International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004 
  
others, the improvement of heading determination and the 
detection of gross errors. 
The current INS/GPS approach to APRS applications is 
that of a single IMU combined with one or two GPS re- 
ceivers. Satellite positioning contributes the long wave- 
length information, while inertial positioning contributes 
the short wavelength information. Although this approach 
has brought remarkable progress to APRS, it has some lim- 
itations so there is need for further research and room for 
further improvement. These limitations range from unob- 
servable heading drifts in long strips to defective sensors 
going undetected for years. One possible cause of this lim- 
itations is the lack of redundant inertial data. This paper 
explores the possible benefits of the Skewed Redundant 
IMU (SRIMU) concept. In a previous paper (Colomina et 
al., 2003) the authors already presented a general overview 
of the SRIMU concept for APRS and some preliminary 
tests. 
2 POTENTIAL ADVANTAGES FOR AIRBORNE 
PHOTOGRAMMETRY AND REMOTE 
SENSING 
2.1 Realistic noise estimation 
Redundancy allows for intrinsic noise estimation and there- 
fore input precision for inertial measurements is realistic 
provided that good calibration of the sensors is achieved. 
Realistic noise estimates eliminate the need for adaptive 
Kalman filtering and improve the performance of robust 
Kalman filtering techniques. 
2.2 Overall navigation performance improvement 
Overall navigation improvement is to be expected as there 
is more input information. By simply adding a sensor to 
the normal 3-axis configuration, an increase by 3396 in 
the amount of information is achieved (Sukkarieh et al., 
2000). Through increased redundancy, a noise reduction 
in the navigation output parameters is expected. 
[n airborne surveys, heading determination accuracy relies 
on the performance of the vertical angular rate sensor and 
the horizontal accelerometers. Long, straight and constant 
speed flight lines do not allow to calibrate these three sen- 
sors properly. Redundant configurations may change this 
situation. 
Redundancy allows for de-contextualization of the cali- 
bration process. In contextual calibration, there is only a 
limited control on the physical correctness of the calibra- 
tion states. In other words, an apparently correct calibra- 
tion at the system level does not necessarily correspond to 
a correct calibration at the sensor level. This may result 
in unpredictable navigation performance when the context 
changes as it uses to be the case in terrestrial navigation. 
2.3 Reliability and integrity improvement 
Redundancy is on the basis of hypothesis testing for er- 
ror detection and isolation. In INS/GPS navigation there is 
160 
no redundancy with the exception of the coordinate update 
observations. With redundant inertial measurements, relia- 
bility aspects may be approached at the IMU level in a way 
that the detection of defective sensors or spurious signals 
can be detected. The authors are aware of defective IMU 
sensors going undetected and being operated for years. 
Recall that INS navigation integrity is many times achieved 
by means of multiple-sensor configurations and that in civil 
aviation, airplanes are frequently equipped with more than 
one IMU. 
3 ALGORITHMIC APPROACHES TO SRIMU 
NAVIGATION 
As mentioned before, the use of redundant inertial mea- 
surements may provide some benefits for INS/GPS trajec- 
tory determination in APRS. However, correctly blending 
the redundant measurements together is of vital importance 
for the performance of the system. There is not a unique 
way to tackle this issue and all of them have their own pros 
and cons. 
Before seizing the data blending issue, it has to be noted 
that when dealing with redundant configurations two op- 
tions arise: the use of a genuine SRIMU (more than 3 + 3 
sensors assembled in a single box) and the use of two or 
more standard inertial units. 
The first option might be the optimal one in that the device 
has been designed to provide redundant data. However, 
nowadays, this kind of devices are not being produced at 
a very high rate for commercial purposes and, to the best 
knowledge of the authors, they are mainly used in research 
or space projects. 
The second option is interesting in the sense that it is enough 
to arrange two IMUS in such a way they are skewed with 
respect to each other to simulate a SRIMU. As mentioned, 
the difficulty of purchasing a genuine SRIMU and the usual 
high cost of ownership of nonstandard product, makes of 
this kind of simulations a very practical, attractive and eco- 
nomical solution. These configurations will be referred to 
as dual IMU configurations. 
The next section discusses these two options, SRIMU and 
dual IMU, in detail. 
31 ONESKEWED REDUNDANT IMU 
In this section a single skewed redundant IMU with n an- 
gular rate sensors and m accelerometers is assumed (n, 
m 2 3) As the focus of this paper is not on SRIMU 
design optimization, a fixed orientation of the n + m in- 
ertial sensors is assumed to be given through the direction 
cosine vectors of each sensor sensing axis. Let b be an in- 
strumental reference frame. Further, let £° be the angular 
rate observation vector produced by the n gyroscopes and 
£^ the linear acceleration vector produced by the mm ac- 
celerometers. If the instrument is subject to angular rates 
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