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THE NAVIGATION MODEL

The "navigation model" is simply a way to describe and conceptualize navigation. Navigation may also be viewed as a process, or an algorithm, or a mathematical theory, or even an art. No particular scheme is more correct than the others, but describing navigation as the creation and maintenance of a model is perhaps the easiest way to explain the concepts involved.

In most cases, modern navigation consists of constructing and maintaining a model of the navigator's environment, including a representation of the navigator's position within that modeled environment. From this model, the navigator can extract information such as current location, future location, physical relationship to surrounding features, and how to get to a specific destination.

The navigation model may take one of several possible forms. A navigator may use a paper chart as a model of the surface over which he or she is traveling, establish relationships to that surface by using navigation instruments to make external measurements, and use those measurements to model a position on the chart by plotting it with a pencil and plotting instruments. The model may be purely mathematical in nature, with equations modeling the relationship of vehicle coordinates to the coordinates of external points. Bowditch [1984] gives examples of these equation systems, particularly in the area of celestial navigation. The model may also be a hybrid of sorts, combining aspects of the physical paper chart model and the more abstract mathematical model. This hybrid model would be expressed in a computer system combining a cartographic database with a computer algorithm.

All of the above systems of creating and maintaining the navigation model require three elements: 1. A representation of the environment the vehicle is traveling through; either a chart, a coordinate system, or a cartographic database. 2. A representation of the vehicle within that environment; either as a point plotted on a chart or as a set of coordinates expressed mathematically or as values in a computer. 3. A means of applying measurements of the actual external environment to the model in order to update the model and insure its fidelity.

There are two general ways of applying external measurements to the navigation model: fixing and dead reckoning. A fix answers the basic question: "Where am I now?" It is defined as an accurate position made without reference to any former position [Bowditch, 1984]. The essence of a fix is that it is uncontaminated by any previous error, and fixes are in practice obtained by the navigator making direct measurements of the external environment. The measurements may be of a bearing and distance to a radio transmitter, they may be obtained by geometric triangulation of bearings to two or more known landmarks, they may be celestial measurements, or range to a set of navigation satellites. A fix may even be obtained by simple map reading when the navigator is at or near a known feature. An example of this would be when the navigator is at a sharp bend in Hadley Rille, or at the central peak of crater Tycho. She may then use this information to update the navigation model. In practice, a fix is expressed as a position plotted on a chart, or as a set of coordinates representing current location.

According to Bowditch [1984], Dead reckoning (DR) is the determination of position by advancing a known position for courses and distances. A DR position may be advanced from a fix or from a previous DR position. Unlike a fix, a position determined by dead reckoning is an approximate one, as its accuracy depends on the accuracy of previous positions as well as the accuracy of course and distance measurements. The advantage of DR is that a position may be established for any time, including in the future, or at any place, even when fixing is impossible or impractical. Dead reckoning is thus considered basic to navigation, and fixing simply a way to reduce or eliminate errors in dead reckoning. The task of the navigator in performing dead reckoning is to determine course and distance and apply that information to the navigation model. Fixing should be accomplished periodically in order to "reset" the process of dead reckoning.

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