1.4.1  The Role of Kalman Filtering
It has been called “navigation’s integration workhorse” [23] for the essential
role it has played in navigation and especially for integrating different navigation  modes.  Ever  since  its  introduction  in  1960  [20],  the  Kalman  filter  has
played a major role in the design and implementation of most new navigation
systems as a statistically optimal method for estimating position using noisy
measurements. Because the filter also produces an estimate of its own accuracy, it has also become an essential part of a methodology for the optimal
design  of  navigation  systems.  The  Kalman  filter  has  been  essential  for  the
design and implementation of every GnSS. It is unlikely that the first GnSS
(GPS) could have been built without it.
using  the  Kalman  filter,  navigation  systems  designers  have  been  able  to
exploit  a  powerful  synergism  between  GnSSs  and  InSs,  which  is  possible
because they have very complementary error characteristics:
• Short-term position  errors  from  the  InS  are  relatively  small,  but  they
degrade significantly over time.
• GnSS position accuracies, on the other hand, are not as good over the
short term, but they do not degrade with time.
The  Kalman  filter  takes  advantage  of  these  characteristics  to  provide  a
common, integrated navigation implementation with performance superior to
that of either subsystem (GnSS or InS). By using statistical information about
the errors in both systems, it is able to combine a system with tens of meters
position uncertainty (GnSS) with another system whose position uncertainty
degrades at kilometers per hour (InS) and achieve bounded position uncertainties in the order of centimeters (with differential GnSS) to meters.
1.4.2  Implementation
The Kalman filter solves for the solution with the least mean-squared error
by  using  data  weighting  proportional  to  statistical  information  content  (the
inverse  of  uncertainty)  in  the  measured  data.  It  combines  GnSS  and  InS
information to
1.  track drifting parameters of the sensors in the InS, so that InS performance does not degrade with time when GnSS is available
2.  improve overall performance even when there are insufficient satellite
signals for obtaining a complete GnSS solution
3.  allow the InS to navigate with improved initial error whenever GnSS
signals become unavailable
4.  improve GnSS  signal  reacquisition  when  GnSS  signals  become  available again by providing better navigation solutions (based on InS data)
5.  use acceleration and attitude rate information from the InS for reducing
the  signal  phase-tracking  filter  lags  in  the  GnSS  receiver,  which  can
significantly improve GnSS reliability during periods of high maneuvering, jamming, or reduced signal availability.
The  more  intimate  levels  of  GnSS/InS  integration  necessarily  penetrate
deeply into each of the subsystems in that it makes use of partial results that
are  not  ordinarily  accessible  to  users. To  take  full  advantage  of  the  offered
integration  potential,  we  must  delve  into  technical  details  of  the  designs  of
both types of systems.
1.4.3  Applications  Military Applications The  rationale  for  developing  the navistar
GPS system was based, in part, on economic considerations—in terms of how
many inertial systems it could replace. However, the ability to integrate GPS
with InS also enabled military applications that were not possible before. It
would lead to a new generation of high-precision military weaponry, improving military effectiveness while reducing collateral damage. Most missiles were
already  using  inertial  sensors  for  guidance  and  control,  so  the  transition  to
integrated GnSS/InS navigation was natural.
Most military applications of inertial navigation were already using other
navigation aids for limiting the growth of inertial navigation errors with time.
The u.S. navy had begun using satellites for aiding shipboard inertial navigation  decades  before  GnSS  became  available,  and  most  military  InSs  were
being adapted to use GPS before it was operational. It has resulted in superior
navigation performance at low marginal cost.  Civilian and Commercial Applications The availability of GnSS
also  allowed  for  integrated  GnSS/InS  navigation  systems  accurate  enough  
32  InTrODuCTIOn
for automated grading, plowing, and surface mining. The resulting relaxation
of inertial sensor stability requirements and advances in fabrication technologies have also combined to lower costs to the point where low-performance
GnSS/InS  systems  can  be  embedded  in  high-end  consumer  products. This
market is likely to grow even more as costs fall due to increasing production
Details of Section 1.4 are given in Chapters 10 through 12