initial commit

samples/python/kalman.py

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+#!/usr/bin/env python
+"""
+   Tracking of rotating point.
+   Rotation speed is constant.
+   Both state and measurements vectors are 1D (a point angle),
+   Measurement is the real point angle + gaussian noise.
+   The real and the estimated points are connected with yellow line segment,
+   the real and the measured points are connected with red line segment.
+   (if Kalman filter works correctly,
+    the yellow segment should be shorter than the red one).
+   Pressing any key (except ESC) will reset the tracking with a different speed.
+   Pressing ESC will stop the program.
+"""
+# Python 2/3 compatibility
+import sys
+PY3 = sys.version_info[0] == 3
+
+if PY3:
+    long = int
+
+import numpy as np
+import cv2 as cv
+
+from math import cos, sin, sqrt
+import numpy as np
+
+def main():
+    img_height = 500
+    img_width = 500
+    kalman = cv.KalmanFilter(2, 1, 0)
+
+    code = long(-1)
+
+    cv.namedWindow("Kalman")
+
+    while True:
+        state = 0.1 * np.random.randn(2, 1)
+
+        kalman.transitionMatrix = np.array([[1., 1.], [0., 1.]])
+        kalman.measurementMatrix = 1. * np.ones((1, 2))
+        kalman.processNoiseCov = 1e-5 * np.eye(2)
+        kalman.measurementNoiseCov = 1e-1 * np.ones((1, 1))
+        kalman.errorCovPost = 1. * np.ones((2, 2))
+        kalman.statePost = 0.1 * np.random.randn(2, 1)
+
+        while True:
+            def calc_point(angle):
+                return (np.around(img_width/2 + img_width/3*cos(angle), 0).astype(int),
+                        np.around(img_height/2 - img_width/3*sin(angle), 1).astype(int))
+
+            state_angle = state[0, 0]
+            state_pt = calc_point(state_angle)
+
+            prediction = kalman.predict()
+            predict_angle = prediction[0, 0]
+            predict_pt = calc_point(predict_angle)
+
+            measurement = kalman.measurementNoiseCov * np.random.randn(1, 1)
+
+            # generate measurement
+            measurement = np.dot(kalman.measurementMatrix, state) + measurement
+
+            measurement_angle = measurement[0, 0]
+            measurement_pt = calc_point(measurement_angle)
+
+            # plot points
+            def draw_cross(center, color, d):
+                cv.line(img,
+                         (center[0] - d, center[1] - d), (center[0] + d, center[1] + d),
+                         color, 1, cv.LINE_AA, 0)
+                cv.line(img,
+                         (center[0] + d, center[1] - d), (center[0] - d, center[1] + d),
+                         color, 1, cv.LINE_AA, 0)
+
+            img = np.zeros((img_height, img_width, 3), np.uint8)
+            draw_cross(np.int32(state_pt), (255, 255, 255), 3)
+            draw_cross(np.int32(measurement_pt), (0, 0, 255), 3)
+            draw_cross(np.int32(predict_pt), (0, 255, 0), 3)
+
+            cv.line(img, state_pt, measurement_pt, (0, 0, 255), 3, cv.LINE_AA, 0)
+            cv.line(img, state_pt, predict_pt, (0, 255, 255), 3, cv.LINE_AA, 0)
+
+            kalman.correct(measurement)
+
+            process_noise = sqrt(kalman.processNoiseCov[0,0]) * np.random.randn(2, 1)
+            state = np.dot(kalman.transitionMatrix, state) + process_noise
+
+            cv.imshow("Kalman", img)
+
+            code = cv.waitKey(100)
+            if code != -1:
+                break
+
+        if code in [27, ord('q'), ord('Q')]:
+            break
+
+    print('Done')
+
+
+if __name__ == '__main__':
+    print(__doc__)
+    main()
+    cv.destroyAllWindows()