity fixing method, positioning device and mobile station |
| CN114994601A (en) * | 2022-06-02 | 2022-09-02 | 合肥联睿微电子科技有限公司 | Generalized Kalman filtering positioning method and system based on distance measurement |
| CN116299615A (en) * | 2022-12-15 | 2023-06-23 | 长安大学 | Phase deviation estimation method for realizing single Beidou real-time PPP fuzzy fixation |
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