A New Approach to Better Low-Cost MEMS IMU Performance Using Sensor Arrays

Over the past decade and a half, the combination of low-cost, lightweight micro-electro-mechanical sensors (MEMS) technology and multisensor integration has enabled inertial sensors to be deployed over a much wider range of navigation applications [1]. Examples include pedestrian dead-reckoning using step detection technology [2, 3], aiding of GNSS signal tracking during jamming [4, 5], and simultaneous localisation and mapping (SLAM) using radio signals [6]. However, for best performance, a MEMS inertial measurement unit (IMU) must be calibrated in the laboratory prior to use, which increases the cost by more than $1000 per unit. In this paper, we examine and present a range of techniques which use an array of inexpensive MEMS sensors to improve the performance of a MEMS IMU without requiring a full calibration prior to use. As the cost of calibration of a high-performance MEMS IMU far outweighs the cost of the hardware, there is considerable scope to improve the performance by adding additional sensors, before the cost of the IMU reaches that of a laboratory calibrated equivalent. Combining MEMS IMUs in an array has been studied before. However, the most common approach was simply to take an average of the input of several identical sensors [7]. If the sensor errors were independent, this could be expected to improve performance by a factor of root-n where, n is the number of IMUs combined. In this paper more sophisticated techniques are investigated that use knowledge of the sensor characteristics to obtain better performance. Three different properties of MEMS sensors may potentially be exploited: 1) The common-mode errors of different sensors of the same design; 2) The different characteristics of in-plane and out-of-plane sensors; and 3) The complementary properties of MEMS sensors with different dynamic ranges. In [8], it is shown that different individual sensors of the same design exhibit similar bias variation with temperature and that improved accuracy may be obtained by differencing the outputs of two gyroscopes mounted with their sensitive axes in opposing directions. Here, this approach will be independently verified and the performance benefits assessed with a range of different MEMS accelerometers and gyros, including Bosch BMA180 accelerometers, Analogue Devices ADXL345 accelerometers, ST Microtronics L3G4200D gyroscopes. Preliminary indications are that there is considerable common bias variation with temperature for the in-plane sensors of L3G4200D gyroscopes, and some common mode behaviour for the low-cost accelerometers. The second idea presented is exploiting the differences between the in-plane and out-of-plane axis outputs of single-chip inertial sensor triads, to improve the performance of an array-based IMU. Early experiment s point to considerable differences between the two which could markedly affect navigation performance. Both accelerometer and gyro triads can exhibit smaller errors from the in-plane sensors than from the out-of-plane sensors. Therefore, experiments were conducted using mutually-perpendicular arrays of accelerometer and gyro triads to determine whether better performance could be obtained using only the in-plane sensors. The third idea is to combine the outputs of MEMS sensors with different dynamic ranges to exploit the lower noise exhibited by some lower-dynamic-range sensors compared to their higher-dynamic-range counterparts. The sensor outputs are thus weighted according to the platform dynamics. That is, predominantly using the high-precision sensor when dynamics are low and using the full-range sensor when the dynamics are high. Several versions of this weighted signal combination will be presented and compared. Early indications are that there can be a significant benefit in this approach for some sensor designs, but not others. Finally, this paper will also examine the efficacy of a once-only static calibration on purchase, performed by the user instead of the supplier, for improving navigation performance. It is essential for a user-performed calibration that the physical movements required of the sensor are very simple and easily understood and completed, even if the underlying method is complex. To this end data, recorded on different days from an array of MEMS sensors within a precisely manufactured rapid prototyped ‘calibration cube’, will be analysed. These measurements are taken at precisely orthogonal angles of the cubes six faces, and allow the scale factor errors, biases and axes alignments of the accelerometers to be determined. The computed calibration corrections over several days will be compared to enable the efficacy of the one-time calibration technique to be assessed. The development of a full calibration routine will be the subject of future research. In summary, this paper will present several new methods for utilising the output of an array of low-cost sensors to improve the performance of a MEMS IMU, and also expands on methods proposed in existing research. As uncalibrated MEMS IMUs are of low performance there is a great potential for new applications if the performance can be improved closer to the level of those which are factory calibrated. / References [1] Groves, P. D., Principles of GNSS, inertial, and multi-sensor integrated navigation systems, Second Edition, Artech House, 2013. [2] Gustafson, D., J. Dowdle, and K. Flueckiger, “A Deeply Integrated Adaptive GPS-Based Navigator with Extended Range Code Tracking,” Proc. IEEE PLANS 2000. [3] Groves, P. D., C. J. Mather and A. A. Macaulay, “Demonstration of Non-Coherent Deep INS/GPS Integration for Optimized Signal to Noise Performance,” Proc. ION GNSS 2007. [4] Ma, Y., W. Soehren, W. Hawkinson, and J. Syrstad, "An Enhanced Prototype Personal Inertial Navigation System," Proc. ION GNSS 2012. [5] Groves, P. D., et al., “Inertial Navigation Versus Pedestrian Dead Reckoning: Optimizing the Integration,” Proc. ION GNSS 2007. [6] Faragher, R. M., C. Sarno, and M. Newman, “Opportunistic Radio SLAM for Indoor Navigation using Smartphone Sensors,” Proc. IEEE/ION PLANS 2012. [7] Bancroft, J. B., and G. Lachapelle, “Data fusion algorithms for multiple inertial measurement units,” Sensors, Vol. 11, No. 7, 2011, pp. 6771-6798. [8] Yuksel, Y., N. El-Sheimy, N., and A. Noureldin, “Error modelling and characterization of environmental effects for low cost inertial MEMS units,” Proc. IEEE/ION PLANS 2010

