There are also excellent tools available which are intended for studying principal effects and for training purposes and are not intended primarily for quantitative and rigorous analysis due to the level of theoretical methods involved. The application of these tools for practical problems and the interpretation of these results should be handled with great care and only within the range of the applicability.

The preferred method for the general complex 3D-analysis is the GTD/UTD-method. It can be applied most efficiently for the tridimensional case of the image type glideslope to optimize the antenna geometry and to determine the monitor position and performance. The above mentioned multilayer method can be added to take into account the snow on the ground (dry, wet and combinations etc.) or to describe more realistically the characteristics of buildings made of concrete.

The general numerical methods are invariant against the system in principle. The GTD/UTD is an example which can be applied for ILS, VOR, TACAN, MLS etc. However, the system analysis part has to be adapted and applied to yield the decisive system parameter(s), i.e. the

• DDM/SDM for ILS
• azimuth accuracy for VOR (TACAN)
• range error for DME
• angular error, PFE, CMN for MLS etc.

The use of numerical methods is a powerful and cost effective technique allowing great flexibility in the prediction of system performance but caution must be exercised to ensure that the method used is appropriate to the application. The achieved accuracy depends to a large extent on the validity and the adequateness of the developed numerical model compared to the real world.

Especially the specified tolerances with respect to the accuracy of the model must be observed very closely. E.g., in the runway region for ILS CATIII the deviation of the system is not to exceed a very small number (i.e. 5µA) where it is hard to achieve an accuracy for the model that makes decisions for models definitive. General practical experience and practical results of analog cases may support the verification of the numerical results.

The reader is referred for further details and for in depth publications to the open literature on numerical methods.

Acknowledgement