Ionospheric Observations from the ISS: Overcoming Noise Challenges in Signal Extraction

A Statistical F ramew ork for Signal Extraction in Noisy Ionospheric Observ ations from the In ternational Space Station Rac hel Ulric h  , Kelly R. Moran  , Ky P otter  , Lauren A. Castro  , Gabriel R. Wilson  , Carlos Maldonado   Statistics, Computing and Articial Intelligence Division, Los Alamos Na- tional Lab oratory  Statistics and A ctuarial Science Departmen t, Simon F raser Univ ersit y  Analytics, In telligence and T echnology Division, Los Alamos National Lab- oratory  Space Science and Applications, Intelligence and Space Research Division, Los Alamos National Lab oratory Marc h 19, 2026 Abstract The Electric Propulsion Electrostatic Analyzer Exp eriment (ÈPÈE) is a compact ion energy bandpass lter deplo y ed on the In ternational Space Station (ISS) in Marc h 2023 and providing con tinuous measuremen ts through April 2024. This perio d co- incides with the Solar Cycle 25 maxim um, capturing unique observ ations of solar activit y extremes in the mid- to low-latitude regions of the topside ionosphere. F rom these in situ sp ectra w e deriv e plasma parameters that inform space-w eather impacts on satellite na vigation and radio comm unication. W e present a statistical pro cessing pip eline for ÈPÈE that (i) estimates the bac kground curren t prole of the instrumen t, (ii) accounts for irregular temp oral sampling, and (iii) extracts ionospheric signals. Rather than discarding data b elo w some current threshold, the method learns an instrumen tal baseline and ts the residual measurement surface using a scaled V ec- c hia Gaussian pro cess appro ximation, decreasing the num b er of observ ation times t ypically rejected by thresholding by ov er 98%. The resulting pro ducts increase data co v erage and enable noise-assisted monitoring of ionospheric v ariabilit y . K eywor ds: Gaussian pro cesses, Scaled V ecc hia, Ionospheric science, signal pro cessing 1 1 In tro duction 1.1 Bac kground on EPEE instrument The Electric Propulsion Electrostatic Analyzer Exp erimen t (ÈPÈE) is a low-cost, rugged, compact laminated electrostatic analyzer (ESA) deploy ed on the International Space Sta- tion (ISS) in Marc h 2023. ÈPÈE provided contin uous measurements from its deplo ymen t through April 2024, spanning the entry into the maximum of Solar Cycle 25 ( Maldonado et al. 2025 ). In space plasma ph ysics, electrostatic analyzers (ESAs) are widely used for measuring particle energy p er unit c harge (   ). By com bining sensor geometry with an applied electric eld to form an energy band-pass lter, ÈPÈE measures ion energy and curren t from lo cal charged particle p opulations ( Maldonado et al. 2025 , 2023 ). F rom these measuremen ts, macroscopic parameters of interest can b e derived. The ISS orbits at   kilometers ab o v e the Earth’s surface, pro viding critical mea- suremen ts of the top-side ionosphere directly ab o v e the F2 p eak that cannot b e obtained from ground-based metho ds ( Maldonado et al. 2025 ). The ionosphere is a lo w-density , ”cold” plasma dictating that curren ts are relativ ely small (rep orted in nanoamp eres) and temp eratures are low (0.1-0.2 electron V olts). A ccurate plasma measuremen ts facilitate understanding of the complex relationships b etw een solar storms, the solar cycle, eclipse, and spacecraft charging. This understanding is essential not only for exploring phenomena of scientic interest (e.g., the Equatorial Ionization Anomaly and T rav eling Ionospheric Disturbances), but also for anticipating space-w eather eects on the gro wing n um ber of lo w Earth orbit satellites that support na vigation, comm unication, and national securit y ( Mino w et al. 2024 ). The ÈPÈE instrument pro vides measurements at a rate of 0.5 Hz, resulting in a single data p oint appro ximately ev ery t w o seconds. Due to the selectiv e lter design, at each 2 timestamp (  ) a measurement of the current ( I ) and energy ( E ) in electron V olts (e V) is recorded for each of 