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132 Autonomous Mobile Robots

In particular, for GPS aiding, the time-of-availability of a GPS measurement
is typically delayed from its time-of-applicability due to latency within the
receiver and communication delay between the receiver and the EKF processor.
A typical latency between the times of applicability and availability is on the
order of a few hundred milliseconds (i.e., typically <0.25 sec). Fortunately,
most receivers provide a one-pulse-per-second (1PPS) output signal that can
be configured to align in time with the GPS second. In addition, assuming
a one second GPS measurement epoch, the time-of-applicability of the GPS
measurement can be aligned with the GPS second. When the EKF processor
receives the 1PPS signal, it saves the INS state. By doing this, the EKF will
have the INS state coincident with the GPS measurement even though the GPS
measurement will not arrive until a significant fraction of a second later. At the
time-of-availability of the EKF estimated correction, the EKF can use the state
transition matrix to propagate the correction from its time-of-applicability to
its time-of-availability.

Example 3.5 Let t denote an integer GPS second. At time t, the EKF pro-
cessor detects the 1PPS signal and saves the INS state x(t). In addition, the
GPS processor saves the receiver tracking data and computes the pseudoranges
ρ(t). The pseudorange measurements are sent to the EKF processor arriving
at time t 1 = t + τ where 0 <τ < 1 sec. At time t 1 the EKF processes the
pseudoranges to compute δx(t) which is available at some t 2 > t 1 . At this
point in time it is not correct to simply add the correction to the current INS
state, since δx(t) = δx(t 2 ) (i.e., x(t 2 ) + δx(t) would not be correct). Note that
the time t 2 is known to the EKF processor and that the processor is already
propagating the state transition matrix by a method such as Equation (3.18),
because is required to propagate the state estimation error covariance matrix.
With these quantities being known and available, it is straightforward for the
EKF processor to propagate the correction from its time-of-applicability to its
time-of-availability t 2 as

δx(t 2 ) = (t 2 , t)δx(t)

Then, δx(t 2 ) can be added to the INS state x(t 2 ) to properly compensate the
system.
Alternative latency compensation methods are described in the literature,
see, for example, Reference 44.

3.5 INTEGRATION OF GPS AND INS
Due to their complementary characteristics, various methods have been sugges-
ted to implement a system to integrate GPS and INS with the goal of achieving

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c003” — 2006/3/31 — 16:42 — page 132 — #34