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install pymap3d\n\nimport pandas as pd  # 添加这行，导入 pandas 库并使用别名 pd\nimport matplotlib.pyplot as plt  # 如果需要绘制图表，也需要导入 matplotlib\nimport numpy as np\nimport pandas as pd\nimport pymap3d as pm\nimport pymap3d.vincenty as pmv\nimport matplotlib.pyplot as plt\nimport glob as gl\nimport scipy.optimize\nfrom tqdm.auto import tqdm\nfrom scipy.interpolate import InterpolatedUnivariateSpline\n\nfrom scipy.spatial import distance\n\nfrom scipy.interpolate import InterpolatedUnivariateSpline\nfrom scipy.spatial import distance\nfrom tensorflow.keras.models import Sequential\nfrom tensorflow.keras.layers import LSTM, Dense, Dropout\nfrom sklearn.preprocessing import StandardScaler\nfrom sklearn.metrics import mean_squared_error\n\n","metadata":{"_cell_guid":"b1076dfc-b9ad-4769-8c92-a6c4dae69d19","_uuid":"8f2839f25d086af736a60e9eeb907d3b93b6e0e5","execution":{"iopub.status.busy":"2025-05-29T02:20:06.866837Z","iopub.execute_input":"2025-05-29T02:20:06.867186Z","iopub.status.idle":"2025-05-29T02:20:10.462702Z","shell.execute_reply.started":"2025-05-29T02:20:06.867156Z","shell.execute_reply":"2025-05-29T02:20:10.461546Z"},"papermill":{"duration":16.534605,"end_time":"2024-01-24T15:31:36.041755","exception":false,"start_time":"2024-01-24T15:31:19.50715","status":"completed"},"tags":[],"trusted":true},"outputs":[],"execution_count":null},{"id":"5ddf2aeb","cell_type":"markdown","source":"# 0 Constants","metadata":{"papermill":{"duration":0.005742,"end_time":"2024-01-24T15:31:36.053566","exception":false,"start_time":"2024-01-24T15:31:36.047824","status":"completed"},"tags":[]}},{"id":"41659121","cell_type":"code","source":"# Constants\nCLIGHT = 299_792_458   # speed of light (m/s)\nRE_WGS84 = 6_378_137   # earth semimajor axis (WGS84) (m)\nOMGE = 7.2921151467E-5  # earth angular velocity (IS-GPS) (rad/s)","metadata":{"execution":{"iopub.status.busy":"2025-05-29T02:20:10.464408Z","iopub.execute_input":"2025-05-29T02:20:10.464738Z","iopub.status.idle":"2025-05-29T02:20:10.469813Z","shell.execute_reply.started":"2025-05-29T02:20:10.464703Z","shell.execute_reply":"2025-05-29T02:20:10.46885Z"},"papermill":{"duration":0.015252,"end_time":"2024-01-24T15:31:36.074751","exception":false,"start_time":"2024-01-24T15:31:36.059499","status":"completed"},"tags":[],"trusted":true},"outputs":[],"execution_count":null},{"id":"26a92d01","cell_type":"markdown","source":"# 1 Satellite Selection\nsatellite_selection(df, column)","metadata":{"papermill":{"duration":0.005554,"end_time":"2024-01-24T15:31:36.086282","exception":false,"start_time":"2024-01-24T15:31:36.080728","status":"completed"},"tags":[]}},{"id":"50ade3fc","cell_type":"code","source":"# Satellite selection using carrier frequency error, elevation angle, and C/N0\ndef satellite_selection(df, column):\n    \"\"\"\n    Args:\n        df : DataFrame from device_gnss.csv\n        column : Column name\n    Returns:\n        df: DataFrame with eliminated satellite signals\n    \"\"\"\n    idx = df[column].notnull()\n    idx &= df['CarrierErrorHz'] < 2.0e6  # carrier frequency error (Hz)\n    idx &= df['SvElevationDegrees'] > 10.0  # elevation angle (deg)\n    idx &= df['Cn0DbHz'] > 15.0  # C/N0 (dB-Hz)\n    idx &= df['MultipathIndicator'] == 0 # Multipath flag\n\n    return df[idx]","metadata":{"execution":{"iopub.status.busy":"2025-05-29T02:20:10.470747Z","iopub.execute_input":"2025-05-29T02:20:10.471057Z","iopub.status.idle":"2025-05-29T02:20:10.508965Z","shell.execute_reply.started":"2025-05-29T02:20:10.471031Z","shell.execute_reply":"2025-05-29T02:20:10.507843Z"},"papermill":{"duration":0.024476,"end_time":"2024-01-24T15:31:36.116614","exception":false,"start_time":"2024-01-24T15:31:36.092138","status":"completed"},"tags":[],"trusted":true},"outputs":[],"execution_count":null},{"id":"0fddcbe7","cell_type":"markdown","source":"# 2 Pseudorange/Doppler Residuals and Jacobian\n los_vector(xusr, xsat);\n jac_pr_residuals(x, xsat, pr, W);\n pr_residuals(x, xsat, pr, W);\n jac_prr_residuals(v, vsat, prr, x, xsat, W);\n prr_residuals(v, vsat, prr, x, xsat, W);\n ","metadata":{"papermill":{"duration":0.005586,"end_time":"2024-01-24T15:31:36.128637","exception":false,"start_time":"2024-01-24T15:31:36.123051","status":"completed"},"tags":[]}},{"id":"a841697e","cell_type":"code","source":"# Compute line-of-sight vector from user to satellite\ndef los_vector(xusr, xsat):\n    \"\"\"\n    Args:\n        xusr : user position in ECEF (m)\n        xsat : satellite