Analysis and Modeling of Inertial Sensors Using Allan Variance

El‐Sheimy, Naser; Hou, Haiying; Niu, Xiaoji

doi:10.1109/tim.2007.908635

Cited by 724 publications

(421 citation statements)

References 10 publications

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“…The AV can be expressed in the frequency domain through the unique relationship between σ 2 y (τ ) and the Power Spectral Density (PSD) S yy (f ) of the intrinsic processes [23]:…”

Section: Allan Hadamard and Total Variance Techniquesmentioning

confidence: 99%

Constrained expectation-maximization algorithm for stochastic inertial error modeling: study of feasibility

Stebler¹,

Guerrier²,

Skaloud³

et al. 2011

Meas. Sci. Technol.

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Abstract. Stochastic modeling is a challenging task for low-cost sensors which errors can have complex spectral structures. This makes the tuning process of the INS/GNSS Kalman filter often sensitive and difficult. For example, first-order Gauss-Markov processes are very often used in inertial sensor models. But the estimation of their parameters is a non-trivial task if the error structure is mixed with other types of noises. Such estimation is often attempted by computing and analyzing Allan variance plots. This contribution demonstrates solving situations when the estimation of error parameters by graphical interpretation is rather difficult. The novel strategy performs direct estimation of these parameters by means of the Expectation-Maximization (EM) algorithm. The algorithm results are first analyzed with a critical and practical point of view using simulations with typically encountered error signals. These simulations show that the EM algorithm seems to perform better than the Allan variance and offers a procedure to estimate first-order Gauss-Markov processes mixed with other types of noises. At the same time, the conducted tests revealed limits of this approach that are related to the convergence and stability issues. Suggestions are given to circumvent or mitigate these problems when complexity of error structure is "reasonable". This work also highlights the fact that the suggested approach via EM algorithm and the Allan variance may not be able to estimate reasonably well parameters of complex error models, and shows the need for new estimation procedures to be developed in this context. Finally, an empirical scenario is presented to support the former findings. There, the positive effect of using the more sophisticated EM-based error modeling on a filtered trajectory is highlighted.

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“…The AV can be expressed in the frequency domain through the unique relationship between σ 2 y (τ ) and the Power Spectral Density (PSD) S yy (f ) of the intrinsic processes [23]:…”

Section: Allan Hadamard and Total Variance Techniquesmentioning

confidence: 99%

Constrained expectation-maximization algorithm for stochastic inertial error modeling: study of feasibility

Stebler¹,

Guerrier²,

Skaloud³

et al. 2011

Meas. Sci. Technol.

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“…Optimization of interface circuitry design will further reduce flicker noise in the system and provide a lower bias instability floor. In addition to random noise errors, deterministic errors due to environmental factors such as linear vibrations and temperature variations will cause a drift rate ramp 24 , which may prevent the gyroscope from reaching the actual bias instability floor. With high-stiffness designs having high resonance frequencies, effects of linear vibrations will be suppressed 4 .…”

Section: Gyroscope Performance Characterizationmentioning

confidence: 99%

Resonant pitch and roll silicon gyroscopes with sub-micron-gap slanted electrodes: Breaking the barrier toward high-performance monolithic inertial measurement units

2017

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This paper presents the design, fabrication, and characterization of a novel high quality factor (Q) resonant pitch/roll gyroscope implemented in a 40 μm (100) silicon-on-insulator (SOI) substrate without using the deep reactive-ion etching (DRIE) process. The featured silicon gyroscope has a mode-matched operating frequency of 200 kHz and is the first out-of-plane pitch/roll gyroscope with electrostatic quadrature tuning capability to fully compensate for fabrication non-idealities and variation in SOI thickness. The quadrature tuning is enabled by slanted electrodes with sub-micron capacitive gaps along the (111) plane created by an anisotropic wet etching. The quadrature cancellation enables a 20-fold improvement in the scale factor for a typical fabricated device. Noise measurement of quadrature-cancelled mode-matched devices shows an angle random walk (ARW) of 0.63°√h − 1 and a bias instability of 37.7°h − 1 , partially limited by the noise of the interface electronics. The elimination of silicon DRIE in the anisotropically wet-etched gyroscope improves the gyroscope robustness against the process variation and reduces the fabrication costs. The use of a slanted electrode for quadrature tuning demonstrates an effective path to reach high-performance in future pitch and roll gyroscope designs for the implementation of single-chip high-precision inertial measurement units (IMUs).

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“…The first type of errors, such as cross-axis misalignment, scale factor, and non-linearity errors, can be determined by calibration before using the IMU for measurements, as suggested in [5]. Stochastic error sources can be quantified by using a time domain analysis technique called Allan variance (AV) or a frequency domain analysis using power spectral decomposition (PSD) analysis [6], [7].…”

Section: Inertial Measurement Unitsmentioning

confidence: 99%

“…It has been successfully applied to model the different measurement errors in rate gyroscope and accelerometer measurements [6]. More details about Allan variance can be found in [9], [10].…”

Section: Inertial Measurement Unitsmentioning

confidence: 99%