NAM: Non-Adversarial Unsupervised Domain Mapping

Several methods were recently proposed for the task of translating images between domains without prior knowledge in the form of correspondences. The existing methods apply adversarial learning to ensure that the distribution of the mapped source domain is indistinguishable from the target domain, which suffers from known stability issues. In addition, most methods rely heavily on `cycle' relationships between the domains, which enforce a one-to-one mapping. In this work, we introduce an alternative method: Non-Adversarial Mapping (NAM), which separates the task of target domain generative modeling from the cross-domain mapping task. NAM relies on a pre-trained generative model of the target domain, and aligns each source image with an image synthesized from the target domain, while jointly optimizing the domain mapping function. It has several key advantages: higher quality and resolution image translations, simpler and more stable training and reusable target models. Extensive experiments are presented validating the advantages of our method.Comment: ECCV 201

Post-critical set and non existence of preserved meromorphic two-forms

We present a family of birational transformations in $CP_2$ depending on two, or three, parameters which does not, generically, preserve meromorphic two-forms. With the introduction of the orbit of the critical set (vanishing condition of the Jacobian), also called ``post-critical set'', we get some new structures, some "non-analytic" two-form which reduce to meromorphic two-forms for particular subvarieties in the parameter space. On these subvarieties, the iterates of the critical set have a polynomial growth in the \emph{degrees of the parameters}, while one has an exponential growth out of these subspaces. The analysis of our birational transformation in $CP_2$ is first carried out using Diller-Favre criterion in order to find the complexity reduction of the mapping. The integrable cases are found. The identification between the complexity growth and the topological entropy is, one more time, verified. We perform plots of the post-critical set, as well as calculations of Lyapunov exponents for many orbits, confirming that generically no meromorphic two-form can be preserved for this mapping. These birational transformations in $CP_2$, which, generically, do not preserve any meromorphic two-form, are extremely similar to other birational transformations we previously studied, which do preserve meromorphic two-forms. We note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned, but drastically different results as far as a more ``probabilistic'' approach of dynamical systems is concerned (Lyapunov exponents). With these examples we see that the existence of a preserved meromorphic two-form explains most of the (numerical) discrepancy between the topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure