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 (2)  The FMCS is programmed to select the navigation mode that provides the best determination of airplane present position and velocity. This selection depends upon sensor status, and availability of navigation aid (DME, VOR/DME, VORTAC) ground stations. The selection process is automatic and controlled solely by the FMC. The FMC contains a nine-state Kalman filter. This filter is used in the DME/DME/IRS and DME/VOR/IRS modes, for navigation aid correction to IRS position and velocity solutions. Also the filter reduces transients in position and velocity. The transients may be caused by differences in correction from one navigation aid to another.
 I. Position Determination
 (1)  
Navigation function processing consists of computations for both the horizontal and vertical position of the airplane. For vertical navigation, the process computes values of altitude and Flight Path Angle (FPA), using data from the IRS and DADC. When the airplane is on the ground the FPA is set to zero. The more involved process of horizontal navigation primarily consists of a dead-reckoning position computation, and a Kalman filtering process for estimating dead-reckoning errors. In the order that they are accomplished, the FMCS navigation processing tasks are:

 (a)  
Navigation mode selection

 (b)  
On-ground navigation

 (c)  
Dead-reckoning

 (d)  
Track angle calculation

 (e)  
Kalman filtering

 (f)  
Position updating

 

 (2)  
Every five seconds the FMC checks the status of all the navigation sensors and makes a selection of the optimum navigation mode available. The transition from a radio-updated navigation mode (DME/DME/IRS, or DME/VOR/IRS) to IRS dead-reckoning occurs 15 seconds after radio measurements are lost. However, this 15-second period does not include time while in the cone of silence of a tuned navigation aid. When the airplane is on the ground, the navigation mode selected is the On-Ground Navigation Mode.

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 (3)  
On-Ground Navigation

 (a)  When the airplane is on the ground, the On-Ground Navigation mode is used, because signals from navigation aid stations are not reliable for position determining. On the ground, the system position and velocity states are initialized, and the navigation outputs are simply the current IRS values. Once the airplane is on the air, and the IRS and DADC are valid, other modes of navigation can be selected.

 (4)  
Dead-Reckoning

 (a)  The dead-reckoning equations for estimate of the horizontal position are processed by the FMC every 100 milliseconds. The basic inputs are latitude, longitude, and north-south and east-west velocity components from the IRS. The basic data from the IRS are refined by corrections available from the Kalman filter process.

 (5)  
Track Angle Calculation

 (a)  The track angle computation simply uses the Kalman filter-corrected values of the airplanes north-south and east-west velocity; and takes the arctangent of the velocity ratio to determine track angle.

 (6)  
Kalman Filtering

 (a)  
The navigation position accuracy depends upon the data used for the Kalman filtering process. If current radio data is available, the Kalman error correction to the basic IRS present position will be more accurate than if the radios are invalid. Depending upon the radio-augmented navigation mode selected by the system, the Kalman filter will use either two DME ranges, or one DME range and one VOR bearing. The complete Kalman filtering process is operated if either of the two radio-augmented navigation modes are available.

 (b)  
If the radio systems become completely invalid for use as navigation data sources, the Kalman filtering process will predict system position errors. The position errors are extrapolated by the Kalman filter from previously received radio information. However, the Kalman filter is not updated with radio information until the radios again become valid. The Kalman filtering process is operated by the FMC every five seconds. DME or VOR measurements are tested for reasonableness, first to decide if the airplane is inside or outside the navigation aids cone of silence, and then for the magnitude of the measured range or bearing error from that navigation aid.
　
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