Simple gyro¶

In this example, a simulated gyro measures a sinusoidal input.

This is the simplest example of gyro simulation in InertialSim. The input is analytically specified and Earth's rotation is ignored.

Create and visualize the input¶

First we create and visualize the input. It is a Vector type that represents the angular rate experienced by the simulated gyro. The input must always be 3-axis, regardless of the number of axes of the simulated sensor. In this example we first simulate a single axis gyro, then a 3-axis gyro.

# -----------------------------------------------------------------------------
# Copyright (c) 2023-2025, Inertial Simulation LLC.
# All rights reserved.
# Do not use or redistribute without permission.
# Email: info@inertialsim.com
# -----------------------------------------------------------------------------
%matplotlib widget

import numpy as np

from inertialsim import plot
from inertialsim.geometry import Vector
from inertialsim.time import span

# Create a time 0:60s time vector sampled at 10Hz
time = span(start=0.0, end=60.0, dt=0.1)

# Create a 3-axis sinusoidal signal with arbitrary frequency and phase.
# Inputs must always be 3-axis.  Set them to zero if needed.
angular_rate = np.zeros((time.size, 3, 1))
angular_rate[:, 0:1] = 0.001 * time - 0.02 * np.sin(0.3 * time) + 0.02
angular_rate[:, 1:2] = -0.002 * time + 0.015 * np.sin(-0.15 * time)
angular_rate[:, 2:3] = 0.0015 * time - 0.03 * np.sin(0.05 * time)
rate_vector = Vector.from_xyz(angular_rate, time)

# Plot the input
rate_plot = plot.TimeSeries(title="Input Angular Rate", ylabel="Angular Rate (rad/s)")
rate_plot.line(time, angular_rate, xlimits=[0, 60])
rate_plot.legend(["X", "Y", "Z"])

Simulate an ideal gyro measuring the input¶

Next we simulate an ideal single-axis gyro measuring the input. An ideal gyro is one with no sources of error. By default, a single-axis sensor will measure the x-axis input but this can be modified as shown below. In this case we simulate a gyro that is sensitive only along the y-axis input.

from inertialsim.sensors import Parameter, SensorModel
from inertialsim.sensors.gyro import Gyro, GyroSpecification

# Create a gyro model and keep the input sampling rate (10Hz) rather than using
# the Analog Devices sampling rate (125Hz).
model = SensorModel()
model.data_interface.simulate_sample_rate = False

# Create the single-axis gyro with a sensitive axis along the y input reference
# axis.
specification = GyroSpecification(axes=1)
specification.misalignment.fixed = Parameter([0, 1, 0], "dimensionless")

gyro = Gyro(model, specification, rng=0)
result = gyro.simulate(angular_rate=rate_vector)

# Plot the gyro measurements
rate_plot = plot.TimeSeries(title="Gyro Measurements", ylabel="Angular Rate (rad/s)")
rate_plot.line(time, result.angular_rate.data, xlimits=[0, 60], color="#4CAF50")
rate_plot.zoom_inset([0.7, 0.4, 0.25, 0.25], [39, 41], [-0.08, -0.07])

As can be seen, the measured output matches the y-axis input exactly.

Simulate a realistic gyro¶

Next we create a realistic gyro using the Analog Devices ADIS16495 specification from the InertialSim devices library. It is a 3-axis sensor. By default axes have a one-to-one alignment with the input. In this case, each axis has the same performance specifications but this is not always the case.

from inertialsim.devices import analog_devices_adis16495

# Create a gyro model and keep the input sampling rate (10Hz) rather than using
# the Analog Devices sampling rate (125Hz).
model = SensorModel()
model.data_interface.simulate_sample_rate = False

# Create the gyro and simulate the output
gyro = Gyro(model, specification=analog_devices_adis16495, rng=3)
result = gyro.simulate(angular_rate=rate_vector)

# Plot the gyro measurements
rate_plot = plot.TimeSeries(title="Gyro Measurements", ylabel="Angular Rate (rad/s)")
rate_plot.line(time, result.angular_rate.data, xlimits=[0, 60])
rate_plot.zoom_inset([0.7, 0.4, 0.25, 0.25], [39, 41], [-0.08, -0.07])
rate_plot.legend(["X", "Y", "Z"])

# Plot the error in measuring the input.  More precise error data can also be
# found in the result.metadata fields.
error_plot = plot.TimeSeries(title="Gyro Errors", ylabel="Angular Rate Error (rad/s)")
error_plot.line(time, result.angular_rate.data - angular_rate, xlimits=[0, 60])
error_plot.legend(["X", "Y", "Z"])
error_plot.figure.set_layout_engine("tight")

Analyzing the result¶

The angular rate errors display the expected trends given the Analog Devices ADIS16495 specification. Random noise, bias (zero-offset), and drift are all observed. The total error is a superposition of deterministic and random components so running the simulation again (with a different rng input) will produce different results.