Angular Random Walk (ARW) es un tipo de error que afecta a los giroscopios y, por extensión, a los sistemas de navegación inercial (INS). Se refiere a las fluctuaciones aleatorias en la la velocidad angular proporcionada por un giroscopio, lo que hace que la orientación angular (por ejemplo, balanceo, cabeceo y guiñada) se desvíe gradualmente con el tiempo.
Características clave del paseo aleatorio angular (ARW):
- Naturaleza aleatoria:
- ARW representa un ruido aleatorio que provoca cambios pequeños e impredecibles en la salida del giroscopio. Este ruido a menudo se modela como un de caminata aleatoria , lo que significa que se acumula con el tiempo, lo que genera errores cada vez mayores en las mediciones angulares.
- Efecto sobre los giroscopios:
- En un sistema de navegación inercial, los giroscopios miden la velocidad angular (es decir, la rapidez con la que el objeto gira alrededor de sus ejes). ARW se manifiesta como un error inherente en esta medición de velocidad, lo que hace que la salida del giroscopio se desvíe ligeramente de manera impredecible, lo que resulta en la deriva acumulativa de las estimaciones de orientación (giro, cabeceo y guiñada).
- Impacto en la navegación inercial:
- Over time, the random fluctuations in angular velocity lead to increasing errors in the calculated orientation (attitude). While the error in angular velocity is small at any given moment, it accumulates over time, leading to progressively larger deviations in the system’s attitude and heading estimates.
- This effect is particularly significant in applications requiring long-duration operations where the inertial system has no external corrections (e.g., GPS or other reference systems).
- Statistical Model:
- ARW is typically described by a power spectral density function, often with units of degrees per square root hour (°/√hr) or radians per square root hour (rad/√hr). This quantifies the rate of angular drift in terms of random noise.
- The error due to ARW increases with the square root of time. In other words, the longer the system operates without correction, the larger the accumulated error.
- Formula Representation:
- ARW can be represented as a random walk of the gyroscope’s angular velocity, where the angular error at time t is proportional to the square root of time. In simple terms, the error grows as:
θ(t) = √(KARW · t)
Where:
- θ(t) is the angular error at time t,
- KARW is a constant that characterizes the magnitude of the ARW noise.
Sources of Angular Random Walk:
- Gyroscope Biases: Imperfections in the gyroscope sensors themselves, such as bias instability or noise in the sensor electronics.
- Environmental Factors: Temperature fluctuations, mechanical vibrations, and other environmental conditions can exacerbate the random noise.
- Manufacturing Variability: Differences in the quality of sensors between units can lead to varying levels of ARW.
Implications for Inertial Navigation:
- Short-Term vs. Long-Term Navigation: In the short term, ARW might not significantly affect the navigation accuracy. However, over extended periods without external correction (like GPS), the accumulation of errors from ARW can lead to significant drift in the system’s attitude and heading.
- Correction Methods: To mitigate ARW’s impact, inertial navigation systems often employ techniques like:
- Kalman Filtering: Integrating the measurements from multiple sensors (such as accelerometers and GPS) to correct the accumulated drift.
- Sensor Fusion: Combining data from gyroscopes with other reference systems (such as GPS, magnetometers, or visual sensors) to reduce the impact of ARW on the system’s accuracy.
Conclusion:
Inertial navigation systems rely heavily on gyroscopes to measure rotational movements, and angular random walk is a critical factor that describes the random fluctuations in these measurements over time. The errors induced by ARW accumulate as a square root of time, leading to gradual orientation drift. This drift can be compensated by using advanced sensor fusion techniques, calibration, and high-quality gyroscopes.