position in ECEF (m)\n    Returns:\n        u: unit line-of-sight vector in ECEF (m)\n        rng: distance between user and satellite (m)\n    \"\"\"\n    u = xsat - xusr\n    rng = np.linalg.norm(u, axis=1).reshape(-1, 1)\n    u /= rng\n    \n    return u, rng.reshape(-1)\n\n\n# Compute Jacobian matrix\ndef jac_pr_residuals(x, xsat, pr, W):\n    \"\"\"\n    Args:\n        x : current position in ECEF (m)\n        xsat : satellite position in ECEF (m)\n        pr : pseudorange (m)\n        W : weight matrix\n    Returns:\n        W*J : Jacobian matrix\n    \"\"\"\n    u, _ = los_vector(x[:3], xsat)\n    J = np.hstack([-u, np.ones([len(pr), 1])])  # J = [-ux -uy -uz 1]\n\n    return W @ J\n\n\n# Compute pseudorange residuals\ndef pr_residuals(x, xsat, pr, W):\n    \"\"\"\n    Args:\n        x : current position in ECEF (m)\n        xsat : satellite position in ECEF (m)\n        pr : pseudorange (m)\n        W : weight matrix\n    Returns:\n        residuals*W : pseudorange residuals\n    \"\"\"\n    u, rng = los_vector(x[:3], xsat)\n\n    # Approximate correction of the earth rotation (Sagnac effect) often used in GNSS positioning\n    rng += OMGE * (xsat[:, 0] * x[1] - xsat[:, 1] * x[0]) / CLIGHT\n\n    # Add GPS L1 clock offset\n    residuals = rng - (pr - x[3])\n\n    return residuals @ W\n\n\n# Compute Jacobian matrix\ndef jac_prr_residuals(v, vsat, prr, x, xsat, W):\n    \"\"\"\n    Args:\n        v : current velocity in ECEF (m/s)\n        vsat : satellite velocity in ECEF (m/s)\n        prr : pseudorange rate (m/s)\n        x : current position in ECEF (m)\n        xsat : satellite position in ECEF (m)\n        W : weight matrix\n    Returns:\n        W*J : Jacobian matrix\n    \"\"\"\n    u, _ = los_vector(x[:3], xsat)\n    J = np.hstack([-u, np.ones([len(prr), 1])])\n\n    return np.dot(W, J)\n\n\n# Compute pseudorange rate residuals\ndef prr_residuals(v, vsat, prr, x, xsat, W):\n    \"\"\"\n    Args:\n        v : current velocity in ECEF (m/s)\n        vsat : satellite velocity in ECEF (m/s)\n        prr : pseudorange rate (m/s)\n        x : current position in ECEF (m)\n        xsat : satellite position in ECEF (m)\n        W : weight matrix\n    Returns:\n        residuals*W : pseudorange rate residuals\n    \"\"\"\n    u, rng = los_vector(x[:3], xsat)\n    rate = np.sum((vsat-v[:3])*u, axis=1) \\\n          + OMGE / CLIGHT * (vsat[:, 1] * x[0] + xsat[:, 1] * v[0]\n                           - vsat[:, 0] * x[1] - xsat[:, 0] * v[1])\n\n    residuals = rate - (prr - v[3])\n\n    return residuals @ W","metadata":{"execution":{"iopub.status.busy":"2025-05-29T02:20:10.511241Z","iopub.execute_input":"2025-05-29T02:20:10.511568Z","iopub.status.idle":"2025-05-29T02:20:10.526586Z","shell.execute_reply.started":"2025-05-29T02:20:10.511543Z","shell.execute_reply":"2025-05-29T02:20:10.525597Z"},"papermill":{"duration":0.024795,"end_time":"2024-01-24T15:31:36.159391","exception":false,"start_time":"2024-01-24T15:31:36.134596","status":"completed"},"tags":[],"trusted":true},"outputs":[],"execution_count":null},{"id":"2d2537ed","cell_type":"markdown","source":"\n# 3 Carrier Smoothing\ncarrier_smoothing(gnss_df):","metadata":{"papermill":{"duration":0.005613,"end_time":"2024-01-24T15:31:36.170912","exception":false,"start_time":"2024-01-24T15:31:36.165299","status":"completed"},"tags":[]}},{"id":"03a6d524","cell_type":"code","source":"# Carrier smoothing of pseudarange\ndef carrier_smoothing(gnss_df):\n    \"\"\"\n    Args:\n        df : DataFrame from device_gnss.csv\n    Returns:\n        df: DataFrame with carrier-smoothing pseudorange 'pr_smooth'\n    \"\"\"\n    carr_th = 1.0 # carrier phase jump threshold [m] 2->1.5 (best)->1.0\n    pr_th =  15.0 # pseudorange jump threshold [m] 20->15\n\n    prsmooth = np.full_like(gnss_df['RawPseudorangeMeters'], np.nan)\n    # Loop for each signal\n    for (i, (svid_sigtype, df)) in enumerate((gnss_df.groupby(['Svid', 'SignalType']))):\n        df = df.replace(\n            {'AccumulatedDeltaRangeMeters': {0: np.nan}})  # 0 to NaN\n\n        # Compare time difference between pseudorange/carrier with Doppler\n        drng1 = df['AccumulatedDeltaRangeMeters'].diff() - df['PseudorangeRateMetersPerSecond']\n        drng2 = df['RawPseudorangeMeters'].diff() - df['PseudorangeRateMetersPerSecond']\n\n        # Check cycle-slip\n        slip1 = (df['AccumulatedDeltaRangeState'].to_numpy() & 2**1) != 0  # reset flag\n        slip2 = (df['AccumulatedDeltaRangeState'].to_numpy() & 2**2) != 0  # cycle-slip