Method of providing relatively accurate position data for a position-reliant device based on output of an inertial measurement unit and position-reliant devices incorporating same

Abstract

The disclosure provides a position-reliant device and method of providing relatively accurate position data to a position-reliant device using an inertial measurement unit (IMU) that involves collecting training data from the particular IMU over a relatively short period of time. The method further involves subjecting the particular IMU to location manipulation during data collection. A reservoir computer is trained using the data collected toward improving navigation accuracy (e.g. error correction and state estimation) of the particular IMU. The method also involves creating a digital twin of the trained reservoir computer and embedding the digital twin with the particular IMU

Description

METHOD OF PROVIDING RELATIVELY ACCURATE POSITION DATA FOR A POSITION-RELIANT DEVICE BASED ON OUTPUT OF AN INERTIAL MEASUREMENT UNIT AND POSITION-RELIANT DEVICES INCORPORATING SAME

[0001] This application claims priority to U.S. Patent Application Serial No. 63 / 632,623, entitled “Reservoir Aided Inertial Navigation Methods” fded April 11, 2024, the disclosure of which is hereby expressly incorporated herein by reference in its entirety.FIELD OF THE INVENTION

[0002] The present invention relates to systems and methods for incorporating improving navigation accuracy for position-reliant devices by learning and correcting for non-ideal behaviors present in Inertial Measurement Units (IMUs).GOVERNMENT SUPPORT CLAUSE

[0003] This invention was made with government support under Contract No: HQ0860-22-C- 7837 awarded by Missile Defense Agency. The government has certain rights in the invention.BACKGROUND

[0004] Air, space, ground, and underwater vehicles require external references to maintain an accurate picture of their current position and orientation (attitude) in space, which allows the vehicle to navigate along a desired path. These external references include the global navigation satellite system (GNSS) when navigating near the Earth, or celestial objects when navigating away from the Earth.

[0005] When external sources of position and attitude data are not available, internal sensors - often called inertial measurement units (IMUs) - may be used for a short time, but the non-ideal characteristics and errors of these sensors inevitably accumulate and eventually cause a loss of accurate position and attitude solutions. Maintaining an accurate navigation solution while relyingsolely on internal sensors is an enormous challenge and speaks to the fundamental limits of both sensor fidelity and the mathematical analysis of the sensor signals.

[0006] Inertial measurements units (IMUs) are devices (i.e., sensors) that translate motion into electrical signals. In particular, IMUs measure and report an object’s acceleration and often its angular rate to provide data on a device’s movement and orientation. IMUs often include one or more accelerometers, one or more gyroscopes and one or more magnetometers. Accelerometers are devices that measure acceleration of an object relative to an observer in free fall often by measuring the response of a spring supporting a damped proof mass using electronic (e.g., piezoelectric, piezoresistive, capacitive), mechanical (e.g., micro-electrical-mechanical systems (“MEMS”)) or optical techniques. Gyroscopes are devices that utilize the principle of angular momentum to measure object orientation and angular velocity. Originally, gyroscopes used a spinning rotor to provide angular momentum of a spin axis supported by at least two gimbals (pivoted supports) each on a respective orthogonal axis. In a more modem approach, a MEMS gyroscope measures angular momentum / velocity by using the Coriolis Effect in association with one or more proof mass(es) attached to a spring. A magnetometer measures magnetic field (e.g., a compass) to provide directional signals. In addition to direction, some magnetometers measure strength and relative change of a magnetic field at a particular location.

[0007] Some IMU devices may comprise one accelerometer, one gyroscope, and magnetometer for each of the three principal axes: pitch, roll and yaw (or x-, y- and z-) axes. Other IMU devices may comprise only a single accelerometer or a single gyroscope. The IMU device selected for a particular device or application may be based on size, weight, power or costs constraints, the intended application including application environment and other application specific factors.

[0008] IMUs are found in various position-reliant devices (i.e., devices that require an awareness of their position, orientation, and / or motion). Some position-reliant devices utilizing IMUs include cameras; drilling tools; industrial / building sensors; smartphones; user-input devices (e.g. mice, smart glasses); video-game controllers; wearables (e.g., fitness trackers, pedometers, smart-glasses, smart-rings, smartwatches, VR headsets); and weapon systems.

[0009] IMUs are also found within Inertial Navigation Systems (INSs). An INS typically includes a plurality of IMUs (or more basic accelerometers and / or gyroscopes), GNSS receiver (or other external source of navigation data (i.e., real-world, geographic truth) and a microprocessor with code designed to fuse data from the plurality of IMUs with the data from the GNSS receiver to provide navigation level data. INSs are used where navigation level data is desired, such as in the air, space, ground and underwater vehicles (manned or autonomous) noted above. GNSS receivers are not without their problems. In addition to their loss-of-signal problems, GNSS data updates may occur slower than the need for up-to-date information for vehicle autopilot, missile navigation, and other weapons systems. Hence, the desire to include IMUs as part of an INS.

[0010] Commercially available IMUs have varying degrees of accuracy, sampling rates, durability, and cost. For example, wearables and recreational unmanned aerial vehicles may require relatively low precision and usually employ MEMS-based IMUs costing cents per unit.