100 discrete energy bins ( B with       ). Energy v alues are discretized in to bins with the total observ ed range spanning appro ximately 0.8 - 185 e V. A t each timestamp we hav e v alues of current across energy bins (   ), or a distribution of curren t that c haracterizes the lo cal space plasma at that momen t in time. Figure 1 displays a heat map of curren t v alues across energy bins for the seven-hour time p erio d that serves as the example for this pap er (Sept 28, 2023 22:00:00 UTC - Sept 29, 2023 05:00:00 UTC). The ma jorit y of higher curren t v alues (ranging from 0-5 nA) o ccur at or b elow energy bin 25, with current v alues recorded near the instrument noise o or (0.15 nA) for higher energy bins. This enhancement pattern recurs approximately ev ery   minutes, consistent with the ISS orbital p erio d. In terpretation of ÈPÈE’s measuremen ts relies on basic principles of plasma physics. Recall- ing that a plasma consists of electrons, ions, and neutrals, each sp ecies can b e describ ed by a distribution function  󰅠  r  v   that ev olv es under external forces and collisions, where r and v are the p osition and velocity vectors and  is time. This function, often referred to as the phase sp ac e density , represen ts the num b er of particles per unit v olume in real and velocity space — that is, the particle density at a given velocity , p osition, and time. Because individual motions cannot b e observed, macroscopic parameters—such as densit y and temp erature—are estimated by taking moments of these distributions ( Ho w ard 2002 ). Due to ÈPÈE’s limited eld of view, the mov ement of space plasma relative to the detector face is primarily along the v elo city vector, allowing the use of a one-dimensional Maxw ellian distribution,     , as an analytical appro ximation to the ion velocity distribution. Here,     is a sp ecies-sp ecic simplication of the general distribution  󰅠  r  v   , assuming spatial and temp oral homogeneity and that p erp endicular v elo cit y comp onents contribute negligibly within ÈPÈE’s narro w eld of view. Ho w ev er, b ecause the plasma cannot b e 3 Figure 1: Heat map of current v alue by energy bin for the time range of in terest (Sept 28, 2023 22:00:00 UTC - Sept 29, 2023 05:00:00 UTC). Color indicates the range of current v alues b et w een 0-5 nA across the 100 discrete energy bins, display ed on the y-axis. Time is on the x-axis (MM-dd:HH). F or this time p erio d, larger current v alues mainly o ccur in energy bins at or b elow bin 25, with the ma jority of curren t v alues recorded near the noise o or (0.15 nA) in higher energy bins. 4 considered to b e in thermal equilibrium o wing to external in terference from the ISS, a drifte d Maxwel lian is used to account for the resulting bulk ow velocity . This distribution dep ends on     and the drift v elo cit y   , where  is the Boltzmann constant,   are sp ecies-sp ecic (with  represen ting the thermal spread in lo cal equilibrium), and  is the total n um b er density serving as the normalizing constant ( Maldonado et al. 2023 ):        󰄛    exp            (1) The form of this distribution is familiar, as it is a special application of the Gaussian distribution. ÈPÈE measures ion current arising from the ux of charged particles transmitted through its energy bandpass at eac h voltage step. The measured current              there- fore reects the v elo cit y distribution weigh ted b y particle sp eed within the analyzer’s se- lected energy-p er-charge window. The current p eak    o ccurs at the most probable energy    linking the drifted Maxwellian form of Eq. 1 to the subsequent energy rela- tion used to infer the spacecraft p oten tial 󰄠  ( Maldonado et al. 2023 ):           󰄠  (2) Th us, selecting the maximum current v alue (   ) and resp ective energy v alue (   ) at a giv en timestamp allo ws us to solv e for spacecraft p oten tial ( 󰄠  ). Recall  is the particle c harge (see Section 1.1 ). Figure 2 demonstrates the distribution of current v alues for a single momen t in time under