flag\n        slip3 = np.fabs(drng1.to_numpy()) > carr_th # Carrier phase jump\n        slip4 = np.fabs(drng2.to_numpy()) > pr_th # Pseudorange jump\n\n        idx_slip = slip1 | slip2 | slip3 | slip4\n        idx_slip[0] = True\n\n        # groups with continuous carrier phase tracking\n        df['group_slip'] = np.cumsum(idx_slip)\n\n        # Psudorange - carrier phase\n        df['dpc'] = df['RawPseudorangeMeters'] - df['AccumulatedDeltaRangeMeters']\n\n        # Absolute distance bias of carrier phase\n        meandpc = df.groupby('group_slip')['dpc'].mean()\n        df = df.merge(meandpc, on='group_slip', suffixes=('', '_Mean'))\n\n        # Index of original gnss_df\n        idx = (gnss_df['Svid'] == svid_sigtype[0]) & (\n            gnss_df['SignalType'] == svid_sigtype[1])\n\n        # Carrier phase + bias\n        prsmooth[idx] = df['AccumulatedDeltaRangeMeters'] + df['dpc_Mean']\n\n    # If carrier smoothing is not possible, use original pseudorange\n    idx_nan = np.isnan(prsmooth)\n    prsmooth[idx_nan] = gnss_df['RawPseudorangeMeters'][idx_nan]\n    gnss_df['pr_smooth'] = prsmooth\n\n    return gnss_df","metadata":{"execution":{"iopub.status.busy":"2025-05-29T02:20:10.527654Z","iopub.execute_input":"2025-05-29T02:20:10.527987Z","iopub.status.idle":"2025-05-29T02:20:10.545951Z","shell.execute_reply.started":"2025-05-29T02:20:10.527957Z","shell.execute_reply":"2025-05-29T02:20:10.545049Z"},"papermill":{"duration":0.020964,"end_time":"2024-01-24T15:31:36.197745","exception":false,"start_time":"2024-01-24T15:31:36.176781","status":"completed"},"tags":[],"trusted":true},"outputs":[],"execution_count":null},{"id":"711aeeed","cell_type":"markdown","source":"# 4 score\nvincenty_distance(llh1, llh2):\ncalc_score(llh, llh_gt)-vincenty_distance(llh, llh_gt)","metadata":{"papermill":{"duration":0.005562,"end_time":"2024-01-24T15:31:36.209313","exception":false,"start_time":"2024-01-24T15:31:36.203751","status":"completed"},"tags":[]}},{"id":"86f9ac83","cell_type":"code","source":"# Compute distance by Vincenty's formulae\ndef vincenty_distance(llh1, llh2):\n    \"\"\"\n    Args:\n        llh1 : [latitude,longitude] (deg)\n        llh2 : [latitude,longitude] (deg)\n    Returns:\n        d : distance between llh1 and llh2 (m)\n    \"\"\"\n    d, az = np.array(pmv.vdist(llh1[:, 0], llh1[:, 1], llh2[:, 0], llh2[:, 1]))\n\n    return d\n\n\n# Compute score\ndef calc_score(llh, llh_gt):\n    \"\"\"\n    Args:\n        llh : [latitude,longitude] (deg)\n        llh_gt : [latitude,longitude] (deg)\n    Returns:\n        score : (m)\n    \"\"\"\n    d = vincenty_distance(llh, llh_gt)\n    score = np.mean([np.quantile(d, 0.50), np.quantile(d, 0.95)])\n\n    return score","metadata":{"execution":{"iopub.status.busy":"2025-05-29T02:20:10.546899Z","iopub.execute_input":"2025-05-29T02:20:10.547215Z","iopub.status.idle":"2025-05-29T02:20:10.564874Z","shell.execute_reply.started":"2025-05-29T02:20:10.547189Z","shell.execute_reply":"2025-05-29T02:20:10.564169Z"},"papermill":{"duration":0.016984,"end_time":"2024-01-24T15:31:36.232148","exception":false,"start_time":"2024-01-24T15:31:36.215164","status":"completed"},"tags":[],"trusted":true},"outputs":[],"execution_count":null},{"id":"fb8b2d55","cell_type":"markdown","source":"# 5 Robust WLS\npoint_positioning(gnss_df)","metadata":{"papermill":{"duration":0.005562,"end_time":"2024-01-24T15:31:36.243622","exception":false,"start_time":"2024-01-24T15:31:36.23806","status":"completed"},"tags":[]}},{"id":"bdc096cb","cell_type":"code","source":"# GNSS single point positioning using pseudorange\n\ndef point_positioning(gnss_df):\n    # Add nominal frequency to each signal\n    # Note: GLONASS is an FDMA signal, so each satellite has a different frequency\n    CarrierFrequencyHzRef = gnss_df.groupby(['Svid', 'SignalType'])[\n        'CarrierFrequencyHz'].median()\n    gnss_df = gnss_df.merge(CarrierFrequencyHzRef, how='left', on=[\n                            'Svid', 'SignalType'], suffixes=('', 'Ref'))\n    gnss_df['CarrierErrorHz'] = np.abs(\n        (gnss_df['CarrierFrequencyHz'] - gnss_df['CarrierFrequencyHzRef']))\n\n    # Carrier smoothing\n    gnss_df = carrier_smoothing(gnss_df)\n\n    # GNSS single point positioning\n    utcTimeMillis = gnss_df['utcTimeMillis'].unique()\n    nepoch = len(utcTimeMillis)\n    x0 = np.zeros(4)  # [x,y,z,tGPSL1]\n    v0 = np.zeros(4)  # [vx,vy,vz,dtGPSL1]\n    x_wls = np.full([nepoch, 3], np.nan)  # For saving position\n    v_wls = np.full([nepoch, 3], np.nan)  # For saving velocity\n\n # Store additional features for each epoch!!!!!!!!!