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Unfortunately, as a general rule, (E , Q) is not a super-set of an exact aggregation of (E, Q). So, we need to [HAD 95, HAD 96b] nd conditions under which such a combination of methods is feasible. In this section, we explain the problems raised by this approach and the results obtained. 11.4.1. Problems Two fundamental problems arise for a combination of these methods: the rst one concerns the speci cation of the studied system and the second one concerns the resolution method used. 11.4.2. The speci cation problem If the system to be modeled has synchronization between the same types of entities (server processes for instance), we can build a synchronized product of submodels, each one modeling the behavior of one entity; but, since we model each entity with one submodel, there is no entity class and we cannot introduce aggregation. An elementary example of this kind of situation is a system of sites running sequential code with a critical section the execution of which is allocated in a cyclic way to each site (virtual token ring). The GSPN and the SWN of such a system (with four sites) are presented in Figure 11.4: starting from the idle state, each site executes an initial task (transition t1 ), then waits for the mutual exclusion token to go on (transition t2 ). When the critical section is over, the site releases the mutual exclusion token (transition t4 ) and goes back to idle. In the SWN model, we have only one base



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We stated previously that a model-based meta data integration architecture requires a formal language capable of representing meta data in terms of shared platform-independent models. In CWM, this language is UML (actually, a very specific subset of UML). UML is an Object Management Group (OMG) standard language for specifying abstract models of discrete systems (Booch et al., 1999; Rumbaugh et al., 1999). UML is the notational basis for CWM, and CWM likewise extends a subset of the UML language to include data warehousing and business analysis domain concepts. CWM relies on the expressiveness and power of UML as a means of defining complex meta data structures and relationships.





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1341 Traditional Techniques As we discussed earlier, TOA and RSS metrics are the most popular in wireless positioning systems for urban and indoor areas TOA metrics provides for a more accurate measure of distance but may need additional infrastructure The RSS is an easier metrics to measure and integrates well with the existing infrastructure, but it is less reliable and often needs more complex algorithms and additional calibration procedure Positioning algorithms using AOA metrics are often simple and use the principles shown in Fig 138 Therefore, our discussion of the algorithms will emphasize TOA and RSS systems With reliable TOA-based distance measurements using UWB technology, simple geometrical triangulation methods can be used to nd the location of a tag or a mobile terminal [Fon01].

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Due to estimation errors of distances at RP receivers caused by inaccurate TOA measurement, the geometrical triangulation technique can only provide a region of uncertainly, instead of a single-position x, for the estimated location of the mobile terminal To obtain an estimate of location coordinates in the presence of measurement errors of location metrics, a variety of direct and iterative statistical positioning algorithms have been developed to solve the problem by formulating it into a set of nonlinear iterative equations In some wireless geolocation applications, the purpose of the positioning systems is to provide visualization of the possible mobile locations instead of an estimate of the location coordinates On the other hand, positional accuracy is not constant across the area of coverage, and poor geometry of the relative positions of the mobile terminal and RP can lead to high geometric dilution of precision.

The output of statistical methods is an estimate of mobile location coordinates, and changes in the shape of the region of uncertainty are not revealed by this method When both region-of-uncertainty information and an estimate of the location are needed, both geometric and statistical triangulation algorithms are used [Pah02] Example 134: LS and RGWH Algorithms for Indoor Geolocation In [Kan04a] the performance of least squares (LS) and residual weighted (RGWH) LS algorithms in a square area with four RPs in the corners of the room is evaluated The LS algorithm is a simple traditional gradient algorithm used in basic GPS systems which iteratively minimizes the square of the error in estimation of the position For two-dimensional applications, considered in this example, it needs a minimum of three RPs With more RPs the algorithm is expected to provide more accurate positioning.

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