Page 192 - 卫星导航2021年第1-2合期

Li et al. Satell Navig (2021) 2:1 Page 6 of 14

represents the vector of the measurement residual, and predicted position is used as an initial value for the PPP
is the corresponding covariance. data processing to replace the Standard Point Position-
k
k
Te error function r = z − h (χ) consists of two ing (SPP) result. On the one hand, SPP produces a posi-
t
t
parts in the fusion model. Part one is the local meas- tion with low accuracy in GNSS-challenged conditions
urement residual, which is formulated as: (Angrisano et al. 2013). On the other hand, the priori
location has a comparable positioning accuracy with PPP
l l l l
r local = z − h (χ) = z − h (x t−1 , x t ) in a short term, which is verifed in the following experi-
t t t t
l −1 l l G −1 G G mental part. Secondly, when the number of available sat-
q (p − p ) q (p − p )
t
t
= t−1 l −1 l t−1 ⊖ t−1 G −1 G t−1
q q q q ellites is less than six, the forecast position will be used
t−1 t t−1 t
(17) as the position constraint in the PPP processing. Tis
the upper equation describes the relative pose error criterion is used mainly to cope with the extremely poor
between time t − 1 and t . Te frst row denotes the rela- observation conditions. Te variance of the predicted
tive position errors, and the second row denotes the rela- position can be determined by:
tive rotation error. ⊖ is the minus operation on the error 2 2 (19)
state of quaternion. Te unifed covariance is applied for σ = (σ 0 + 0.01 × D)
all local measurements in our framework. Part two is the where σ 0 = σ + σ + σ is the standard deviation of
2
2
2
x 0
y 0
z 0
global measurement residual, which can be written as: the global location used in last graph optimization;
2
2
2
G
G
G
G
r global = z − h (χ) = z − h (x t ) = p ppp − p G (σ , σ , σ ) is the variances of position in ECEF; D
x 0
y 0
z 0
t
t
t
t
t
t
(18) denotes the diving distance from the vehicle state of last
ppp graph optimization to current vehicle state in meters; 1%
where p t is the position measurement from the multi- is the degradation rate of the local positioning accuracy
GNSS PPP. Te global location is directly used as the (Qin et al. 2019). Te unifed variance σ is applied for
2
position constraint for every node. It should be noted that diferent axes of the position vector p =[p , p , p ] in our
e
e
e
y
z
x
the local-level frame (ENU, East-North-Up) is adopted algorithm for the degradation rate of the local position-
to represent the global reference frame G , and the ori- ing accuracy is hard to be decomposed to diferent axes.
gin point is located at the frst global location from the Te position feedback mechanism in our solution is
multi-GNSS PPP solution during the global fusion. Fur- bootable when the number of the global locations main-
thermore, the subsequent global positioning results are tained in the global fusion processor exceeds a certain
converted from the Earth-Centered Earth-Fixed (ECEF) threshold.
frame to the ENU frame with respect to the frst global
location. Te proposed triple integrated system can pro-
vide the covariances of the global locations, which con- Implementation of multi‑GNSS PPP/S‑VINS algorithm
tributes to a better use of the position information from Te architecture of the proposed semi-tightly cou-
the GNSS. In comparison, the original work in Qin et al. pled multi-GNSS PPP/S-VINS integration is shown
(2019) determines the covariance only by the number of in Fig. 2. A sliding window-based nonlinear optimi-
the visible satellites. zation is operated for state updates after fnishing the
Te nature of the fusion method is a rigid base frame visual-inertial initialization. Te newest local state
alignment problem between a local reference frame is converted to the corresponding global state by the
and a global reference frame. Te multi-sensor-fusion transformation between the local frame and the global
positioning in the global frame can be realized by car- frame. In addition, the transformation matrix is initially
rying out this alignment process. Te transformation set to the identity matrix and gets updated after each
between the local and the global reference frame will be global optimization. Te IF combinations of GNSS raw
updated after each global optimization. Te subsequent pseudorange and phase measurements are applied to
positioning results from S-VINS can be converted from the PPP data processing. Once the feedback mechanism
the local frame to the global frame by this transforma- is activated, the predicted positions from S-VINS can
tion. Moreover, the predicted positions maintain a high be utilized in the PPP processing. When the PPP solu-
accuracy in a short term, which can be utilized in the tion is completed, the global position with its uncer-
multi-GNSS PPP data processing. Tus, we transmit tainty will be transferred to the global fusion processor.
the global forecast position to the multi-GNSS PPP Nevertheless, only the positioning result that passes the
processor as the a priori information. quality check will be used in the global fusion. Practi-
Te a priori information is used for the following pur- cally, the measurements from the local (S-VINS) and
poses in the multi-GNSS PPP processing. Firstly, the global (PPP) processor have diferent sampling rates. If