\n    features = []\n    gdop_values = []  # 初始化 gdop_values 数组\n    # Loop for epochs\n    for i, (t_utc, df) in enumerate(tqdm(gnss_df.groupby('utcTimeMillis'), total=nepoch)):\n        # Valid satellite selection\n        df_pr = satellite_selection(df, 'pr_smooth')\n        df_prr = satellite_selection(df, 'PseudorangeRateMetersPerSecond')\n\n        # Corrected pseudorange/pseudorange rate\n        pr = (df_pr['pr_smooth'] + df_pr['SvClockBiasMeters'] - df_pr['IsrbMeters'] -\n              df_pr['IonosphericDelayMeters'] - df_pr['TroposphericDelayMeters']).to_numpy()\n        prr = (df_prr['PseudorangeRateMetersPerSecond'] +\n               df_prr['SvClockDriftMetersPerSecond']).to_numpy()\n\n        # Satellite position/velocity\n        xsat_pr = df_pr[['SvPositionXEcefMeters', 'SvPositionYEcefMeters',\n                         'SvPositionZEcefMeters']].to_numpy()\n        xsat_prr = df_prr[['SvPositionXEcefMeters', 'SvPositionYEcefMeters',\n                           'SvPositionZEcefMeters']].to_numpy()\n        vsat = df_prr[['SvVelocityXEcefMetersPerSecond', 'SvVelocityYEcefMetersPerSecond',\n                       'SvVelocityZEcefMetersPerSecond']].to_numpy()\n\n        # Weight matrix for peseudorange/pseudorange rate\n        Wx = np.diag(1 / df_pr['RawPseudorangeUncertaintyMeters'].to_numpy())\n        Wv = np.diag(1 / df_prr['PseudorangeRateUncertaintyMetersPerSecond'].to_numpy())\n#####\n# Compute additional features for this epoch\n        num_sats = len(df_pr)\n        avg_elevation = df_pr['SvElevationDegrees'].mean()\n        avg_cn0 = df_pr['Cn0DbHz'].mean()\n        max_cn0 = df_pr['Cn0DbHz'].max()\n        min_cn0 = df_pr['Cn0DbHz'].min()\n        std_cn0 = df_pr['Cn0DbHz'].std()\n\n# 在循环中保存GDOP值\n        if len(df_pr) >= 4:\n    # 计算GDOP# Compute GDOP (Geometric Dilution of Precision)\n            u, _ = los_vector(np.zeros(3), xsat_pr)\n            G = np.hstack([-u, np.ones([len(pr), 1])])\n            Q = np.linalg.inv(G.T @ G)\n            gdop = np.sqrt(np.trace(Q))\n        else:\n             gdop = np.nan\n\n        gdop_values.append(gdop)  # 保存GDOP值\n\n# 在函数结束前，将GDOP值作为额外返回值\n        \n  \n        # Store features\n        features.append([num_sats, avg_elevation, avg_cn0, max_cn0, min_cn0, std_cn0, gdop])\n\n#######\n\n        # Robust WLS requires accurate initial values for convergence,\n        # so perform normal WLS for the first time\n        if len(df_pr) >= 4:\n            # Normal WLS\n            if np.all(x0 == 0):\n                opt = scipy.optimize.least_squares(\n                    pr_residuals, x0, jac_pr_residuals, args=(xsat_pr, pr, Wx))\n                x0 = opt.x \n            # Robust WLS for position estimation\n            opt = scipy.optimize.least_squares(\n                 pr_residuals, x0, jac_pr_residuals, args=(xsat_pr, pr, Wx), loss='soft_l1')\n            if opt.status < 1 or opt.status == 2:\n                 print(f'i = {i} position lsq status = {opt.status}')\n            else:\n                 x_wls[i, :] = opt.x[:3]\n                 x0 = opt.x\n                 \n        # Velocity estimation\n        if len(df_prr) >= 4:\n            if np.all(v0 == 0): # Normal WLS\n                opt = scipy.optimize.least_squares(\n                    prr_residuals, v0, jac_prr_residuals, args=(vsat, prr, x0, xsat_prr, Wv))\n                v0 = opt.x\n            # Robust WLS for velocity estimation\n            opt = scipy.optimize.least_squares(\n                prr_residuals, v0, jac_prr_residuals, args=(vsat, prr, x0, xsat_prr, Wv), loss='soft_l1')\n            if opt.status < 1:\n                print(f'i = {i} velocity lsq status = {opt.status}')\n            else:\n                v_wls[i, :] = opt.x[:3]\n                v0 = opt.x\n # Convert features to numpy array\n    features = np.array(features)\n\n    return utcTimeMillis, x_wls, v_wls,features, np.array(gdop_values)\n","metadata":{"execution":{"iopub.status.busy":"2025-05-29T02:20:10.566103Z","iopub.execute_input":"2025-05-29T02:20:10.566391Z","iopub.status.idle":"2025-05-29T02:20:10.582799Z","shell.execute_reply.started":"2025-05-29T02:20:10.56637Z","shell.execute_reply":"2025-05-29T02:20:10.581723Z"},"papermill":{"duration":0.02729,"end_time":"2024-01-24T15:31:36.277718","exception":false,"start_time":"2024-01-24T15:31:36.250428","status":"completed"},"tags":[],"trusted":true},"outputs":[],"execution_count":null},{"id":"11f33322","cell_type":"markdown","source":"# 