WO2020247721A1 - Systems and methods to improve geo-referencing using a combination of magnetic field models and in situ measurements - Google Patents

Abstract

Various embodiments of the present technology provide for systems and methods for predicting the global external magnetic field due to electrical current systems in the ionosphere and magnetosphere. Some embodiments combine knowledge of the physics of the system, in addition to decades of satellite and ground measurements to obtain a global model of the climatology of the magnetic field. Then, data assimilation is used to ingest real-time and near real-time observations to make corrections to the climatological global model, leading to more accurate results on small local scales. In some embodiments, a global magnetic field model is constructed and then combined with satellite data and ground data to generate an enhanced modeling prediction describing global magnetic field perturbations. Data may be combined with the global magnetic field model using machine learning and/or data assimilation techniques.

Description

SYSTEMS AND METHODS TO IMPROVE GEO-REFERENCING

USING A COMBINATION OF MAGNETIC FIELD MODELS AND IN SITU MEASUREMENTS

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims priority to U.S. Provisional Application No.

62/857,553 filed June 5, 2019 titled“SYSTEMS AND METHODS TO IMPROVE GEO- REFERENCING USING A COMBINATION OF MAGNETIC FIELD MODELS AND IN SITU MEASUREMENTS” which is incorporated herein by reference in its entirety for all purposes.

BACKGROUND

[0002] The Earth’s magnetic field measured at or near the surface is a superposition of fields from several different sources. The primary source is a fluid dynamo generated in the Earth's core which is responsible for the large-scale structure of the total field.

Localized magnetic anomalies in the Earth's crust contribute additional magnetic field signatures. Finally, electrical currents owing in the Earth's outer atmosphere (ionosphere) and the magnetosphere generate magnetic fields detectable on the planet's surface.

[0003] The external magnetic field, coming from the ionosphere and magnetosphere, exhibits complex spatial and temporal structure, and is notoriously difficult to predict accurately. While much progress has been made in recent decades, a full understanding of the physics of all the different current systems contributing to the field still eludes researchers. For example, many of the current models still miss much of the localized field variations that change rapidly in time.

[0004] It is with respect to this general technical environment that aspects of the present technology disclosed herein have been contemplated. Furthermore, although a general environment has been discussed, it should be understood that the examples described herein should not be limited to the general environment identified in the background.

BRIEF SUMMARY OF THE INVENTION

[0005] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter. [0006] Various embodiments herein related to systems and methods for improved georeferencing. More specifically, some embodiments relate to predicting the external magnetic field at and near the Earth's surface using a combination of modeling and measurements. In an embodiment, a method of generating an enhanced modeling prediction comprises constructing a global magnetic field model (GMFM), wherein the GMFM is configured to produce a modeling prediction describing global magnetic field perturbations based on one or more input parameters. The method further comprises obtaining satellite data comprising data related to at least one solar wind parameter and at least one magnetic field component, obtaining ground data comprising data related to geomagnetic variations, and generating an enhanced modeling prediction based on the modeling prediction, the satellite data, and the ground data. The modeling prediction and the enhanced modeling prediction may represent patterns of magnetic perturbations due to one or more solar inputs in some implementations.

[0007] In some embodiments, generating the enhanced modeling prediction comprises using at least one data assimilation technique to combine the modeling prediction with the satellite data and the ground data. In other embodiments, generating the enhanced modeling prediction comprises using at least one machine learning technique to combine the modeling prediction with the satellite data and the ground data. The one or more input parameters, in some implementations, comprise one or more of solar flux intensity, solar wind velocity, interplanetary magnetic field components, magnetospheric ring current strength, and high-latitude ionospheric current strengths. The at least one solar wind parameters and the at least one magnetic field component of the satellite data may comprise solar wind parameters and interplanetary magnetic field components collected from one or more satellites positioned in space between Sun and Earth. The data related to geomagnetic variations may comprise data collected at one or more of a ground magnetic observatory and a variometer station. In some embodiments, the satellite data further comprises one or more of electric field measurements of a geomagnetic field, electric field measurements of a geoelectric field, magnetic field measurements of a geomagnetic field, and magnetic field measurements of a geoelectric field.

[0008] In another embodiment a system for generating enhanced modeling predictions comprises one or more computer-readable storage media having stored thereon a GMFM, wherein the GMFM is configured to produce a modeling prediction describing global magnetic field perturbations due to solar inputs based on one or more input parameters, a processing system operatively coupled with the one or more computer- readable storage media, and program instructions stored on the one or more computer- readable storage media for generating an enhanced modeling prediction. The program instructions, when read and executed by the processing system, direct the processing system to at least obtain satellite data comprising data related to at least one solar wind parameter and at least one magnetic field component, obtain ground data comprising data related to geomagnetic variations, and generate an enhanced modeling prediction based on the modeling prediction, the satellite data, and the ground data.

[0009] In some embodiments, to generate an enhanced modeling prediction, the program instructions further direct the processing system to provide the modeling prediction, the satellite data, and the ground data to a machine learning engine configured at least to combine the modeling prediction, the satellite data, and the ground data. In other embodiments, to generate an enhanced modeling prediction, the program instructions further direct the processing system to provide the modeling prediction, the satellite data, and the ground data to an assimilation engine that assimilates real-time measurements from the satellite data and the ground data into the global magnetic field model to generate the enhanced modeling prediction. The assimilation engine may further comprise a forecasting module to generate an estimate of a state at a current time by propagating past state forward in time using physical constraints and an analysis module to correct the modeling prediction based on real-time observations. In some embodiments, to generate the enhanced modeling prediction, the program instructions direct the processing system to predict a value of a magnetic component based on a present input value and past input values within a time window.

[0010] In yet another embodiment one or more computer-readable storage media have program instructions stored thereon for generating enhanced global magnetic field predictions. The program instructions, when read and executed by a processing system, direct the processing system to construct a global magnetic field model, wherein the global magnetic field model is configured to produce a modeling prediction describing global magnetic field perturbations based on one or more input parameters, obtain satellite data comprising data related to at least one solar wind parameter and at least one magnetic field component, obtain ground data comprising data related to geomagnetic variations, and provide the modeling prediction, the satellite data, and the ground data to a machine learning engine configured to combine the modeling prediction, the satellite data, and the ground data and produce an enhanced modeling prediction describing global magnetic field perturbations.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Many aspects of the disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily drawn to scale. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views. While several embodiments are described in connection with these drawings, the disclosure is not limited to the embodiments disclosed herein. On the contrary, the intent is to cover all alternatives, modifications, and equivalents.

