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balzer82 · Jul 2, 2014 · b581875 · b581875
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diff --git a/.ipynb_checkpoints/Kalman-Filter-CA-Ball-checkpoint.ipynb b/.ipynb_checkpoints/Kalman-Filter-CA-Ball-checkpoint.ipynb
diff --git a/Kalman-Filter-CA-Ball-StateEstimated.png b/Kalman-Filter-CA-Ball-StateEstimated.png
diff --git a/Kalman-Filter-CA-Ball-Trajectory.png b/Kalman-Filter-CA-Ball-Trajectory.png
diff --git a/Kalman-Filter-CA-Ball.ipynb b/Kalman-Filter-CA-Ball.ipynb
diff --git a/Kalman-Filter-CA-Ball.py b/Kalman-Filter-CA-Ball.py
@@ -338,7 +338,7 @@
 
 fig = plt.figure(figsize=(16,9))
 ax = fig.add_subplot(111, projection='3d')
-ax.scatter(Xm, Ym, Zm)
+ax.scatter(Xm, Ym, Zm, c='gray')
 ax.set_xlabel('X')
 ax.set_ylabel('Y')
 ax.set_zlabel('Z')
@@ -621,8 +621,8 @@
 
 fig = plt.figure(figsize=(16,9))
 ax = fig.add_subplot(111, projection='3d')
-ax.scatter(xt, yt, zt, label='Estimate', c='k')
-ax.plot(Xr, Yr, Zr, c='g', label='Real')
+ax.plot(xt,yt,zt, label='Kalman Filter Estimate')
+ax.plot(Xr, Yr, Zr, label='Real')
 ax.set_xlabel('X')
 ax.set_ylabel('Y')
 ax.set_zlabel('Z')
@@ -637,7 +637,7 @@
 ax.set_xlim(mean_x - max_range, mean_x + max_range)
 ax.set_ylim(mean_y - max_range, mean_y + max_range)
 ax.set_zlim(mean_z - max_range, mean_z + max_range)
-#plt.savefig('BallTrajectory-Computervision-Kalman.png', dpi=150, bbox_inches='tight')
+plt.savefig('Kalman-Filter-CA-Ball-Trajectory.png', dpi=150, bbox_inches='tight')
 
 # <headingcell level=1>
 

diff --git a/README.md b/README.md
@@ -5,12 +5,10 @@ Some Python Implementations of the Kalman Filter
 
 ####See [Vimeo](https://vimeo.com/album/2754700/sort:preset/format:detail) for some Explanations.
 
-![Kalman Filter Step](https://raw.github.com/balzer82/Kalman/master/Kalman-Filter-Step.png)
+![Kalman Filter Step](Kalman-Filter-Step.png)
 
 ## Kalman Filter with Constant Velocity Model
 
-![State Vector](http://www.texify.com/img/%5CLARGE%5C%21x%3D%20%5Cleft%5B%20%5Cmatrix%7B%20x%20%26%20y%20%26%20%5Cdot%20x%20%26%20%5Cdot%20y%7D%20%5Cright%5D%5ET.gif)
-
 Situation covered: You drive with your car in a tunnel and the GPS signal is lost. Now the car has to determine, where it is in the tunnel. The only information it has, is the velocity in driving direction. The x and y component of the velocity (x˙ and y˙) can be calculated from the absolute velocity (revolutions of the wheels) and the heading of the vehicle (yaw rate sensor).
 
 ####[View IPython Notebook](http://nbviewer.ipython.org/github/balzer82/Kalman/blob/master/Kalman-Filter-CV.ipynb?create=1)
@@ -19,9 +17,7 @@ Situation covered: You drive with your car in a tunnel and the GPS signal is los
 
 ### 2D
 
-![State Vector](http://www.texify.com/img/%5CLARGE%5C%21x%3D%20%5Cleft%5B%20%5Cmatrix%7B%20x%20%26%20y%20%26%20%5Cdot%20x%20%26%20%5Cdot%20y%20%26%20%5Cddot%20x%20%26%20%5Cddot%20y%7D%20%5Cright%5D%5ET.gif)
-
-Situation covered: You have an acceleration sensor (in 2D: x¨ and y¨) and try to calculate velocity (x˙ and y˙) as well as position (x and y) of a person holding a smartphone in his/her hand.
+Situation covered: You have an acceleration sensor (in 2D: $\ddot x¨ and y¨) and try to calculate velocity (x˙ and y˙) as well as position (x and y) of a person holding a smartphone in his/her hand.
 
 ####[View IPython Notebook](http://nbviewer.ipython.org/github/balzer82/Kalman/blob/master/Kalman-Filter-CA.ipynb?create=1)
 
@@ -34,8 +30,6 @@ Situation covered: You have an acceleration sensor (in 2D: x¨ and y¨) and a Po
 
 Third example is in 3D space, so the state vector is 9D. This model is for ball tracking or something else in 3D space.
 
-![State Vector](http://www.texify.com/img/%5CLARGE%5C%21x%3D%20%5Cleft%5B%20%5Cmatrix%7B%20x%20%26%20y%20%26%20z%20%26%20%5Cdot%20x%20%26%20%5Cdot%20y%20%26%20%5Cdot%20z%20%26%20%5Cddot%20x%20%26%20%5Cddot%20y%20%26%20%5Cddot%20z%7D%20%5Cright%5D%5ET.gif)
-
 ####[View IPython Notebook](http://nbviewer.ipython.org/github/balzer82/Kalman/blob/master/Kalman-Filter-CA-Ball.ipynb?create=1)
 
 ## Adaptive Kalman Filter with Constant Velocity Model
@@ -52,9 +46,6 @@ Here the Measurement Covariance Matrix R is calculated dynamically via the maxim
 
 Situation covered: You have an velocity sensor which measures the vehicle speed (v) in heading direction (ψ) and a yaw rate sensor (ψ˙) which both have to fused with the position (x & y) from a GPS sensor.
 
-![CTRV Model](https://raw.github.com/balzer82/Kalman/master/CTRV-Model.png)
-![State Vector](http://www.texify.com/img/%5CLARGE%5C%21x_k%3D%20%5Cleft%5B%20%5Cmatrix%7B%20x%20%26%20y%20%26%20%5Cpsi%20%26%20v%20%26%20%5Cdot%5Cpsi%7D%20%5Cright%5D%20%5ET.gif)
-
 ####[View IPython Notebook](http://nbviewer.ipython.org/github/balzer82/Kalman/blob/master/Extended-Kalman-Filter-CTRV.ipynb?create=1)
 
 ## Adaptive Extended Kalman Filter with Constant Turn Rate and Velocity (CTRV) Model
@@ -63,8 +54,6 @@ Situation covered: You have an velocity sensor which measures the vehicle speed
 
 Because of poor GPS signal quality, the position measurement is pretty inaccurate. Especially, when the car is standing still, the position error is high. Therefore, an Adaptive Extended Kalman Filter is used here. It calculates the measurement noise covariance `R` in every filterstep depending on the `speed` and `EPE` (Estimated Position Error from GPS).
 
-![Adaptively calculated R](https://raw.github.com/balzer82/Kalman/master/Extended-Kalman-Filter-CTRV-Adaptive-R.png)
-
 The trajectory is exportet to a [.kmz](https://github.com/balzer82/Kalman/blob/master/Extended-Kalman-Filter-CTRV-Adaptive.kmz?raw=true), which can best viewed with Google Earth.
 
 ####[View IPython Notebook](http://nbviewer.ipython.org/github/balzer82/Kalman/blob/master/Extended-Kalman-Filter-CTRV-Adaptive.ipynb?create=1)