straight and level flight, for example, the Q will be overly pessimistic and will force

processing too much noise from the measurements due to larger Kalman gains than

needed.

The answer is to adapt Q, by setting it as small as possible, then using some other

observation to boost Q when needed.  Some schemes tried in GPS receivers

include making Q a function of the ratio of the observed measurement residuals

with the assumed measurement noise.  The only danger here is that if Q is allowed

to adapt too quickly, the filter can get into a positive feedback loop and cause

instability.  This happens when observed noise opens Q which creates more noise,

etc.  The resolution of this problem is to make Q adaptation very slow so that only

longer trend conditions cause a change in Q.  In practice, the adaptation may be

implemented directly on the covariance rather than the Q  term, but the effect is

similar.

9.4  KALMAN FILTERING FOR AIDED/INTEGRATED GPS

9.4.1  The Integrated Navigation Solution

GPS provides accurate position, velocity and time and is designed to perform in

all weather, at any time of the day, and under specified conditions of jamming and

HV dynamics.  Despite its superb performance, many integrators choose to go one

step further and combine GPS with other navigation sensors and systems available

in the HV into an integrated navigation solution.  Similar to the basic GPS

navigation equations, this integrated solution is using a Kalman filter to combine the

individual navigation solutions.

Since GPS is the most accurate positioning system with worldwide coverage

currently available, the integrated system navigation solution will essentially be

based on the GPS solution when GPS is available.  The system design will be

driven by the unifying concern for continued high quality navigation when the GPS

solution is unavailable because of jamming, dynamics or satellite failures.

Technical considerations for integrations of GPS with other sensors include the

choice of system architecture, the hosting of the Kalman filter, and the

characterization and modeling of additional measurements added by the other

sensors.  The most important integration is the one in which GPS is combined with

an INS.  Besides the combination of GPS and INS, the integration can also benefit

from sensors in the HV such as a precise clock, barometric altimeter or an AHRS in

the absence of an INS.

9.4.2  Kalman Filtering and GPS/INS

9.4.2.1  System Architecture

There are basically four different architectures possible in the combined GPS/INS

implementation, depending on the choice of hosting the Kalman filter and the

choice of open or closed loop technique.  Whether the integrated filter uses

position and velocity derived  from the GPS Kalman filter or uses pseudoranges and

deltaranges is usually referred  as loosely coupled or tightly coupled respectively.

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