[0012] Fig. 1 illustrates a methodology that may be used in accordance with various embodiments of the present technology.

[0013] Fig. 2 is a flow chart illustrating a series of steps for improved georeferencing in accordance with some embodiments of the present technology.

[0014] Fig. 3 is a flow chart illustrating a series of steps for improved georeferencing in accordance with some embodiments of the present technology.

[0015] Fig. 4 illustrates an example of the north pole (left) and south pole (right) magnetic signatures of ionospheric polar current systems from one year of satellite data recorded in accordance with various embodiments of the present technology.

[0016] Fig. 5A illustrates declination data recorded at Deadhorse observatory overlaid with predictions from GMFM in LEO in accordance with various aspects of the present technology.

[0017] Fig. 5B illustrates total field data recorded at Deadhorse observatory overlaid with predictions from GMFM in LEO in accordance with various aspects of the present technology.

[0018] Fig. 5C illustrates inclination data recorded at Deadhorse observatory overlaid with predictions from GMFM in LEO in accordance with various aspects of the present technology.

[0019] Fig. 6 illustrates an example of an artificial neural network architecture that may be used in accordance with various embodiments of the present technology.

[0020] Fig. 7 illustrates an example of a recurrent neural network design for magnetic prediction that may be used in accordance with some embodiments of the present technology.

[0021] Fig. 8A shows declination data collected that demonstrates the improvement which can be achieved through various embodiments that combine global modeling, satellite data, and ground data through machine learning in accordance with some embodiments of the present technology.

[0022] Fig. 8B shows total field data collected that demonstrates the improvement which can be achieved through various embodiments that combine global modeling, satellite data, and ground data through machine learning in accordance with some embodiments of the present technology.

[0023] Fig. 8C shows inclination data collected that demonstrates the improvement which can be achieved through various embodiments that combine global modeling, satellite data, and ground data through machine learning in accordance with some embodiments of the present technology.

[0024] Fig. 9 is a block diagram illustrating an example machine representing the computer systemization of the estimation system that may be used in some embodiments.

[0025] The drawings have not necessarily been drawn to scale. Similarly, some components and/or operations may be separated into different blocks or combined into a single block for the purposes of discussion of some of the embodiments of the present technology. Moreover, while the technology is amenable to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and are described in detail below. The intention, however, is not to limit the technology to the particular embodiments described. On the contrary, the technology is intended to cover all modifications, equivalents, and alternatives falling within the scope of the technology as defined by the appended claims.

DETAILED DESCRIPTION

[0026] The following description and associated figures teach the best mode of the invention. For the purpose of teaching inventive principles, some conventional aspects of the best mode may be simplified or omitted. The following claims specify the scope of the invention. Note that some aspects of the best mode may not fall within the scope of the invention as specified by the claims. Thus, those skilled in the art will appreciate variations from the best mode that fall within the scope of the invention. Those skilled in the art will appreciate that the features described below can be combined in various ways to form multiple variations of the invention. As a result, the invention is not limited to the specific examples described below, but only by the claims and their equivalents.

[0027] Various embodiments of the present technology generally relate to prediction and estimation of the magnetic field in the Earth’s environment. More specifically, some embodiments relate to systems and methods to make real-time predictions of the external magnetic field at and near the Earth's surface. The Earth's magnetic field measured at or near the surface is a superposition of fields from several different sources. The primary source is a fluid dynamo generated in the Earth's core which is responsible for the large- scale structure of the total field. Localized magnetic anomalies in the Earth's crust contribute additional magnetic field signatures. Finally, electrical currents owing in the Earth's outer atmosphere (ionosphere) and the magnetosphere generate magnetic fields detectable on the planet's surface.

[0028] The external magnetic field, coming from the ionosphere and magnetosphere, exhibits complex spatial and temporal structure, and is notoriously difficult to predict accurately. While much progress has been made in recent decades, a full understanding of the physics of all the different current systems contributing to the field still eludes researchers. Various embodiments of the present technology provide for novel systems and methods to make real-time predictions of the external magnetic field at and near the Earth's surface, by combining decades of observations from both satellites and ground stations, knowledge of the physics responsible for the generation of the electrical current systems, and state-of-the-art methods in data assimilation and machine learning to ingest real-time and near real-time data streams to update the model's accuracy. The

geomagnetic perturbations associated with these current systems can adversely affect ground magnetic referencing such as compass navigation in ships and planes,

aeromagnetic surveys, and directional drilling.

[0029] Some embodiments of the present technology construct a global magnetic field model (GMFM) which describes the global magnetic field perturbations due to electric current systems owing in the ionosphere and magnetosphere, as well as their induced counterparts in the conducting Earth. This model can be used to describe the large-scale average patterns of the magnetic perturbations due to solar inputs (solar flux levels, solar wind parameters, interplanetary magnetic field (IMF) parameters). In some embodiments, this model can accept as input various parameters related to the solar wind and current systems in the ionosphere and magnetosphere. Example input parameters can include, but are not limited to, the following: solar flux intensity, solar wind velocities, IMF components, magnetospheric ring current strength, and high-latitude ionospheric current strengths.

[0030] Real-time (RT) and near real-time (NRT) data can be ingested from satellites which record parameters related to the solar wind and geomagnetic field. These satellites can include: (a) satellites situated in deep space between the Sun and Earth which record solar wind parameters (velocity components) and interplanetary magnetic field components; and (b) satellites in low Earth orbit (LEO) which record electric and/or magnetic field measurements of the geomagnetic and geoelectric field. The RT and NRT data can also be ingested from ground magnetic observatories and variometer stations. For example, this data may be ingested from a global network of stations which record geomagnetic variations due to external and induced electric current systems. Using all of the data collected, GMFM prediction accuracy on local/regional scales can be enhanced, in near real-time, using data assimilation techniques or machine learning for combining measured data with modeling output.

