Lab Report Data Analysis

8/2/2019 Lab Report Data Analysis

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ContentsDescription of Purpose And Background.......................................................................................... 3

Theoretical Basis of Data Analysis .................................................................................................... 4

Results ................................................................................................................................................... 6

Conclusion ............................................................................................................................................. 8

Discussion ............................................................................................................................................. 9

Appendix .............................................................................................................................................. 10


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Description of Purpose And Background

The aim of this experiment is to analyse the data produced during reception of laser

light from an emitter to a receiver via a reflector. The time difference between pulse

emission and reception is recorded in the computer system. This time difference is

directly proportional to the distance between the receiver and object(time of flight).

A full scan covers 1800. A reading is taken every 0.50 giving a total number of 361 counts

per frame. Each of the 361 counts consist of 13 effective bits of integer. If there is no

reflection, then the value provided by the laser is R = 213 -1. This represents an infinitedistance and is the maximum vale the laser can return. The normal values lie between 0

and 213-2 giving a maximum range of 8190 Centimetres. The data is then converted into a

Cartesian coordinate system. The conversion equation are

Figure 1 Laser Scanner Operation

Figure 2 Laser Scanner- Coordinate System


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Theoretical Basis of Data Analysis

Given a data set obtained under fixed conditions, random scatter will occur in the data

values. There exist a number of statistical techniques for the analysis of such a data set.

These techniques provide an effective model for the interpretation of the data.

The first step in analysing the data is too conduct a Least-Squares Regression Analysis.

This allows a polynomial to be plotted against the data set. The regression analysis for a

single variable function is given by the equation :

(3)

The a0 value is determined by the equation

(4)

The a1 value is determined by the equation

(5)

xi = independent variable (input data)

yi = dependent variable (function of x)

A histogram is needed to supply a graphical representation of the discrete set of data. This

can then be characterized by a probability density function.

To plot the histogram of the data set, we must first calculate the number of bins (K).

(4)

A Gaussian distribution is plotted on the same graph with equal standard deviation and

mean values. This is used to compare and contrast between the Normal Gaussian

distribution and the histogram obtained from the dataset.

The Gaussian distribution is given according to the equation:

(5)


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Results

1 M 0 DEGREES

1 M 15 DEGREES

2 M 0 DEGREES

2 M 15 DEGREES

1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.20

100

200

300

400

500

600

700

y(m)

count

95% interval = 1.1014 to 1.1495

Estimated mean = 1.1254 to 1.1256

Estimated variance = 0.000142


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4 M 0 DEGREES

4 M 15 DEGREES

1.95 2 2.05 2.1 2.15 2.2 2.25 2.3 2.350

50

100

150

200

250

300

y(m)

count

95% interval = 2.0203 to 2.2430

Estimated mean = 2.1311 to 2.1323

Estimated variance = 0.003008


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Conclusion


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Discussion


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Appendix

%%%Giving a choice to select a file from a list[fn,pn,bn] = uigetfile('*.mat');

% Checking if a file is selected and loads itif bn>0

load(fn);end%%%Angles in radians

[h,w] = size(X.Scans);q = linspace(0,pi,w);


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%Conversion to cartesianfor k = 1:h

x(k,:) = X.Scans(k,:).* cos(q);y(k,:) = X.Scans(k,:).* sin(q);

end

%%% Plotting of the data scansfig(1) = figure('units','normalized','position',[rand*0.1+0.4 rand*0.1+0.40.35 0.35],'color','w');plot(x,y,'b.');xlabel('x(m)');ylabel('y(m)');axis([-4 4 0 8]);

%%z1 = find(fn=='m');z2 = find(fn=='d');deg = fn(z1(1) + 1:z2(1) - 1);set(gcf, 'name', sprintf('Object Inclination = %s(deg)', deg));

%% Make the data select optionwaitforbuttonpress;p1 = get(gca,'CurrentPoint');finalRect = rbbox;p2 = get(gca,'CurrentPoint');title('');p1=p1(1,1:2);p2=p2(1,1:2);if sum(p1==p2)>1,%no selectiontitle('No data selected');returnend;

x1 = p1(1,1);y1 = p1(1,2);x2 = p2(1,1);y2 = p2(1,2);

%selects the min and max x n yx2min = min(x1,x2);x2max = max(x1,x2);y2min = min(y1,y2);y2max = max(y1,y2);

% Indices for the point inside the selectionz= find((x>x2min & xy2min & y


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K = 1.87 * ((N-1)^0.4) + 1;% Limits of the data to be plottedy2min = min(yss);y2max = max(yss);zy = linspace(y2min,y2max,K);%Plots the histogram and Stairs

[hy,iy] = hist(yss,zy); hold on;stairs(iy,hy);

%Selected data meany2mean = mean(yss);%Selected data Standard Deviationy2stdev= std(yss);%Normal distribution of the selected dataGy = normpdf(iy,y2mean,y2stdev); Gy= Gy/sum(Gy) * N;%Plotting normal distributionplot(iy,Gy,'r');xlabel('y(m)');ylabel('count');

%Generate t tablesPr = 0.95; t = 1- (1-Pr)/2; v = N-1; tt=tinv(t,v);

% Sxbar Defined hereSxbar = y2stdev/ sqrt(N);

% High low pair of confidence intervalConf_intev1 = y2mean + 2 *y2stdev;Conf_intev2 = y2mean - 2* y2stdev;

% range of the estimated means

Rmean1 = y2mean + t* Sxbar;Rmean2 = y2mean - t* Sxbar;

% Generating the vertical axis indices from norm distribution[xx ind]= min(abs(iy-Rmean1));[xx2 ind2]= min(abs(iy-Rmean2));

% Plotting the estimated mean and confidence intervalplot(Conf_intev1,0,'bd',Conf_intev2,0,'bd','MarkerFaceColor','b');plot(Rmean1,Gy(ind),'b^',Rmean2,Gy(ind2),'b^','MarkerFaceColor','r');

% Interval of varianceclimit_1 = (1-Pr)/2; climit_1 = chi2inv(climit_1,K-1);climit_2 = 1 - (1-Pr)/2 ; climit_2 = chi2inv(climit_2,K-1);

% Goodness Fitchi = sum((hy-Gy).^2./Gy);cfit_1 = (1-Pr)/2; cfit_1 = chi2inv(cfit_1,N-1);cfit_2 = 1 - (1-Pr)/2; cfit_2 = chi2inv(cfit_2,N-1);

% Estimated range of variancecv_1 = ((N-1) * (y2stdev^2)) / cfit_1;cv_2 = y2stdev^2;cv_3 = ((N-1) * (y2stdev^2)) / cfit_2;

%checking chi of the datapoints to be within chi values with 95% confidenceif chi < climit_1 || chi > climit_2answer = 'REJECT';


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elseanswer = 'ACCEPT';

end

% Sorting for printing on the screenConf_intmin = min(Conf_intev1,Conf_intev2);

Conf_intmax = max(Conf_intev1,Conf_intev2);Rmean_min = min(Rmean1,Rmean2);Rmean_max = max(Rmean1,Rmean2);A = [cv_1, cv_2, cv_3];RVar = sort(A);title(sprintf('95%% interval = %2.4f to %2.4f \n Estimated mean = %2.4f ...to %2.4f\n Estimated variance = %2.6f

Lab Report Data Analysis

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