[0011] Also, IMUs based on micro-electro-mechanical systems (MEMS) exhibit typical nonideal behaviors caused by, among other potential issues, misalignment of the axes of the accelerometers and / or gyroscopes, sensor bias (offset of the voltage for zero linear acceleration and angular rotation, respectively), drift in the bias, noise in the sensor voltage reading, and vibration. Any of these behaviors may give rise to a random walk in the attitude (velocity) estimate, cross-coupling of the angular acceleration to the linear accelerometer and the linearacceleration to the gyroscope, among other disadvantages. These types of IMUs also commonly suffer from the nonlinear response of the proof mass at high linear and angular accelerations, where the proof mass motion is no longer linearly related to the linear or angular acceleration. Non- MEMS-based IMUs also experience errors from axis misalignment, temperature variation, and noise, among other potential problems. While IMU manufacturers try to calibrate and correct for most of these errors, they have done little to meaningfully correct for the nonlinear response of the proof mass. Moreover, vibration and gravitational-force issues have proven too complex to be successfully mitigated by practically implementable solutions.

[0012] Most, if not all, IMUs have at least a small microcontroller (e.g., an embedded computer, application-specific integrated circuit (ASIC), or edge computing device) integrated with the sensor to provide calibration and apply corrections to the generalized non-ideal behavior of the sensor and filter output data based on user settings. As more fully discussed below, this filtered data — particular in INSs— may be further processed by an unscented Kalman Filter (UKF) to arrive at a navigation solution. Historically, IMU manufacturers have provided the code used in applying and filtering the sensor data to facilitate end-user implementation of their own UKF or other navigation correction efforts.

[0013] In contrast, military aircraft and satellites may employ high-precision laser and fiberoptic-based Inertial Navigation Systems (INS) costing tens of thousands of dollars each. Even these expensive Inertial Navigation Systems experience error from misalignment, installation deviations, model simplification, nonlinearity, and prediction latency.

[0014] Hypersonic missiles present a greater challenge requiring a balance of factors, demanding utmost accuracy in a small package while generating navigation information at a high rate. Hypersonic vehicle navigation is especially difficult because flight profiles often includehigh accelerations and velocities during maneuvers, and vehicles may pass through parts of the atmosphere — or develop a plasma sheath — that degrades GNSS signals and celestial navigation landmarks. These characteristics may require the navigation system to make predictions at a high rate (at least 200 Hz) and perform dead reckoning navigation during GNSS signal dropouts of 200 seconds or more. Also important is the ability of the system to rapidly correct the navigation solution once GNSS or other landmarks are available after a period of dead reckoning. Hypersonic missile applications, in particular, call for accuracy, high-speed, low-power, and small size.

[0015] Autonomous cars, for example, also need to maintain a position estimate much more accurate than a road-lane width when passing through tunnels, where GPS signals (a type of GNSS signal) are often blocked.

[0016] Inertial navigation has inherent instabilities that limit dead reckoning navigation precision; position errors grow to tens of meters or more over a 200 second interval using tactical grade IMUs. A better solution is needed to ensure success when positional accuracy is paramount.

[0017] There is also a need to improve the accuracy and reduce the latency of algorithms that process raw signals from IMUs beyond the current state-of-the-art, motivated, in part, by the emergence of new technologies such as autonomous vehicles and hypersonic vehicles.

[0018] The standard approach for processing raw EMU data and improving navigation accuracy is to use a non-linear extension to a Kalman filter: either an extended Kalman filter (EKF) or an unscented Kalman filter (UKF). EKF uses linearization while UKF incorporates a six degrees-of- freedom (6DOF) model of vehicle dynamics and a noise model of the EMU to make a more optimal prediction, especially for highly non-linear systems. Unfortunately, nonlinear model evaluation and attitude and position prediction— using either EKF or UKF— are computationally intensive tasks, making the high-rate prediction required for precise autonomous vehicle or hypersonicnavigation difficult to achieve, especially in a low size, weight, power, and cost (SWAP-C) environment. And, for best performance, Kalman filters require “tuning” based on knowledge of the system’s underlying behavior, which may be poorly understood and difficult to model, especially at the edges of the flight envelope.

[0019] Generally speaking, machine learning (ML) could be used to provide error correction and state prediction for an IMU. However, most machine learning approaches will be at least as computationally intensive as using non-linear Kalman filters.

[0020] As the physics of inertial sensors (IMUs), INS devices, and advanced vehicles become more complex, traditional methods of modeling these behaviors become too cumbersome for edge computing hardware to produce state estimation within application latency requirements. As such, new methods and systems are required to create computationally efficient and accurate models that can evaluate at high speeds.SUMMARY OF THE DISCLOSURE

[0021] In some aspects, the techniques described herein relate to a method of providing relatively accurate position data for a position-reliant device based on output of an inertial measurement unit, the method including: - collecting training data over a first period of time from the output of the inertial measurement unit; - subjecting the inertial measurement unit to one or more forms of sufficient location manipulation during at least a portion of the first period of time; - training a reservoir computer using training data collected over the first period of time to improve error correction and state estimation accuracy of the inertial measurement unit, wherein the reservoir computer includes a digital twin; - improving accuracy of the output of the inertial measurement unit by embedding the digital twin with the inertial measurement unit to form animproved-accuracy inertial measurement unit; and - embedding the improved-accuracy inertial measurement unit in the position-reliant device.

