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At least 397 records · Page 22

Extended Kalman Filter Performance on the Artemis-1 Mission

The Artemis Program is NASA’s campaign to explore the Moon and beyond. Artemis-1, the uncrewed exoLEO test flight of the Orion spacecraft, was completed in 2022. There were four navigation Extended Kalman Filters (EKFs) that are part of the Orion navigation system. The Atmospheric Extended Kalman Filter (ATMEKF) estimates the vehicle position, velocity, and attitude (referred to as the vehicle state) during the ascent and entry phases of flight. Once Orion is outside of Earths atmosphere, the Earth Orbit Extended Kalman Filter (EOEKF) and CisLunar Extended Kalman Filter (CLEKF) estimate the translational states, depending on the phase of flight, while the Attitude Extended Kalman Filter (ATTEKF) estimates the rotational state of the vehicle. The Kalman filters propagate the vehicle state forward in time using a combination of dynamics models and the output data from the Inertial Measurement Unit (IMU). The filters update the vehicle states and associated uncertainties, in the form of the covariance matrix, using pseudorange measurements from GPS (in ATMEKF/EOEKF), optical navigation measurements of the Earth or Moon (in CLEKF), and star tracker measurements (in ATTEKF). Simultaneously, the Kalman filters estimate error sources in the sensors, which are included in the state vectors as Exponentially Correlated Random Variables (ECRVs). This paper will summarize the performance of these filters during the Artemis-1 mission.

Artemis-1↗

ACS3 - Flight Dynamics for A Solar Sail Technology Demonstration Mission

The NASA's Advanced Composite Solar Sail System (ACS3) mission consist of a spacecraft that will deploy an 80 m 2 solar sail in a 1000 km sun-synchronous orbit. The main objective of the mission is to demonstrate that the solar wind can impulse the spacecraft to change the semimajor-axis and obtain a different orbit altitude. The sail will be composed of a combination of composite materials with distinct properties, and it will be deployed with lightweight booms from a 12U CubeSat bus, developed by Nanoavionics. The spacecraft will be launched aboard an Electron launch vehicle from Rocket LAB Launch Complex in New Zealand no earlier than July 2023. This paper covers the orbital mechanics and navigation developments to support the mission, from the solar sail trajectory model to the actual flight dynamics system to provide the orbit determination analysis prior to flight. First, we introduce a description of our high-fidelity propagation that accounts for the solar radiation pressure to produce predictive ephemeris of the solar sail performance with several spacecraft attitude modes. As part of our results, we present plots of the expected altitudes achieved by the spacecraft once the solar sail is deployed under various assumptions of the solar weather. In addition to that, we present a full description of our orbit determination process which relies in GPS state vectors to accurately estimate the position and velocity uncertainties at a frequent cadence during the mission. The outcome of this process will be critical to achieving the objective of determining effective altitude change produced by the solar sail.

Solar Sail↗

ACS3: Flight Dynamics

The NASA's Advanced Composite Solar Sail System (ACS3) mission consist of a spacecraft that will deploy an 80 m2 solar sail in Low Earth Orbit (LEO). The main objective of the mission is to demonstrate that the solar wind can impulse the spacecraft to change the semimajor-axis and obtain a different orbit altitude. The sail will be composed of a combination of composite materials with distinct properties, and it will be deployed with lightweight booms from a 12U CubeSat bus, developed by Nanoavionics. The spacecraft will be launched aboard an Electron launch vehicle from Rocket LAB Launch Complex in New Zealand. This paper covers the orbital mechanics and navigation developments to support the mission, from the solar sail trajectory model to the actual flight dynamics system to provide the orbit determination analysis prior to flight. First, we introduce a description of our high-fidelity propagation that accounts for the solar radiation pressure to produce predictive ephemeris of the solar sail performance with several spacecraft attitude modes. As part of our results, we present plots of the expected altitudes achieved by the spacecraft once the solar sail is deployed under various assumptions of the solar weather. In addition to that, we present a full description of our orbit determination process which relies in GPS state vectors to accurately estimate the position and velocity uncertainties at a frequent cadence during the mission. The outcome of this process will be critical to achieving the objective of determining effective altitude change produced by the solar sail.