[0031] Various embodiments of the present technology provide for a wide range of technical effects, advantages, and/or improvements to computing systems and

components. For example, various embodiments include one or more of the following technical effects, advantages, and/or improvements: 1 ) intelligent prediction of Earth’s magnetic field variations ; 2) integrated use of machine learning to generate real-time predictions of magnetic fields; 3) dynamic integration of decades of observations (e.g., from satellites, ground stations, etc.), knowledge of the physics responsible for the generation of the electrical current systems, and state-of-the-art methods in data assimilation and machine learning to ingest real-time and near real-time data streams in the real-time prediction of magnetic field variations ; 4) use of unconventional and non-routine computer operations to provide improved estimates of localized magnetic field variations; 5) cross- platform integration of machine learning to more efficiently estimate magnetic fields in realtime; 6) changing the manner in which a navigational systems estimate direction and position; and/or 7) changing the manner in which a computing system generates surveys.

[0032] Fig. 1 is a schematic of a methodology that may be used in various embodiments of the present technology. Schematic 100 includes sun 105, Earth 1 10, satellite 1 15, satellite 120, and a corona ejection/solar storm at position 130, position 135, and position 140. Satellite 1 15 measures solar wind data in accordance with some implementations. Satellite 120 is a LEO satellite that measures magnetic signatures. Data may be recorded from satellites in deep space (i.e., satellite 1 15), satellites in low-Earth orbit (i.e., satellite 120), and ground stations (various positions on Earth 110). The data may be combined with physical modeling results using data assimilation and machine learning to predict magnetic field perturbations near Earth. For example, in some embodiments, a global magnetic field model is constructed. The GMFM can describe the global magnetic field perturbations due to electric current systems owing in the ionosphere and magnetosphere, as well as their induced counterparts in the conducting Earth.

[0033] The GMFM represents the large-scale global magnetic perturbation field due to electric currents flowing in the ionosphere and magnetosphere, as well as their induced secondary fields in the conducting Earth. The magnetic field due to these sources exhibits a high degree of spatial and temporal variability and is extremely challenging to model accurately. This magnetic field is driven primarily by input from the Sun (solar cycle variations on longer time scales and solar wind variations on shorter timescales). There currently exist decades of magnetic measurements of the global magnetic perturbation field from both ground stations and satellites, under a wide variety of solar conditions.

[0034] The GMFM may also describe the large-scale average patterns of the magnetic perturbations due to solar inputs (solar flux levels, solar wind parameters, interplanetary magnetic field (IMF) parameters). In accordance with various embodiments, the GMFM may be unable to capture the small-scale temporal and spatial variations in a local region. This model may also accept as input various parameters related to the solar wind and current systems in the ionosphere and magnetosphere. Example input parameters may include but are not limited to solar flux intensity, solar wind velocities, IMF components, magnetospheric ring current strength, and high-latitude ionospheric current strengths.

[0035] Real-time and near real-time data can be ingested from satellites which record parameters related to the solar wind and geomagnetic field. These satellites may include but are not limited to satellites situated in deep space between the Sun and Earth which record solar wind parameters (velocity components) and interplanetary magnetic field components and satellites in low Earth orbit (LEO) which record electric and/or magnetic field measurements of the geomagnetic and geoelectric field. The RT and NRT data can also be ingested from ground magnetic observatories and variometer stations. For example, this data can be ingested from a global network of stations which record geomagnetic variations due to external and induced electric current systems. Using all of the data collected, GMFM prediction accuracy on local/regional scales can be enhanced, in near real-time, using data assimilation techniques or machine learning for combining measured data with modeling output.

[0036] Fig. 2 is a flowchart illustrating process 200 for generating enhanced predictions by combining modeling predictions with collected satellite and ground data. In step 205, a global magnetic field model is constructed that is configured to produce modeling predictions describing global magnetic field perturbations based on input parameters characterizing solar wind and IMF conditions. Examples of input parameters may include but are not limited to solar flux intensity, solar wind velocities, IMF

components, magnetosphere ring current strength, and high-latitude ionospheric current strengths. In step 210, satellite data comprising data related to at least one solar wind parameter and at least one magnetic field component is obtained. Step 210 may include ingesting real-time and near real-time data from satellites which record parameters related to the solar wind and geomagnetic field. These satellites may include satellites situated in deep space between the Sun and Earth (e.g., satellite 1 15) which record solar wind parameters (i.e., velocity components, etc.) and interplanetary magnetic field components. These satellites may further include satellites in low Earth orbit (e.g., satellite 120) which record electric and/or magnetic field measurements of the geomagnetic and geoelectric field.

[0037] In step 215, ground data comprising data related to geomagnetic variations is obtained. Step 215 may include ingesting real-time and near real-time data from ground magnetic observatories and variometer stations (e.g., positions shown on Earth 1 10).

These data may be ingested from a global network of stations which record geomagnetic variations due to external and induced electric current systems. In step 220, an enhanced modeling prediction based on the modeling prediction, the satellite data, and the ground data is generated. The data collected via satellites and ground collection methods can help enhance GMFM prediction accuracy on local/regional scales in near real-time. Data assimilation techniques and/or machine learning may be used to combine the measured data with the GMFM modeling output to generate the enhanced prediction.

[0038] Fig. 3 is a flow chart illustrating process 300 for generating enhanced GMFM predictions in accordance with certain embodiments of the present technology. In step 305, a system in accordance with the present disclosure constructs a GMFM describing global magnetic field perturbations due to electric current systems flowing in the ionosphere and magnetosphere and their induced counterparts. In some examples, the GMFM describes the large-scale average patterns of the magnetic perturbations due to solar inputs (e.g., solar flux levels, solar wind parameters, IMF parameters). The GMFM may accept as input various parameters related to the solar wind and current systems in the magnetosphere and ionosphere. In step 310, the system ingests RT and NRT data from satellites that record parameters related to solar wind and geomagnetic field (e.g., satellite 1 15 and satellite 120). In step 315, the system ingests RT and NRT data from ground magnetic observatories and variometer stations (e.g., stations on Earth 1 10). In step 320, the system uses the satellite data and ground data to enhance GMFM prediction accuracy in NRT by combining the measured data with the modeling output. In some examples, combining the measured data with the modeling output includes implementation one or more machine learning techniques (e.g., neural networks, k-nearest neighbor, random forest, etc.).