[0022] In some aspects, the techniques described herein relate to a method further including: - subjecting a first trusted location measurement unit to one or more types of location manipulation simultaneously with the inertial measurement unit during the at least a portion of the first period of time; and - collecting truth data over the first period of time from the first trusted location measurement unit physically associated in a known fixed-relationship with the inertial measurement unit, wherein training of the reservoir computer further includes using truth data collected over the first period of time to improve location accuracy of the inertial measurement unit.

[0023] In some aspects, the techniques described herein relate to a method wherein embedding the digital twin with the inertial measurement unit further including combining the digital twin with software originally associated with the inertial measurement unit.

[0024] In some aspects, the techniques described herein relate to a method wherein the one or more forms of sufficient location manipulation are selected from a group including a centrifugal rotation stage and a vibration table.

[0025] In some aspects, the techniques described herein relate to a method, wherein the position-reliant device further includes an external source of navigation data, the method further including: - collecting new truth data over a second period of time from the external source of navigation data; - collecting new training data over the second period of time from the output of the inertial measurement unit; and - retraining the digital twin using the new truth data and the new training data collected over the second period of time.

[0026] In some aspects, the techniques described herein relate to a method further including: - monitoring for a retraining condition; and - triggering collecting of new truth and training data and retraining of the digital twin upon the retraining condition.

[0027] In some aspects, the techniques described herein relate to a method wherein monitoring for the retraining condition includes calculating an error rate between the output of the inertial measurement unit and the output of the external source of navigation data signaling the retraining condition upon the error rate exceeding a predetermined threshold.

[0028] In some aspects, the techniques described herein relate to a method wherein retraining the digital twin begins with prior weights of the digital twin.

[0029] In some aspects, the techniques described herein relate to a method wherein the external source of navigation data includes a GNSS receiver.

[0030] The techniques described herein also may relate to a position-reliant device including: - a processor; - a power supply; and - an improved-accuracy inertial measurement unit that outputs accurate position data to the processor, the improved-accuracy inertial measurement unit including an inertial measurement unit and a digital twin of a reservoir computer trained using training output from the inertial measurement unit collected over a first period of time while being subjected to one or more forms of location manipulation.

[0031] In some aspects, the techniques described herein relate to a position-reliant device further including an external source of navigation data that provides accurate position data to the processor, wherein the processor relies on the improved-accuracy inertial measurement unit when the external source of navigation data is not providing valid position data.

[0032] In some aspects, the techniques described herein relate to a position-reliant device wherein the digital twin is also trained using truth data from a first trusted location unit collectedover the first period of time during which the inertial measurement unit and the first trusted location unit are physically associated in a known-fixed relationship and simultaneously subjected to one or more forms of location manipulation.

[0033] In some aspects, the techniques described herein relate to a position-reliant device further including an external source of navigation data that provides accurate position data to the processor, wherein the processor relies on the improved-accuracy inertial measurement unit when the external source of navigation data is not providing valid position data.

[0034] In some aspects, the techniques described herein relate to a position-reliant device further including: - memory to store new truth data collected over a second period of time from the external source of navigation data and new training data collected over the second period of time from the improved-accuracy inertial measurement unit; and - a processor to retrain the digital twin using the new truth data and the new training data collected over the second period of time.

[0035] In some aspects, the techniques described herein relate to a position-reliant device wherein the processor is the digital twin.

[0036] In some aspects, the techniques described herein relate to a position -reliant device further including a mechanism to monitor for a retraining condition, the mechanism causing the memory to collect the new truth data and the new training data and the processor to retrain the digital twin.

[0037] In some aspects, the techniques described herein relate to a position-reliant device wherein the mechanism calculates an error rate between an output of the improved-accuracy inertial measurement unit and the output of the external source of navigation data causing the retraining condition upon the error rate exceeding a predetermined threshold.

[0038] In some aspects, the techniques described herein relate to a position-reliant device wherein the external source of navigation data is a GNSS receiver.

[0039] In some aspects, the techniques described herein relate to a position-reliant device wherein the external source of navigation data is a GNSS receiver.BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The present application can be understood by reference to the following description taken in conjunction with the accompanying figures.

[0041] Fig. 1 of the drawings illustrates the overall systems and methods of the present invention.

[0042] Fig. 1A of the drawings illustrates one embodiment of logical embedding of various aspects of the Reservoir Aided Inertial Navigation (RAIN) framework in association with a particular Inertial Measurement Unit (IMU).

[0043] Fig. 2 of the drawings illustrates one embodiment of logical embedding of various aspects of the Reservoir Aided Inertial Navigation (RAIN) framework in association with a particular Inertial Navigation System (INS).

[0044] Fig. 3 of the drawings illustrates the impact the present teachings had in reducing crossaxis signal in a y-axis gyroscope when the particular IMU was subjected to vibration in the z-axis.

[0045] Fig. 4 of the drawings illustrates the substantial reduction of vibration rectification error (VRE) provided by the present teachings.DETAILED DESCRIPTION

[0046] The following description sets forth exemplary methods, systems, parameters and the like. It should be recognized by a person having ordinary skill in the art having the presentspecification and drawings before them that such description is not intended as a limitation on the scope of the present disclosure but is instead provided as a description of exemplary embodiments.