6 outlier detection\nexclude_interpolate_outlier(x_wls, v_wls)","metadata":{"papermill":{"duration":0.005514,"end_time":"2024-01-24T15:31:36.289193","exception":false,"start_time":"2024-01-24T15:31:36.283679","status":"completed"},"tags":[]}},{"id":"a9a7906c","cell_type":"code","source":"# Simple outlier detection and interpolation\ndef exclude_interpolate_outlier(x_wls, v_wls,features):\n    # Up velocity threshold\n    v_up_th = 2.0 # m/s\n\n    # Coordinate conversion\n    x_llh = np.array(pm.ecef2geodetic(x_wls[:, 0], x_wls[:, 1], x_wls[:, 2])).T\n    v_enu = np.array(pm.ecef2enuv(\n        v_wls[:, 0], v_wls[:, 1], v_wls[:, 2], x_llh[0, 0], x_llh[0, 1])).T\n\n    # Up velocity jump detection\n    # Cars don't jump suddenly!\n    idx_v_out = np.abs(v_enu[:, 2]) > v_up_th\n    v_wls[idx_v_out, :] = np.nan\n    \n    # Interpolate NaNs at beginning and end of array\n    x_df = pd.DataFrame({'x': x_wls[:, 0], 'y': x_wls[:, 1], 'z': x_wls[:, 2]})\n    x_df = x_df.interpolate(limit_area='outside', limit_direction='both')\n    \n    # Interpolate all NaN data\n    v_df = pd.DataFrame({'x': v_wls[:, 0], 'y': v_wls[:, 1], 'z': v_wls[:, 2]})\n    v_df = v_df.interpolate(limit_area='outside', limit_direction='both')\n    v_df = v_df.interpolate('spline', order=3)\n\n    return x_df.to_numpy(), v_df.to_numpy(), features","metadata":{"execution":{"iopub.status.busy":"2025-05-29T02:20:10.583753Z","iopub.execute_input":"2025-05-29T02:20:10.584084Z","iopub.status.idle":"2025-05-29T02:20:10.602618Z","shell.execute_reply.started":"2025-05-29T02:20:10.584056Z","shell.execute_reply":"2025-05-29T02:20:10.601776Z"},"papermill":{"duration":0.017978,"end_time":"2024-01-24T15:31:36.313048","exception":false,"start_time":"2024-01-24T15:31:36.29507","status":"completed"},"tags":[],"trusted":true},"outputs":[],"execution_count":null},{"id":"be2fedb0","cell_type":"markdown","source":"# 7 Kalman \nKalman_filter(zs, us, phone)\nKalman_smoothing(x_wls, v_wls, phone):\nApplication of Kalman smoother; integration of velocity and position obtained by WLS. The covariance matrix is a fixed value.","metadata":{"papermill":{"duration":0.005512,"end_time":"2024-01-24T15:31:36.324505","exception":false,"start_time":"2024-01-24T15:31:36.318993","status":"completed"},"tags":[]}},{"id":"81d97e09","cell_type":"code","source":"#Kalman filter\ndef Kalman_filter(zs, us, phone):\n    # Parameters\n    # I don't know why only XiaomiMi8 seems to be inaccurate ... \n    sigma_v = 0.6 if phone == 'XiaomiMi8' else 0.1 # velocity SD m/s\n    sigma_x = 5.0  # position SD m\n    sigma_mahalanobis = 30.0 # Mahalanobis distance for rejecting innovation\n    \n    n, dim_x = zs.shape\n    F = np.eye(3)  # Transition matrix\n    Q = sigma_v**2 * np.eye(3)  # Process noise\n\n    H = np.eye(3)  # Measurement function\n    R = sigma_x**2 * np.eye(3)  # Measurement noise\n\n    # Initial state and covariance\n    x = zs[0, :3].T  # State\n    P = sigma_x**2 * np.eye(3)  # State covariance\n    I = np.eye(dim_x)\n\n    x_kf = np.zeros([n, dim_x])\n    P_kf = np.zeros([n, dim_x, dim_x])\n\n    # Kalman filtering\n    for i, (u, z) in enumerate(zip(us, zs)):\n        # First step\n        if i == 0:\n            x_kf[i] = x.T\n            P_kf[i] = P\n            continue\n\n        # Prediction step\n        x = F @ x + u.T\n        P = (F @ P) @ F.T + Q\n\n        # Check outliers for observation\n        d = distance.mahalanobis(z, H @ x, np.linalg.pinv(P))\n\n        # Update step\n        if d < sigma_mahalanobis:\n            y = z.T - H @ x\n            S = (H @ P) @ H.T + R\n            K = (P @ H.T) @ np.linalg.inv(S)\n            x = x + K @ y\n            P = (I - (K @ H)) @ P\n        else:\n            # If no observation update is available, increase covariance\n            P += 10**2*Q\n\n        x_kf[i] = x.T\n        P_kf[i] = P\n\n    return x_kf, P_kf\n\n\n# Forward + backward Kalman filter and smoothing\ndef Kalman_smoothing(x_wls, v_wls, phone):\n    n, dim_x = x_wls.shape\n\n    # Forward\n    v = np.vstack([np.zeros([1, 3]), (v_wls[:-1, :] + v_wls[1:, :])/2])\n    x_f, P_f = Kalman_filter(x_wls, v, phone)\n\n    # Backward\n    v = -np.flipud(v_wls)\n    v = np.vstack([np.zeros([1, 3]), (v[:-1, :] + v[1:, :])/2])\n    x_b, P_b = Kalman_filter(np.flipud(x_wls), v, phone)\n\n    # Smoothing\n    x_fb = np.zeros_like(x_f)\n    P_fb = np.zeros_like(P_f)\n    for (f, b) in zip(range(n), range(n-1, -1, -1)):\n        P_fi = np.linalg.inv(P_f[f])\n        P_bi = np.linalg.inv(P_b[b])\n\n        P_fb[f] = np.linalg.inv(P_fi + P_bi)\n        x_fb[f] = P_fb[f] @ (P_fi @ x_f[f] + P_bi @ x_b[b])\n\n    return x_fb, x_f, np.flipud(x_b)","metadata":{"execution":{"iopub.status.busy":"2025-05-29T02:20:10.603755Z","iopub.execute_input":"2025-05-29T02:20:10.604034Z","iopub.status.idle":"2025-05-29T02:20:10.619929Z","shell.execute_reply.started":"2025-05-29T02:20:10.604008Z","shell.execute_reply":"2025-05-29T02:20:10.619052Z"},"papermill":{"duration":0.024951,"end_time":"2024-01-24T15:31:36.355983","exception":false,"start_time":"2024-01-24T15:31:36.331032","status":"completed"},"tags":[],"trusted":true},"outputs":[],"execution_count":null},{"id":"46b06965","cell_type":"markdown","source":"# 8 lstm\nenhanced_lstm_prediction(x_kf, v_wls, features, sequence_length=10)\nevaluate_model(llh_pred, llh_gt, method_name):","metadata":{}},{"id":"33239169","cell_type":"code","source":"from tensorflow.keras.models import Sequential\nfrom tensorflow.keras.layers import LSTM, Dense, Dropout\nfrom sklearn.preprocessing import StandardScaler\nimport numpy as np\nfrom tensorflow.keras.models import load_model\nimport os\n\ndef enhanced_lstm_prediction(x_kf, v_wls, features, sequence_length=10, model_path=\"lstm_model.h5\"):\n    \"\"\"\n    训练 LSTM 模型并保存（仅用于 train 阶段）。\n    \"\"\"\n    all_features = np.hstack([x_kf, v_wls, features])\n    scaler = StandardScaler()\n    normalized_features = scaler.fit_transform(all_features)\n\n    n_samples = len(normalized_features) - sequence_length\n    n_features = normalized_features.shape[1]\n    X = np.zeros((n_samples, sequence_length, n_features))\n    y = np.zeros((n_samples, 3))\n    for i in range(n_samples):\n        X[i] = normalized_features[i:i+sequence_length]\n        y[i] = x_kf[i+sequence_length]\n\n    model = Sequential()\n    model.add(LSTM(64, activation='relu', input_shape=(sequence_length, n_features)))\n    model.add(Dropout(0.2))\n    model.add(Dense(3))\n    model.compile(optimizer='adam', loss='mse')\n\n    print(\"开始训练 LSTM 模型...\")\n    model.fit(X, y, epochs=10, batch_size=128, verbose=1)\n\n    # 保存模型\n    model.save(model_path)\n    print(f\"LSTM 模型已保存至 {model_path}\")\n\n    # 用训练好的模型预测训练数据，返回 x_lstm\n    x_lstm = np.copy(x_kf)\n    for i in range(sequence_length, len(x_kf)):\n        input_features = normalized_features[i-sequence_length:i].reshape((1, sequence_length, n_features))\n        x_lstm[i] = model.predict(input_features, verbose=0)\n\n    return x_lstm\n","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2025-05-29T02:20:10.62233Z","iopub.execute_input":"2025-05-29T02:20:10.62259Z","iopub.status.idle":"2025-05-29T02:20:10.639252Z","shell.execute_reply.started":"2025-05-29T02:20:10.622564Z","shell.execute_reply":"2025-05-29T02:20:10.638364Z"}},"outputs":[],"execution_count":null},{"id":"29aaca02","cell_type":"code","source":"from tensorflow.keras.models import load_model\nfrom sklearn.preprocessing import StandardScaler\nimport numpy as np\n\ndef predict_with_lstm_model(x_kf, v_wls, features, sequence_length=10, model_path=\"lstm_model.h5\"):\n    \"\"\"\n    加载训练好的模型，做预测（仅用于 test 阶段）\n    \"\"\"\n    model = load_model(model_path)\n    all_features = np.hstack([x_kf, v_wls, features])\n    scaler = StandardScaler()\n    normalized_features = scaler.fit_transform(all_features)\n\n    x_lstm = np.copy(x_kf)\n    n_features = normalized_features.shape[1]\n    for i in range(sequence_length, len(x_kf)):\n        input_features = normalized_features[i-sequence_length:i].reshape((1, sequence_length, n_features))\n        x_lstm[i] = model.predict(input_features, verbose=0)\n\n    return x_lstm\n","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2025-05-29T02:20:10.640239Z","iopub.execute_input":"2025-05-29T02:20:10.640557Z","iopub.status.idle":"2025-05-29T02:20:10.656003Z","shell.execute_reply.started":"2025-05-29T02:20:10.64053Z","shell.execute_reply":"2025-05-29T02:20:10.655132Z"}},"outputs":[],"execution_count":null},{"id":"a940a374","cell_type":"code","source":"# Evaluate model performance\ndef evaluate_model(llh_pred, llh_gt, method_name):\n    \"\"\"\n    Evaluate the performance of a positioning method.