Mean acquisition time in a multi-dwell hybrid or parallel acquisition structure in GNSS

Mean acquisition time calculation for the acquisition of GNSS signals (GPS, Galileo, Glonass, ...)

%The main function is Fct_MeanTacq_hybr_and_parr, which computes the mean acquisition
%time in a multi-dwell hybrid or parallel structure in GNSS.
%It is based on the formulas derived and presented in:
%%Lohan, E.-S. , Lakhzouri, A. , Renfors, M, "Selection of the multiple-dwell hybrid-search strategy for the acqusition
%of Galileo signals in fading channels",
%IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, PIMRC
%Volume 4, 2004, Pages 2352-2356
%The function is called via:
%Tacq=Fct_MeanTacq_hybr_and_parr(Pd, Pfa_H0, Pfa_H1, tau_d, Kpenalty, Nr_states);
%where we have the following input parameters
%
%INPUTS
%Pd = vector of detection probabilities for each dwell =[Pd1,
% Pd2,..PdK]; there are K dwells. For example, for a 2 dwell
% structure with 95% acquisition probability in the first dwell
% and 94% acquisition probability in the second dwell, Pd=[0.95
% 0.94];
% Pfa_H0 = vector of false alarm probabilities under the hypothesis
% that we are in an incorrect window; For example, for a 2 dwell
% structure with 1% false alarm probability in the first dwell
% and 0.5% acquisition probability in the second dwell in the incorrect windows, Pfa_H0=[0.01
% 0.005];
% Pfa_H1 = vector of false alarm probabilities under the hypothesis
% that we are in a correct window (typically, at high
% CNRs, this is zero, i.e: Pfa_H1=[0 0] for a 2-dwell acquisition)
%tau_d = vector of dwell times [in seconds], i.e. the time to take a decision,
% usually equal to the integration times in each dwell. For
% example, for a 2-dwell approach, if we use 2 ms coherent
% integration time and 1 block non-coherent integration in the first dwell and a 4ms coherent
% integration time and 2 blocks non-coherent integration in the
% second dwell , tau_d=[2 8]*1e-3 [seconds];
%Kpenalty = penatlty factor for the last dwell, associated with a
% false alarm [in seconds]. This is a scalar value, some example is
% Kpenalty=1e6;
%Nr_states= the number of windows(states) to cover the whole
% time-frequency uncertainty; if Nr_states==1 => fully parallel;
% otherwise (Nr_states >1), we have hybrid acquisition. For
% example, if we use a window size of 2046 half-chips and 1 frequency bin and we want to cover a
% full uncertainty space of 9 frequency bins and 4098 chips code
% length, Nr_states=9*4=36.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%OUTPUT
%Tacq = mean acquisition time in seconds