Angular Random Walk (ARW) est un type d'erreur qui affecte les gyroscopes et, par extension, les systèmes de navigation inertielle (INS). Il fait référence aux fluctuations aléatoires de la la vitesse angulaire orientation angulaire du système (par exemple, roulis, tangage et lacet) au fil du temps.
Caractéristiques clés de la marche aléatoire angulaire (ARW) :
- Nature aléatoire:
- ARW représente un bruit aléatoire qui entraîne de petits changements imprévisibles dans la sortie du gyroscope. Ce bruit est souvent modélisé comme un de marche aléatoire , ce qui signifie qu'il s'accumule au fil du temps, conduisant à des erreurs de plus en plus importantes dans les mesures angulaires.
- Effet sur les gyroscopes:
- Dans un système de navigation inertielle, les gyroscopes mesurent le taux de vitesse angulaire (c'est-à-dire la vitesse à laquelle l'objet tourne autour de ses axes). ARW se manifeste comme une erreur inhérente à cette mesure de vitesse, provoquant une légère déviation de la sortie du gyroscope de manière imprévisible, entraînant une dérive cumulative des estimations d'orientation (roulis, tangage et lacet).
- Impact on Inertial Navigation:
- 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.
