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For a low elevation, the antenna collects rather high noise contributions from the atmosphere a1) (the lower the elevation, the longer the length of the rays in the atmosphere) and also from the ground a2), through that part of the radiation diagram which hits the ground (ie side lobes, including back lobes and, even possibly, a part of the main lobe in the case of the wide lobes radiated by small antennas) For illustration, Figure 25 gives an example (from Recommendation ITU-R PI3726) of the sky noise temperature for an earth station antenna (for frequencies between 1 and 55 GHz, with the elevation angle as a parameter) This diagram is the result of a calculation using a model of the atmosphere Contribution a1) only is included, in the case of a "clear sky", assuming various hypotheses, as quoted.

Under these conditions, the sky noise temperature is called "brightness temperature" in Recommendation ITU-R PI3726 The figure is given simply to show the general trends and, in particular, the important increase around 23 GHz (due to resonance in the water vapour absorption) In practical cases and notwithstanding contributions a2) and b), noise.

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( 3. Finally, the initial set SkM1) for the next time stamp is produced by drifting + ( the unweighted particles Sk0) according to the dynamic model with the largest covariance matrix, Wmax.

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/********************************************************************************** MonteCarloBasket : values a basket option on three stocks [in] double price1 : initial price of stock1 double price2 : initial price of stock2 double price3 : initial price of stock3 double strike : strike price double vol1 : volatility of stock 1 double vol2 : volatility of stock 2 double vol3 : volatility of stock 3 double rate : risk-free rate double div1 : dividend yield on stock1 double div2 : dividend yield on stock2 double div3 : dividend yield on stock3 double T : maturity of option double rho12 : correlation between stock 1 and 2 double rho13 : correlation between stock 1 and 3 double rho23 : correlation between stock 2 and 3 char type : type of basket option: (C)all or (P)ut long M : number of simulations long N : number of time steps [out] double : price of basket option **********************************************************************************/ double BasketOption::calcMonteCarloBasket(double price1, double price2, double price3, double strike, double vol1,double vol2, double vol3, double rate, double

numbers so that the ith bit of the number is nonzero. The effect is such that the bits toggle on and off at different rates. The kth bit switches once in 2k 1 steps so that the least signi cant bit switches the fastest, and the most signi cant bit switches the slowest. Each different Sobol sequence (or component of an n-dimensional sequence) is based on a different primitive polynomial over the integers modulo 2, that is, a polynomial whose coef cients are either 0 or 1, and which generates a maximal length shift register sequence. 10 Following Press et al. (1992), suppose P is such a polynomial, of degree q, P = xq + a1xq 1 + a2xq 2 + . . . + aq 1x + 1 De ne a sequence of integers Mi by the q-term recurrence relation, Mi = 2a1Mi 1 22a2Mi 2 2q 1 Mi q+1aq 1 (2qMi q Mi q) The bitwise XOR operator is denoted . The starting values for this recurrence are that M1, . . . , Mq can be arbitrary odd integers less than 2, . . . , 2q, respectively. Then, the direction numbers Vi are given by11 Vi = Mi /2i i = 1, . . . , w

where the ensemble state statistics sk are updated by integrating the current 1 O measurements Zk = (Zk , , Zk ) associated with all targets, together with the set Zk 1 of all measurements up to k 1, all included into the last posterior distribution, sk 1, through state dynamics and measurement likelihood. In most cases, this scheme is split into O independent single-target trackers,

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