[0039] An example of polar current climatology as seen in one year of low-Earth orbiting CHAMP satellite measurements is shown in Fig. 4. Fig. 4 illustrates an example of north pole 410 and south pole 420 magnetic signatures of ionospheric polar current systems as recorded from one year of Challenging Minisatellite Payload (CHAMP) data. Fig. 4 further includes scale 430 measuring nanoteslas from -300 to 300. Some embodiments may use the CHAMP satellite data (and other magnetic satellite

observations) and a database of observations to build a model of the climatology (or average) field under different solar conditions. This climatological model can capture the primary spatial patterns and temporal changes in the field and may rely on a number of state parameters (e.g., solar flux intensity, solar wind velocity, IMF components, etc.). This model may be unable to capture the small-scale spatial and temporal field fluctuations in some examples, and so the model can be supplemented with real-time data assimilation from a global network of ground stations and satellites.

[0040] Traditional models may be built with similar methodologies, using several years of ground and/or satellite observations to derive the climatology of the ionospheric and magnetospheric field at the Earth’s surface and in LEO. However, these existing models suffer from inaccuracies on short temporal and spatial scales since the physical mechanisms producing these complex electrical currents are not sufficiently understood in order to capture small-scale variations.

[0041] In contrast, various embodiments of the present technology may use a custom model of the large-scale global magnetic field which assume that primary source electrical currents flow in a thin shell at an altitude of 1 10 km. The magnetic field generated by these currents above or below the shell can be expressed as a solution to Laplace’s equation in spherical coordinates,

where represent the magnetic field components in a spherical coordinate system

represents the model coefficients, a is a reference radius, and is the

spherical harmonic of degree n and order m.

[0042] The model coefficients,

fully specify the magnetic perturbation field and represent the novel step forward in the approach. In the approach, a form of the model parameters

derived from physical knowledge of the solar wind parameters driving the magnetic field is specified a-priori. The model parameters are given by the following:

where B_T represents the magnitude of the tangential IMF field in the Y-Z plane with a clock angle q_c, V_sw represents the solar wind velocity, t represents the dipole tilt angle in radians, and F10.7 is the solar flux index. The coefficients may be initially determined through a least squares analysis to maps built from satellite and ground stations. Then, according to some embodiments, the coefficients can be subsequently refined by ingesting real-time and near real-time data, as discussed below.

[0043] Fig. 5A, Fig. 5B, and Fig. 5C show examples of applying the GMFM to various datasets recorded by the Deadhorse magnetic observatory during a geomagnetic storm in June 2015. The thinner curves in Fig. 5A, Fig. 5B, and Fig. 5C show the observed declination, observed total field, and observed inclination. The thicker curves show the predicted values from GMFM. Fig. 5A includes declination graph 500 which includes GMFM prediction curve 505 and recorded data curve 510. Total field graph 520 of Fig. 5B shows GMFM prediction curve 525 and recorded data curve 530. Dip graph 540 of Fig. 5C shows GMFM prediction curve 545 and recorded data curve 550.

[0044] Some deep space satellite missions exist (such as Advanced Composition

Explore (ACE) and the Deep Space Climate Observatory (DSCOVR)) whose mission is to provide continuous measurements of solar wind velocity and IMF conditions. These measurements can provide valuable information for forecasting upcoming changes in the external field. Additionally, satellites in LEO continually monitor the geomagnetic field, whose observations can supplement the solar wind observations to help determine more precisely the solar-induced changes in the external disturbance field. These satellites move at around 7km/s through the geomagnetic field and can track spatial variations very well. The measurements from all of these satellites may be combined to provide updates to the climatological GMFM to enhance its accuracy on small local and regional scales.

[0045] Satellites such as ACE and DSCOVR are operational missions with significant support to provide real-time data streams. The GMFM may take advantage of these or similar data streams to update model predictions in real-time. Other satellites, such as those in LEO, may provide data in NRT or with a delay of a few days. Such data can still be useful for modeling purposes in some embodiments by providing observations of the magnetic field close to the Earth’s surface and allowing corrections to the climatological spatial maps produced by the GMFM.

[0046] Some embodiments make use of the global network of ground magnetic observatories and variometer stations to further enhance the accuracy of the GMFM.

Ground stations are adept in tracking temporal variations in the global geomagnetic field and are able to provide valuable information on the short-scale time variations in the disturbance field. This information can be assimilated into the climatological predictions of GMFM to enhance its accuracy.

[0047] Many ground observatories part of the INTERMAGNET network already have the capability of providing real-time data streams (typically for a fee). Also, data provided with a short delay may be useful for correcting the disturbance field model on smaller regional scales.

[0048] There exist various methods of assimilating real-time measurements into a model in order to enhance its ability to accurately predict real world phenomena. Some embodiments can use a two-step process that includes a forecast step and an analysis step. In the forecast step, a past state of the system can be propagated forward in time using physical constraints of the system in order to obtain an estimate of the system state at the current time. Then, in the analysis step, real-time observations can be combined with the physical prediction in order to make a correction to the model which more closely matches the observations. The Kalman filter is an example of such a scheme that may be used in some embodiments.

[0049] A completely different approach, that may be used in other embodiments, is based on machine learning, by which an artificial neural network (ANN) can be trained with a large input dataset to predict a known outcome. Then, once the ANN has a good understanding of the relationship between inputs and outputs, it can be used to make predictions in the future from real-time and near real-time data streams.

[0050] Some embodiments can use these data assimilation techniques to combine the climatological model with real-time observations from the network of satellites and ground stations in order to enhance the accuracy of the disturbance field prediction on small local scales.

[0051] The Kalman filter equations can be expressed as:

where x(t) is the best estimate of the state vector at time t (the model parameters of GMFM), x^F(t + 1) is the forecast value of state vector at time t + 1 (prior to assimilation of new data), F(ί + 1; t) is the matrix which evolves state vector from time t to t + 1, u(t) is the vector representing process noise, P(t) is the covariance matrix of state vector at time t, P^F(t + 1) is the forecast estimate of covariance matrix at time t + 1 (prior to assimilating new data), Q(t) is the covariance matrix of process noise, y(t + 1) is the measurement vector at time t + 1, M(t) is the matrix relating measurements to state vector x^F(t + 1), v(t) is the vector of measurement noise, K(t + 1) is the Kalman gain matrix, R(t) is the measurement error covariance matrix.

