{"metadata":{"kernelspec":{"language":"python","display_name":"Python 3","name":"python3"},"language_info":{"name":"python","version":"3.10.13","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"},"kaggle":{"accelerator":"none","dataSources":[{"sourceId":60095,"databundleVersionId":6542333,"sourceType":"competition"}],"dockerImageVersionId":30673,"isInternetEnabled":true,"language":"python","sourceType":"notebook","isGpuEnabled":false}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"code","source":"# This Python 3 environment comes with many helpful analytics libraries installed\n# It is defined by the kaggle/python Docker image: https://github.com/kaggle/docker-python\n# For example, here's several helpful packages to load\n\nimport numpy as np # linear algebra\nimport pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)\n\n# Input data files are available in the read-only \"../input/\" directory\n# For example, running this (by clicking run or pressing Shift+Enter) will list all files under the input directory\n\nimport os\nfor dirname, _, filenames in os.walk('/kaggle/input'):\n    for filename in filenames:\n        print(os.path.join(dirname, filename))\n\n# You can write up to 20GB to the current directory (/kaggle/working/) that gets preserved as output when you create a version using \"Save & Run All\" \n# You can also write temporary files to /kaggle/temp/, but they won't be saved outside of the current session","metadata":{"_uuid":"8f2839f25d086af736a60e9eeb907d3b93b6e0e5","_cell_guid":"b1076dfc-b9ad-4769-8c92-a6c4dae69d19","execution":{"iopub.status.busy":"2024-03-31T13:06:23.559125Z","iopub.execute_input":"2024-03-31T13:06:23.559527Z","iopub.status.idle":"2024-03-31T13:06:29.59222Z","shell.execute_reply.started":"2024-03-31T13:06:23.559492Z","shell.execute_reply":"2024-03-31T13:06:29.591051Z"},"trusted":true},"execution_count":1,"outputs":[{"name":"stdout","text":"/kaggle/input/smartphone-decimeter-2023/sdc2023/sample_submission.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/metadata/constellation_type_mapping.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/metadata/accumulated_delta_range_state_bit_map.json\n/kaggle/input/smartphone-decimeter-2023/sdc2023/metadata/raw_state_bit_map.json\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-09-14-20-32-us-ca-mtv-k/pixel4/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-09-14-20-32-us-ca-mtv-k/pixel4/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-09-14-20-32-us-ca-mtv-k/pixel4/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-08-17-20-37-us-ca-mtv-g/pixel5/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-08-17-20-37-us-ca-mtv-g/pixel5/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-08-17-20-37-us-ca-mtv-g/pixel5/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-09-20-19-03-us-ca-mtv-l/pixel4/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-09-20-19-03-us-ca-mtv-l/pixel4/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-09-20-19-03-us-ca-mtv-l/pixel4/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2022-02-23-22-35-us-ca-lax-m/pixel5/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2022-02-23-22-35-us-ca-lax-m/pixel5/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2022-02-23-22-35-us-ca-lax-m/pixel5/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2023-05-25-17-32-us-ca-pao-j/pixel6pro/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2023-05-25-17-32-us-ca-pao-j/pixel6pro/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2023-05-25-17-32-us-ca-pao-j/pixel6pro/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2023-06-06-22-43-us-ca-sjc-he2/pixel5/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2023-06-06-22-43-us-ca-sjc-he2/pixel5/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2023-06-06-22-43-us-ca-sjc-he2/pixel5/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2022-04-25-22-36-us-ca-ebf-z/pixel5/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2022-04-25-22-36-us-ca-ebf-z/pixel5/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2022-04-25-22-36-us-ca-ebf-z/pixel5/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2020-12-11-19-30-us-ca-mtv-e/pixel4xl/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2020-12-11-19-30-us-ca-mtv-e/pixel4xl/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2020-12-11-19-30-us-ca-mtv-e/pixel4xl/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2022-03-14-19-57-us-ca-mtv-pe1/xiaomimi8/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2022-03-14-19-57-us-ca-mtv-pe1/xiaomimi8/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2022-03-14-19-57-us-ca-mtv-pe1/xiaomimi8/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2023-06-15-18-49-us-ca