>, too. The 
raw GPS 
when less 
enefit in a 
vhere the 
bstruction 
  
tecture 
the EKF 
h serious 
ements. In 
the quality 
's place in 
f reflected 
> Adaptive 
ly-coupled 
nent noise 
maximum 
ate weight 
onal EKF 
1e update 
> matrix Q 
MES 
. adaptive 
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culate the 
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asurement 
jn. Hence, 
satisfy the 
t source of 
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se of AKF 
statistical 
| time. 
scheme is 
.E scheme 
is used to 
1ce matrix 
study, the 
pdate with 
update the 
adaptively 
replace the measurement weights through the latest estimated 
covariance matrices R. Figure 4 depicts the implementation of 
IAE procedure. 
Ze 
  
Compute C, bod Compute R | Kalman Filter 
Loop 
Figure 4. IAE computing procedure 
  
In the IAE approach, the measurement covariance matrix R and 
system noise covariance matrix Q are tuned by measurements of 
different time. The study focuses on the influence of the 
qualities of measurements, so only the measurement covariance 
matrix R is variable. The formulations of AKF are shown below 
(R-only) (Schwarz and Mohamed, 1999). 
Vp Zí 7 Hu (1) 
^ | 7 
C.=— > yvy @) 
Vk 2? J 
R, 2C, HP HT (3) 
Where V, represents the innovation sequence and C. is the 
covariance of innovation sequence at epoch À. jy is the first 
epoch of estimation window, and it would be calculated 
by Jo — k — N 1 and N is the size of window. 
The integrated algorithm in this study is applied for land vehicle 
navigation. Therefore, the velocity of land vehicle navigation 
constraints is derived assuming that the vehicle does not slip, 
which is a close representation for travel in a constant direction. 
A second assumption is that the vehicle stays on the ground, i.e. 
it does not jump of the ground. If both assumptions are true, 
non-holonomic constraints (NHC) are defined as the fact that 
unless the vehicle jumps off the ground or slides on the ground, 
the velocity of the vehicle in the plane perpendicular to the 
forward direction is almost zero (Sukkarieh, 2000; Nassar et al., 
2006; Godha, 2006). Figure 5 shows the scenario of non- 
holonomic constraints in the b-frame. Therefore, two constraints 
can be considered as measurement updates to the Kalman 
filtering navigation: 
b 
v, e 0 (4) 
b 
v, &0 
  
Voc 
Figure 5. The two non-holonomic constraints in the b-frame 
The body frame velocity can be given as: 
$26" (Cw (5) 
Perturbing Equation 5 expresses: 
voa rid - E" yc; p. o" + dv) = chu -EÜ"ys"..", (0) 
Collecting terms to the first order, the velocity error dynamics 
can be written as: 
on’ = ca + CE = C^óy" il C^(v"x) e" (7) 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
Then the measurement matrix can be given as: 
Zr SLY (8) 
mue qe Ciz Car 32, 7 DC22 SEC, *DÉID 
0 3o C13 0€) Cg imr pCog X vgCSa VDE 
053 9x3 0 4 (9) 
053 053 0 0 2x17 
Cy: the (i, j) elements from the DCM C7 
In general, the velocity output of the inertial navigation 
mechanization V" can be transformed to the body frame 
velocity y? by the attitude error dynamics DCM C T . And the 
NHC . : 
Z, is used as the measurements in the Kalman filter. The 
estimated errors will be fed back to the mechanization then. 
Finally, the implementation of the Kalman filters with non- 
holonomic constraints in INS-based tightly-coupled integrated 
systems can be illustrated as Figure 6. 
  
  
  
  
  
  
  
  
  
  
Figure 6. INS-based tightly-coupled integrated systems with NHC 
4. RESULTS AND ANALYSIS 
To validate the performance of proposed algorithm, the field 
scenario of the land vehicle was conducted in the downtown 
area of Tainan. Reference and test systems were installed on the 
test vehicle. The geodetic GPS receiver with double frequency 
board and the low-cost GPS receiver with single frequency 
board were applied in the field scenario. In the case of INSs, the 
two tactical grade INSs were applied. 
4.1 Test Instrument 
Table 1 and Table 2 show the specifications of the GPS 
receivers and INSs used in the field scenario. 
Table 1. The specifications of the GPS receivers 
  
NovAtel OEMV-3 | U-blox AEK-4T 
  
  
    
   
    
   
  
  
   
    
   
   
    
     
    
  
    
   
   
     
   
     
    
   
    
   
     
   
    
    
    
   
  
  
  
  
   
   
  
  
  
  
(Geodetic) (Low-cost) 
; Channels 14 L1,14 L2,6 L5 16 LI 
Receiver C/A code, P code, 
Type Data type Carrier Phase C/A Code 
Accuracy SPP (m) L11.8 Li+E2:1.5 3.0 
(RMS) DGPS (m) 0.45 2.4 
  
  
Table 2. The specifications of the INSs 
Type of IMU Grade Gyro Drift | Acc. Drift 
SPAN-CPT Tactical 1 deg/hr 0.75 
C-MIGITS III | Tactical 3 deg/hr 0.2