[0047] The present disclosure teaches the use of a reservoir computer to learn the particular dynamics of the non-ideal characteristics of a particularly manufactured Inertial Measurement Unit toward providing error correction and state estimation for the internal non-idealities of that particular IMU. Reservoir computers, which may also be known as Echo State Networks (ESN), process information generated by dynamic systems using observed time-series data. Reservoir computers require very small training data sets and use linear optimization even though the ML model is inherently nonlinear. So, they require minimal computing resources. Generally speaking, reservoir computers comprise an input layer, a reservoir (i.e., a fixed, artificial neural network (ANN) with recurrent links between nonlinear, time-dependent neurons, often called nodes), and a trainable output layer.

[0048] Unlike other machine learning methods (such as Deep Learning), the classic reservoir computer has a small number of weights (typically less than one hundred) trained using supervised learning. This smaller number of weights reduces the size of the labelled datasets required for initial training and subsequent retraining. The smaller number of trainable weights also vastly simplifies the mathematical function, making it open to interpretability, where each of the weights can be associated with a different physical effect in the dynamics of the host system. While a person having ordinary skill in the art with the present specification and drawings before them might assume that a restricted training set (as taught above) would offer inferior results for time series data processing and prediction, head-to-head comparisons between deep learning ANNs with long short-term memory and traditional reservoir computing techniques showed surprisinglysimilar performance despite training times that are 103to 106times less than the conventional deep learning approaches.

[0049] Classic reservoir computing uses randomly sampled matrices to define the reservoir. A next generation reservoir computer has more recently been introduced that uses nonlinear vector autoregression in place of randomly sampled matrices. See, Gauthier et al., “Next generation reservoir computing,” NATURE COMMUNICATIONS 12:5564 (2021) https: / / doi.org / 10.1038 / s41467-021-25801-2. As explained in the 2021 Gauthier paper, the next generation approach to reservoir computing results in fewer metaparameters. While nextgeneration reservoir computing still required supervised learning, it required smaller training data sets and, thus, shorter training time. The next generation reservoir computer also provides more easily interpretable results than classic reservoir computers. In the present specification, unless the specific context dictates otherwise, classical and next generation reservoir computers are collectively referred to as reservoir computers.

[0050] The use of the term “particular IMU” in this specification refers to a particular model of IMU produced by a particular manufacturer. One example of a particular IMU would be the ADIS16575 Precision MEMS IMU Module manufactured by Analog Devices (Wilmington, DE). The HG5700 Inertial Measurement Unit manufactured by Honeywell Aerospace Technologies (Norcross, GA) and the IIS3DHHCTR Accelerometer manufactured by STMicroelectronics (Geneva, Switzerland) would be examples of other particular IMUs. As would be understood by a person having ordinary skill in the art having the present specification and drawings before them, the present teachings have further potential utility in optimizing for a specific IMU, e.g., ADIS16575 Precision MEMS IMU Module bearing Serial No. 1234567, in other words a one-of- a-kind reservoir computer.

[0051] After training for a particular Inertial Measurement Unit, the reservoir computer is used to process the sensor level data from that particular IMU to produce output with greater positional accuracy and reduced time to generate a prediction (that is, reduces the latency of prediction) particularly in comparison to an unscented Kalman fdter (UKF).

[0052] In some embodiments, the reservoir computer may be trained outside the position-reliant device in which it will be utilized. In other embodiments, the reservoir computer may be trained within the position-reliant device in which it is being deployed based on known accurate position and attitude information obtained, for example, from an associated GNSS receiver (particularly in association with Earth-based applications). In the various embodiments, the reservoir computer may be retrained in the field based on the same known accurate position and attitude information. In these embodiments, navigation information, together with the calibration and IMU measurements, may be used to “retrain” the reservoir computer to ensure accurate data generated by the IMU, even if drifting in calibration occurs. In one embodiment, such retraining may be triggered by a user (e g., a few minutes before a missile launches). In another embodiment of the invention, an automatic detection algorithm may monitor and detect a drifting calibration and initiate an appropriate retraining, if necessary (i.e., when the calculated error rate has exceeded a predetermined threshold).

[0053] The reservoir computer, which may be represented by software code (i.e. a digital twin), may be referred to as a Reservoir Aided Inertial Navigation (RAIN) framework. The RAIN framework may be used to improve sensor-level accuracy by learning and correcting for non-ideal behaviors present in a particular IMU. For example, nearly all IMUs utilize a low pass filter (LPF) with a cutoff frequency set to the Nyquist frequency to avoid signal aliasing during analog-to- digital conversion (ADC) of the raw analog sensor signal. The Nyquist limited analog sampleintroduces sufficient distortion to cause meaningful non-ideal signal behaviors. In some embodiments, the RAIN framework may be used to both learn the physics of the LPF and generate an inverse digital filter to eliminate the resulting distortion before further signal processing.

[0054] The RAIN framework may also be used to improve navigation level accuracy in a particular INS by learning and correcting for non-ideal behaviors of one or more of the particular IMUs; particular GNSS receiver and other sensors in the particular INS. The RAIN framework may also be used in some embodiments to improve the fusing of data within an INS from these sources.