Solar sail↗

Forward and Inverse Models for Satellite Remote Sensors using Principal Component Analysis

Satellite remote sensors such as AIRS on Aqua, CrIS on S-NPP, NOAA20 and JPSS-2, IASI on Metop A, B, and C make millions of observations each day with thousands of spectral channels for each observation; this poses challenges for efficiently inversion of the inherently large dataset as needed to retrieve atmospheric and surface properties. This presentation will illustrate the use of Principal Component Analysis (PCA) to speed up radiative transfer forward model calculations and to stabilize the inversion algorithms. A Principal Component-based radiative transfer model (PCRTM) developed at NASA Langley Research Center can simulate top of atmosphere (TOA) radiance or reflectance spectra from 50 cm-1 to 50000 cm-1 (200 m to 0.20 m quickly and accurately. PCRTM demonstrated very high accuracy relative to reference line-by-line radiative transfer models and it saves orders of magnitude computational time. Examples of the PCRTM model developed for hyperspectral sensors such as AIRS, CrIS, IASI, NAST-I, SHIS, CPF, TEMPO, SBG, OMI, and SCIAMACHY will be presented. In addition to using the PCRTM as forward model, the NASA Langley developed inversion algorithm also uses PCA to compress the state vector into a compressed dimension to speed up and stabilize the inversion process. Examples of retrieved atmospheric temperature, water vapor, CO2, CO, CH4, N2O, and O3 profiles, cloud properties (optical depth, size, phase, and height), and surface properties (surface emissivity spectra and skin temperatures) will be presented. This algorithm is being transitioned to the NASA Sounder SIPS and NASA's Goddard Earth Sciences Data and Information Services Center (GES DISC).

forward model↗

Surrogate Optimization for Quantum Circuits

Variational quantum Eigensolvers are touted as a near-term algorithm capable of impacting many applications. However, the potential has yet to be realized with few claims of quantum advantage and high resource estimates mainly due to the need for optimization in the presence of noise. Finding algorithms and methods to improve the convergence is essential to accelerate the capabilities of near-term hardware for VQE or more broad applications of hybrid methods in which optimization is required. To this goal we look to use modern approaches recently developed in circuit simulations and stochastic classical optimization that can be combined in a surrogate optimization approach to classical circuits. Using an approximate state vector simulator, we efficiently calculate an approximate Hessian, fed as an input for a detailed quantum circuit simulator. We demonstrate the capabilities of such an approach with and without sampling noise. We also show that this method outperforms Powell in the presence of quantum circuit shot noise by a factor of 2-4

quantum computing↗

Navigation for the ACS3 Solar Sail Mission

NASA’s Advanced Composite Solar Sail System (ACS3) mission consists of a spacecraft that plans to be launched in early 2024. The spacecraft carries an 80 m2 solar sail that can produce effective thrust to alter the initial 1000 km sun-synchronous orbit. The main objective of the mission is to demonstrate the capabilities of the solar sail to effectively change various orbital parameters such as the semi-major axis and the inclination. Various composite materials were used to produce the sail, together with lightweight booms that will deploy from a 12U CubeSat bus. The astrodynamics team at NASA Ames Research Center has built a Flight Dynamics System (FDS) to provide mission navigation and to produce regular ephemeris once in orbit. The FDS can compute the trajectories that the spacecraft will perform once the sail is deployed. To achieve that, GPS data is obtained from the spacecraft telemetry and then is used with a Kalman filter and a smoother to obtain an orbit determination solution. The outcome of this process reduces the position and velocity uncertainty in a daily cadence. After that, the state vector output is used to feed a propagation model that includes the updated attitude and orbit of the spacecraft at that given moment. The trajectory model considers the updated attitude plan of the spacecraft as well as the environment conditions such as the solar weather to compute the associated drag and solar radiation pressure. This paper explains in detail the implementation of the FDS, as well as the solar sail solar radiation pressure trajectory model. We also present the results of several potential trajectory models under various assumptions of orbit parameters, attitude, environment, and material properties. In addition, we introduce a trajectory model for potential interplanetary use of an equivalent solar sail in the future. The outcome of this process will be critical to achieving the objective of determining effective altitude change produced by the solar sail.