\n    \n    Args:\n        llh_pred: Predicted positions (latitude, longitude)\n        llh_gt: Ground truth positions (latitude, longitude)\n        method_name: Name of the positioning method\n        \n    Returns:\n        score: Competition score (mean of 50th and 95th percentile errors)\n        rmse: Root mean squared error\n        errors: Individual position errors\n    \"\"\"\n    # Calculate distance errors\n    errors = vincenty_distance(llh_pred, llh_gt)\n    \n    # Calculate metrics\n    score = calc_score(llh_pred, llh_gt)\n    rmse = np.sqrt(np.mean(errors**2))\n    percentile_50 = np.percentile(errors, 50)\n    percentile_95 = np.percentile(errors, 95)\n    \n    # Print results\n    print(f\"\\n{method_name} Performance:\")\n    print(f\"  Score (mean of 50th and 95th percentile): {score:.4f} m\")\n    print(f\"  RMSE: {rmse:.4f} m\")\n    print(f\"  50th percentile error: {percentile_50:.4f} m\")\n    print(f\"  95th percentile error: {percentile_95:.4f} m\")\n    \n    return score, rmse, errors\n","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2025-05-29T02:20:10.65686Z","iopub.execute_input":"2025-05-29T02:20:10.657107Z","iopub.status.idle":"2025-05-29T02:20:10.676383Z","shell.execute_reply.started":"2025-05-29T02:20:10.657083Z","shell.execute_reply":"2025-05-29T02:20:10.675452Z"}},"outputs":[],"execution_count":null},{"id":"a694f75d","cell_type":"markdown","source":"# 9 lstm修改模型","metadata":{}},{"id":"c08205b6","cell_type":"markdown","source":"# Train Data","metadata":{"papermill":{"duration":0.005551,"end_time":"2024-01-24T15:31:36.367477","exception":false,"start_time":"2024-01-24T15:31:36.361926","status":"completed"},"tags":[]}},{"id":"05858c3a","cell_type":"code","source":"from tensorflow.keras.models import Sequential\nfrom tensorflow.keras.layers import LSTM, Dense, Dropout\nimport numpy as np\nimport pandas as pd  # 添加这行，导入 pandas 库并使用别名 pd\nimport matplotlib.pyplot as plt  # 如果需要绘制图表，也需要导入 matplotlib\n\n# Target course/phone换回去\n\npath = '/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-07-22-48-us-ca-routebc2/pixel4xl'\n\ndrive, phone = path.split('/')[-2:]\n\n# Read data\ngnss_df = pd.read_csv(f'{path}/device_gnss.csv')  # GNSS data\ngt_df = pd.read_csv(f'{path}/ground_truth.csv')  # ground truth\n\n\n# Point positioning\n#utc, x_wls, v_wls = point_positioning(gnss_df)\nutc, x_wls, v_wls, features, gdop_values = point_positioning(gnss_df)\n\n ##### Extract GDOP values from features (7th column)\ngdop_values = features[:, 6]\n    \n'''  ##### # 可视化 GDOP 值\nplt.figure(figsize=(12, 6))\nplt.plot(utc, gdop_values, label='GDOP')\nplt.axhline(y=5, color='r', linestyle='--', label='Poor GDOP Threshold (5)')\nplt.axhline(y=3, color='y', linestyle='--', label='Fair GDOP Threshold (3)')\nplt.axhline(y=2, color='g', linestyle='--', label='Good GDOP Threshold (2)')\nplt.title('Geometric Dilution of Precision (GDOP) over Time')\nplt.xlabel('Time (UTC)')\nplt.ylabel('GDOP')\nplt.legend()\nplt.grid(True)\nplt.tight_layout()\nplt.show()\n  '''  \n\n# Exclude velocity outliers\n#x_wls, v_wls = exclude_interpolate_outlier(x_wls, v_wls)\nx_wls, v_wls, features = exclude_interpolate_outlier(x_wls, v_wls, features)\n\n# Kalman smoothing\nx_kf, _, _ = Kalman_smoothing(x_wls, v_wls, phone)\n\n# 训练 LSTM 模型并保存\nx_lstm = enhanced_lstm_prediction(x_kf, v_wls, features, model_path=\"lstm_model.h5\")\n\n# Convert to latitude and longitude！！！（3排）\nllh_wls = np.array(pm.ecef2geodetic(x_wls[:, 0], x_wls[:, 1], x_wls[:, 2])).T\nllh_kf = np.array(pm.ecef2geodetic(x_kf[:, 0], x_kf[:, 1], x_kf[:, 2])).T\nllh_lstm = np.array(pm.ecef2geodetic(x_lstm[:, 0], x_lstm[:, 1], x_lstm[:, 2])).T\n\n# Baseline\nx_bl = gnss_df.groupby('TimeNanos')[\n    ['WlsPositionXEcefMeters', 'WlsPositionYEcefMeters', 'WlsPositionZEcefMeters']].mean().to_numpy()\nllh_bl = np.array(pm.ecef2geodetic(x_bl[:, 0], x_bl[:, 1], x_bl[:, 2])).T\n\n# Ground truth\nllh_gt = gt_df[['LatitudeDegrees', 'LongitudeDegrees']].to_numpy()\n# 可视化比较\nplt.figure(figsize=(12, 6))\nplt.plot(utc, llh_kf[:,0], label='Kalman Filter')\nplt.plot(utc, llh_lstm[:,0], label='Kalman + LSTM')\nplt.title('Latitude Comparison')\nplt.xlabel('Time')\nplt.ylabel('Latitude')\nplt.legend()\nplt.show()\n\n# Distance from ground truth！！！！（4排）\nvd_bl = vincenty_distance(llh_bl, llh_gt)\nvd_wls = vincenty_distance(llh_wls, llh_gt)\nvd_kf = vincenty_distance(llh_kf, llh_gt)\nvd_lstm = vincenty_distance(llh_lstm, llh_gt)\n\n# Score！！！！（4排）\nscore_bl = calc_score(llh_bl, llh_gt)\nscore_wls = calc_score(llh_wls, llh_gt)\nscore_kf = calc_score(llh_kf[:-1, :], llh_gt[:-1, :])\nscore_lstm = calc_score(llh_lstm[:-1, :], llh_gt[:-1, :])\n\n#！！！！（4排）\nprint(f'Score Baseline   {score_bl:.4f} [m]')\nprint(f'Score Robust WLS {score_wls:.4f} [m]')\nprint(f'Score KF         {score_kf:.4f} [m]')\nprint(f'Score LSTM       {score_lstm:.4f} [m]')\n\n# Plot distance error！！！！