Comparison of number-theoretic and Monte Carlo methods in combat simulation

Sami Helle

doi:10.1117/12.486818

4 September 2003 Comparison of number-theoretic and Monte Carlo methods in combat simulation

Sami Helle

Proceedings Volume 5091, Enabling Technologies for Simulation Science VII; (2003) https://doi.org/10.1117/12.486818
Event: AeroSense 2003, 2003, Orlando, Florida, United States

Abstract

Number-theoretic methods (NTM) or quasi-Monte Carlo methods are a class of techniques to generate points of the uniform distribution in the s-dimensional unit cube. NTM is a special method, which represents a combination of number theory and numerical analysis. The uniformly scattered set of points in the unit cube obtained by NTM is usually called a set of quasi-random numbers or a number-theoretic net (NT-net), since it may used instead of random numbers in many statistical problems. NT-net can be defined as representative points of the uniform distribution. There are different criterions to measure uniformity and methods how to generate NT-nets. Theoretically the rate of convergence of the NTM is better when compared to the Monte Carlo method. The high-resolution force-on-force combat simulation is usually modeled as stochastic Monte Carlo type model and discrete event system. In high-resolution Monte Carlo combat simulations a large amount of random numbers has to be generated. In Monte Carlo type combat simulation models every unit has certain probabilities for detecting and affecting each enemy unit at each time interval. Usually Monte Carlo method is used to calculate expected value of some property of the model. This is matter of numerical integration with Monte Carlo method. In this paper the effectiveness of NTM's are compared with Monte Carlo method in simulated high-resolution combat simulation case. Some methods how to generate NT-nets are introduced. The estimates of NTM and Monte Carlo simulations are studied by comparing statistical properties of the estimates.

Citation Download Citation

Sami Helle "Comparison of number-theoretic and Monte Carlo methods in combat simulation", Proc. SPIE 5091, Enabling Technologies for Simulation Science VII, (4 September 2003); https://doi.org/10.1117/12.486818

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KEYWORDS

Monte Carlo methods

Computer simulations

Statistical analysis

Error analysis

Numerical integration

Quasi-Monte Carlo methods

Stochastic processes

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