Andres Dono Perez↗

Navigation for the ACS3 Solar Sail Mission

NASA’s Advanced Composite Solar Sail System (ACS3) mission consists of a spacecraft that plans to be launched no earlier than April 2024. The spacecraft carries an 81 m2 solar sail that can produce effective ΔV to alter the initial 1000 km sun-synchronous orbit. The main objective of the mission is to demonstrate the capabilities of the solar sail to effectively change the semi-major axis of its initial orbit. Various composite materials were used to produce the sail, together with lightweight booms that will deploy from a 12U CubeSat bus. The ACS3 navigation team at NASA Ames Research Center has built a Flight Dynamics System (FDS) to provide mission navigation and to produce regular ephemeris once in orbit. The FDS can compute the orbit transfers that the spacecraft will perform once the sail is deployed. To achieve that, GPS data is obtained from the spacecraft telemetry and then is used with a Kalman filter and a smoother to obtain an orbit determination solution. The outcome of this process reduces the position and velocity uncertainty in a daily cadence. After that, the state vector output is used to feed a propagation model that includes the updated attitude and orbit of the spacecraft at that given moment. The trajectory model considers the updated attitude plan of the spacecraft as well as the environment conditions such as the solar weather to compute the associated drag and solar radiation pressure. This paper explains in detail the implementation of the FDS, as well as the solar sail solar radiation pressure trajectory model. We also present the results of several potential trajectory models under various assumptions of orbit parameters, attitude, environment, and material properties. In addition, we introduce a trajectory model for potential interplanetary use of an equivalent solar sail in the future. The outcome of this process will be critical to achieving the objective of determining effective semi-major axis change produced by the solar sail.

Andres Dono↗

Exploring Resonance Structures in the Partial-Wave Analysis of ¿p0 Photoproduction at GlueX

This thesis studies what happens when a photon (¿) collides with a proton (p) and produces a neutral omega (¿) and pion (p0) pair, with a recoiling proton (p'), expressed as ¿p ¿ ¿p0p'. We study this and other reactions to better understand the strong nuclear force; one of the four fundamental forces that govern all the physics of the universe. This force is specifically responsible for the binding and decay of subatomic particles, such as the ones here. While we understand the ¿ and p0, what we are actually interested in is a short-lived unknown particle X that decays via X ¿ ¿p0. There are a multitude of possible particles X can be, and so our focus in this work is to find out what X is by determining its properties from the particles we measure. We do this via an intricate analysis procedure known as “partial-wave analysis”. By analogy, one can think of our particle detector as a buoy, and the particles we want to analyze (X) as pebbles hitting a pond. The waves created by the pebble will move our buoy, giving us information about the pebble that produced the wave. However, when multiple pebbles hit our pond, the waves overlap and interfere with each other. Our buoy only can measure the complicated interfering result of all the waves. To disentangle this, our partial-wave analysis works by modeling this interference pattern so that we may infer the properties of the pebbles (particles) we produced. In this thesis, we review the relevant experimental history in photoproduction and related production mechanisms, as well as the theoretical foundations that motivate our measurement. We describe the methods used to collect our data at the GlueX experiment stationed at the Jefferson Lab accelerator facility in Newport News, Virginia. We then detail the selections we apply to ensure our events are almost exclusively ¿p ¿ ¿p0p'. We cover the intensity model, how we verify its capabilities, and finally present our results together with systematic studies. Our primary result is the detection of a b1(1235) meson interfering with a wide JPC = 1-- vector state, measured via a mass-independent partial-wave analysis. It provides precise experimental results that can be used as input for theoretical models of the reaction, yielding conclusions about the procedures responsible for how our universe behaves at its most basic level.

Scheuer, Kevin [College of William and Mary, Willi↗

Recent Developments In Theory Of Balanced Linear Systems

Report presents theoretical study of some issues of controllability and observability of system represented by linear, time-invariant mathematical model of the form. x = Ax + Bu, y = Cx + Du, x(0) = xo where x is n-dimensional vector representing state of system; u is p-dimensional vector representing control input to system; y is q-dimensional vector representing output of system; n,p, and q are integers; x(0) is intial (zero-time) state vector; and set of matrices (A,B,C,D) said to constitute state-space representation of system.

