Trajectory usage

The examples in this section demonstrate how to use the trajectory interface to create and evaluate trajectories. These examples use the CubicSplineTrajectory implementation, that is the suggested default implementation.

Basic construction from state vectors

Creating a trajectory object from state vectors (time tagged sensor positions and velocities).

Trajectory from state vectors

import numpy as np

from perseo_core.geometry.navigation import CubicSplineTrajectory
from perseo_core.timing.precise_datetime import PreciseDateTime

# discrete state vectors 
time_axis_origin = PreciseDateTime.from_utc_string("13-FEB-2023 09:33:56.000000")
time_axis = np.arange(8) * 0.5 + time_axis_origin

positions = np.array(
    [
        [-2542286.449576481, -5094859.4894666, 3901083.7183820857],
        [-2542066.5079547316, -5092594.238796566, 3904175.2612526673],
        [-2541845.6347068036, -5090327.468904538, 3907265.6186505724],
        [-2541623.8297894364, -5088059.180544005, 3910354.7896390846],
        [-2541401.0931600337, -5085789.374468956, 3913442.7732819766],
        [-2541177.424776237, -5083518.051433686, 3916529.5686432645],
        [-2540952.8245959855, -5081245.212193193, 3919615.1747874315],
        [-2540727.2925774334, -5078970.857502782, 3922699.5907792132],
    ]
)

velocities = np.array(
    [
        [439, 4529, 6184],
        [440, 4532, 6181],
        [442, 4535, 6179],
        [444, 4538, 6177],
        [446, 4544, 6174],
        [448, 4547, 6172],
        [450, 4550, 6170],
        [452, 4552, 6167],
    ]
)

# create the trajectory
trajectory = CubicSplineTrajectory(
    times=time_axis,
    positions=positions,
    velocities=velocities
)

Evaluation

Once constructed, the trajectory can be evaluated at arbitrary times within its domain to retrieve position, velocity, and acceleration.

Evaluating trajectory components

# query at a single time point
query_time = 0.75 + time_axis_origin

# these evaluations return array with shape (3,)
position = trajectory.position(query_time)
velocity = trajectory.velocity(query_time)
acceleration = trajectory.acceleration(query_time)

# query at multiple time points
query_times = np.array([0.25, 0.5, 0.75, 1.0, 1.5]) + time_axis_origin

# these evaluations return array with shape (query_times.size, 3)
positions = trajectory.position(query_times)
velocities = trajectory.velocity(query_times)
accelerations = trajectory.acceleration(query_times)

Domain and Time Validation

Each trajectory has a defined time domain accessible via the domain property:

Checking trajectory domain

# Get the valid time range
domain_start, domain_end = trajectory.domain
print(f"Trajectory valid from {domain_start} to {domain_end}")

Extrapolation is forbidden

Attempting to evaluate the trajectory outside its defined domain will raise a RuntimeError:

Python

# This will raise RuntimeError - outside domain
trajectory.position(-1.0)  # Error: before start time
trajectory.position(3.0)   # Error: after end time

Use Cases

The trajectory object evaluated as shown in the previous section can be used to perform a variety of tasks:

it can be used to evaluate sensor positions and velocities at specific azimuth times for geocoding computations
it can be directly provided to functions to perform inverse geocoding operations, ground velocity computations, doppler computations, etc.

Here are some examples:

Indirect trajectory usage

from perseo_core.geometry.geocoding.direct import direct_geocoding_monostatic

query_times = np.array([0.5, 1.2, 2.8]) + time_axis_origin

ground_points = direct_geocoding_monostatic(
    sensor_positions=trajectory.position(query_times),
    sensor_velocities=trajectory.velocity(query_times),
    range_times=0.0036229998783991087,
    doppler_frequencies=0.0,
    wavelength=1.0,
    look_direction="RIGHT",
    altitude=0.0,
)

Direct trajectory usage

from perseo_core.geometry.geocoding.inverse import inverse_geocoding_monostatic

ground_points = np.array(
    [
        [-2244336.5269435 , -4736678.06390127,  3622022.95230392],
        [-2244084.37158288, -4733735.65581756,  3625996.93151137],
        [-2243501.43978246, -4726996.21905426,  3635077.07787725]
    ]
)

azimuth_times, range_times = inverse_geocoding_monostatic(
    trajectory=trajectory,
    ground_points=ground_points,
    doppler_frequencies=0,
    wavelength=1,
    az_initial_time_guesses=time_axis_origin,
)