OPTIMIZING THE INS/GPS HYBRID Michael J. Dyment 
Navstar/GPS Product Manager 
FOR_NAVIGATION* Canadian Marconi Company 
]. INTRODUCTION anata, Ontario 
  
  
An excellent combination for precise, all weather navigation is the Inertial Navigation System/ 
Global Positioning System. When optimized through a fully closed loop Kalman filter, the systems 
perform mutual aiding: The INS provides the GPS receiver tracking loops with accurate velocity infor- 
mation. This enables the tracking loops ‘to be pre-positioned in phase to sustain lock or to reacquire. 
The assistance allows the tracking loops to have lower loop noise bandwidths, which improve measurement 
RMS error. The GPS receiver then supplies the inertial navigator with periodic pseudo-range 
information. However, the pseudo-range errors can become strongly correlated with the errors in the 
velocity aid. If the system navigation filter does not model these correlated errors instabilities 
vill result. This paper examines the various stability and performance aspects of mutually aided 
systems. Conventional aiding is analysed and various compensation techniques proposed in the literature 
are considered. A decorrelated measurement approach is suggested which eliminates the instability and 
makes the Kalman filter optimal. The implications of the decorrelated measurement approach for 
navigation in 3 dimensions are pointed out, as modifications to GPS receiver signal processing software 
are necessary. 
2, ALTERNATIVES FOR INS/GPS HYBRIDIZATION 
  
Several alternatives exist for INS/GPS integration which provide trade-offs in performance, 
software sophistication and hardware architecture. Performance aspects include positional accuracy, 
velocity accuracy, angular accuracy and the capability of rapid or dynamic initialization of the INS. 
While the INS/GPS hybrid should be suitable for the intended application, performance should also be 
weighed against the cost of engineering design. 
No differentiation is made here between strapdown and gimballed INS mechanizations. The systems, 
although mechanically different, are mathematically equivalent. This means that the various integration 
schemes investigated here will in general entail similar software cost tradeoffs. The major difference 
lies with performance. For those applications where positional accuracy is important, the systems are 
equivalent. The strapdown INS shows far superior performance however, when angular accuracy is required. 
This is due primarily to gimbal flexure, which can be on the order of 1 - 2 minutes of arc and is 
unmodelable. The final performance consideration is dynamic alignment, which is more difficult to 
achieve with a gimballed INS than with SINS, because the gimbals and gyros have dynamic torquing 
limitations. 
Two of the most important hybrid designs are compared below. Other designs are deemed special 
cases of these, and are therefore excluded so that clear differences can be pointed out in the actual 
mechanization. 
2.1 Open Loop Kalman Mechanization 
  
The open loop Kalman mechanization is characterized by the one-way flow of information from the INS 
and GPS set (Figure 2-1). The INS observes specific forces and angular rates and, based on initial 
conditions, computes raw states of position, velocity and attitude, which are passed to the Kalman 
filter. The GPS set observes and translates satellite signal phase measurements into pseudo ranges 
and pseudo range rates. These measurements and relevant ephemeris information are passed to the 
Kalman filter for processing. The Kalman filter, in addition to modeling primary error states 
(position, velocity and angular errors), is designed to model secondary errors that are not of direct 
use, such as GPS clock offset and drift, gyro drift and various INS biases. 
The advantage of the above mechanization lies with the straightforward hardware and software design. 
Off-the-shelf sensors can be used as there is no need to modify the internal design of these sensors. 
The complete integration function is handled by a Kalman filter which resides in an external processor, 
and which utilizes information that exists on the standard interface bus of the INS and GPS sets. 
The principle weakness of this mechanization is that the GPS pseudo-ranges and pseudo range rates 
are subject to errors induced by vehicle motion. For low dynamic applications such as drill rig 
positioning this is not a consideration. For applications that require antenna installation on the 
mast of a rolling ship, or fuselage of an aircraft, the measurement statistics must be deweighted to 
account for the unmodelable dynamically induced error component. This error component can be an order 
of magnitude worse that components due to normal system errors. A simple method of correcting for 
antenna lever arm effects can assist in reducing the error, but tracking loop phase error will still 
exist, especially when the GPS set is of a single or two channel design. Normally tracking loop 
bandwidths are wide enough to allow phase lock under these unassisted dynamic conditions.  Pseudo-range 
and range rate precision are proportional to these bandwidths. 
Antenna lever arm effects can be critical (Figure 2-2). If the Kalman filter uses velocity damping, 
the Kalman filter could be unstable if the statistics are not accurate, or do not reflect the relative 
velocity between the INS accelerometer triad and the GPS antenna. 
Hence the open loop Kalman mechanization of the INS/GPS hybrid is adequate for low dynamic applic- 
ations where lever arm effects are small. Positional error should not exceed that of the GPS position 
fixes (16m for P-code, 35m for differential C/A code and velocity to better than 0.1m/sec). When 
dynamics come into play these precisions will degrade, and the Kalman filter will be unstable if the 
measurements are not deweighted to account for the dynamic transients and unmodeled lever arm effects. 
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