Gawronski, Wodek↗

Nonlinear filtering for spacecraft attitude estimation

Nonlinear filtering techniques are applied to spacecraft attitude estimation using quaternion parameterization for the attitude kinematics. By replacing the angular velocity vector by the gyro output vector, a state dependent noise vector is introduced in the seven-dimensional system equations. The resulting conditional probability density function from the Ito differential rule is governed by the Fokker Planck partial differential equation which is approximated by the second order mean and covariance differential equations. In order to minimize computer loading, the covariance propagation is carried out in six-dimensional state space using a matrix transformation. The star tracker data is used to update the covariance matrix in the seven-dimensional space. The algorithm is simulated for an earth pointing spacecraft mission, using Monte Carlo samples of gyro and star measurements. The performance of the second order filter is compared with the extended Kalman Filter through several simulation runs and drift rates have been identified.

Vathsal, S.↗

Application of a recursive distortion estimator to the geodetic correction of thematic mapper imagery

It is pointed out that the higher resolution provided by the Thematic Mapper increases the demands on the accuracy needed by the ground processing in correcting for geodetic errors deriving from internal misalignments and uncertainties in the knowledge of spacecraft ephemeris and attitude. In addition, the Thematic Mapper will also process longer imagery intervals than previous missions. The recursive distortion estimator to be used is a Kalman filter. Here, a minimum variance spacecraft state error vector is estimated for known initial covariance of the elements of that vector and known image noise. Tests of the recursive distortion estimator with various spacecraft models carried out using a simulation of real world state vector dynamics are described. A determination is made of the density of control points needed to meet specified geometric correction requirements; it is expressed as a function of imagery interval length and control point measurement error.

Arnold, P.↗

The harmonic oscillator and nuclear physics

The three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It is shown that the three-dimensional harmonic oscillator features a rich variety of coherent states, including vibrations of the monopole, dipole, and quadrupole types, and rotations of the rigid flow, vortex flow, and irrotational flow types. Nuclear collective states exhibit all of these flows. It is also shown that the coherent state representations, which have their origins in applications to the dynamical groups of the simple harmonic oscillator, can be extended to vector coherent state representations with a much wider range of applicability. As a result, coherent state theory and vector coherent state theory become powerful tools in the application of algebraic methods in physics.

Rowe, D. J.↗

HarDWR - Harmonized Water Rights Records

For a detailed description of the database of which this record is only one part, please see the HarDWR meta-record. Here we present a new dataset of western U.S. water rights records. This dataset provides consistent unique identifiers for each spatial unit of water management across the domain, unique identifiers for each water right record, and a consistent categorization scheme that puts each water right record into one of 7 broad use categories. These data were instrumental in conducting a study of the multi-sector dynamics of intersectoral water allocation changes through water markets (Grogan et al., in review). Specifically, the data were formatted for use as input to a process-based hydrologic model, WBM, with a water rights module (Grogan et al., in review). While this specific study motivated the development of the database presented here, U.S. west water management is a rich area of study (e.g., Anderson and Woosly, 2005; Tidwell, 2014; Null and Prudencio, 2016; Carney et al, 2021) so releasing this database publicly with documentation and usage notes will enable other researchers to do further work on water management in the U.S. west. The raw downloaded data for each state is described in Lisk et al. (in review), as well as here. The dataset is a collection of objects stored within an RDate file, stateWaterRightsHarmonized.RData. Each object either describes how one should interact with the other objects, or contains the harmonized water rights data. Here is each object described in detail: states: A character vector containing the state names for those states in which data was collected for. More importantly, the index of the state name is also the index in which that state's data can be found in the various following list objects. For example, if California is the third index in this object, the data for California will also be in the third index for each accompanying list. rightsByState_ground: A list of data frames with the cleaned ground water rights collected from each state. The column headers for each data frame are: waterRightID - The unique identifying ID of the water right, the same identifier as its state uses. basinNum - The alpha-numeric identifier of the WMA the record belongs to. priorityDate - The priority date associated with the right. allocatedFlow - The maximum flow of the allocation in cubic feet per second (ft3s-1). source - Whether the right is for surface water or groundwater. origWaterUse - The original stated water use from the state. waterUse - The water use category under the unified use categories established here. rightsByState_surface: A list of the cleaned surface water rights collected from each state. See rightsByState_ground for more details on how the data is formatted. fullRightsRecs: A list of the combined groundwater and surface water records for each state. Essentially, these lists are the merging of rightsByState_ground and rightsByState_surface by state. See rightsByState_ground for more details on how the data is formatted. projProj: The spatial projection used for map creation in the beginning of the project. Specifically, the World Geodetic System (WGS84) as a coordinate reference system (CRS) string in PROJ.4 format. wmaStateLabel: The name and/or abbreviation for what each state legally calls their WMAs. h2oUseByState: A list of spatial polygon data frames which contain the area(s) in which each water right is claimed to be used. It should be noted that not all water right records have a listed area(s) of use in this object. Currently, only Idaho and Washington provided valid data to be included in this object. h2oDivByState: A list of spatial points data frames which identifies the location of the Point of Diversion for the state's water rights. It should be noted that not all water right records have a listed Point of Diversion in this object. spatialWMAByState: A list of spatial polygon data frames which contain the spatial WMA boundaries for each state. The only data contained within the table are identifiers for each polygon. It is worth reiterating that Arizona is the only state in which the surface and groundwater WMA boundaries are not the same. wmaIDByState: A list which contains the unique ID values of the WMAs for each state. plottingDim: A character vector used to inform mapping functions for internal map making. Each state is classified as either "tall" or "wide", to maximize space on a typical 8x11 page.

