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.

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.

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.

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737-300/400/500MAINTENANCE MANUAL
 (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 radio again becomes 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.
 (7)  Position Updating
 (a)  When the Kalman filter has made an acceptable estimate of the errors in the basic IRS present position; the lateral position data used for airplane navigation is updated. If significant error exists between the present and update position, the present position data (used for steering guidance) is slewed at a controlled rate to match the update position.
 I.  Magnetic Variation
 (1)  The FMC computes the current value of magnetic variation at the airplanes present position. This magnetic variation is based upon the known angle between true north and magnetic north, at the nearest VOR facility in the navigation data base.
 J.  Navigation Aid Cone of Silence
 (1)  Before computing airplane present position, the FMC determines if the airplanes estimated position is within the cone of silence of a tuned navigation aid. If the airplane is estimated to be within the cone of silence of a tuned navigation aid, the DME range received from that station will not be used for navigation calculations.
 10. Navigation Aid and Tuning Management____________________________________
 A.  The FMCS relies upon a combination of VHF NAV, DME, IRS, and DADC inputs to provide position, heading, and velocity information for an optimal navigation solution. Most of the sensors provide this information independently, without requiring the attention of either the crew or the FMCS. There are, however two types of sensors that require some form of external control; these are the airplane's VOR receivers and DME interrogators.
 B.  Tuning Commands from the FMC go to the VORs and DMEs by way of the DAA. The receiver/interrogator pairs may be operated in either of two basic modes: manual or automatic. A MODE selector switch is located on each of the VHF NAV control panels. If a MODE switch is in the MAN position, the frequency command for tuning the VOR/DME pair comes from the control panel and is the frequency manually selected by the crew. When the switch is in the AUTO position, the frequency command originates in the FMC. The FMC automatically generates tuning commands, as a function of the available navigation aid ground stations relative to the navigation position estimate and the airplane altitude, by the station selection processes in the FMC software program. When both VHF NAV control panels are in the MAN mode, the FMC will use its normal navigation mode hierarchy as long as navaid geometry and range criteria are met.
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