[0055] Because the RAIN framework is incredibly lightweight (i.e., small code size and fast evaluation), it may be embedded in the particularly manufactured IMU for which it was trained- even on the smallest of microcontrollers or ASIC-based processors found in commercial IMUs— either operating as a final -processing step or by combining the correction framework with the original manufacturer’s IMU signal processing code. In this manner, the RAIN framework may perform both IMU signal correction and navigation state estimation at high rates (e.g., higher than 4 kHz). In an embodiment where the RAIN framework provides navigation state estimation based on IMU sensor-level data, the prediction may be improved or corrected soon after once slower- generated, navigation level RAIN data becomes available.

[0056] The RAIN framework is intended to be a complete replacement for nonlinear (extended or unscented) Kalman filters providing higher accuracy and a fraction of their latency, making it especially ideal for hypersonic navigation applications. The lightweight nature of the RAIN framework also means that it consumes at least a factor of two less power than a Kalman filter in operation. And as discussed more fully below, because the RAIN framework may be trained usingonly semi-supervised and even unsupervised learning, the time, power, and computing effort required are greatly reduced over classic and even next-generation reservoir computing.

[0057] As illustrated in Fig. 1, the RAIN framework is integrated with a particular IMU or particular INS in three phases: collecting training data (120); reservoir computer training (130); and reservoir computer deployment (140-160).

[0058] Collecting Training Data (120): A training phase is performed on the particular IMU (i.e., Inertial Measurement Unit-A 57), while the particular IMU is being subjected to sufficient linear and / or angular accelerations. The type and amount of linear and / or angular accelerations sufficient to provide training depends primarily on the particular IMU used and the intended application. As illustrated in Fig. 1, for an IMU sensor-level implementation, this manipulation may be accomplished by placing the particular IMU (i.e., Inertial Measurement Unit-A 57) on a location manipulation device 126. The location manipulation device 126 may comprise a centrifugal rotation stage, vibration table, and / or tilt table. When working with a particular IMU, for example, it may be sufficient to subject the particular IMU to vibrations along at least a set of orthogonal axes (x / y / z, yaw / pitch / roll), simultaneously, seriatim or some combination thereof. Subjecting the particular IMU to sufficient location manipulation in three orthogonal axes may be accomplished using a vibration table in conjunction with a tilt table. As further illustrated by Fig 1, the location manipulation may take place in the presence of physical field parameters 127, such as the Earth’s local gravitational acceleration or an induced magnetic field.

[0059] In some embodiments, while collecting training data, an auxiliary high-accuracy sensor (i.e., trusted location measurement unit 125) is placed in a known fixed relationship (“d”) to the particular IMU (i.e., Inertial Measurement Unit-A 57) to provide “truth” data for use in some of the training process. This would be particularly important for an INS navigation-levelimplementation. Navigation-level training requires some real-world, actual location truth data, the type of data that would be generated by a GNSS receiver. However, other location-data might suffice. For example, traveling in a straight line from a known geographic position in a vehicle with an accurate time-keeping device and source of velocity information (and tires with a known- radius), one can quickly generate a set of location data to inform the training of a navigation-level RAIN framework.

[0060] The training and truth data are collected over time from the Inertial Measurement Unit- A 57 and the trusted location measurement unit 125, respectively over a first period of time. The first period of time may be on the order of seconds, even milliseconds depending upon the particular EMU and intended application. In some embodiments, the trusted location and inertial measurement units may only be simultaneously subjected to one or more forms of location manipulation during only a portion of this first period of time.

[0061] Reservoir Computer Training (130): Training data collected in step 120 is used to train a reservoir computer 200. In some embodiments, the training may take place on a standard computer. In other embodiments, the training may be performed directly on a microcontroller physically embedded in the particular IMU. In the context of reservoir computers, training works to adjust the strength of the weights of links in the output stage of the reservoir computer, where desirable, to “learn” the non-ideal behavior of the particular IMU. In most embodiments, the training may be either semi-supervised or unsupervised. For example, when “truth” data is available for training, it can be used in a supervised, semi -supervised or unsupervised procedure for finding the optimal weights. When “truth” data is not available, an unsupervised method can be used to find the weights.

[0062] Reservoir Computer Deployment (140-160): Once the reservoir computer is trained, the reservoir computer model / implementation (i.e., “the RAIN framework”) comprises computer code (i.e. a digital twin 210) that simulates the artificial neural network of reservoir computer, element 140. The digital twin 210 is deployed on the particular IMU 57 to correct for the nonideal behaviors in that particular IMU-A 57. In particular, the digital twin 210 may be embedded 160 in the particular IMU manufacturer’s signal chain. In some embodiments, signals generated by the sensor in the particular IMU-A 57 undergo preliminary processing using the original IMU manufacturer’s code and are then passed to the digital twin 210 to correct for non-ideal sensor behavior. Digital twin 210 then hands the data back to the particular IMU manufacturer’s code to finalize the data processing. In other embodiments, where the manufacturer of the IMU-A 57 has provided access to the IMU’s internal software code (e.g., firmware), embedding 160 of the digital twin 210 may involve logically combining the digital twin 210 into the particular original IMU manufacturer’s code so that all processing happens within the same code base, element 150. As would be understood a person having ordinary skill in the art having the present specification and drawings before them, this logical combination of the digital twin 210 with the IMU-A manufacturer’s original code may involve streamlining the two codes into one more cohesive code. In either embodiment, the processing between original manufacturer’s code and digital twin 210 happens in real time with minimum latency so that the data output from the particular IMU 57 is temporally correlated with the accelerations and rotation of the particular IMU 57.