[0052] An implementation of a full Kalman filter for models with a large number of parameters (state vector) is computationally prohibitive. The most expensive steps are the calculation of the evolution matrix F, the propagation of errors (P^F(t + 1)), and the updating of the covariance matrix (P(t + 1)). These difficulties have led to a search for methods to approximate the covariance matrix and its evolution, such as the ensemble Kalman filter. Some embodiments can use the GMFM to propagate the state vector forward in time, making the calculation of F unnecessary. In order to approximate the covariance matrix, some embodiments may utilize an ensemble of state vectors, each driven with different solar wind and IMF inputs in order to capture a wide range of physical states corresponding to physical quantities that cannot be perfectly measured. The covariance matrix can then be estimated as the covariance between the state vectors of the ensemble members in some embodiments.

[0053] In accordance with various embodiments, the state vector x(t) can contain the spherical harmonic coefficients of the GMFM (i.e.,

which can be used to generate the climatological spatial patterns of the disturbance magnetic field at any altitude from the surface to LEO. Since GMFM relies on input parameters characterizing the solar wind and IMF conditions, the forecast vector x^F(t + 1) can be calculated simply by running the GMFM for the next time step with the corresponding input parameters. This allows some embodiments to completely avoid calculating the F matrix, which would require a large computational burden, as all of the relevant physics of the ionosphere and magnetosphere would be needed to fully specify this matrix accurately.

[0054] The forecast covariance matrix can be calculated according to the approximation

where n is the number of model parameters (length of x(t)), and M is the number of members in the ensemble. This equation can be used to estimate the covariance between the different members of the ensemble and may be used in place of

[0055] The matrix M(t) relating the state vector and observations is straightforward - it represents the Green's functions of the expansion of the GMFM relating spherical harmonic coefficients to magnetic field observations at the Earth's surface and in LEO.

[0056] With the covariance matrix P^F(t + 1) and Green's function matrix M(t) specified, the Kalman gain K(t + 1) can be readily calculated. Once K(t + 1) is computed, some embodiments can compute the new state vector x(t + 1), with assimilation of the RT and NRT observations y(t + 1) by using the equation for x(t + 1). Finally, the covariance matrix can be updated according to the equation for P(t + 1) using the approximation of P^F(t + 1).

[0057] Fig. 6 is an example architecture of an artificial neural network that may be used in accordance with various embodiments of the present technology. Neural network architecture 600 includes input layer 605, hidden layer 610, output layer 615, input 620, input 625, input 630, input 635, output 640, and transfer function example 645. Neural network architecture 600 is an example of a feed-forward neural net architecture. Artificial neural networks are a commonly used machine learning technique. An artificial neural network is an information processing system composed of a large number of processing elements called neurons, which are modeled on the functions of neurons in the human brain. A neural network has the ability to adaptively discriminate or learn through repeated exposure to examples and in their robustness in the presence of high-noise levels. Neural networks do not require a priori knowledge concerning the noise distribution of the physics of the system under study, like its statistical or physics-based counterparts. Unlike conventional methods, which incorporate a fixed algorithm to solve a particular problem, neural networks perform a highly non-linear mapping between the input and output data, which allows the network to acquire important information on the problem being solved.

[0058] One of the most widely used types of artificial neural network, the feed- forward artificial neural network is shown in Fig. 6. It consists of a layer of neurons that accept various inputs (the input layer). These inputs are fed to further layers of neurons (hidden layers) and ultimately to the output layer, which produces a response. The aim of the technique is to train the network such that its response to a given set of inputs is as close as possible to a desired output. A number of algorithms are available for training a neural network. Back propagation is the most popular training algorithm and may be used in various embodiments of the present technology. [0059] During neural network training, each hidden and output neuron process inputs by multiplying each input by its weights. The products can be summed and processed using an activation function, here, a sigmoid function

to produce an output with reasonable discriminating power. The neural network learns by modifying the weights of the neurons in response to the errors between the actual and targeted output values. For a given set or vector of N inputs the output of

node j is computed as

where W_ji is the weight of the connection between the i -th and j -th neurons. The learning rule for the adjustments in the weight between neurons i and j can be expressed as

where o_i is either the output of node i or an input, h is a positive constant called the learning rate and is the error term of node j. Thus

where

[0060] In contrast, various embodiments of the present technology may use a custom model of the large-scale global magnetic field which assume that primary source electrical currents flow in a thin shell at an altitude of 1 10 km. The magnetic field generated by these currents above or below the shell can be expressed as a solution to Laplace’s equation in spherical coordinates.

[0061] Here, is the target value for the j -th node and o_j is the output for the j -th

node. The value is computed as

if the node is not an output unit. To improve the convergence characteristics, a momentum gain b can be added to the weight correction term, which stabilizes oscillations during the learning process, i.e.

where n is the iteration index. The training of the network can be indicated as complete, in some embodiments, if the convergence of weighting coefficients has been achieved. The convergence criterion may require that the sum square error at the output must be less than a desired tolerable error.

[0062] While training a network, we start with arbitrary values for the weights It

is usual to choose random numbers in the range 0 to 1. Next, the outputs (O) and errors (E) for that set of weights can be computed. Then, the derivatives of E with respect to all of the weights can be calculated. If increasing a given weight would lead to more error, the weight may be adjusted downwards. If increasing a weight leads to a reduced error, the weight may be adjusted upwards. After adjusting the weights up or down, the process may start over again and the system can keep going through this process until the error is close to zero. The sequence of presenting the entire training database, calculating the network response, comparing the result with the assigned class, propagating the error backwards and adjusting the weights is called an epoch. A few thousand such training epochs are usually required by a neural network to reach zero error. However, if the number of training patterns exceeds the number of weights in the network it may not be possible for the sum squared error (SSE) to reach zero.

[0063] Fig. 7 illustrates an example of a recurrent neural network design for magnetic prediction that may be used in some embodiments. While artificial neural networks work very well for classification of time series, it may require adaptation for prediction of time series because the predicted value of a magnetic component depends not only on the present input values but also on past input values within a certain time window. In other words, the current systems in the ionosphere, magnetosphere and their induced counter parts in the Earth and ocean have memory of the past variations. In order to account for the connection between past and present values, some embodiments use a variation of a neural network called Recurrent Neural Network (RNN) as presented in Fig. 7.

