Page 189 - 卫星导航2021年第1-2合期

Li et al. Satell Navig (2021) 2:1 Page 3 of 14

Methodology be denoted by ε P IF = γε P s + (1 − γ )ε P s and
r,2
r,1
In this section, we frstly introduce the PPP observation s + (1 − γ )ε L . Additionally, d r,j is absorbed
ε L IF = γε L r,1 s r,2
model. Ten, a tightly coupled stereo VIO algorithm is in receiver clock ofset, and d is corrected in the IF com-
s
j
described. Subsequently, the semi-tightly coupled multi- binations when applying the precise clock products. Te
GNSS PPP/S-VINS fusion method is presented. Finally, tropospheric delay T in Eqs. (1) and (2) is made up of the
the algorithm implementation of the developed multi- dry and wet components which can be expressed by the
sensor fusion framework is explained. zenith delays ( T dry , T wet ) and the corresponding mapping
functions ( m dry , m wet ). An empirical model can be used
PPP observation model to correct the dry delay part ( m dry · T dry ) (Saastamoinen
Te GNSS observation equations for raw pseudorange 1972), while the wet component delay ( m wet · T wet ) can
and carrier phase are formulated as (Li et al. 2015): be estimated from the observations.
When multi-GNSS observations are involved, the dif-
s
s
s
s
P s r,j = ρ + c(t r − t ) + c(d r,j − d ) + µ j I r,1 + T + �ρ + ε P r,j s ferent signal structures and diferent hardware delays for
j
r
(1)
each GNSS system will result in diferent code biases in
s
s
L s r,j = ρ + c(t r − t ) + j (b r,j − b ) one multi-GNSS receiver (Li et al. 2015). Te diferences
j
+ j N s − µ j I s s s between these biases are usually called Inter-System Biases
r,j r,1 + T + �ρ + ε L r,j (2) (ISB) or Inter-Frequency Biases (IFB) for GLONASS sat-
r
where the symbols s , r , and j represent the satellite, ellites. ISB/IFB parameters must be introduced into the
receiver and carrier frequency, respectively; ρ is the geo- multi-GNSS estimator. Te IF combinations of the multi-
metric distance between the satellite and receiver; c is the GNSS code and phase observations can be written as:
s
speed of light in vacuum; t r and t denote the receiver and sys s
s
satellite clock ofsets, respectively; d r,j and d are the code P IF = ρ T + c · t r + ISB − c · t + m wet · T wet + ε P IF
(5)
j
hardware delays for the receiver and the satellite, respec-
tively; I is the ionospheric delay at the frst carrier fre- L IF = ρ T + c · t r + ISB sys − c · t s
s
r,1
2
quency, and µ j = f 2 f is the ionospheric coefcient + IF N IF + m wet · T wet + ε L IF (6)
j 1
associated to a frequency f j ; T is the tropospheric delay; where t r denotes the receiver clock ofset of the reference
s
r
j and N denote the wavelength and the integer ambi- GNSS system, namely GPS; ISB represents the ISB of
s
sys
r,j
guity; b r,j and b are the phase delays in receiver and satel- the non-reference GNSS system. As for GLONASS, the
s
j
lite sides (Ge et al. 2008; Li et al. 2011); �ρ denotes the ISB parameter will be set for each frequency. ρ T rep-
sys
other corrections which should be considered in the PPP resents the sum of the geometric distance and the dry
model, such as phase wind-up efect, antenna Phase tropospheric delay. Te linearized equations of the IF
Center Ofset (PCO) and Phase Center Variation (PCV), combination can be expressed as:
relativity efect, and earth rotation efect (Wu et al. 1993;
Schmid et al. 2007); ε P and ε L represent the sum of p IF =−u · δp + c · t r + ISB sys + m wet · T wet + ε P IF
s
s
r,j r,j
measurement noises and multipath errors for code and (7)
phase, respectively. l IF =−u · δp + c · t r + ISB sys + IF N IF + m wet · T wet + ε L IF
Te Ionospheric-Free (IF) combinations are usually (8)
applied to eliminate the ionospheric delay in the PPP where p IF and l IF signify observed-minus-computed
model. Te dual-frequency IF combinations can be writ- pseudorange and phase IF measurement residuals; u rep-
ten as: resents the unit vector of the direction from the receiver
s
P IF = γ P 1 + (1 − γ)P 2 = ρ + c(t r − t ) to the satellite; δp is the position correction vector. In this
paper, the GNSS raw measurements are processed by the
(3)
+ m dry · T dry + m wet · T wet + ε P IF individual multi-GNSS PPP module of the multi-sensor
fusion system. Te detailed information on the multi-
s GNSS data processing in PPP is listed in Table 1.
L IF = γ L 1 + (1 − γ)L 2 = ρ + c(t r − t ) + IF N IF
+ m dry · T dry + m wet · T wet + ε L IF
(4) Stereo visual‑inertial odometry formulation
2
2
where γ = f 2 (f − f ) , f 1 and f 2 are the frequencies of Te visual front-end processes the stereo pairs from the
1 1 2 stereo camera. For each new stereo pair, the Kanade–
s
s
two carriers; IF N IF = γ( 1 (N r,1 + b r,1 − b )) + (1 − γ) Lucas–Tomasi (KLT) sparse optical fow algorithm
1
s
s
( 2 (N r,2 + b r,2 − b )) is the IF ambiguity in meters. Te is applied to perform feature tracking of existing fea-
2
measurements noises of IF pseudorange and phase can
tures (Lucas and Kanade 1981). In addition, the forward