def kalman_initial(q): kf = KalmanFilter(transition_matrices=np.mat([[1, 0.1], [0, 1]]), observation_matrices=np.mat([1, 0])) ''' kf.transition_matrices = np.mat([[1, 0, 0, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1]]) kf.observation_matrices = np.mat([[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]]) kf.observation_covariance = np.eye(3) # kf0.initial_state_covariance = np.eye(6) kf.transition_covariance = np.eye(6) kf.n_dim_obs = 3 kf.n_dim_state = 6 ''' # 定义初始状态协方差矩阵 kf.initial_state_covariance = np.mat([[1, 0], [0, 1]]) # 定义状态转移矩阵,因为每秒钟采一次样,所以delta_t = 1 kf.transition_matrices = np.mat([[1, 1], [0, 1]]) # 定义状态转移协方差矩阵,这里我们把协方差设置的很小,因为觉得状态转移矩阵准确度高 kf.transition_covariance = np.mat([[q, 0], [0, q]]) # 定义观测矩阵 kf.observation_matrices = np.mat([1, 0]) # 定义观测噪声协方差 kf.observation_covariance = np.mat([758]) return kf
def demo(): img = np.zeros((768, 1024, 3), np.uint8) trajs = deque(maxlen=200) trajs_filterd = deque(maxlen=200) def draw(event, x, y, flags, param): kf, fm, fo = param if event == cv2.EVENT_MOUSEMOVE: fm[:], fo[:] = kf.filter_update(fm, fo, np.array([x, y])) fx = int(fm[0]) fy = int(fm[1]) trajs.append((x, y)) trajs_filterd.append((fx, fy)) cv2.namedWindow("image") kf = KalmanFilter(n_dim_state=4, n_dim_obs=2) kf.transition_matrices = np.array([[1, 0, 1, 0], [0, 1, 0, 1], [0, 0, 1, 0], [0, 0, 0, 1]]) kf.observation_matrices = np.array([[1, 0, 0, 0], [0, 1, 0, 0]]) kf.transition_covariance = 1e-3 * np.eye(4) kf.observation_covariance = 10 * np.eye(2) kf.initial_state_mean = np.array([0, 0, 0, 0]) kf.initial_state_covariance = np.eye(4) fm = kf.initial_state_mean fo = kf.initial_state_covariance cv2.setMouseCallback("image", draw, (kf, fm, fo)) while True: img = np.zeros((768, 1024, 3), np.uint8) for i in range(len(trajs) - 1): cv2.line(img, trajs[i], trajs[i + 1], (0, 255, 0), 1) cv2.line(img, trajs_filterd[i], trajs_filterd[i + 1], (0, 0, 255), 1) map(lambda pt: cv2.circle(img, pt, 3, (0, 255, 0), 1), trajs) map(lambda pt: cv2.circle(img, pt, 3, (0, 0, 255), 1), trajs_filterd) cv2.imshow("image", img) if cv2.waitKey(5) & 0xFF == ord("q"): return
def main(argv): config = read_parser(argv, Inputs, InputsOpt_Defaults) if config['mode'] == 'normal': print('nothing') n = 500 x_pure = np.arange(n) * 0.1 x = x_pure + np.random.normal(scale=0.25, size=n) y = np.cos(x) # y = 2*x+ 6 kf = KalmanFilter(initial_state_mean=0, n_dim_obs=1, random_state=1) # measurements = [[x[i], y[i]] for i in range(int(n))] measurements = [[y[i]] for i in range(int(n / 2))] # measurements_full = [[y[i]] for i in range(int(n))] kf.em(measurements) # print(kf.initial_state_mean) # print(kf.initial_state_covariance) # print(type(kf.initial_state_mean)) # print(type(kf.initial_state_covariance)) # exit() z = kf.filter(measurements) means = z[0] covs = z[1] it_mean = means[len(means) - 1] it_cov = covs[len(covs) - 1] h = list(means) r = h # kf2 = KalmanFilter(initial_state_mean=it_mean, initial_state_covariance=it_cov, n_dim_obs=1) # kf2.em(measurements) f = list( kf.sample(int(n / 2), initial_state=it_mean, random_state=1)[0]) # f = h + list(np.array(f) + it_mean) f = h + f for i in range(int(n / 2)): it_z = kf.filter_update(filtered_state_mean=it_mean, filtered_state_covariance=it_cov, observation=[y[i + int(n / 2)]]) it_mean = it_z[0] it_cov = it_z[1] h.append(it_mean) plt.plot(x_pure, h, 'r') plt.plot(x_pure, y) plt.plot(x_pure, f, 'g') plt.show() elif config['mode'] == 'ukalman': print('Ukalman') n = 1000 x_pure = np.arange(n) * 0.1 x = x_pure + np.random.normal(scale=0.5, size=n) y = np.cos(x) # y = 2*x kf = AdditiveUnscentedKalmanFilter(n_dim_obs=1) measurements = [[y[i]] for i in range(int(n / 2))] kf.initial_state_mean = np.array([0.]) kf.initial_state_covariance = np.array([[0.1]]) it_mean = kf.initial_state_mean it_cov = kf.initial_state_covariance print(kf.initial_state_mean) print(kf.initial_state_covariance) # exit() h = [] for element in measurements: it_z = kf.filter_update(filtered_state_mean=it_mean, filtered_state_covariance=it_cov, observation=element) it_mean = it_z[0] it_cov = it_z[1] h.append(it_mean) f = list(kf.sample(int(n / 2), initial_state=it_mean)[0]) # f = h + list(np.array(f) + it_mean) f = h + f plt.plot(x_pure, y) plt.plot(x_pure, f, 'g') plt.show() return