[0064] As illustrated in Fig. 7, are the input at time steps

t - 2 to t + 2. For example, x may be the X, Y or Z component of the magnetic field at a ground observatory. Some embodiments may concatenate the time series of X, Y and Z with a fixed length and provide the network as one time series. W_h1h1 represent the weights that connect the hidden states of the network in layer 1 . W_h2h2 are similarly defined for layer 2. The second layer is optional and may only be added if network performance is sub-optimal in some examples. W_h1t_₂ through W_h1t+2 represent the weights that connect the hidden states of the network in layer 2. S_t_₂, ... ,S_t+2 represent the hidden states corresponding to time steps t - 2 to t + 2. They are the“memory" of the network. S_t is calculated based on the previous hidden state and the input at the current step: S_t = f(x_t + W_h1h1). The function f is the sigmoid function (f(x)) that maps the inputs nonlinearly to values between -1 to 1 . The first hidden state is typically initialized to all zeroes. The outputs are represented by at steps t - 2 to t + 2. For example, some

embodiments can predict the X component at some spatial location it would be a time series of X measured by an input ground station, coinciding in time with the input time series.

[0065] The theory behind error back-propagation and weight adjustment during the training of an RNN is similar to that of an artificial neural net described in the previous section. Some embodiments may use a python-based software for the training and prediction of magnetic data which can be adapted to real-time use.

[0066] Fig. 8A, Fig. 8B, and Fig. 8C show improvements achieved through various embodiments of the present technology that combine global modeling, satellite data, and ground data through machine learning. The thick, solid curves show the declination, total field and inclination data measured at Deadhorse magnetic observatory during a storm in June 2015. The thin, solid curves show the GMFM predictions, which tend to capture longer time scales but do poorly in prediction rapid small-scale variations. The dotted curves show the improvement offered by techniques disclosed herein wherein the GMFM prediction is improved by combining it with collected data via machine. The improved prediction manages to capture many of the small-scale variations in the signal.

[0067] Fig.8 A includes declination graph 800 which shows collected data curve 805

(solid, thick), GMFM curve 810 (solid, thin), and enhanced curve 815 (dotted). Fig. 8B includes total field graph 820. Total field graph 820 includes collected data curve 825 (solid, thick), GMFM curve 830 (solid, thin), and enhanced curve 835 (dotted). Fig. 8C includes dip graph 840. Dip graph 840 includes collected data curve 845 (solid, thick), GMFM curve 850 (solid, thin), and enhanced curve 855 (dotted). As is shown by the enhanced curves, the present technology improved predictions by managing to capture small-scale variations in the signal. [0068] Aspects and implementations of the magnetic field estimation system of the disclosure have been described in the general context of various steps and operations. A variety of these steps and operations may be performed by hardware components or may be embodied in computer-executable instructions, which may be used to cause a general- purpose or special-purpose processor (e.g., in a computer, server, cloud-based computing platform, or other computing device) programmed with the instructions to perform the steps or operations. For example, the steps or operations may be performed by a combination of hardware, software, and/or firmware.

[0069] In the following description, for the purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of embodiments of the present technology. It will be apparent, however, to one skilled in the art that embodiments of the present technology may be practiced without some of these specific details. Moreover, various embodiments may be implemented as a cloud-based platform or service in which local devices can access and request estimates. In other embodiments, the techniques introduced here can be embodied as special-purpose hardware (e.g., circuitry), as programmable circuitry appropriately programmed with software and/or firmware, or as a combination of special-purpose and programmable circuitry. Hence, embodiments may include a machine-readable medium having stored thereon instructions which may be used to program a computer (or other electronic devices) to perform a process. The machine-readable medium may include, but is not limited to, floppy diskettes, optical disks, compact disc read-only memories (CD-ROMs), magneto-optical disks, ROMs, random access memories (RAMs), erasable programmable read-only memories

(EPROMs), electrically erasable programmable read-only memories (EEPROMs), magnetic or optical cards, flash memory, or other type of media / machine-readable medium suitable for storing electronic instructions.

[0070] Fig. 9 is a block diagram illustrating an example machine representing the computer systemization of the estimation system that may be used in some embodiments. Controller 900 may be in communication with entities including one or more users 925 client/terminal devices 920, user input devices 905, peripheral devices 910, an optional co- processor device(s) (e.g., cryptographic processor devices) 915, and networks 930. Users may engage with the controller 900 via terminal devices 920 over networks 930.

[0071] Computers may employ central processing unit (CPU) or processor to process information. Processors may include programmable general-purpose or special- purpose microprocessors, programmable controllers, application-specific integrated circuits (ASICs), programmable logic devices (PLDs), embedded components, combination of such devices and the like. Processors execute program components in response to user and/or system-generated requests. One or more of these components may be implemented in software, hardware or both hardware and software. Processors pass instructions (e.g., operational and data instructions) to enable various operations.

[0072] The controller 900 may include clock 965, CPU 970, memory such as read only memory (ROM) 985 and random-access memory (RAM) 980 and co-processor 975 among others. These controller components may be connected to a system bus 960, and through the system bus 960 to an interface bus 935. Further, user input devices 905, peripheral devices 910, co-processor devices 915, and the like, may be connected through the interface bus 935 to the system bus 960. The interface bus 935 may be connected to a number of interface adapters such as processor interface 940, input output interfaces (I/O) 945, network interfaces 950, storage interfaces 955, and the like.

[0073] Processor interface 940 may facilitate communication between co-processor devices 915 and co-processor 975. In one implementation, processor interface 940 may expedite encryption and decryption of requests or data. Input output interfaces (I/O) 945 facilitate communication between user input devices 905, peripheral devices 910, coprocessor devices 915, and/or the like and components of the controller 900 using protocols such as those for handling audio, data, video interface, wireless transceivers, or the like (e.g., Bluetooth, IEEE 1394a-b, serial, universal serial bus (USB), Digital Visual Interface (DVI), 802.1 1 a/b/g/n/x, cellular, etc.). Network interfaces 950 may be in communication with the network 930. Through the network 930, the controller 900 may be accessible to remote terminal devices 920. Network interfaces 950 may use various wired and wireless connection protocols such as, direct connect, Ethernet, wireless connection such as IEEE 802.1 1 a-x, and the like.