（7排）\nplt.figure()\nplt.title('Distance error')\nplt.ylabel('Distance error [m]')\nplt.plot(vd_bl, label=f'Baseline, Score: {score_bl:.4f} m')\nplt.plot(vd_wls, label=f'Robust WLS, Score: {score_wls:.4f} m')\nplt.plot(vd_kf, label=f'Robust WLS + KF, Score: {score_kf:.4f} m')\nplt.plot(vd_lstm, label=f'Robust WLS + KF + LSTM, Score: {score_lstm:.4f} m')\nplt.legend()\nplt.grid()\nplt.ylim([0, 30])\nplt.hist(vd_kf, bins=100)\n\n\n# Compute velocity error\nspeed_wls = np.linalg.norm(v_wls[:, :3], axis=1)\nspeed_gt = gt_df['SpeedMps'].to_numpy()\nspeed_rmse = np.sqrt(np.sum((speed_wls-speed_gt)**2)/len(speed_gt))\n'''\n# Plot velocity error\nplt.figure()\nplt.title('Speed error')\nplt.ylabel('Speed Error [m/s]')\nplt.plot(speed_wls - speed_gt, label=f'Speed RMSE: {speed_rmse:.4f} m')\nplt.legend()\nplt.grid()'''","metadata":{"execution":{"iopub.status.busy":"2025-05-29T02:20:10.67747Z","iopub.execute_input":"2025-05-29T02:20:10.677795Z","iopub.status.idle":"2025-05-29T02:20:10.742622Z","shell.execute_reply.started":"2025-05-29T02:20:10.677769Z","shell.execute_reply":"2025-05-29T02:20:10.741259Z"},"papermill":{"duration":35.562316,"end_time":"2024-01-24T15:32:11.935664","exception":false,"start_time":"2024-01-24T15:31:36.373348","status":"completed"},"tags":[],"trusted":true},"outputs":[],"execution_count":null},{"id":"0ea40cf4","cell_type":"markdown","source":"# Test and submission","metadata":{"papermill":{"duration":0.007848,"end_time":"2024-01-24T15:32:11.951744","exception":false,"start_time":"2024-01-24T15:32:11.943896","status":"completed"},"tags":[]}},{"id":"a5200920","cell_type":"code","source":"path = '/kaggle/input/smartphone-decimeter-2023/sdc2023'\n\n# Target course/phone\n\n\n\nsample_df = pd.read_csv(f'{path}/sample_submission.csv')\ntest_dfs = []\n\n# Loop for each trip\nfor i, dirname in enumerate(tqdm(sorted(gl.glob(f'{path}/test/*/*/')))):\n    #drive, phone = dirname.split('/')[-3:-1]\n    drive, phone =dirname.split('\\\\')[-3:-1]\n    tripID = f'{drive}/{phone}'\n    print(tripID)\n\n    # Read data\n    gnss_df = pd.read_csv(f'{dirname}/device_gnss.csv')\n\n    # Exclude velocity outliers\n    #x_wls, v_wls = exclude_interpolate_outlier(x_wls, v_wls)\n    utc, x_wls, v_wls, features, gdop_values = point_positioning(gnss_df)\n\n    # Kalman smoothing\n    x_kf, _, _ = Kalman_smoothing(x_wls, v_wls, phone)\n    print(f\"卡尔曼平滑后 x_kf 长度: {len(x_kf)}\")\n\n    # LSTM prediction！！！！\n    x_lstm = predict_with_lstm_model(x_kf, v_wls, features, model_path=\"lstm_model.h5\")\n    print(f\"异常值处理后 x_wls 长度: {len(x_wls)}\")\n    print(f\"x_lstm 长度: {len(x_lstm)}\")\n\n # Convert to latitude and longitude\n    #llh_kf = np.array(pm.ecef2geodetic(x_kf[:, 0], x_kf[:, 1], x_kf[:, 2])).T\n    llh_lstm = np.array(pm.ecef2geodetic(x_lstm[:, 0], x_lstm[:, 1], x_lstm[:, 2])).T\n    print(f\"llh_lstm 长度: {len(llh_lstm)}\")\n# 打印 utc 和 llh_kf 的前10个元素（用于调试）\n   \n     # 确保 utc 和 llh_lstm 长度一致\n    min_len = min(len(utc), len(llh_lstm))\n    utc = utc[:min_len]\n    llh_lstm = llh_lstm[:min_len]\n\n    # Interpolation for submission\n    UnixTimeMillis = sample_df[sample_df['tripId'] == tripID]['UnixTimeMillis'].to_numpy()\n    \n    lat = InterpolatedUnivariateSpline(utc, llh_lstm[:,0], ext=3)(UnixTimeMillis)+0.00001\n    lng = InterpolatedUnivariateSpline(utc, llh_lstm[:,1], ext=3)(UnixTimeMillis)-0.000001\n    trip_df = pd.DataFrame({\n        'tripId' : tripID,\n        'UnixTimeMillis': UnixTimeMillis,\n        'LatitudeDegrees': lat,\n        'LongitudeDegrees': lng\n        })\n\n    test_dfs.append(trip_df)\n\n# Write submission.csv\ntest_df = pd.concat(test_dfs)\ntest_df.to_csv('submission.csv', index=False)\n","metadata":{"execution":{"iopub.status.busy":"2025-05-29T02:20:10.743405Z","iopub.status.idle":"2025-05-29T02:20:10.743758Z","shell.execute_reply.started":"2025-05-29T02:20:10.743587Z","shell.execute_reply":"2025-05-29T02:20:10.743602Z"},"papermill":{"duration":1270.083999,"end_time":"2024-01-24T15:53:22.043967","exception":false,"start_time":"2024-01-24T15:32:11.959968","status":"completed"},"tags":[],"trusted":true},"outputs":[],"execution_count":null},{"id":"810d6303","cell_type":"code","source":"","metadata":{"papermill":{"duration":0.017946,"end_time":"2024-01-24T15:53:22.079945","exception":false,"start_time":"2024-01-24T15:53:22.061999","status":"completed"},"tags":[],"trusted":true},"outputs":[],"execution_count":null}]}