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99 lines
4.2 KiB
Python
Executable File
99 lines
4.2 KiB
Python
Executable File
#!/usr/bin/env python
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"""
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Tracking of rotating point.
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Point moves in a circle and is characterized by a 1D state.
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state_k+1 = state_k + speed + process_noise N(0, 1e-5)
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The speed is constant.
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Both state and measurements vectors are 1D (a point angle),
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Measurement is the real state + gaussian noise N(0, 1e-1).
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The real and the measured points are connected with red line segment,
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the real and the estimated points are connected with yellow line segment,
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the real and the corrected estimated points are connected with green line segment.
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(if Kalman filter works correctly,
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the yellow segment should be shorter than the red one and
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the green segment should be shorter than the yellow one).
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Pressing any key (except ESC) will reset the tracking.
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Pressing ESC will stop the program.
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"""
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import numpy as np
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import cv2 as cv
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from math import cos, sin, sqrt, pi
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def main():
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img_height = 500
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img_width = 500
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kalman = cv.KalmanFilter(2, 1, 0)
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code = -1
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num_circle_steps = 12
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while True:
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img = np.zeros((img_height, img_width, 3), np.uint8)
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state = np.array([[0.0],[(2 * pi) / num_circle_steps]]) # start state
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kalman.transitionMatrix = np.array([[1., 1.], [0., 1.]]) # F. input
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kalman.measurementMatrix = 1. * np.eye(1, 2) # H. input
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kalman.processNoiseCov = 1e-5 * np.eye(2) # Q. input
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kalman.measurementNoiseCov = 1e-1 * np.ones((1, 1)) # R. input
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kalman.errorCovPost = 1. * np.eye(2, 2) # P._k|k KF state var
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kalman.statePost = 0.1 * np.random.randn(2, 1) # x^_k|k KF state var
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while True:
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def calc_point(angle):
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return (np.around(img_width / 2. + img_width / 3.0 * cos(angle), 0).astype(int),
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np.around(img_height / 2. - img_width / 3.0 * sin(angle), 1).astype(int))
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img = img * 1e-3
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state_angle = state[0, 0]
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state_pt = calc_point(state_angle)
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# advance Kalman filter to next timestep
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# updates statePre, statePost, errorCovPre, errorCovPost
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# k-> k+1, x'(k) = A*x(k)
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# P'(k) = temp1*At + Q
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prediction = kalman.predict()
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predict_pt = calc_point(prediction[0, 0]) # equivalent to calc_point(kalman.statePre[0,0])
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# generate measurement
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measurement = kalman.measurementNoiseCov * np.random.randn(1, 1)
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measurement = np.dot(kalman.measurementMatrix, state) + measurement
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measurement_angle = measurement[0, 0]
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measurement_pt = calc_point(measurement_angle)
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# correct the state estimates based on measurements
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# updates statePost & errorCovPost
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kalman.correct(measurement)
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improved_pt = calc_point(kalman.statePost[0, 0])
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# plot points
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cv.drawMarker(img, measurement_pt, (0, 0, 255), cv.MARKER_SQUARE, 5, 2)
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cv.drawMarker(img, predict_pt, (0, 255, 255), cv.MARKER_SQUARE, 5, 2)
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cv.drawMarker(img, improved_pt, (0, 255, 0), cv.MARKER_SQUARE, 5, 2)
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cv.drawMarker(img, state_pt, (255, 255, 255), cv.MARKER_STAR, 10, 1)
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# forecast one step
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cv.drawMarker(img, calc_point(np.dot(kalman.transitionMatrix, kalman.statePost)[0, 0]),
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(255, 255, 0), cv.MARKER_SQUARE, 12, 1)
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cv.line(img, state_pt, measurement_pt, (0, 0, 255), 1, cv.LINE_AA, 0) # red measurement error
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cv.line(img, state_pt, predict_pt, (0, 255, 255), 1, cv.LINE_AA, 0) # yellow pre-meas error
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cv.line(img, state_pt, improved_pt, (0, 255, 0), 1, cv.LINE_AA, 0) # green post-meas error
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# update the real process
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process_noise = sqrt(kalman.processNoiseCov[0, 0]) * np.random.randn(2, 1)
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state = np.dot(kalman.transitionMatrix, state) + process_noise # x_k+1 = F x_k + w_k
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cv.imshow("Kalman", img)
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code = cv.waitKey(1000)
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if code != -1:
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break
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if code in [27, ord('q'), ord('Q')]:
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break
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print('Done')
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if __name__ == '__main__':
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print(__doc__)
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main()
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cv.destroyAllWindows()
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