[0074] Examples of network 930 include the Internet, Local Area Network (LAN),

Metropolitan Area Network (MAN), a Wide Area Network (WAN), wireless network (e.g., using Wireless Application Protocol WAP), a secured custom connection, and the like. Network interfaces 950 can include a firewall which can, in some aspects, govern and/or manage permission to access/proxy data in a computer network, and track varying levels of trust between different machines and/or applications. The firewall can be any number of modules having any combination of hardware and/or software components able to enforce a predetermined set of access rights between a particular set of machines and applications, machines and machines, and/or applications and applications, for example, to regulate the flow of traffic and resource sharing between these varying entities. The firewall may additionally manage and/or have access to an access control list which details permissions including, for example, the access and operation rights of an object by an individual, a machine, and/or an application, and the circumstances under which the permission rights stand. Other network security functions performed or included in the functions of the firewall, can be, for example, but are not limited to, intrusion-prevention, intrusion detection, next-generation firewall, personal firewall, etc., without deviating from the novel art of this disclosure.

[0075] Storage interfaces 955 may be in communication with a number of storage devices such as, storage devices 990, removable disc devices, and the like. The storage interfaces 955 may use various connection protocols such as Serial Advanced Technology Attachment (SATA), IEEE 1394, Ethernet, Universal Serial Bus (USB), and the like.

[0076] User input devices 905 and peripheral devices 910 may be connected to I/O interface 945 and potentially other interfaces, buses and/or components. User input devices 905 may include card readers, fingerprint readers, joysticks, keyboards, microphones, mouse, remote controls, retina readers, touch screens, sensors, and/or the like. Peripheral devices 910 may include antenna, audio devices (e.g., microphone, speakers, etc.), cameras, external processors, communication devices, radio frequency identifiers (RFIDs), scanners, printers, storage devices, transceivers, and/or the like. Coprocessor devices 915 may be connected to the controller 900 through interface bus 935, and may include microcontrollers, processors, interfaces or other devices.

[0077] Computer executable instructions and data may be stored in memory (e.g., registers, cache memory, random access memory, flash, etc.) which is accessible by processors. These stored instruction codes (e.g., programs) may engage the processor components, motherboard and/or other system components to perform desired operations. The controller 900 may employ various forms of memory including on-chip CPU memory (e.g., registers), RAM 980, ROM 985, and storage devices 990. Storage devices 990 may employ any number of tangible, non-transitory storage devices or systems such as fixed or removable magnetic disk drive, an optical drive, solid state memory devices and other processor-readable storage media. Computer-executable instructions stored in the memory may include one or more program modules such as routines, programs, objects, components, data structures, and so on that perform particular tasks or implement particular abstract data types. For example, the memory may contain operating system (OS) component 995, modules and other components, database tables, and the like.

These modules/components may be stored and accessed from the storage devices, including from external storage devices accessible through an interface bus. [0078] The database components can store programs executed by the processor to process the stored data. The database components may be implemented in the form of a database that is relational, scalable and secure. Examples of such database include DB2, MySQL, Oracle, Sybase, and the like. Alternatively, the database may be implemented using various standard data-structures, such as an array, hash, list, stack, structured text file (e.g., XML), table, and/or the like. Such data-structures may be stored in memory and/or in structured files.

[0079] The controller 900 may be implemented in distributed computing

environments, where tasks or modules are performed by remote processing devices, which are linked through a communications network, such as a Local Area Network ("LAN"), Wide Area Network ("WAN"), the Internet, and the like. In a distributed computing environment, program modules or subroutines may be located in both local and remote memory storage devices. Distributed computing may be employed to load balance and/or aggregate resources for processing. Alternatively, aspects of the controller 900 may be distributed electronically over the Internet or over other networks (including wireless networks). Those skilled in the relevant art(s) will recognize that portions of the system may reside on a server computer, while corresponding portions reside on a client computer. Data structures and transmission of data particular to aspects of the controller 900 are also encompassed within the scope of the disclosure.

[0080] Unless the context clearly requires otherwise, throughout the description and the claims, the words "comprise," "comprising," and the like are to be construed in an inclusive sense, as opposed to an exclusive or exhaustive sense; that is to say, in the sense of "including, but not limited to." As used herein, the terms "connected," "coupled," or any variant thereof means any connection or coupling, either direct or indirect, between two or more elements; the coupling or connection between the elements can be physical, logical, or a combination thereof. Additionally, the words "herein," "above," "below," and words of similar import, when used in this application, refer to this application as a whole and not to any particular portions of this application. Where the context permits, words in the above Detailed Description using the singular or plural number may also include the plural or singular number respectively. The word "or," in reference to a list of two or more items, covers all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of the items in the list.

[0081] The phrases "in some embodiments," "according to some embodiments," "in the embodiments shown," "in other embodiments," and the like generally mean the particular feature, structure, or characteristic following the phrase is included in at least one implementation of the present technology, and may be included in more than one implementation. In addition, such phrases do not necessarily refer to the same

embodiments or different embodiments.

[0082] The above Detailed Description of examples of the technology is not intended to be exhaustive or to limit the technology to the precise form disclosed above. While specific examples for the technology are described above for illustrative purposes, various equivalent modifications are possible within the scope of the technology, as those skilled in the relevant art will recognize. For example, while processes or blocks are presented in a given order, alternative implementations may perform routines having steps, or employ systems having blocks, in a different order, and some processes or blocks may be deleted, moved, added, subdivided, combined, and/or modified to provide alternative or

subcombinations. Each of these processes or blocks may be implemented in a variety of different ways. Also, while processes or blocks are at times shown as being performed in series, these processes or blocks may instead be performed or implemented in parallel, or may be performed at different times. Further any specific numbers noted herein are only examples: alternative implementations may employ differing values or ranges.

[0083] The teachings of the technology provided herein can be applied to other systems, not necessarily the system described above. The elements and acts of the various examples described above can be combined to provide further implementations of the technology. Some alternative implementations of the technology may include not only additional elements to those implementations noted above, but also may include fewer elements.

