# US 11,442,178 B2 · Method for achieving space-based autonomous navigation of global navigation satellite system (GNSS) satellites

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- Number: US 11,442,178 B2
- Document ID: US11442178B2
- Status: Granted
- Kind: B2
- Application number: 16/837,158
- Filed: 2020-04-01
- Published: 2020-10-08
- Granted: 2022-09-13
- Earliest claimed: 2019-04-02
- Assignees: Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences
- Applicants: Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences
- Inventors: Wenbin Wang; Yang Gao; Leizheng Shu; Jiangkai Liu
- Web page: https://patentgrep.com/patent/US11442178B2

## CPC

- G01S 19/02: Details of the space or ground control segments
- G01S 19/393: {Trajectory determination or predictive tracking, e.g. Kalman filtering}
- B64G 1/1007: {Communications satellites}
- B64G 1/1014: {Navigation satellites}
- B64G 1/1085: {Swarms and constellations}
- B64G 1/244: {Spacecraft control systems}
- G01S 19/421: {by combining or switching between position solutions or signals derived from different satellite radio beacon positioning systems; by combining or switching between position solutions or signals derived from different modes of operation in a single system}
- G06F 17/13: Differential equations (using digital differential analysers G06F7/64)
- G06F 17/16: Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)}
- 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
- B64G: COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

Disclosed is a method for achieving space-based autonomous navigation of global navigation satellite system (GNSS) satellites, and relates to the field of satellite navigation technologies. The method includes the following steps: optimizing a DRO, and establishing a dynamic model of an earth-moon space satellite orbit; establishing measurement links, by a low earth orbit (LEO) data relay satellite, with an earth-moon space DRO satellite and a GNSS respectively, and measuring an inter-satellite distance for modeling and linearization; adopting an extended Kalman filter (EKF) method to process inter-satellite measurement data, and autonomously determining a position and velocity of the global navigation satellite system without depending on the ground measurement and control support.

## Claims

### Claim 1

A method for achieving space-based autonomous navigation of global navigation satellite system (GNSS) satellites, comprising the following steps:
S1: optimizing an earth-moon space DRO, and establishing a dynamic model of an earth-moon space satellite orbit;
S2: establishing measurement links, by a low earth orbit (LEO) data relay satellite, with an earth-moon space DRO satellite and a GNSS satellite respectively, and measuring an inter-satellite distance for modeling and linearization; and
S3: adopting a data processing method to process inter-satellite measurement data, and achieving autonomous navigation of the GNSS satellite without depending on the ground measurement and control support.

### Claim 2 (depends on 1)

The method for achieving autonomous navigation of GNSS satellites according to claim 1, wherein in step S1, the optimizing an earth-moon space DRO specifically comprises:
A1: deducing an earth-moon DRO family with periodic characteristics from a circular restricted three-body problem (CRTBP) model; and
A2: calculating gravity asymmetry of each orbit, and selecting an orbit with high gravity asymmetry as a preferred earth-moon DRO.

### Claim 3 (depends on 1)

The method for achieving autonomous navigation of GNSS satellites according to claim 1, wherein in step S1, the establishing a dynamic model of an earth-moon space satellite orbit specifically comprises:
B 1: establishing satellite state vectors: at any time t, yDj(t), jMk(t) and yTl(t) denote position and velocity state vectors of a j-th DRO satellite, a k-th navigation satellite and an l-th LEO data relay satellite, respectively, namely yDj(t)=[rDj(t)T,vDj(t)T]T, yMj(t)=[rMj(t)T,vMj(t)T]T and yTj(t)=[rTj(t)T,vTj(t)T]T;
wherein the numbers of satellites participating in orbit determination are J, K and L respectively, j=0, . . . ,J−1, k=0, . . . ,K−1 and l=0, . . . ,L−1 , and the state vector of each type of satellites is denoted as:
yD(t)=[yD0(t)T, . . . ,yDJ−1(t)T)]T (1)
and
yM(t)=[yM0(t)T, . . . ,yMK−1(t)T)]T (2)
and
yT(t)=[yT0(t)T, . . . ,yTL−1(t)T)]T (3)
which are further combined into a state vector:
X(t)=[yD(t)T,yM(t)T,yT(t)T]T (4);
B2: a differential equation of an orbital motion state of any satellite is:
[
r
.
v
.
]
=
[
v
a
E
+
a
M
+
a
S
+
a
SRP
+
a
D
]
(
5
)
wherein aE and aM are spherical harmonic gravity acceleration models of the earth and the moon respectively, aS is a gravity acceleration of the solar particle, aSRP is an acceleration of solar radiation light pressure, and aD is mainly an atmospheric drag acceleration suffered by an LEO satellite; and
B3: calculating a state transition matrix Φi□Φ(ti,ti−1)=∂X(ti)/∂X(ti−1) from any time ti−1 to any time ti.