[0063] In some embodiments, these three phases may be supplemented by updating the weights in the digital twin 210 in the field. As such, this embodiment addresses the notion that the characteristics of the particular IMU 57 or INS may change over time so that a factory calibration procedure may no longer be accurate. This change could be due, for example, to aging of thedevice, among other reasons. Especially for a critical mission requiring the highest navigation accuracy, accurate position and attitude data can be collected just before the beginning of the mission and transferred to the particular IMU 57. The particular EMU 57 uses this data to correct for its position and attitude prediction and to adjust the weights of the artificial neural network (or its mathematical representation) underlying the reservoir computer / digital twin. In some embodiments, the prior weights associated with the reservoir computer / digital may be a starting point for this retaining process to improve the process of finding new weights.

[0064] Because initial training and retraining of the reservoir computer / digital twin may be accomplished directly on-device (i.e., using the existing microcontroller hardware in the particular IMU) — there are embodiments contemplated where no companion computer would be required. Once trained, the RAIN framework allows for ultra-fast updating which can be accomplished in parallel to normal host system operation.

[0065] As further illustrated by Fig. 1, position-reliant device 50a includes at least one particular IMU (e.g., Inertial Measurement Unit-A 57), which translates motion into electrical signals indicative of the movement and orientation of position-reliant device 50. As would be understood by a person of ordinary skill in the art having the present specification and drawings before them, position-reliant device 50 may include additional Inertial Measurement Units such that an EMU may be dedicated to measuring each principal axis of motion of the position-reliant device 50a. Nevertheless, to simplify description of the present teachings, the specification focuses on a single Inertial Measurement Unit-A 57 with the understanding that the teachings with respect to this single Inertial Measurement Unit-A would be applied independently to each Inertial Measurement Unit 57 found in the position-reliant device 50.

[0066] Moreover, while each IMU in the position-reliant device 50a may be the same part from the same manufacture, it is contemplated that one or more of the IMUs may be different (i.e., have a different part number or from different manufacturer). This may occur, for example, in application where the motion along only one axis is significant to the position-reliant device 50. It is similarly contemplated that the designer / manufacturer of the position-reliant device 50 may only wish to apply the present teachings to less than all of the IMUs deployed within the device.

[0067] In certain embodiments, the RAIN framework may include multiple parallel reservoir computers (or their digital twins) to maximize the ability of the RAIN framework to learn and correct for physical behaviors in the particular IMU that give rise to errors over the particular IMU’s full range of dynamics. In one potential approach to this embodiment, the RAIN framework may include another reservoir computer (or its digital twin) to blend the output of each of the multiple parallel reservoir computers (or their digital twins). In another potential approach to this embodiment, each of the multiple parallel reservoir computers (or their digital twins) are given a weight and summed together to arrive at a composite prediction.

[0068] In further embodiments, the multiple parallel reservoir computers / digital twins may be combined with the output of an associated GNSS receiver (or other source of navigation truth data) to create a highly accurate state estimation. These embodiments, are believed to provide minimal navigation solution drift in between GNSS updates and error prediction rates that are well within the latency requirements of high-speed flight, let alone autonomous cars, gaming devices and VR headsets / wearables.

[0069] Fig. 1A illustrates one embodiment of logical embedding of various aspects of the Reservoir Aided Inertial Navigation (RAIN) framework in association with a particular Inertial Measurement Unit (IMU). Inertial Measurement UnitA 57 is a particular IMU (i.e. a particularmodel number from a particular manufacturer. (The inclusion of the subscript “A” is to denote that it is a particular IMU. Other particular IMUs may benefit from the application of the teachings found throughout this specification. Those other particular IMUs would be denoted IMUB, IMUC, . . . IMUN. By way of illustration and not limitation, IMUA may be ADIS16575 Precision MEMS IMU Module manufactured by Analog Devices while IMUB may be ADIS 16577 Precision MEMS IMU Module also manufactured by Analog Devices, a HG5700 Inertial Measurement Unit manufactured by Honeywell Aerospace Technologies, or an IIS3DHHCTR Accelerometer manufactured by STMicroelectronics. The point being that under the teachings of this disclosure, each particular IMU has a RAIN framework that has been particularly trained to correct the nonideal behaviors of that particular IMU.

[0070] As illustrated in Fig. 1A, IMUA 57 may have a plurality of sensors to measure acceleration, angular rate / velocity, and / or orientation. In particular IMUA is illustrated as having three sensors, corresponding to the three independent orthogonal axes of potential motion. These sensors generate raw analog sensor data that is commonly translated into a digital signal. As further illustrated in Fig. 1A, the analog output of the sensors is fed into a low pass filter (LPF). The LPFs have a cutoff frequency set to the Nyquist frequency to avoid signal aliasing during the analog-to-digital conversion (ADC) of the raw analog sensor signal. Commonly, the output of the ADC in an Inertial Measurement Unit remains as a Nyquist limited signal. Having recognized that even this slight signal distortion on the digital sensor output leads to significant position error, the embodiment shown in Fig. 1A illustrates the preferable application of an inverse digital low-pass (LP) filter at the earliest possible signal processing stage following the analog-to-digital conversion. As illustrated by inclusion of this optional module in the RAIN-IMUA Processing 100 block, the inverse digital LP filter may be generated by applying the technical principals of theRAIN framework to compare the unfiltered and filter output over time to generate a digital twin component to correct the Nyquist limited signal and included within the RAIN framework code base.

