Question

I am trying to translate a function in a book into code, using MATLAB and C#.

I am first trying to get the function to work properly in MATLAB.

Here are the instructions:

The variables are:

xt and m can be ignored.
zMax = Maximum Sensor Range (100)
zkt = Sensor Measurement (49)
zkt* = What sensor measurement should have been (50)
oHit = Std Deviation of my measurement (5)

I have written the first formula, N(zkt;zkt*,oHit) in MATLAB as this:

hitProbabilty = (1/sqrt( 2*pi * (oHit^2) ))...
                * exp(-0.5 * (((zkt- zktStar) ^ 2) / (oHit^2))  );

This gives me the Gaussian curve I expect.

I have an issue with the definite integral below, I do not understand how to turn this into a real number, because I get horrible values out my code, which is this:

func = @(x) hitProbabilty * zkt * x;
normaliser = quad(func, 0, max) ^ -1;  
hitProbabilty = normaliser * hitProbabilty;

Can someone help me with this integral? It is supposed to normalize my curve, but it just goes crazy…. (I am doing this for zkt 0:1:100, with everything else the same, and graphing the probability it should output.)

Answer 1

You should use the error function ERF (available in basic MATLAB)

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EDIT1:

As @Jim Brissom mentioned, the cumulative distribution function (CDF) is related to the error function by:

normcdf(X) = (1 + erf(X/sqrt(2)) / 2 ,   where X~N(0,1)

Note that NORMCDF requires the Statistics Toolbox

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EDIT2:

I think there’s been a small confusion seeing the comments.. The above only compute the normalizing factor, so if you want to compute the final probability over a certain range of values, you should do this:

zMax = 100;                         %# Maximum Sensor Range
zktStar = 50;                       %# What sensor measurement should have been
oHit = 5;                           %# Std Deviation of my measurement

%# p(0<z<zMax) = p(z<zMax) - p(z<0)
ncdf = diff( normcdf([0 zMax], zktStar, oHit) );
normaliser = 1 ./ ncdf;

zkt = linspace(0,zMax,500);         %# Sensor Measurement, 500 values in [0,zMax]
hitProbabilty = normpdf(zkt, zktStar, oHit) * normaliser;

plot(zkt, hitProbabilty)
xlabel('z^k_t'), ylabel('P_{hit}(z^k_t)'), title('Measurement Probability')