diff --git a/Kalman_Filter_Tutorial/Kalman_filt_for_Ninjam.m b/Kalman_Filter_Tutorial/Kalman_filt_for_Ninjam.m
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+% written by StudentDave
+%for licensing and usage questions
+%email scienceguy5000 at gmail. com
+
+%Bayesian Ninja tracking Quail using kalman filter
+
+clear all
+%% define our meta-variables (i.e. how long and often we will sample)
+duration = 10; %how long the Quail flies
+dt = .1; %The Ninja continuously looks for the birdy,
+%but we'll assume he's just repeatedly sampling over time at a fixed interval
+
+%% Define update equations (Coefficent matrices): A physics based model for where we expect the Quail to be [state transition (state + velocity)] + [input control (acceleration)]
+A = [1 dt; 0 1] ; % state transition matrix: expected flight of the Quail (state prediction)
+B = [dt^2/2; dt]; %input control matrix: expected effect of the input accceleration on the state.
+C = [1 0]; % measurement matrix: the expected measurement given the predicted state (likelihood)
+%since we are only measuring position (too hard for the ninja to calculate speed), we set the velocity variable to
+%zero.
+
+%% define main variables
+u = 1.5; % define acceleration magnitude
+Q= [0; 0]; %initized state--it has two components: [position; velocity] of the Quail
+Q_estimate = Q; %x_estimate of initial location estimation of where the Quail is (what we are updating)
+QuailAccel_noise_mag = 0.05; %process noise: the variability in how fast the Quail is speeding up (stdv of acceleration: meters/sec^2)
+NinjaVision_noise_mag = 10; %measurement noise: How mask-blinded is the Ninja (stdv of location, in meters)
+Ez = NinjaVision_noise_mag^2;% Ez convert the measurement noise (stdv) into covariance matrix
+Ex = QuailAccel_noise_mag^2 * [dt^4/4 dt^3/2; dt^3/2 dt^2]; % Ex convert the process noise (stdv) into covariance matrix
+P = Ex; % estimate of initial Quail position variance (covariance matrix)
+
+%% initize result variables
+% Initialize for speed
+Q_loc = []; % ACTUAL Quail flight path
+vel = []; % ACTUAL Quail velocity
+Q_loc_meas = []; % Quail path that the Ninja sees
+
+
+%% simulate what the Ninja sees over time
+figure(2);clf
+figure(1);clf
+for t = 0 : dt: duration
+
+ % Generate the Quail flight
+ QuailAccel_noise = QuailAccel_noise_mag * [(dt^2/2)*randn; dt*randn];
+ Q= A * Q+ B * u + QuailAccel_noise;
+ % Generate what the Ninja sees
+ NinjaVision_noise = NinjaVision_noise_mag * randn;
+ y = C * Q+ NinjaVision_noise;
+ Q_loc = [Q_loc; Q(1)];
+ Q_loc_meas = [Q_loc_meas; y];
+ vel = [vel; Q(2)];
+ %iteratively plot what the ninja sees
+ plot(0:dt:t, Q_loc, '-r.')
+ plot(0:dt:t, Q_loc_meas, '-k.')
+ axis([0 10 -30 80])
+ hold on
+ pause
+end
+
+%plot theoretical path of ninja that doesn't use kalman
+plot(0:dt:t, smooth(Q_loc_meas), '-g.')
+
+%plot velocity, just to show that it's constantly increasing, due to
+%constant acceleration
+%figure(2);
+%plot(0:dt:t, vel, '-b.')
+
+
+%% Do kalman filtering
+%initize estimation variables
+Q_loc_estimate = []; % Quail position estimate
+vel_estimate = []; % Quail velocity estimate
+Q= [0; 0]; % re-initized state
+P_estimate = P;
+P_mag_estimate = [];
+predic_state = [];
+predic_var = [];
+for t = 1:length(Q_loc)
+ % Predict next state of the quail with the last state and predicted motion.
+ Q_estimate = A * Q_estimate + B * u;
+ predic_state = [predic_state; Q_estimate(1)] ;
+ %predict next covariance
+ P = A * P * A' + Ex;
+ predic_var = [predic_var; P] ;
+ % predicted Ninja measurement covariance
+ % Kalman Gain
+ K = P*C'*inv(C*P*C'+Ez);
+ % Update the state estimate.
+ Q_estimate = Q_estimate + K * (Q_loc_meas(t) - C * Q_estimate);
+ % update covariance estimation.
+ P = (eye(2)-K*C)*P;
+ %Store for plotting
+ Q_loc_estimate = [Q_loc_estimate; Q_estimate(1)];
+ vel_estimate = [vel_estimate; Q_estimate(2)];
+ P_mag_estimate = [P_mag_estimate; P(1)]
+end
+
+% Plot the results
+figure(2);
+tt = 0 : dt : duration;
+plot(tt,Q_loc,'-r.',tt,Q_loc_meas,'-k.', tt,Q_loc_estimate,'-g.');
+axis([0 10 -30 80])
+
+
+%plot the evolution of the distributions
+figure(3);clf
+for T = 1:length(Q_loc_estimate)
+clf
+ x = Q_loc_estimate(T)-5:.01:Q_loc_estimate(T)+5; % range on x axis
+
+ %predicted next position of the quail
+ hold on
+ mu = predic_state(T); % mean
+ sigma = predic_var(T); % standard deviation
+ y = normpdf(x,mu,sigma); % pdf
+ y = y/(max(y));
+ hl = line(x,y,'Color','m'); % or use hold on and normal plot
+
+ %data measured by the ninja
+ mu = Q_loc_meas(T); % mean
+ sigma = NinjaVision_noise_mag; % standard deviation
+ y = normpdf(x,mu,sigma); % pdf
+ y = y/(max(y));
+ hl = line(x,y,'Color','k'); % or use hold on and normal plot
+
+ %combined position estimate
+ mu = Q_loc_estimate(T); % mean
+ sigma = P_mag_estimate(T); % standard deviation
+ y = normpdf(x,mu,sigma); % pdf
+ y = y/(max(y));
+ hl = line(x,y, 'Color','g'); % or use hold on and normal plot
+ axis([Q_loc_estimate(T)-5 Q_loc_estimate(T)+5 0 1]);
+
+
+ %actual position of the quail
+ plot(Q_loc(T));
+ ylim=get(gca,'ylim');
+ line([Q_loc(T);Q_loc(T)],ylim.','linewidth',2,'color','b');
+ legend('state predicted','measurement','state estimate','actual Quail position')
+ pause
+end
\ No newline at end of file
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