Page 153 - Autonomous Mobile Robots

136 Autonomous Mobile Robots

x –
Du, Dv INS x
IMU
equations + + Position
velocity
Ephemeris
Measurement dx attitude
prediction
Predicted measurements
Measurements – Residuals
GPS Kalman filter
+

FIGURE 3.5 Block diagram of a tightly coupled GPS aided INS.

From Section 3.3, the range measurement residual is

 e 
h 1 C , 1  
n δn
e
h 2 C ,
 δe
n 1  
 

.   (3.70)
.
y = δρ =  

 .  δd 
e
h m C ,1 b u
n
e
where C is the rotation matrix for transforming the representation of vectors
n
in navigation frame to the ECEF frame that is valid at the measurement epoch.
When using this implementation approach, the designer is responsible for
accommodating the receiver clock bias. As an alternative to including clock
bias states in the error model, the clock bias can be addressed by subtracting
the measurement of one satellite from the measurement of all other satel-
lites, but the resulting differenced signals then have correlated measurement
errors.
T
T T
T
T
T ˙
If the INS error state is ordered as δx =[δp , b u , δv , b u , δρ , x , x ] with
a g
the INS error dynamics as in Equation (3.68) and the receiver clock dynamics
as in Section 3.3.3.1; then, for Step 4 of the EKF algorithm, the linearized
pseudorange measurement matrix is
e
H k =[HC , 0]
n
where H is defined in Equation (3.47), 0 is an m by 13 matrix of zeros, and m is
the number of satellites available. Note that the components of the error in this
vector of measurements are uncorrelated. Whether or not the measurement error
can be considered white depends on which GPS error correction approaches
are used and the time between measurement epochs. If significantly correl-
ated measurement errors exist, then they should be addressed through state
© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c003” — 2006/3/31 — 16:42 — page 136 — #38