IMU Simulation

This is the foundational, noise-free model that calculates the true kinematic quantities based on the simulated robot's state. It provides the ground-truth linear acceleration and angular velocity that a perfect sensor would measure.

• Inputs: The simulated robot's precise position, orientation, and their derivatives from the physics engine.
• Outputs: Perfect linear acceleration vector (in the sensor's local frame, excluding gravity) and perfect angular velocity vector.
• Purpose: Serves as the baseline signal before the application of error models. It is the reference against which sensor fusion algorithms in the real system are ultimately trying to converge.

Bias represents a constant offset error in the sensor's output. In simulation, bias is modeled to be time-varying and temperature-dependent, mimicking real hardware imperfections.

• Types: Includes turn-on bias (random constant per simulation run), in-run bias (slow drift over time), and temperature-dependent bias.
• Modeling: Often implemented as a random walk process or a first-order Gauss-Markov process. For example: bias_{t+1} = bias_t + random_noise.
• Impact: A primary source of drift in dead-reckoning; simulation must inject this to train estimators (like Kalman filters) to identify and compensate for it.

This component adds random, high-frequency error to the ideal signal. The noise is typically characterized by its statistical properties, most commonly as Additive White Gaussian Noise (AWGN) or correlated noise.

• Angle Random Walk (Gyro) / Velocity Random Walk (Accel): The fundamental noise specification, defining the standard deviation of the noise per root Hertz. It is the dominant source of short-term uncertainty.
• Power Spectral Density (PSD): Used to define the frequency distribution of the noise. White noise has a flat PSD.
• Implementation: Noise is sampled from a Gaussian distribution N(0, σ²) where σ is derived from the sensor's datasheet noise density and the simulation timestep.

These are deterministic error models representing imperfections in the sensor's manufacturing. They transform the true kinematic vector into the sensor's reported measurement through a linear transformation.

• Scale Factor Error: A multiplicative error. A true angular velocity of 10 rad/s might be reported as 10.1 rad/s (1% scale error).
• Misalignment (Cross-Axis Sensitivity): The axes of the sensor are not perfectly orthogonal. Acceleration along the X-axis may cause a small, erroneous reading on the Y-axis.
• Composite Model: Often combined into a single 3x3 transformation matrix applied to the true kinematic vector: measurement = (I + M + S) * truth, where M is the misalignment matrix and S is a diagonal scale factor matrix.

High-fidelity models simulate how sensor performance degrades or varies with operating conditions, which is critical for systems deployed in non-laboratory environments.

• Temperature-Dependent Bias: The sensor's bias offset changes as its internal temperature changes, following a characterized curve.
• Noise Variation: The magnitude of stochastic noise (Angle Random Walk) may increase at temperature extremes.
• Scale Factor Drift: The scaling factor between input and output can also vary with temperature.
• Use Case: Essential for simulating long-duration missions or outdoor robotics where ambient temperature is not controlled.

This component enforces the physical limits of the simulated sensor, ensuring synthetic data respects the manufacturer's specifications for maximum measurable values.

• Saturation: Any true kinematic value exceeding the sensor's Full-Scale Range (FSR) is clipped to the maximum (or minimum) reportable value. For example, an accelerometer with a ±16g range will output 16g for any true acceleration ≥ 16g.
• Dynamic Range: The ratio between the largest and smallest measurable signal. This implicitly models the sensor's resolution.
• Importance: Prevents simulation from generating physically impossible data and tests the robustness of control algorithms to sensor saturation events.