[0071] Fig. 1 A further illustrates that the RAIN framework codebase / RAIN-IMUA Processing 100 block further comprises non-linear error correction, improved state estimation, and improved data fusing functions. Each of these sensor data correcting functions are generated through the reservoir computer training 130 methodology discussed above and integrated into the code base. Fig. 1A finally illustrates that the output of IMUAhas been processed by RAIN-IMUA Processing 100 via the digital signal processor / microprocessor physically associated with IMUA 57. In approaches where the particular IMU does not have an onboard microprocessor or the onboard microprocessor is not accessible or otherwise precluded from accepting code updates, the operations of RAIN-IMUA Processing 100 may be applied to the signal generated by the IMU using a separate microprocessor (not shown).

[0072] Fig. 2 illustrates one embodiment of logical embedding of various aspects of the Reservoir Aided Inertial Navigation (RAIN) framework in association with a particular Inertial Navigation System (INS). As illustrated in this figure, INS 500 may include certain hardware: a particular IMUA 57, a GNSS receiver 55, other sensors 510 and a microprocessor 520. The other sensors 510 may comprise one or more of the following: a vehicle data sensor (e.g., measuring revolutions of a wheel of known diameter); a visual information sensor (e.g. celestial navigation or pilotage); a radio frequency beacon receiver; a Received Signal Strength Indicator (RSSI), and a remote sensor system. These sensors and the GNSS receiver may all be collectively referred to as external sources of navigation data.

[0073] The microprocessor 520 initially contains the manufacturer’s code 521 designed and deployed by the manufacturer of the INS to control the other elements in INS 500 and provide rudimentary error correction and data fusing toward providing navigation level position information 550. In one application of the present teachings, the RAIN framework techniques may be applied to any and all of IMUA 57, a GNSS receiver 55, and other sensors 510 to provide error correction and state estimation preferably unique to each particular device (at manufacturer / serial number level). Then, as logically illustrated in Fig. 2, the various RAIN framework digital twins 100, 525, and 526 may be embedded in microprocessor 520 to correct the data provided from the respective device that framework was trained to service. A last code contribution, RAIN data fusion 527, may also be embedded in microprocessor 520. RAIN data fusion is trained like the other RAIN frameworks to fuse the data from the various sensor inputs together to arrive at a more accurate navigation system that is quicker to update. It should be understood by those of ordinary skill in the art having the present specification and drawings, that each of these logical RAIN components may be combined with the manufacturer’s code to create a more efficient, lower latency approach to correction.

[0074] Fig. 3 illustrates the impact the present teachings had in reducing cross-axis signal in a y-axis gyroscope when the IMU was subjected to vibration in the z-axis. This is commonly referred to as cross-axis coupling. As illustrated, shaking in the z-axis causes unwanted deterministic signals in the y-axis. For this experimental illustration, 1,000 data points collected over less than 2 seconds of IMU operation were used. Even with this minimal data, the system and method was able to learn the physics of how these vibrations propagated and affected the off-axis sensor. The resulting model can then be used to predict and subtract out the cross-axis signal, effectively decoupling and reducing the false indication of motion.

[0075] Fig. 4 illustrates the substantial reduction of Vibration Rectification Error (VRE) error provided by the present invention, showing in particular the high-speed IMU x-axis results from a live shaker table testing in the x-axis. This example shows reservoir-aided inertial navigation (RAIN) ability to learn and “undo” and prefiltering of the IMU’ s raw signal occurring in the signal chain prior to the microcontroller hosting the RAIN algorithm. Though this adds to its computational complexity, the deployed model (in the compiled C language) that produced the results in Figure 3 is still only 500 bytes and evaluates in less than 250 microseconds on microcontroller hardware.

[0076] Using a simulated hypersonic trajectory dataset, the ability of RAIN to perform state estimation using inertial signals from a tactical grade IMU was tested. After training on as little as 70 seconds of position and attitude truth data, RAIN’s predictions were at least as accurate as a state-of-the-art Unscented Kalman Filter (UKF), through predictions processed ten times faster than UKF.

[0077] Certain embodiments may include an automated technique for “feature selection” of a nonlinear model which identifies the inputs that are most important for prediction. Automated feature selection involves testing each term in a RAIN framework one-by-one and selecting the term that reduces the prediction error of the RAIN framework the most. In one embodiment, automated feature selection then performs a mathematical procedure known as orthogonalization on the remaining terms. See, e.g., S. Chen, “Local regularization assisted orthogonal least squares regression” Neurocomputing 69 (2006) 559-585. Orthogonalization makes the remaining terms as distinct from each other as possible. Then each of these orthogonalized model terms are tested one-by-one, and the term that reduces the error the most is selected. This procedure is repeated recursively until a criterion is satisfied, known as an information criterion. In this embodiment,the information criterion is based on a statistical method that estimates how much information is contained in a signal and stops the procedure when the reservoir computing model generates the same information content.

