9.4.2.3  The INS Kalman Filter States

For an INS Kalman filter implementation, 15 states are often used to describe the

INS navigation process and its error sources:

3 INS position errors

3 INS velocity errors

3 platform orientation errors

3 accelerometer biases

3 gyro drift rates

For some applications, particularly if the mission scenario calls for only short

periods of time without GPS data, it may be possible to model an INS with fewer

states.

There are many other sources of error in an INS in addition to the states given

above as noted previously: gyro and accelerometer scale factor errors, gyro and

accelerometer input axis misalignment angles, gyro g  sensitivity, etc.  Usually the

effects of these errors are accounted for in the computation of the process noise

covariance matrix Q.  Failure to account for the effects of these errors will almost

always result in optimistic filter performance; that is, the true estimation error

standard deviations will be larger than the standard deviations in the covariance

matrix computed by the Kalman filter.  In addition, the INS manufacturer attempts to

minimize their effects by providing calibration coefficients and test data on the INS

themselves.

9.4.3  Kalman Filtering and GPS/Precise Clock

In case an external clock is used for GPS time reference, its phase and frequency

error can be included as states in the Kalman filter. Corrections are calculated and

either maintained in the mission computer (open loop) or directly applied to the

clock continuously (closed loop).

When the receiver starts to navigate with only three satellites, the calibrated clock

can then be used to maintain accurate GPS system time. This also applies to a two

satellite situation if receiver altitude is known.  What accuracy can be maintained

and for how long depends on the detail of the error models and the disturbance to

the clock during the outage period. Examples of such disturbances are temperature

changes, pressure changes, crystal aging, accelerations and vibrations.

9.4.4  Kalman Filtering and GPS/Barometric Altimeter

A barometric altimeter is typically included in a stand  alone INS for damping of its

otherwise unstable vertical loop.  In a GPS/INS integration, inclusion of a

barometric altimeter is recommended both for aiding poor vertical geometry

situations under nominal conditions and for three satellite situations.  If GPS

outages occur for extended periods of time, then  some other type  of reference

altitude is required to stabilize the vertical channel.

The barometric altimeter can be processed as a measurement to the Kalman filter

since the vertical channel is effectively stabilized through the optimal Kalman filter

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