-sjc-ce1/pixel7pro/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2023-06-15-18-49-us-ca-sjc-ce1/pixel7pro/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2023-06-15-18-49-us-ca-sjc-ce1/pixel7pro/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-08-31-20-37-us-ca-mtv-e/sm-g988b/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-08-31-20-37-us-ca-mtv-e/sm-g988b/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-08-31-20-37-us-ca-mtv-e/sm-g988b/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-11-30-20-59-us-ca-mtv-m/mi8/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-11-30-20-59-us-ca-mtv-m/mi8/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2021-11-30-20-59-us-ca-mtv-m/mi8/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2023-05-23-21-06-us-ca-mtv-de1/pixel5/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/test/2023-05-23-21-06-us-ca-mtv-de1/pixel5/device_imu.csv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el5/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-05-23-07-us-ca-routen/pixel5/supplemental/span_log.nmea\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-05-23-07-us-ca-routen/pixel7pro/ground_truth.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-05-23-07-us-ca-routen/pixel7pro/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-05-23-07-us-ca-routen/pixel7pro/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-05-23-07-us-ca-routen/pixel7pro/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-05-23-07-us-ca-routen/pixel7pro/supplemental/span_log.nmea\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-08-04-00-20-us-ca-sb-mtv-101/pixel4xl/ground_truth.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-08-04-00-20-us-ca-sb-mtv-101/pixel4xl/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-08-04-00-20-us-ca-sb-mtv-101/pixel4xl/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-08-04-00-20-us-ca-sb-mtv-101/pixel4xl/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-08-04-00-20-us-ca-sb-mtv-101/pixel4xl/supplemental/span_log.nmea\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-08-04-00-20-us-ca-sb-mtv-101/pixel5/ground_truth.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-08-04-00-20-us-ca-sb-mtv-101/pixel5/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-08-04-00-20-us-ca-sb-mtv-101/pixel5/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-08-04-00-20-us-ca-sb-mtv-101/pixel5/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-08-04-00-20-us-ca-sb-mtv-101/pixel5/supplemental/span_log.nmea\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2021-12-08-18-52-us-ca-lax-b/mi8/ground_truth.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2021-12-08-18-52-us-ca-lax-b/mi8/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2021-12-08-18-52-us-ca-lax-b/mi8/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2021-12-08-18-52-us-ca-lax-b/mi8/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2021-12-08-18-52-us-ca-lax-b/mi8/supplemental/span_log.nmea\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2021-12-08-18-52-us-ca-lax-b/pixel6pro/ground_truth.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2021-12-08-18-52-us-ca-lax-b/pixel6pro/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2021-12-08-18-52-us-ca-lax-b/pixel6pro/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2021-12-08-18-52-us-ca-lax-b/pixel6pro/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2021-12-08-18-52-us-ca-lax-b/pixel6pro/supplemental/span_log.nmea\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/pixel5/ground_truth.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/pixel5/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/pixel5/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/pixel5/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/pixel5/supplemental/span_log.nmea\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/mi8/ground_truth.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/mi8/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/mi8/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/mi8/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/mi8/supplemental/span_log.nmea\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/pixel6pro/ground_truth.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/pixel6pro/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/pixel6pro/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/pixel6pro/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2022-04-01-18-22-us-ca-lax-t/pixel6pro/supplemental/span_log.nmea\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-07-17-22-27-us-ca-mtv-sf-280/pixel4/ground_truth.