Abstract
We present a filtering technique that allows estimating the time derivative of slowly changing temperature measured via quantized sensor output in real time. Due to quantization, the output may appear constant for several minutes in a row with the temperature actually changing over time. Another issue is that measurement errors do not represent any kind of white noise. Being typically the case in high-grade inertial navigation systems, these phenomena amid slow variations of temperature prevent any kind of straightforward assessment of its time derivative, which is required for compensating hysteresis-like thermal effects in inertial sensors. The method is based on a short-term temperature prediction represented by an exponentially decaying function, and on the finite-impulse-response Kalman filtering in its numerically stable square-root form, employed for estimating model parameters in real time. Instead of using all of the measurements, the estimation involves only those received when quantized sensor output is updated. We compare the technique against both an ordinary averaging numerical differentiator and a conventional Kalman filter, over a set of real samples recorded from the inertial unit.
Highlights
In inertial measurement units (IMU) of navigation grade, thermal effects usually have a substantial impact on inertial sensor errors
We suggest using a technique relying on the physical nature of the internal thermal processes taking place inside the IMU, employing Kalman filtering [3] to optimize their model parameters in real time
Since the second sample comes from the more thermally dynamic interior of an accelerometer, where the heating rate reaches its peak twice faster than in the record from a ring laser gyroscope, the above values were appropriately adjusted to be 3 and 2 min, respectively. Their temperature time derivative estimates overlay the reference within a tolerable margin, having an apparent few-minute phase delay when the slope changes too fast, which seems to be unavoidable to a certain extent
Summary
In inertial measurement units (IMU) of navigation grade, thermal effects usually have a substantial impact on inertial sensor errors. To compensate (see [2]) for the described effects, apart from an appropriate model, we need an actual value of the rate at which the temperature changes. Obtaining this value, becomes a challenge in such devices, due to the combination of several issues commonly inherent to inertial systems of navigation grade. Prior to coming to real time filtering, let us first consider the background description of thermal processes in inertial measurement units [5].
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