Economics↗

HarDWR - Harmonized Water Rights Records

For a detailed description of the database of which this record is only one part, please see the HarDWR meta-record. Here we present a new dataset of western U.S. water rights records. This dataset provides consistent unique identifiers for each spatial unit of water management across the domain, unique identifiers for each water right record, and a consistent categorization scheme that puts each water right record into one of 7 broad use categories. These data were instrumental in conducting a study of the multi-sector dynamics of intersectoral water allocation changes through water markets (Grogan et al., in review). Specifically, the data were formatted for use as input to a process-based hydrologic model, WBM, with a water rights module (Grogan et al., in review). While this specific study motivated the development of the database presented here, U.S. west water management is a rich area of study (e.g., Anderson and Woosly, 2005; Tidwell, 2014; Null and Prudencio, 2016; Carney et al, 2021) so releasing this database publicly with documentation and usage notes will enable other researchers to do further work on water management in the U.S. west. The raw downloaded data for each state is described in Lisk et al. (in review), as well as here. The dataset is a series of various files organized by state sub-directories. The first two characters of each file name is the abbreviation for the state the in which the file contains data for. After the abbreviation is the text which describes the contents of the file. Here is each file type described in detail: XXFullHarmonizedRights.csv: A file of the combined groundwater and surface water records for each state. Essentially, this file is the merging of XXGroundwaterHarmonizedRights.csv and XXSurfaceWaterHarmonizedRights.csv by state. The column headers for each of this type of file are: state - The name of the state the data comes from. FIPS - The two-digit numeric state ID code. waterRightID - The unique identifying ID of the water right, the same identifier as its state uses. priorityDate - The priority date associated with the right. origWaterUse - The original stated water use(s) from the state. waterUse - The water use category under the unified use categories established here. source - Whether the right is for surface water or groundwater. basinNum - The alpha-numeric identifier of the WMA the record belongs to. CFS - The maximum flow of the allocation in cubic feet per second (ft3s-1). Arizona is unique among the states, as its surface and groundwater resources are managed with two different sets of boundaries. So, for Arizona, the basinNum column is missing and instead there are two columns: surBasinNum - The alpha-numeric identifier of the surface water WMA the record belongs to. grdBasinNum - The alpha-numeric identifier of the groundwater WMA the record belongs to. XXStatePOD.shp: A shapefile which identifies the location of the Points of Diversion for the state's water rights. It should be noted that not all water right records in XXFullHarmonizedRights.csv have coordinates, and therefore may be missing from this file. XXStatePOU.shp: A shapefile which contains the area(s) in which each water right is claimed to be used. Currently, only Idaho and Washington provided valid data to include within this file. XXGroundwaterHarmonizedRights.csv: A file which contains only harmonized groundwater rights collected from each state. See XXFullHarmonizedRights.csv for more details on how the data is formatted. XXSurfaceWaterHarmonizedRights.csv: A file which contains only harmonized surface water rights collected from each state. See XXFullHarmonizedRights.csv for more details on how the data is formatted. Additionally, one file, stateWMALabels.csv, is not stored within a sub-directory. While we have referred to the spatial boundaries that each state uses to manage its water resources as WMAs, this term is not shared across all states. This file lists the proper name for each boundary set, by state. For those whom may be interested in exploring our code more in depth, we are also making available an internal data file for convenience. The file is in .RData format and contains everything described above as well as some minor additional objects used within the code calculating the cumulative curves. For completeness, here is a detailed description of the various objects which can be found within the .RData file: states: A character vector containing the state names for those states in which data was collected for. More importantly, the index of the state name is also the index in which that state's data can be found in the various following list objects. For example, if California is the third index in this object, the data for California will also be in the third index for each accompanying list. rightsByState_ground: A list of data frames with the cleaned ground water rights collected from each state. This object holds the the data that is exported to created the xxGroundwaterHarmonizedRights.csv files. rightsByState_surface: A list of data frames with the cleaned surface water rights collected from each state. This object holds the the data that is exported to created the xxSurfaceWaterHarmonizedRights.csv files. fullRightsRecs: A list of the combined groundwater and surface water records for each state. This object holds the the data that is exported to created the xxFullHarmonizedRights.csv files. projProj: The spatial projection used for map creation in the beginning of the project. Specifically, the World Geodetic System (WGS84) as a coordinate reference system (CRS) string in PROJ.4 format. wmaStateLabel: The name and/or abbreviation for what each state legally calls their WMAs. h2oUseByState: A list of spatial polygon data frames which contain the area(s) in which each water right is claimed to be used. It should be noted that not all water right records have a listed area(s) of use in this object. Currently, only Idaho and Washington provided valid data to be included in this object. h2oDivByState: A list of spatial points data frames which identifies the location of the Point of Diversion for the state's water rights. It should be noted that not all water right records have a listed Point of Diversion in this object. spatialWMAByState: A list of spatial polygon data frames which contain the spatial WMA boundaries for each state. The only data contained within the table are identifiers for each polygon. It is worth reiterating that Arizona is the only state in which the surface and groundwater WMA boundaries are not the same. wmaIDByState: A list which contains the unique ID values of the WMAs for each state. plottingDim: A character vector used to inform mapping functions for internal map making. Each state is classified as either "tall" or "wide", to maximize space on a typical 8x11 page. The code related to the creation of this dataset can be viewed within HarDWR GitHub Repository/dataHarmonization.