### Claim 4 (depends on 3)

The method for achieving autonomous navigation of GNSS satellites according to claim 3, wherein in step B2, a first-order dynamic differential equation used as a basis is:
{dot over (X)}(t)=f(X(t),t) (6) and
in step B3, the state transition matrix for state calculation follows a variational equation:
Φ
.
i
=
∂
f
⁡
(
t
i
,
X
⁡
(
t
i
)
)
∂
X
⁡
(
t
i
)
⁢
Φ
i
.
(
7
)

### Claim 5 (depends on 1)

The method for achieving autonomous navigation of GNSS satellites according to claim 1, wherein step S2 specifically comprises:
S21: at any time ti, an inter-satellite measurement model of an l-th LEO satellite and a j-th DRO satellite and a k-th navigation satellite being as follows:
{
z
DT
,
i
j
⁢
l
=
h
D
⁢
T
j
⁢
l
(
y
D
j
(
t
i
)
,
y
T
l
(
t
i
)
)
+
ε
D
⁢
L
=
|
r
D
j
(
t
i
)
-
r
T
l
(
t
i
)
|
+
ε
D
⁢
L
z
MT
,
i
k
⁢
l
=
h
M
⁢
T
k
⁢
l
(
y
M
k
(
t
i
)
,
y
T
l
(
t
i
)
)
+
ε
M
⁢
L
=
|
r
M
k
(
t
i
)
-
r
T
l
(
t
i
)
|
+
ε
M
⁢
L
(
8
)
wherein z is a measured value, h is a model value, and ε is a measurement noise;
S22: Xi−[(yD,i−)T,(yM,i−)T,(yT,i−)T]T being a known initial state of a satellite, and linearizing the measurement model (8) near the state:
z
DT
,
i
j
⁢
l
=
h
D
⁢
T
j
⁢
l
(
y
D
,
i
j
,
-
,
y
T
,
i
l
,
-
)
+
H
DD
,
i
jl
·
Δ
⁢
y
D
,
i
j
+
H
DT
,
i
jl
·
Δ
⁢
y
T
,
i
l
+
ε
DT
(
9
)
z
MT
,
i
kl
=
h
MT
kl
(
y
M
,
i
k
,
-
,
y
T
,
i
j
,
-
)
+
H
MM
,
i
kl
·
Δ
⁢
y
M
,
i
k
+
H
MT
,
i
kl
·
Δ
⁢
y
T
,
i
l
+
ε
MT
wherein
⁢
H
DD
,
i
jl
⁢
▯
⁢
∂
h
DT
,
i
jl
∂
y
D
,
i
j
,
-
,
H
DT
,
i
jl
⁢
▯
⁢
∂
h
DT
,
i
jl
∂
y
T
,
i
l
,
-
,
H
MM
,
i
kl
⁢
▯
⁢
∂
h
MT
,
i
kl
∂
y
M
,
i
k
,
-
,
H
MT
,
i
kl
⁢
▯
⁢
∂
h
MT
,
i
kl
∂
y
T
,
i
l
,
-
,
and there are relations HDT,ijl=−HDD,ijl and HMT,ikl=−HMM,ikl;
ΔXi=[(ΔyD,i−)T,(ΔyM,i−)T,(ΔyT,i−)T]T is set to be an increment of a to-be-estimated state with respect to an initial value state, and then ΔXi=Xi−Xi−;
S23: combining all measured values into zi=[zDT,iT,zMT,iT]T, with a component denoted as:
z
DT
,
i
=
[
z
DT
,
i
00
,
…
,
z
DT
,
i
J
-
1
,
0
,
…
,
z
DT
,
i
0
,
L
-
1
,
…
,
z
DT
,
1
J
-
1
,
L
-
1
]
T
⁢
z
MT
,
i
=
[
z
MT
,
i
00
,
…
,
z
MT
,
i
K
-
1
,
0
,
…
,
z
MT
,
i
0
,
L
-
1
,
…
,
z
MT
,
i
K
-
1
,
L
-
1
]
T
(
10
)
wherein a corresponding model value hi(Xi)=[hDT,iT,hMT,iT]T, and a measurement error is ε=[(εDL)T,(εML)T];
standard deviations of microwave measurement and laser measurement errors are σDL and σML respectively; and
S24: at the time ti, a linearization measurement model comprising all measured values is:
[
z
DT
,
i
z
MT
,
i
]
=
[
h
DT
,
i
(
X
i
-
)
h
MT
,
i
(
X
i
-
)
]
+
[
H
DD
,
i
0
H
DT
,
i
0
H
MM
,
i
H
MT
,
i
]
·
[
Δ
⁢
y
D
,
i
Δ
⁢
y
M
,
i
Δ
⁢
y
T
,
i
]
+
[
ε
D
ε
M
]
(
11
)
which is further simplified as:
zi=hi(Xi−)+Hi·ΔXi+ε (12)

