Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 470

y ( t n ) in place of the observed state, our state vector has become the estimated error of
the state, more commonly known as the error state vector, instead of the estimated
state. One can then periodically (usually every filter cycle) apply the estimated cor-
rection to the output data and reset the filter error states to zero. By doing this, the
magnitude of the variables used in the filter are small, minimizing round off and
nonlinearity errors. This also minimizes some of the computation errors by setting
many of the elements in our matrices operation to zero. This method allows the mea-
surement processing and Kalman filtering to execute at different frequencies. For
example, one can process measurements at 100 Hz and run the filter at 1 Hz. Before
outputting the data, the latest correction from the filter is applied to the data.

9.2.4 GPSI Integration Methods
Integration of GPS and inertial navigation systems was initiated in the early 1980s
[5, 9] with a configuration that later came to be known as a loosely integrated or
loosely coupled configuration. This configuration typically includes a GPS receiver
with an 8-state Kalman filter, an IMU, a navigation processor that contains a 15- to
18-state Kalman filter, navigation equations to convert the

s from the
IMU to platform attitude, position, and velocity, as well as other functions that we
will discuss later in Sections 9.2.4.1 through 9.2.4.3. The configuration, as shown in
Figure 9.8, accepts GPS position from the GPS receiver, and

∆θ s and ∆ν

s from the
inertial unit. Although used in many initial applications, this system has a feed for-
ward loop from the navigation processor and two separate filters that open the pos-
sibility of instability caused by mutual feedback. Mission scenarios for this
configuration must be thoroughly simulated to ensure the stability of the filter. In
situations where instability occurs, the gains in the filter are reduced, which may
result in sluggish system operation. Today, most GPSI systems are tightly integrated ,
as shown in Figure 9.9. This configuration is also referred to as tightly coupled .In
tightly integrated systems, the Kalman filter in the GPS receiver is eliminated, and
pseudorange and pseudorange rate data from the GPS channel processor is sent

∆θ s and ∆ν

IMU

s, s ∆θ ∆ν

3 gyros
3 accel.

GPS receiver

Navigation
processor

Navigation
processor

Channel
processor

P, V, T
and attitu de P, V, T

.

N-state
Kalman filter

ρρ

,

8-state
Kalman filter

1-6 channels

V

Figure 9.8 Loosely integrated GPSI system.