Economics↗

Time-controlled descent guidance in uncertain winds

A procedure has been developed for constructing a statistical model of the altitude-dependent mean wind profile from the historical record of wind measurements at particular locations. The model is constructed by fitting a Markov process, with altitude as the stage variable, to the historical wind data. The wind model, together with the aircraft dynamics and the error characteristics of the navigation system, are incorporated in the design of a state estimator, which gives the minimum variance estimate of the aircraft state and the wind vector. The state and wind estimates are used as inputs to a linear feedback law for guiding the aircraft along the nominal trajectory. An example design of a time-constrained (4D RNAV) descent guidance system is presented, showing tracking accuracy, control activity, and probability of arrival time with and without the wind estimator.

Menga, G.↗

An atomic orbital-based formulation of analytical gradients and nonadiabatic coupling vector elements for the state-averaged complete active space self-consistent field method on graphical processing units

We recently presented an algorithm for state-averaged complete active space self-consistent field (SA-CASSCF) orbital optimization that capitalizes on sparsity in the atomic orbital basis set to reduce the scaling of computational effort with respect to molecular size. Here, we extend those algorithms to calculate the analytic gradient and nonadiabatic coupling vectors for SA-CASSCF. Combining the low computational scaling with acceleration from graphical processing units allows us to perform SA-CASSCF geometry optimizations for molecules with more than 1000 atoms. The new approach will make minimal energy conical intersection searches and nonadiabatic dynamics routine for molecular systems with O(10{sup 2}) atoms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Model predictive control and optimization for battery charging and discharging

An apparatus for model predictive control (“MPC”) is disclosed. A method and system also perform the functions of the apparatus. The apparatus includes a measurement module that receives battery status information from one or more sensors receiving information from a battery cell, and a Kalman filter module that uses a Kalman filter and the battery status information to provide a state estimate vector. The apparatus includes a battery model module that inputs the state estimate vector and battery status information into a battery model and calculates a battery model output, the battery model representing the battery cell, and an MPC optimization module that inputs one or more battery model outputs and an error signal in a model predictive control algorithm to calculate an optimal response. The optimal response includes a modification of the error signal.

Trimboli, Michael Scott↗