### Claim 6 (depends on 1)

The method for achieving autonomous navigation of GNSS satellites according to claim 1, wherein the data processing method in step S3 is an extended Kalman filter (EKF) method, which specifically comprises:
S31: adding a process noise u(t) to a dynamic equation:
{dot over (X)}(t)=f(X(t),u(t),t) (13)
wherein u(t) is a white Gaussian noise with zero mean; correspondingly, a process noise conversion matrix is:
Γ
⁡
(
t
i
,
t
i
-
1
)
=
∂
X
⁡
(
t
i
)
∂
u
⁡
(
t
i
-
1
)
;
(
14
)
and
S32: given an initial state and time of the satellite, processing, by an extended Kalman filter (EKF), measurement data based on continuous measurement epochs, and updating a to-be-estimated state.

### Claim 7 (depends on 6)

The method for achieving autonomous navigation of GNSS satellites according to claim 6, wherein step S32 specifically comprises:
A. time update
wherein a satellite orbit state and a state estimation covariance are advanced from the previous time ti−1 to the current observation time ti:
Xi−=X(ti;X(ti−1)=Xi−1+)+Γ(ti,ti−1)u(ti−1)
Pi−=Φ(ti,ti−)Pi−1+ΦT(ti,ti−1)+Γ(ti,ti−1)QcΓT(ti,ti−1) (15)
wherein P is an orbit state covariance matrix, Qc is a process noise covariance matrix and is a (3J+3K+3L)-dimensional diagonal matrix, a diagonal value is related to dynamic model accuracy of each satellite, and a variance of an acceleration error is set as σc2; a format of the process noise conversion matrix Γ is:
Γ
=
[
Γ
0
0
Γ
1
⋱
0
Γ
J
+
K
+
L
⁢
‐
⁢
1
]
(
16
)
wherein a diagonal submatrix is denoted as:
Γ
k
=
[
Δ
⁢
t
2
/
2
×
I
3
×
3
Δ
⁢
t
×
I
3
×
3
]
6
×
3
(
17
)
where Δt=ti−ti−1, I is an identity matrix, 0 is a zero matrix, and k=0,1, . . . ,J+K+L−1.
B. measurement update
where the solution of a satellite orbit state and update of an orbit state covariance are completed by using measurement data:
Ki=Pi−HiT(Ri+HiPi−HiT)−1
Xi+=Xi−+Ki(zi−h(Xi−))
Pi+=(I−KiHi)Pi−(I−KiHi)T+KiRiKiT (18)
wherein Ki is a Kalman gain, Hi is a design matrix and is calculated by equation (12), I is an identity matrix, Ri is a measuring noise covariance diagonal matrix, a diagonal element value corresponding to laser measurement data is σDL2, and a diagonal element value corresponding to microwave measurement data is σML2.

### Claim 8 (depends on 1)

The method for achieving autonomous navigation of GNSS satellites according to claim 1, wherein the method is applicable to all navigation systems, comprising at least one of a GPS system, a Beidou system, a Glonass system, a Galileo system and a quasi-zenith navigation system.

### Claim 9 (depends on 2)

The method for achieving autonomous navigation of GNSS satellites according to claim 2, wherein the method is applicable to all navigation systems, comprising at least one of a GPS system, a Beidou system, a Glonass system, a Galileo system and a quasi-zenith navigation system.

### Claim 10 (depends on 3)

The method for achieving autonomous navigation of GNSS satellites according to claim 3, wherein the method is applicable to all navigation systems, comprising at least one of a GPS system, a Beidou system, a Glonass system, a Galileo system and a quasi-zenith navigation system.

### Claim 11 (depends on 4)

The method for achieving autonomous navigation of GNSS satellites according to claim 4, wherein the method is applicable to all navigation systems, comprising at least one of a GPS system, a Beidou system, a Glonass system, a Galileo system and a quasi-zenith navigation system.

### Claim 12 (depends on 5)

The method for achieving autonomous navigation of GNSS satellites according to claim 5, wherein the method is applicable to all navigation systems, comprising at least one of a GPS system, a Beidou system, a Glonass system, a Galileo system and a quasi-zenith navigation system.

### Claim 13 (depends on 6)

The method for achieving autonomous navigation of GNSS satellites according to claim 6, wherein the method is applicable to all navigation systems, comprising at least one of a GPS system, a Beidou system, a Glonass system, a Galileo system and a quasi-zenith navigation system.

### Claim 14 (depends on 7)

The method for achieving autonomous navigation of GNSS satellites according to claim 7, wherein the method is applicable to all navigation systems, comprising at least one of a GPS system, a Beidou system, a Glonass system, a Galileo system and a quasi-zenith navigation system.