[0084] These and other changes can be made to the technology in light of the above Detailed Description. While the above description describes certain examples of the technology, and describes the best mode contemplated, no matter how detailed the above appears in text, the technology can be practiced in many ways. Details of the system may vary considerably in its specific implementation, while still being encompassed by the technology disclosed herein. As noted above, particular terminology used when describing certain features or aspects of the technology should not be taken to imply that the terminology is being redefined herein to be restricted to any specific characteristics, features, or aspects of the technology with which that terminology is associated. In general, the terms used in the following claims should not be construed to limit the technology to the specific examples disclosed in the specification, unless the above Detailed Description section explicitly defines such terms. Accordingly, the actual scope of the technology encompasses not only the disclosed examples, but also all equivalent ways of practicing or implementing the technology under the claims.

[0085] To reduce the number of claims, certain aspects of the technology are presented below in certain claim forms, but the applicant contemplates the various aspects of the technology in any number of claim forms. For example, while only one aspect of the technology is recited as a computer-readable medium claim, other aspects may likewise be embodied as a computer-readable medium claim, or in other forms, such as being embodied in a means-plus-function claim. Any claims intended to be treated under 35 U.S.C. § 1 12(f) will begin with the words "means for", but use of the term "for" in any other context is not intended to invoke treatment under 35 U.S.C. § 1 12(f). Accordingly, the applicant reserves the right to pursue additional claims after filing this application to pursue such additional claim forms, in either this application or in a continuing application.

Claims

CLAIMS What is claimed is:

1. A method comprising: constructing a global magnetic field model (GMFM), wherein the GMFM is configured to produce a modeling prediction describing global magnetic field perturbations based on one or more input parameters;

obtaining satellite data comprising data related to at least one solar wind parameter and at least one magnetic field component;

obtaining ground data comprising data related to geomagnetic variations; and generating an enhanced modeling prediction based on the modeling prediction, the satellite data, and the ground data.

2. The method of claim 1 , wherein generating the enhanced modeling prediction comprises using at least one data assimilation technique to combine the modeling prediction with the satellite data and the ground data.

3. The method of claim 1 , wherein generating the enhanced modeling prediction comprises using at least one machine learning technique to combine the modeling prediction with the satellite data and the ground data.

4. The method of claim 1 , wherein the modeling prediction and the enhanced modeling prediction represent patterns of magnetic perturbations due to one or more solar inputs.

5. The method of claim 1 , wherein the one or more input parameters comprise one or more of solar flux intensity, solar wind velocity, interplanetary magnetic field components, magnetospheric ring current strength, and high-latitude ionospheric current strengths.

6. The method of claim 1 , wherein the at least one solar wind parameter and the at least one magnetic field component of the satellite data comprise solar wind parameters and interplanetary magnetic field components collected from one or more satellites positioned in space between Sun and Earth.

7. The method of claim 1 , wherein the data related to geomagnetic variations comprises data collected at one or more of a ground magnetic observatory and a variometer station.

8. The method of claim 1 , wherein the satellite data further comprises one or more of: electric field measurements of a geomagnetic field; electric field measurements of a geoelectric field;

magnetic field measurements of a geomagnetic field; and magnetic field measurements of a geoelectric field.

9. A system comprising: one or more computer-readable storage media having stored thereon a global magnetic field model (GMFM), wherein the GMFM is configured to produce a modeling prediction describing global magnetic field perturbations due to solar inputs based on one or more input parameters;

a processing system operatively coupled with the one or more computer-readable storage media; and

program instructions stored on the one or more computer-readable storage media for generating an enhanced modeling prediction, wherein the program instructions, when read and executed by the processing system, direct the processing system to at least: obtain satellite data comprising data related to at least one solar wind parameter and at least one magnetic field component;

obtain ground data comprising data related to geomagnetic variations; and generate an enhanced modeling prediction based on the modeling prediction, the satellite data, and the ground data.

10. The system of claim 9, wherein to generate an enhanced modeling prediction, the program instructions further direct the processing system to provide the modeling prediction, the satellite data, and the ground data to a machine learning engine configured at least to combine the modeling prediction, the satellite data, and the ground data.

1 1 . The system of claim 9, wherein to generate an enhanced modeling prediction, the program instructions further direct the processing system to provide the modeling prediction, the satellite data, and the ground data to an assimilation engine that assimilates real-time measurements from the satellite data and the ground data into the global magnetic field model to generate the enhanced modeling prediction.

12. The system of claim 11 , wherein the assimilation engine further comprises: a forecasting module to generate an estimate of a state at a current time by propagating past state forward in time using physical constraints; and an analysis module to correct the modeling prediction based on real-time observations.

13. The system of claim 9, wherein to generate the enhanced modeling prediction, the program instructions direct the processing system to predict a value of a magnetic component based on a present input value and past input values within a time window.

14. The system of claim 9, wherein the modeling prediction and the enhanced modeling prediction represent patterns of magnetic perturbations due to one or more solar inputs.

15. The system of claim 9, wherein the one or more input parameters comprise one or more of solar flux intensity, solar wind velocity, interplanetary magnetic field components, magnetospheric ring current strength, and high-latitude ionospheric current strengths.

16. The system of claim 9, wherein the at least one solar wind parameter and the at least one magnetic field component of the satellite data comprise solar wind parameters and interplanetary magnetic field components collected from one or more satellites positioned in space between Sun and Earth.

17. One or more computer-readable storage media having program instructions stored thereon for generating enhanced global magnetic field predictions, wherein the program instructions, when read and executed by a processing system, direct the processing system to: construct a global magnetic field model (GMFM), wherein the GMFM is configured to produce a modeling prediction describing global magnetic field perturbations based on one or more input parameters;

obtain satellite data comprising data related to at least one solar wind parameter and at least one magnetic field component;

obtain ground data comprising data related to geomagnetic variations; and provide the modeling prediction, the satellite data, and the ground data to a machine learning engine configured to combine the modeling prediction, the satellite data, and the ground data and produce an enhanced modeling prediction describing global magnetic field perturbations.

18. The one or more computer-readable storage media of claim 17, wherein the machine learning engine comprises a recurrent neural network.

19. The one or more computer-readable storage media of claim 17, wherein the modeling prediction and the enhanced modeling prediction represent patterns of magnetic perturbations due to one or more solar inputs.

20. The one or more computer-readable storage media of claim 17, wherein the one or more input parameters comprise one or more of solar flux intensity, solar wind velocity, interplanetary magnetic field components, magnetospheric ring current strength, and high-latitude ionospheric current strengths.