Combining redundant inertial sensors to create a virtual sensor output
Included are embodiments for determining an inertial quantity. One embodiment of a method includes combining readings from a plurality of inertial sensors to produce an estimate of the value of an inertial quantity in a manner that is fault-tolerant, more accurate than traditional sensor arrangements, and able to handle non-linear and non-Gaussian systems. Embodiments of a method also include utilizing a Monte Carlo estimation-based inference system to adaptively combine the inertial sensor outputs into a fault-tolerant highly-accurate inertial quantity estimate, an axis-reversed-paired physical arrangement of inertial sensors to minimize effects of environmental and process noise, and cross-associating sensors to ensure good sensor associations and reduce the effects of sample impoverishment.
1. A method of determining an inertial quantity of a single physical system with linear, non-linear, Gaussian, or non-Gaussian characteristics or combinations thereof, the method comprising:
associating a plurality of angular rate sensor devices with a substrate of the single physical system;
acquiring inertial sensor data from the plurality of angular rate sensor devices;
utilizing a computing device for processing the inertial sensor data by application of a Monte Carlo estimation-based inference system configured to produce estimates in systems with linear, non-linear, Gaussian, and non-Gaussian characteristics, wherein the computing device produces a virtual connection between at least two of the plurality of angular rate sensor devices, resulting in a virtual sensor output value, the virtual sensor output value being of a degree of accuracy exceeding that which would otherwise be attributable to one of the single angular rate sensor devices, and wherein the Monte Carlo estimation-based inference system is selected dynamically from a set of Monte Carlo estimation-based inference systems based on a set of operating and performance characteristic criteria including algorithmic execution time or accuracy; and
utilizing the virtual sensor output value as at least part of a tangible indication of the inertial quantity.
2. The method of claim 1 , wherein the Monte Carlo estimation-based inference system comprises an Unscented Particle Filter, incorporating an Unscented Kalman Filter to perform predictions of time updates and measurement updates for each particle.
3. The method of claim 1 , wherein the computing device comprises a firmware controlled digital processor, a programmed portion of a digital software controlled computer, a logic circuit, or an application-specific integrated circuit for performing the recited function.
4. The method of claim 1 , wherein the Monte Carlo estimation-based inference system is an Unscented Particle Filter, configured to perform the following:
read initial inertial sensor data from the plurality of angular rate sensor devices;
establish an initial estimation of the initial inertial sensor data;
create a set of particles and establishing a position for each particle in the set of particles;
initialize a covariance matrix for an Unscented Kalman Filter for each particle;
execute an Unscented Particle Filter update process at least one time, comprising:
read current iteration of inertial sensor data from the plurality of angular rate sensor devices;
scatter particle positions for each particle by adding noise to them according to a probability density function which may be determined experimentally or may be based on noise characteristics of the angular rate sensor devices being used;
use an Unscented Kalman Filter to update the position for each particle further by way of prediction;
perform an importance sampling by assigning a weight to each particle based on the probability of the current iteration of inertial sensor data given that this particle's position is treated as a sensor data element;
normalize the importance weights of all particles with respect to the total of all particle importance weights:
apply selective-importance-resampling to the particles to adjust each particle's importance weighting by comparing each particle to the set of inertial sensor data obtained from the plurality of angular rate sensor devices;
generate the virtual sensor output value using an importance weighted sum of the particles; and
output the virtual sensor output value as a tangible indication of the inertial quantity.
5. The method of claim 1 , in which the Monte Carlo estimation-based inference system is a Particle Filter, Sampling Importance Resampling Filter, Auxiliary Particle Filter, Extended Kalman Particle Filter, Condensation Particle Filter, Ensemble Kalman Filter, or Markov Chain Monte Carlo process.
6. The method of claim 1 , wherein each individual angular rate sensor device of the plurality of angular rate sensor devices is a MEMS-based device.
7. The method of claim 1 wherein each individual angular rate sensor device of the plurality of angular rate sensor devices is a non-MEMS-based device.
8. The method of claim 1 , wherein the plurality of angular rate sensor devices is configured as one or more axis-reversed pairs of angular rate sensor devices positioned on the substrate.
9. A method of determining an inertial quantity of a single physical system with linear, non-linear, Gaussian, or non-Gaussian characteristics or combinations thereof, the method comprising:
associating a plurality of angular rate sensor devices with a substrate of the single physical system;
acquiring inertial sensor data from the plurality of angular rate sensor devices; and
utilizing a computing device for processing the inertial sensor data by application of a Monte Carlo estimation-based inference system configured to produce estimates in systems with linear, non-linear, Gaussian, and non-Gaussian characteristics, wherein the computing device produces a virtual sensor output value from the inertial sensor data of the plurality of angular rate sensor devices, and wherein the Monte Carlo estimation-based inference system is selected dynamically from a set of Monte Carlo estimation-based inference systems based on a set of operating and performance characteristic criteria including algorithmic execution time or accuracy.
10. The method of claim 9 , further comprising utilizing the virtual sensor output value as at least part of a tangible indication of the inertial quantity.
11. The method of claim 9 , wherein the Monte Carlo estimation-based inference system comprises an Unscented Particle Filter, incorporating an Unscented Kalman Filter to perform predictions of time updates and measurement updates for each particle.
12. The method of claim 9 , wherein the Monte Carlo estimation-based inference system is an Unscented Particle Filter, configured to perform the following:
read initial inertial sensor data from the plurality of angular rate sensor devices;
establish an initial estimation of the initial inertial sensor data;
create a set of particles and establishing a position for each particle in the set of particles;
initialize a covariance matrix for an Unscented Kalman Filter for each particle;
execute an Unscented Particle Filter update process at least one time, comprising:
read current iteration of inertial sensor data from the plurality of angular rate sensor devices;
scatter particle positions for each particle by adding noise to them according to a probability density function which may be determined experimentally or may be based on noise characteristics of the angular rate sensor devices being used;
use an Unscented Kalman Filter to update the position for each particle further by way of prediction;
perform an importance sampling by assigning a weight to each particle based on the probability of the current iteration of inertial sensor data given that this particle's position is treated as a sensor data element;
normalize the importance weights of all particles with respect to the total of all particle importance weights:
apply selective-importance-resampling to the particles to adjust each particle's importance weighting by comparing each particle to the set of inertial sensor data obtained from the plurality of angular rate sensor devices;
generate the virtual sensor output value using an importance weighted sum of the particles; and
output the virtual sensor output value as a tangible indication of the inertial quantity.
13. The method of claim 9 , in which the Monte Carlo estimation-based inference system is a Particle Filter, Sampling Importance Resampling Filter, Auxiliary Particle Filter, Extended Kalman Particle Filter, Condensation Particle Filter, Ensemble Kalman Filter, or Markov Chain Monte Carlo process.
14. The method of claim 9 , wherein each individual angular rate sensor device of the plurality of angular rate sensor devices is a MEMS-based device.
15. The method of claim 9 wherein each individual angular rate sensor device of the plurality of angular rate sensor devices is a non-MEMS-based device.
16. The method of claim 9 , wherein the plurality of angular rate sensor devices is configured as one or more axis-reversed pairs of angular rate sensor devices positioned on the substrate.