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91 lines
3.7 KiB
C++
91 lines
3.7 KiB
C++
/**
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* FILENAME: FieldNoise
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* DESCRIPTION: efficient computation of relative probabilities (for the noise model of the RoboCup 3DSSL)
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* AUTHOR: Miguel Abreu (m.abreu@fe.up.pt)
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* DATE: 2021
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*/
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#pragma once
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#include "math.h"
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class FieldNoise{
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public:
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/**
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* Log probability of real distance d, given noisy radius r
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*/
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static double log_prob_r(double d, double r);
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/**
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* Log probability of real horizontal angle h, given noisy angle phi
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*/
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static double log_prob_h(double h, double phi);
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/**
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* Log probability of real vertical angle v, given noisy angle theta
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*/
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static double log_prob_v(double v, double theta);
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private:
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FieldNoise(){}; //Disable construction
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/**
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* Log probability of normally distributed random variable X from interval1 to interval2:
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* Log Pr[interval1 < X < interval2]
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* @param mean mean of random variable
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* @param std standard deviation of random variable
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* @param interval1 minimum value of random variable
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* @param interval2 maximum value of random variable
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*/
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static double log_prob_normal_distribution(double mean, double std, double interval1, double interval2);
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/**
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* This function returns ln(1-sgn(a)*erf(a)), but sgn(a)*erf(a) = |erf(a)|, because sgn(a) == sgn(erf(a))
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* So, it returns: ln(1-|erf(a)|), which is <=0
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*
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* NOTE: condition to guarantee high precision: |a|>= 1
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*
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* how to compute erf(a) ?
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* erf(a) = sgn(a)(1-e^erf_aux(a))
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*
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* how to compute erf(a)+erf(b) ?
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* erf(a)+erf(b) = sgn(a)(1-e^erf_aux(a)) + sgn(b)(1-e^erf_aux(b))
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* assuming a<0 and b>0:
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* = e^erf_aux(a) -1 + 1 - e^erf_aux(b)
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* = e^erf_aux(a) - e^erf_aux(b)
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*
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* example: erf(-7)+erf(7.1)
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* if we computed it directly:
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* erf(-7)+erf(7.1) = -0.9999999(...) + 0.9999999(...) = -1+1 = 0 (due to lack of precision, even if using double)
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* if we use the proposed method:
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* e^erf_aux(-7) - e^erf_aux(7.1) = -1.007340e-23 - -4.183826e-23 = 3.176486E-23
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*
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* how to compute ln(erf(a)+erf(b)) ?
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* assuming a<0 and b>0:
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* ln(erf(a)+erf(b)) = ln( exp(erf_aux(a)) - exp(erf_aux(b)) )
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* = ln( exp(erf_aux(a)-k) - exp(erf_aux(b)-k) ) + k
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* where k = min(erf_aux(a), erf_aux(b))
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*
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* how to compute ln(erf(a)-erf(b)) ? (the difference is just the assumption)
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* assuming a*b >= 0
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*
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* ln(erf(a)-erf(b)) = ln( sgn(a)(1-e^erf_aux(a)) - sgn(a)(1-e^erf_aux(b)) ), note that sgn(a)=sgn(b)
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*
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* rule: log( exp(a) - exp(b) ) = log( exp(a-k) - exp(b-k) ) + k
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*
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* if(a>0)
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* ln(erf(a)-erf(b)) = ln( 1 - e^erf_aux(a) - 1 + e^erf_aux(b))
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* = ln( exp(erf_aux(b)) - exp(erf_aux(a)) )
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* = ln( exp(erf_aux(b)-erf_aux(b)) - exp(erf_aux(a)-erf_aux(b)) ) + erf_aux(b)
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* = ln( 1 - exp(erf_aux(a)-erf_aux(b)) ) + erf_aux(b)
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* if(a<0)
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* ln(erf(a)-erf(b)) = ln( -1 + e^erf_aux(a) + 1 - e^erf_aux(b))
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* = ln( exp(erf_aux(a)) - exp(erf_aux(b)) )
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* = ln( exp(erf_aux(a)-erf_aux(a)) - exp(erf_aux(b)-erf_aux(a)) ) + erf_aux(a)
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* = ln( 1 - exp(erf_aux(b)-erf_aux(a)) ) + erf_aux(a)
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*
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*/
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static double erf_aux(double a);
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}; |