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Continuing to neglect the ie ie p term from eqn (1114), we have 1 0 0 g 0 1 0 pn (1121) gn = R 0 0 2 where g = GM and gn = [ gn , ge , gd ] R2 The e ect of the gravity error on the velocity error dynamics is considered in detail in Section 1143 In that section, the vertical component of the position error is height above the ellipse h, not error in the down component d of the geodetic vector The fact that h = d inserts one extra negative sign in the error analysis of that section 1 0 0 n g 0 1 0 e (1122) gn = R 0 0 2 h The following two paragraphs brie y discuss simple models for the horizontal and vertical error dynamics The purpose is to introduce the important e ects that gravity has on the inertial system navigation systems In the navigation frame, the lateral position error di erential equations can be represented as = gn + n n = ge + e e where all error sources other than those due to gravity are combined into the terms n and e The full error model that de nes n and e will be discussed in Section 1141 From eqn (1122), gn = g n and ge = R g R e; therefore, the dependence of the lateral position error on the gravity error has the form + n g n R g + e e R = n = e

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which are forced harmonic oscillators with natural frequency equal to the g Schuler frequency s = R If the gravity error terms were absent, then the lateral position errors would be the pure integral of the errors n and

Imagine that you are in a space ship traveling through deep space The ship s rockets are fired, and the vessel accelerates at an extreme rate Suppose that the laser apparatus described earlier in this chapter is in the ship, but instead of a mirror on the wall opposite the laser, there is a screen Before the acceleration begins, you align the laser so that it shines at the center of the screen (Fig 16-6) What will happen when the rockets are fired and the ship accelerates

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e We see that the gravity error terms in the lateral dynamics have a stabilizing e ect Because they are small and stable, they are often dropped in the error analysis For the vertical error dynamics, the situation is di erent The vertical position error di erential equation can be written as d = gd + d

where d represent all other error sources except for those due to gravity g and from eqn (1121) we have gd = 2 R d Therefore, the vertical position error model is g d 2 d = d R

approaches lies in which layers query subjects, relationships, filters, and calculations are placed We suggest names for the view namespaces, but you can use different names The simplest is a two layer approach with a Database View namespace and a Presentation View namespace The Database View contains all data source query subjects and any model query subjects necessary to solve modeling challenges It also contains all relationships, filters, and calculations The Presentation View contains only star schema groupings based directly on the database view objects You will need to give your data source query items business names so your users will not be exposed to cryptic database column names This approach is fast to model, but possibly more difficult to maintain and to port to a different database type It can work if your source is a data warehouse that will present few modeling challenges and will require little reorganization and renaming of query items An alternative is a three layer isolation approach, with a Database View, a Business View, and a Presentation View The Database View namespace contains all the data source query subjects, but no model query subjects or relationships In the Business View namespace, you create a model query subject for each data source query subject plus any that you need to resolve challenges, and you create the relationships between the model query subjects in this layer The Business View also contains all filters and calculations A Presentation View contains the star schema groupings based on the Business View This approach is the most time consuming to create because you are creating redundant query subjects, but it is also the most portable because the Business View provides a layer of insulation between the source database and the reports based on the Presentation Layer The consolidation approach also uses three layers The Database View namespace contains all data source query subjects, any model query subjects necessary to resolve challenges, and all relationships Little or no renaming is done in the database view except when creating aliases The Business View namespace contains model query subjects that organize the query items, all named for business users For instance, you can put all customer related query items in one model query subject, and all inventory status indicators in another Place filters and calculations in the Business View unless you need to place them in the Database View for maximum reuse The Presentation View contains the star schema groupings based on the Business View This is a compromise approach that provides some insulation between the reports and the data source, but does not require as much modeling effort as the isolation approach It is a good place to start for most projects.

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