filters.als_tpu

A PDAL filter to generate per-point total propagated uncertainty (TPU) for airborne laser scanning (ALS) point clouds when supplied:

1. An ALS point cloud of a single flightline
2. A trajectory for the flightline.
3. A JSON file containing sensor measurement standard deviations (uncertainties).

The generated TPU consists of 3x3 covariance matrix elements added as extra dimensions to each point: x, y, and z variances (diagonal elements) and xy, xz, and yz covariances (symmetric off-diagonal elements).

The filter is only applicable to data generated by ALS systems with oscillating (sawtooth ground pattern) or rotating (parallel line ground pattern) mirrors.

Generic Pipeline Example

[
    {
        "type": "readers.las",
        "filename": "my-flightline.laz",
        "tag": "cloud"
    },
    {
        "type": "readers.sbet",
        "filename": "my-flightline-trajectory.sbet",
        "tag": "trajectory"
    },
    {
        "type": "filters.als_tpu",
        "uncertainty_file": "my-sensor-uncertainties.json",
        "inputs": [
            "cloud",
            "trajectory"
        ],
        "extended_output": "true"
    },
    {
        "type": "writers.las",
        "minor_version": 4,
        "extra_dims": "all",
        "filename": "my-flightline-tpu.laz"
    }
]

Generic JSON Measurement Uncertainty Example

Sensor measurement uncertainties (measurement standard devations and laser beam divergence) must be supplied in a JSON file. The angular values must be given in degrees, linear units in meters, and laser beam divergence must use the 1/e^2 definition and be given in milliradians. The filter only uses the name and value keys in the uncertainties array; the remaining keys are an optional means to document the provenance of the uncertainty values.

{
    "system": "Make and model of my ALS laser scanner and inertial navigation system",
    "uncertainties": [
        {
            "name": "std_lidar_range",
            "source": "My laser scanner datasheet",
            "value": 0.008
        },
        {
            "name": "std_scan_angle",
            "source": "my laser scanner datasheet",
            "value": 0.001
        },
        {
            "name": "std_sensor_xy",
            "source": "my inertial navigation system datasheet",
            "value": 0.01
        },
        {
            "name": "std_sensor_z",
            "source": "my inertial navigation system datasheet",
            "value": 0.02
        },
        {
            "name": "std_sensor_rollpitch",
            "source": "my inertial navigation system datasheet",
            "value": 0.005
        },
        {
            "name": "std_sensor_yaw",
            "source": "my inertial navigation system datasheet",
            "value": 0.007
        },
        {
            "name": "std_bore_rollpitch",
            "source": "my survey metadata, rule of thumb, or custom source",
            "value": 0.001
        },
        {
            "name": "std_bore_yaw",
            "source": "my survey metadata, rule of thumb, or custom source",
            "value": 0.004
        },
        {
            "name": "std_lever_xyz",
            "source": "my survey metadata, rule of thumb, or custom source",
            "value": 0.02
        },
        {
            "name": "beam_divergence",
            "source": "my laser scanner datasheet",
            "value": 0.49
        }
    ]
}

Options

• include_inc_angle: Boolean flag to include the influence of the laser beam to ground incidence angle in the TPU. Requires normal vectors on each point (see filters.normal). [Default=true]

• max_inc_angle:: Maximum allowable incidence angle specified in degrees and less than 90 degrees. Incidence angles approaching 90 degrees will produce very large TPU values. [Default=85.0]

• no_data_value: Value to assign to TPU dimensions when trajectory information is not available. [Default=-1.0]]

• extended_output: Option to export inverted range and scan angle measurements, interpolated trajectory position and attitude values, and coordinate standard deviations (just the square root of the x, y, and z variances; a convenience). [Default=false]

Installation

Only tested on Linux via Windows WSL2 with a Conda environment.

Dependencies

1. PDAL (version 2.3.0)
   • Install into your Conda environment: conda install -c conda-forge pdal
   • Tell CMake to look inside the Conda environment for the PDAL package: conda env config vars set CMAKE_MODULE_PATH=${CONDA_PREFIX}
2. nlohmann's JSON library
   • Install into your Conda environment: conda install -c conda-forge nlohmann_json

Build and Install:

Clone this repository, navigate to the main directory, and:

mkdir build && cd build
cmake -D CMAKE_INSTALL_PREFIX=${CONDA_PREFIX} ..
cmake ..
make
sudo make install

Check that the plugin is installed:

$ pdal --drivers | grep als_tpu
filters.als_tpu              Per-point airborne lidar Total Propagated Uncertainty (TPU) via a generic sensor model

You can test the filter using the point cloud, trajectory, uncertainty JSON, and pipeline files provided in the test directory:

$ pdal pipeline test/pipeline/als_tpu.json

This will produce a file named 112-five-seconds-tpu.laz in the test/data directory that you can view in CloudCompare or other point cloud viewing software of your choice.

Additional Detail and Example Workflows

1. The general approach of the algorithm is reviewed here.
2. A technical document detailing the math and assumptions used in the algorithm in more depth is found here.
3. A complex example that starts with imperfect tiled LAS point cloud data from a triple channel ALS and works through the process of generating a clean set of LAZ tiles cropped to an area of interest and containing per-point TPU can be found here. A simpler example should be created as a first step for new users.

Tests

If there is interest in maintaining/updating this repository, tests (via GoogleTest, which PDAL uses) should be created. The test/data/112-one-scan-cycle.laz was initially created for this purpose.