A proposed method of processing the outputs of multiple gyroscopes to increase the accuracy of rate (that is, angular- velocity) readings has been developed theoretically and demonstrated by computer simulation. Although the method is applicable, in principle, to any gyroscopes, it is intended especially for application to gyroscopes that are parts of microelectromechanical systems (MEMS). The method is based on the concept that the collective performance of multiple, relatively inexpensive, nominally identical devices can be better than that of one of the devices considered by itself. The method would make it possible to synthesize the readings of a single, more accurate gyroscope (a “virtual gyroscope”) from the outputs of a large number of microscopic gyroscopes fabricated together on a single MEMS chip. The big advantage would be that the combination of the MEMS gyroscope array and the processing circuitry needed to implement the method would be smaller, lighter in weight, and less power-hungry, relative to a conventional gyroscope of equal accuracy.

Readings From Multiple Gyroscopes would be combined by use of an optimal (minimum-variance) filter, thereby synthesizing the readings of what amounts to a more accurate virtual gyroscope.
The method (see figure) is one of combining and filtering the digitized outputs of multiple gyroscopes to obtain minimum-variance estimates of rate. In the combining-and-filtering operations, measurement data from the gyroscopes would be weighted and smoothed with respect to each other according to the gain matrix of a minimum-variance filter. According to Kalman-filter theory, the gain matrix of the minimum-variance filter is uniquely specified by the filter covariance, which propagates according to a matrix Riccati equation. The present method incorporates an exact analytical solution of this equation.

The analytical solution reveals a wealth of theoretical properties and enables the consideration of several practical implementations. Among the most notable theoretical properties are the following:

  • Even though the terms of the Riccati equation grow in an unbounded fashion, the Kalman gain can be shown to approach a steady-state matrix. This result is fortuitous because it simplifies implementation and can serve as a basis of practical schemes for realizing the optimal filter by use of a constant- gain matrix.
  • The analytical solution enables the development of a complete statistical theory that characterizes the drift of the virtual gyroscope and provides theoretical limits of improvement obtainable by use of an ensemble of correlated sensors as a single virtual sensor.
  • The minimum-variance gain matrix has been analyzed in detail. The structure of the gain matrix indicates the presence of a marginally unstable pole, which would make implementation impossible if it were not properly understood and compensated. In addition, a simple algebraic method for computing the optimal gain matrix has been developed, making it possible to avoid the Riccati equation completely.
  • The notion of statistical commonmode rejection (CMR) has been characterized mathematically. For statistically uncorrelated gyroscopes, it is shown that the component drift variances add like parallel resistors (e.g., in units of rad2/sec3). For identical devices, this means that the combined drift is reduced by a factor of 1√N compared to the individual gyroscope drift, where N is the number of gyroscopes being combined.
  • Potential improvement in drift is much more impressive when the devices are correlated. For correlated gyroscopes, an exact mathematical expression is developed for the combined drift. The expression indicates that the internal noise sources count to the extent that they infect multiple devices coherently (e.g., with common sign), and can be removed to the extent that they infect multiple devices incoherently (e.g., with randomized signs). Noise eliminated by correlations between devices can potentially reduce the virtual gyroscope drift far beyond the 1√N factor attainable using uncorrelated devices.

This work was done by David S. Bayard of Caltech for NASA’s Jet Propulsion Laboratory.

In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to

Intellectual Assets Office JPL Mail Stop 202-233 4800 Oak Grove Drive Pasadena, CA 91109 (818) 354-2240 E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Refer to NPO-30533, volume and number of this NASA Tech Briefs issue, and the page number.

Topics:
Analysis methodologies Computer simulation Information Technology Microelectromechanical devices Motion Control Noise Sensors and actuators Simulation and modeling Statistical analysis
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Combining Multiple Gyroscope Outputs for Increased Accuracy

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Motion Control Tech Briefs Magazine

This article first appeared in the June, 2003 issue of Motion Control Tech Briefs Magazine (Vol. 27 No. 6).

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Overview

The document is a technical report prepared under the sponsorship of NASA, focusing on the development of high-accuracy inertial sensors using inexpensive components, particularly Microelectromechanical Systems (MEMS) gyroscopes. Authored by David S. Bayard and Scott R. Ploen from the Jet Propulsion Laboratory (JPL), the report outlines the need for small, lightweight, and low-power inertial sensing devices to support various future NASA missions, including Mars landings, rendezvous and docking, and other complex navigation tasks.

The primary objective of the research is to address the limitations of current MEMS devices, which, despite their advantages in size and power consumption, exhibit low-grade performance that cannot compete with established high-accuracy sensors. The report presents a systematic method for combining multiple MEMS gyroscopes to enhance their collective performance, potentially surpassing that of any single device. This approach leverages the principle that the performance of multiple correlated devices can be improved through analytical combination, akin to how parallel resistors function in electrical circuits.

The document details a theoretical framework for an optimal minimum variance method that filters and combines measurements from multiple gyroscopes. This method produces a "virtual gyro," which provides a more accurate rate estimate than individual sensors. The report emphasizes that by utilizing the collective behavior of numerous MEMS devices, it is possible to offset the deficiencies of single-device performance, making MEMS technology a viable option for high-accuracy applications in future NASA missions.

Additionally, the report includes a notice that references to specific commercial products or manufacturers do not imply endorsement by the U.S. Government or JPL. The work is positioned as a significant advancement in the field of inertial navigation, with the potential to reduce mass and power requirements in emerging low-cost microspacecraft missions.

In summary, this document highlights a novel approach to improving inertial sensing technology through the innovative use of MEMS gyroscopes, paving the way for enhanced navigation capabilities in space exploration and other applications.