[0078] Automated feature selection may result in an additional two times or greater reduction in the size of the reservoir computer / digital twin, in turn reducing training time and model evaluation by a factor of at least four. Feature selection may also provide additional insights into the most important physical quantities within the particular IMU, lending to the RAIN frameworks interpretability (i.e., features in the model have an underlying physical interpretation as would be understood by a person versed in the sensor art).

[0079] The specific embodiments and examples described herein are exemplary only and are not limiting to the invention defined in the claims. Additionally, while the present invention has been illustrated by the description of embodiments thereof, and while the embodiments have been described in considerable detail, such descriptions are not intended to restrict or in any way limit the scope of the appended claims to such detail. Additional advantages and modifications will readily appear to those skilled in the art. Therefore, the invention, in its broader aspects, is not limited to the specific details, the representative compositions and processes, or illustrative examples shown and described. Accordingly, departures may be made from such details without departing from the spirit or scope of the general inventive concept.

Claims

CLAIMSWHAT IS CLAIMED IS:

1. A method of providing relatively accurate position data for a position-reliant device based on output of an inertial measurement unit, the method comprising: collecting training data over a first period of time from the output of the inertial measurement unit; subjecting the inertial measurement unit to one or more forms of sufficient location manipulation during at least a portion of the first period of time; training a reservoir computer using training data collected over the first period of time to improve error correction and state estimation accuracy of the inertial measurement unit, wherein the reservoir computer comprises a digital twin; improving accuracy of the output of the inertial measurement unit by embedding the digital twin with the inertial measurement unit to form an improved-accuracy inertial measurement unit; and embedding the improved-accuracy inertial measurement unit in the position- reliant device.

2. The method of Claim 1 further comprising: subjecting a first trusted location measurement unit to one or more types of location manipulation simultaneously with the inertial measurement unit during the at least a portion of the first period of time; and collecting truth data over the first period of time from the first trusted location measurement unit physically associated in a known fixed-relationship with the inertial measurement unit, wherein training of the reservoir computer further comprises using truth data collected over the first period of time to improve location accuracy of the inertial measurement unit.

3. The method of Claim 1 wherein embedding the digital twin with the inertial measurement unit further comprising combining the digital twin with software originally associated with the inertial measurement unit.

4. The method according to Claim 1 wherein the one or more forms of sufficient location manipulation are selected from a group comprising a centrifugal rotation stage and a vibration table.

5. The method of Claim 2, wherein the position-reliant device further includes an external source of navigation data, the method further comprising: collecting new truth data over a second period of time from the external source of navigation data; collecting new training data over the second period of time from the output of the inertial measurement unit; and retraining the digital twin using the new truth data and the new training data collected over the second period of time.

6. The method of Claim 5 further comprising: monitoring for a retraining condition; and triggering collecting of new truth and training data and retraining of the digital twin upon the retraining condition.

7. The method of Claim 6 wherein monitoring for the retraining condition includes calculating an error rate between the output of the inertial measurement unit and the output of the external source of navigation data signaling the retraining condition upon the error rate exceeding a predetermined threshold.

8. The method of Claim 5 wherein retraining the digital twin begins with prior weights of the digital twin.

9. The method of Claim 5 wherein the external source of navigation data comprises a GNSS receiver.

10. A position-reliant device comprising: a processor; a power supply; and an improved-accuracy inertial measurement unit that outputs accurate position data to the processor, the improved-accuracy inertial measurement unit including an inertial measurement unit and a digital twin of a reservoir computer trained using training output from the inertial measurement unit collected over a first period of time while being subjected to one or more forms of location manipulation.

11. The position-reliant device of Claim 10 further comprising an external source of navigation data that provides accurate position data to the processor, wherein the processor relies on the improved-accuracy inertial measurement unit when the external source of navigation data is not providing valid position data.

12. The position-reliant device of Claim 10 wherein the digital twin is also trained using truth data from a first trusted location unit collected over the first period of time during which the inertial measurement unit and the first trusted location unit are physically associated in a known- fixed relationship and simultaneously subjected to one or more forms of location manipulation.

13. The position-reliant device of Claim 12 further comprising an external source of navigation data that provides accurate position data to the processor, wherein the processor relies on the improved-accuracy inertial measurement unit when the external source of navigation data is not providing valid position data.

14. The position-reliant device of Claim 13 further comprising: memory to store new truth data collected over a second period of time from the external source of navigation data and new training data collected over the second period of time from the improved-accuracy inertial measurement unit; and a processor to retrain the digital twin using the new truth data and the new training data collected over the second period of time.

15. The position-reliant device of Claim 14 wherein the processor is the digital twin.

16. The position-reliant device of Claim 14 further comprising a mechanism to monitor for a retraining condition, the mechanism causing the memory to collect the new truth data and the new training data and the processor to retrain the digital twin.

17. The position-reliant device of Claim 16 wherein the mechanism calculates an error rate between an output of the improved-accuracy inertial measurement unit and the output of the external source of navigation data causing the retraining condition upon the error rate exceeding a predetermined threshold.

18. The position-reliant device of Claim 11 wherein the external source of navigation data is a GNSS receiver.

19. The position-reliant device of Claim 13 wherein the external source of navigation data is a GNSS receiver.

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