def test_circle():
    from filterpy.kalman import KalmanFilter
    from math import radians
    def hx(x):
        radius = x[0]
        angle = x[1]
        x = cos(radians(angle)) * radius
        y = sin(radians(angle)) * radius
        return np.array([x, y])

    def fx(x, dt):
        return np.array([x[0], x[1]+x[2], x[2]])

    std_noise = .1

    sp = JulierSigmaPoints(n=3, kappa=0.)
    f = UKF(dim_x=3, dim_z=2, dt=.01, hx=hx, fx=fx, points=sp)
    f.x = np.array([50., 90., 0])
    f.P *= 100
    f.R = np.eye(2)*(std_noise**2)
    f.Q = np.eye(3)*.001
    f.Q[0,0]=0
    f.Q[2,2]=0

    kf = KalmanFilter(dim_x=6, dim_z=2)
    kf.x = np.array([50., 0., 0, 0, .0, 0.])

    F = np.array([[1., 1., .5, 0., 0., 0.],
                  [0., 1., 1., 0., 0., 0.],
                  [0., 0., 1., 0., 0., 0.],
                  [0., 0., 0., 1., 1., .5],
                  [0., 0., 0., 0., 1., 1.],
                  [0., 0., 0., 0., 0., 1.]])

    kf.F = F
    kf.P*= 100
    kf.H = np.array([[1,0,0,0,0,0],
                     [0,0,0,1,0,0]])


    kf.R = f.R
    kf.Q[0:3, 0:3] = Q_discrete_white_noise(3, 1., .00001)
    kf.Q[3:6, 3:6] = Q_discrete_white_noise(3, 1., .00001)

    measurements = []
    results = []

    zs = []
    kfxs = []
    for t in range (0,12000):
        a = t / 30 + 90
        x = cos(radians(a)) * 50.+ randn() * std_noise
        y = sin(radians(a)) * 50. + randn() * std_noise
        # create measurement = t plus white noise
        z = np.array([x,y])
        zs.append(z)

        f.predict()
        f.update(z)

        kf.predict()
        kf.update(z)

        # save data
        results.append (hx(f.x))
        kfxs.append(kf.x)
        #print(f.x)

    results = np.asarray(results)
    zs = np.asarray(zs)
    kfxs = np.asarray(kfxs)

    print(results)
    if DO_PLOT:
        plt.plot(zs[:,0], zs[:,1], c='r', label='z')
        plt.plot(results[:,0], results[:,1], c='k', label='UKF')
        plt.plot(kfxs[:,0], kfxs[:,3], c='g', label='KF')
        plt.legend(loc='best')
        plt.axis('equal')
dataset/ETHPy150Open rlabbe/filterpy/filterpy/kalman/tests/test_ukf.py/test_circle/original