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-07-17-22-27-us-ca-mtv-sf-280/pixel4/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-07-17-22-27-us-ca-mtv-sf-280/pixel4/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-07-17-22-27-us-ca-mtv-sf-280/pixel4/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-07-17-22-27-us-ca-mtv-sf-280/pixel4/supplemental/span_log.nmea\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-07-22-48-us-ca-routebc2/pixel4xl/ground_truth.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-07-22-48-us-ca-routebc2/pixel4xl/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-07-22-48-us-ca-routebc2/pixel4xl/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-07-22-48-us-ca-routebc2/pixel4xl/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-07-22-48-us-ca-routebc2/pixel4xl/supplemental/span_log.nmea\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-07-22-48-us-ca-routebc2/pixel5a/ground_truth.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-07-22-48-us-ca-routebc2/pixel5a/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-07-22-48-us-ca-routebc2/pixel5a/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-07-22-48-us-ca-routebc2/pixel5a/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2023-09-07-22-48-us-ca-routebc2/pixel5a/supplemental/span_log.nmea\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-12-10-22-17-us-ca-sjc-c/mi8/ground_truth.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-12-10-22-17-us-ca-sjc-c/mi8/device_gnss.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-12-10-22-17-us-ca-sjc-c/mi8/device_imu.csv\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-12-10-22-17-us-ca-sjc-c/mi8/supplemental/gnss_log.txt\n/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2020-12-10-22-17-us-ca-sjc-c/mi8/supplemental/span_log.nmea\n","output_type":"stream"}]},{"cell_type":"code","source":"!pip install pymap3d\n\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\nfrom scipy.spatial import distance\n\n# 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":"2024-03-31T13:07:31.211592Z","iopub.execute_input":"2024-03-31T13:07:31.212009Z","iopub.status.idle":"2024-03-31T13:07:48.572823Z","shell.execute_reply.started":"2024-03-31T13:07:31.211975Z","shell.execute_reply":"2024-03-31T13:07:48.571527Z"},"trusted":true},"execution_count":3,"outputs":[{"name":"stdout","text":"Collecting pymap3d\n  Downloading pymap3d-3.1.0-py3-none-any.whl.metadata (8.7 kB)\nDownloading pymap3d-3.1.0-py3-none-any.whl (60 kB)\n\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m60.6/60.6 kB\u001b[0m \u001b[31m931.1 kB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0ma \u001b[36m0:00:01\u001b[0m\n\u001b[?25hInstalling collected packages: pymap3d\nSuccessfully installed pymap3d-3.1.0\n","output_type":"stream"}]},{"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":"2024-03-31T13:15:19.39254Z","iopub.execute_input":"2024-03-31T13:15:19.392979Z","iopub.status.idle":"2024-03-31T13:15:19.399196Z","shell.execute_reply.started":"2024-03-31T13:15:19.392942Z","shell.execute_reply":"2024-03-31T13:15:19.398133Z"},"trusted":true},"execution_count":18,"outputs":[]},{"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 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":"2024-03-31T13:14:47.615842Z","iopub.execute_input":"2024-03-31T13:14:47.616262Z","iopub.status.idle":"2024-03-31T13:14:47.631969Z","shell.execute_reply.started":"2024-03-31T13:14:47.616231Z","shell.execute_reply":"2024-03-31T13:14:47.630933Z"},"trusted":true},"execution_count":11,"outputs":[]},{"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 = 1.5 # carrier phase jump threshold [m] ** 2.0 -> 1.5 **\n    pr_th =  20.0 # pseudorange jump threshold [m]\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":"2024-03-31T13:14:49.268336Z","iopub.execute_input":"2024-03-31T13:14:49.269439Z","iopub.status.idle":"2024-03-31T13:14:49.282255Z","shell.execute_reply.started":"2024-03-31T13:14:49.269403Z","shell.execute_reply":"2024-03-31T13:14:49.281199Z"},"trusted":true},"execution_count":12,"outputs":[]},{"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":"2024-03-31T13:14:49.809873Z","iopub.execute_input":"2024-03-31T13:14:49.81027Z","iopub.status.idle":"2024-03-31T13:14:49.817873Z","shell.execute_reply.started":"2024-03-31T13:14:49.81024Z","shell.execute_reply":"2024-03-31T13:14:49.816484Z"},"trusted":true},"execution_count":13,"outputs":[]},{"cell_type":"code","source":"# GNSS single point positioning using pseudorange\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    cov_x = np.full([nepoch, 3, 3], np.nan) # For saving position covariance\n    cov_v = np.full([nepoch, 3, 3], np.nan) # For saving velocity covariance\n\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        # 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                # Covariance estimation\n                cov = np.linalg.inv(opt.jac.T @ Wx @ opt.jac)\n                cov_x[i, :, :] = cov[:3, :3]\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                # Covariance estimation\n                cov = np.linalg.inv(opt.jac.T @ Wv @ opt.jac)\n                cov_v[i, :, :] = cov[:3, :3]\n                v_wls[i, :] = opt.x[:3]\n                v0 = opt.x\n\n    return utcTimeMillis, x_wls, v_wls, cov_x, cov_v","metadata":{"execution":{"iopub.status.busy":"2024-03-31T13:14:50.21277Z","iopub.execute_input":"2024-03-31T13:14:50.213177Z","iopub.status.idle":"2024-03-31T13:14:50.23557Z","shell.execute_reply.started":"2024-03-31T13:14:50.213147Z","shell.execute_reply":"2024-03-31T13:14:50.2344Z"},"trusted":true},"execution_count":14,"outputs":[]},{"cell_type":"code","source":"# Simple outlier detection and interpolation\ndef exclude_interpolate_outlier(x_wls, v_wls, cov_x, cov_v):\n    # Up velocity / height threshold\n    v_up_th = 2.6  # m/s  2.0 -> 2.6\n    height_th = 200.0 # m\n    v_out_sigma = 3.0 # m/s\n    x_out_sigma = 30.0 # m\n    \n    # Coordinate conversion\n    x_llh = np.array(pm.ecef2geodetic(x_wls[:, 0], x_wls[:, 1], x_wls[:, 2])).T\n    x_llh_mean = np.nanmean(x_llh, axis=0)\n    v_enu = np.array(pm.ecef2enuv(\n        v_wls[:, 0], v_wls[:, 1], v_wls[:, 2], x_llh_mean[0], x_llh_mean[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    idx_v_out |= np.isnan(v_enu[:, 2])\n    v_wls[idx_v_out, :] = np.nan\n    cov_v[idx_v_out] = v_out_sigma**2 * np.eye(3)\n    print(f'Number of velocity outliers {np.count_nonzero(idx_v_out)}')\n\n    # Height check\n    hmedian = np.nanmedian(x_llh[:, 2])\n    idx_x_out = np.abs(x_llh[:, 2] - hmedian) > height_th\n    idx_x_out |= np.isnan(x_llh[:, 2])\n    x_wls[idx_x_out, :] = np.nan\n    cov_x[idx_x_out] = x_out_sigma**2 * np.eye(3)\n    print(f'Number of position outliers {np.count_nonzero(idx_x_out)}')\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(), cov_x, cov_v","metadata":{"execution":{"iopub.status.busy":"2024-03-31T13:14:50.679917Z","iopub.execute_input":"2024-03-31T13:14:50.680319Z","iopub.status.idle":"2024-03-31T13:14:50.694815Z","shell.execute_reply.started":"2024-03-31T13:14:50.680285Z","shell.execute_reply":"2024-03-31T13:14:50.69351Z"},"trusted":true},"execution_count":15,"outputs":[]},{"cell_type":"code","source":"# Kalman filter\ndef Kalman_filter(zs, us, cov_zs, cov_us, phone):\n    # Parameters\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    H = np.eye(3)  # Measurement function\n\n    # Initial state and covariance\n    x = zs[0, :3].T  # State\n    P = 5.0**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        Q = cov_us[i] # Estimated WLS velocity covariance\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.inv(P))\n\n        # Update step\n        if d < sigma_mahalanobis:\n            R = cov_zs[i] # Estimated WLS position covariance\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 observation update is not 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, cov_x, cov_v, phone):\n    n, dim_x = x_wls.shape\n\n    # For some unknown reason, the speed estimation is wrong only for XiaomiMi8\n    # so the variance is increased\n    if phone == 'XiaomiMi8':\n        v_wls = np.vstack([(v_wls[:-1, :] + v_wls[1:, :])/2, np.zeros([1, 3])])\n        cov_v = 1000.0**2 * cov_v\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, cov_x, cov_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    cov_xf = np.flip(cov_x, axis=0)\n    cov_vf = np.flip(cov_v, axis=0)\n    x_b, P_b = Kalman_filter(np.flipud(x_wls), v, cov_xf, cov_vf, 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":"2024-03-31T13:14:51.246249Z","iopub.execute_input":"2024-03-31T13:14:51.246655Z","iopub.status.idle":"2024-03-31T13:14:51.267557Z","shell.execute_reply.started":"2024-03-31T13:14:51.246623Z","shell.execute_reply":"2024-03-31T13:14:51.266501Z"},"trusted":true},"execution_count":16,"outputs":[]},{"cell_type":"code","source":"# Target course/phone\npath = '/kaggle/input/smartphone-decimeter-2023/sdc2023/train/2021-03-16-19-00-us-ca-mtv-a/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# Point positioning\nutc, x_wls, v_wls, cov_x, cov_v = point_positioning(gnss_df)\n\n# Exclude velocity outliers\nx_wls, v_wls, cov_x, cov_v = exclude_interpolate_outlier(x_wls, v_wls, cov_x, cov_v)\n\n# Kalman smoothing\nx_kf, _, _ = Kalman_smoothing(x_wls, v_wls, cov_x, cov_v, phone)\n\n# Convert to latitude and longitude\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\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\n# Distance from ground truth\nvd_bl = vincenty_distance(llh_bl, llh_gt)\nvd_wls = vincenty_distance(llh_wls, llh_gt)\nvd_kf = vincenty_distance(llh_kf, llh_gt)\n\n# Score\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, :])\n\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]')\n\n# Plot distance error\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.legend()\nplt.grid()\nplt.ylim([0, 30])\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":"2024-03-31T13:22:43.242743Z","iopub.execute_input":"2024-03-31T13:22:43.243172Z","iopub.status.idle":"2024-03-31T13:24:24.512826Z","shell.execute_reply.started":"2024-03-31T13:22:43.243142Z","shell.execute_reply":"2024-03-31T13:24:24.511119Z"},"trusted":true},"execution_count":19,"outputs":[{"output_type":"display_data","data":{"text/plain":"  0%|          | 0/2092 [00:00<?, ?it/s]","application/vnd.jupyter.widget-view+json":{"version_major":2,"version_minor":0,"model_id":"77d000382fe545189c7794c4f3c66438"}},"metadata":{}},{"name":"stdout","text":"Number of velocity outliers 4\nNumber of position outliers 0\n","output_type":"stream"},{"traceback":["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m","\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)","Cell \u001b[0;32mIn[19], line 32\u001b[0m\n\u001b[1;32m     29\u001b[0m llh_gt \u001b[38;5;241m=\u001b[39m gt_df[[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mLatitudeDegrees\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mLongitudeDegrees\u001b[39m\u001b[38;5;124m'\u001b[39m]]\u001b[38;5;241m.\u001b[39mto_numpy()\n\u001b[1;32m     31\u001b[0m \u001b[38;5;66;03m# Distance from ground truth\u001b[39;00m\n\u001b[0;32m---> 32\u001b[0m vd_bl \u001b[38;5;241m=\u001b[39m \u001b[43mvincenty_distance\u001b[49m\u001b[43m(\u001b[49m\u001b[43mllh_bl\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mllh_gt\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     33\u001b[0m vd_wls \u001b[38;5;241m=\u001b[39m vincenty_distance(llh_wls, llh_gt)\n\u001b[1;32m     34\u001b[0m vd_kf \u001b[38;5;241m=\u001b[39m vincenty_distance(llh_kf, llh_gt)\n","Cell \u001b[0;32mIn[13], line 10\u001b[0m, in \u001b[0;36mvincenty_distance\u001b[0;34m(llh1, llh2)\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvincenty_distance\u001b[39m(llh1, llh2):\n\u001b[1;32m      3\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;124;03m    Args:\u001b[39;00m\n\u001b[1;32m      5\u001b[0m \u001b[38;5;124;03m        llh1 : [latitude,longitude] (deg)\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;124;03m        d : distance between llh1 and llh2 (m)\u001b[39;00m\n\u001b[1;32m      9\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m---> 10\u001b[0m     d, az \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray(\u001b[43mpmv\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvdist\u001b[49m\u001b[43m(\u001b[49m\u001b[43mllh1\u001b[49m\u001b[43m[\u001b[49m\u001b[43m:\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mllh1\u001b[49m\u001b[43m[\u001b[49m\u001b[43m:\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mllh2\u001b[49m\u001b[43m[\u001b[49m\u001b[43m:\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mllh2\u001b[49m\u001b[43m[\u001b[49m\u001b[43m:\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m)\n\u001b[1;32m     12\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m d\n","File \u001b[0;32m/opt/conda/lib/python3.10/site-packages/pymap3d/vincenty.py:157\u001b[0m, in \u001b[0;36mvdist\u001b[0;34m(Lat1, Lon1, Lat2, Lon2, ell, deg)\u001b[0m\n\u001b[1;32m    155\u001b[0m lon1 \u001b[38;5;241m=\u001b[39m lon1 \u001b[38;5;241m%\u001b[39m (\u001b[38;5;241m2\u001b[39m \u001b[38;5;241m*\u001b[39m pi)\n\u001b[1;32m    156\u001b[0m lon2 \u001b[38;5;241m=\u001b[39m lon2 \u001b[38;5;241m%\u001b[39m (\u001b[38;5;241m2\u001b[39m \u001b[38;5;241m*\u001b[39m pi)\n\u001b[0;32m--> 157\u001b[0m L \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mabs\u001b[39m(\u001b[43mlon2\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mlon1\u001b[49m)\n\u001b[1;32m    159\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m    160\u001b[0m     L[L \u001b[38;5;241m>\u001b[39m pi] \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m2\u001b[39m \u001b[38;5;241m*\u001b[39m pi \u001b[38;5;241m-\u001b[39m L[L \u001b[38;5;241m>\u001b[39m pi]\n","\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (2091,) (2092,) "],"ename":"ValueError","evalue":"operands could not be broadcast together with shapes (2091,) (2092,) ","output_type":"error"}]},{"cell_type":"code","source":"","metadata":{},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"","metadata":{},"execution_count":null,"outputs":[]},{"cell_type":"code","source":"","metadata":{},"execution_count":null,"outputs":[]}]}