Added test harness for random number generation routine to ensure statistical properties

tools/RandomNumberVerification/gaussian_noise.cpp

+/****************************************************************************
+ *
+ *   Copyright (C) 2015 PX4 Development Team. All rights reserved.
+ *   Author: Eddy Scott <scott.edward@aurora.aero>
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+
+
+#include <cstdlib>
+#include <cmath>
+#include <ctime>
+#include <limits>
+#include <iostream> // not needed
+#include <fstream> // not needed
+using namespace std;
+float generateGaussianNoise(float mu, float variance)
+{
+	/* Calculate normally distributed variable noise with mean = mu and variance = variance.  Calculated according to 
+	Box-Muller transform */
+	static const float epsilon = std::numeric_limits<float>::min(); //used to ensure non-zero uniform numbers
+	static const float two_pi = 2.0*3.14159265358979323846; // 2*pi
+	static float z0; //calculated normal distribution random variables with mu = 0, var = 1;
+	float u1, u2;		 //random variables generated from c++ rand();
+	/*Generate random variables in range (0 1] */
+	do
+	{
+	    u1 = rand() * (1.0 / RAND_MAX);
+	    u2 = rand() * (1.0 / RAND_MAX);
+	}
+	while ( u1 <= epsilon );  //Have a catch to ensure non-zero for log()
+
+	z0 = sqrt(-2.0 * log(u1)) * cos(two_pi * u2); //calculate normally distributed variable with mu = 0, var = 1
+	float noise = z0 * (variance*variance) + mu; //calculate normally distributed variable with mu = mu, std = var^2
+	return noise
+}
+int main(int argc, char *argv[])
+{
+  ofstream fid;
+  fid.open ("generated_noise.csv");
+  float mu = atof(argv[1]); // Define the mean of the noise, for gaussian = 0
+  float variance = atof(argv[2]); //Define the variance of the noise
+  int num_runs = atoi(argv[3]); //Define number of runs
+  int num_samples = atoi(argv[4]);
+  srand(time(NULL)); //Seed rand() function so same random variables are not calculated
+  cout << "Desired Mean: " << mu << "\n";
+  cout << "Desired Variance: " << variance << "\n";
+  cout << "Desired number of runs: " << num_runs << "\n";
+  cout << "Desired number of samples per run: " << num_samples << "\n";
+  for(int j=0;j<num_runs;j++){
+  	if(j!=0){
+  		fid <<"\n";
+  	}
+  	for(int i=0;i<num_samples;i++){
+    	fid << generateGaussianNoise(mu, variance) << ",";
+  	}
+}
+  fid.close();
+  return 0;
+}

tools/RandomNumberVerification/noise_characteristics.m

+% ****************************************************************************
+%  *
+%  *   Copyright (C) 2015 PX4 Development Team. All rights reserved.
+%  *   Author: Eddy Scott <scott.edward@aurora.aero>
+%  *
+%  * Redistribution and use in source and binary forms, with or without
+%  * modification, are permitted provided that the following conditions
+%  * are met:
+%  *
+%  * 1. Redistributions of source code must retain the above copyright
+%  *    notice, this list of conditions and the following disclaimer.
+%  * 2. Redistributions in binary form must reproduce the above copyright
+%  *    notice, this list of conditions and the following disclaimer in
+%  *    the documentation and/or other materials provided with the
+%  *    distribution.
+%  * 3. Neither the name PX4 nor the names of its contributors may be
+%  *    used to endorse or promote products derived from this software
+%  *    without specific prior written permission.
+%  *
+%  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+%  * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+%  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+%  * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+%  * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+%  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+%  * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+%  * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+%  * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+%  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+%  * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+%  * POSSIBILITY OF SUCH DAMAGE.
+%  *
+%  ****************************************************************************/
+%% Clean work environment
+clear all
+close all
+clc
+%% Load the generated noise values
+noise_val = load('generated_noise.csv');
+for i = 1:size(noise_val
+

tools/RandomNumberVerification/verify_noise_characteristics.m

+% ****************************************************************************
+%  *
+%  *   Copyright (C) 2015 PX4 Development Team. All rights reserved.
+%  *   Author: Eddy Scott <scott.edward@aurora.aero>
+%  *
+%  * Redistribution and use in source and binary forms, with or without
+%  * modification, are permitted provided that the following conditions
+%  * are met:
+%  *
+%  * 1. Redistributions of source code must retain the above copyright
+%  *    notice, this list of conditions and the following disclaimer.
+%  * 2. Redistributions in binary form must reproduce the above copyright
+%  *    notice, this list of conditions and the following disclaimer in
+%  *    the documentation and/or other materials provided with the
+%  *    distribution.
+%  * 3. Neither the name PX4 nor the names of its contributors may be
+%  *    used to endorse or promote products derived from this software
+%  *    without specific prior written permission.
+%  *
+%  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+%  * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+%  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+%  * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+%  * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+%  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+%  * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+%  * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+%  * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+%  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+%  * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+%  * POSSIBILITY OF SUCH DAMAGE.
+%  *
+%  ****************************************************************************/
+%% Clean work environment
+clear all
+close all
+clc
+%% Compile and run the noise cpp program
+system('g++ gaussian_noise.cpp -o generate_noise_csv');
+mu_des = 0.0;
+std_des = 0.02;
+var_desired = sqrt(std_des);
+num_samples = 10000;
+num_runs = 100;
+if exist('generated_noise.csv','file')
+    system('rm generated_noise.csv')
+end
+system(sprintf('./generate_noise_csv %s %s %s %s',num2str(mu_des),num2str(var_desired),num2str(num_runs),num2str(num_samples)))
+%% Load the generated noise values
+noise_vals = load('generated_noise.csv');
+for i = 1:size(noise_vals,1);
+    run_mean = mean(noise_vals(i,:));
+    run_std = std(noise_vals(i,:));
+    mean_array(i) = run_mean;
+    std_array(i) = run_std;
+end
+%%%%% Display statisitcs of means generated
+max_mean = max(mean_array);
+min_mean = min(mean_array);
+max_std = max(std_array);
+min_std = min(std_array);
+
+figure
+hist(mean_array)
+ylabel('Occurances')
+xlabel('Mean Value')
+title('Histogram of mean values')
+
+figure
+hist(std_array)
+ylabel('Occurances')
+xlabel('Std Value')
+title('Histogram of std values')
+
+table(min_mean, mu_des, max_mean, min_std, std_des, max_std)
+
+
+
+