the conditions in whic h a Maxw ellian is a reasonable appro ximation. The p eak current v alue describ es the most likely v alue and is matched to the energy v alue for the resp ectiv e energy bin. 5 Figure 2: Distribution of current v alues across energy bins for a single timestamp (2023-09- 29 00:33:18 UTC). Discrete current observ ations are mark ed by p oints and the underlying empirical distribution is t with a line. Energy bin is on the x-axis and curren t is on the y-axis (nA) with color referring to energy v alue (e V). Energy v alue is discretized by bins; energy v alues increase as bin n um b er increases. This is referenced with indigo blues fading to azure as energy v alue increases across the x-axis. Gra y lines indicate the intersection of the maxim um v alues for current and energy . 6 1.2 Bac kground on Spacecraft Charging The electrical c harging physics of the ISS are complex. In brief, the design and motion of the ISS and in teraction with the ionosphere pro duce conditions p oten tially hazardous to astronauts during extrav ehicular activit y , and to the surface of the ISS itself (please see Hastings ( 1995 ) for a detailed explanation). Initially , the Floating P oten tial Measurement Unit (FPMU) w as deplo yed in 2006 as a permanent diagnostic tool of charging ph ysics, designed with four separate instrumen ts that together pro duced reliable measurements of am bien t plasma densit y and electron temp erature in addition to frame p otential. These observ ations ha ve redundan t measuremen ts o v er several instrumen ts: Density is directly measured by the Wide-sw eep Langmuir Prob e (WLP) and the Narro w-Sweep Langm uir Prob e (NLP), and derived from measurements tak en b y the Plasma Imp edance Prob e (PIP) while spacecraft charge is measured b y the WLP and NLP , and referenced by the FPP ( Sw enson et al. 2003 , Mino w et al. 2023 ). These redundancies facilitate cross-v alidation b et w een instruments, rendering measuremen ts from the FPMU to b e the general source of truth b y the scientic communit y . Although intended for only three years op eration, the FPMU has provided observ ations of lo cal space plasma for nearly t w o decades ( Minow et al. 2023 ). How ever, these data were not a contin uous record, rendering EPEE the main provider of data for its limited lifetime deplo ymen t. A seven-hour p erio d of ov erlap exists b etw een the t w o data sets in 2023, on Julian days 271 and 272. This perio d of ov erlap will b e used as the case example - and opp ortunit y for comparison - for the remainder of the analysis in instances where subsets of the data record are most ecacious for visualization. As shown in Equation ( 2 ), determining spacecraft charge at a given timestamp requires the selection of the maximum current v alue and resp ective energy v alue, resulting in data formatted with a single current v alue, energy bin, energy v alue and spacecraft charge v alue 7 p er timestamp. If, ho w ev er, our assumed underlying distribution do es not reasonably ap- pro ximate the data, taking the maxim um curren t v alue do es not align with our exp ectation. Belo w, Figure 3 shows an empirical distribution of curren t v alues for a single timestamp with no clear maxim um. Figure 3: Empirical distribution of current v alues across energy bins for a single timestamp (2023-09-28 23:05:20 UTC). Energy bin is on the x-axis and curren t is on the y-axis (nA). The increase in energy v alue (e V) is represen ted through a lightening blue color palette, with indigo blues indicating low er energy v alues and azure blues indicating higher energy v alues. In this instance, choosing a maximum v alue is not clear, and the ma jority of observ ations fall in close pro ximit y to the actual maximum. Figure 3 demonstrates another, related issue. Although not alw a ys the case, the times- tamps that present diculties in prop erly selecting the maximum v alue are often hov ering at or b elo w the instrumen t noise o or (0.15 nA). Observ ations near the instrument’s sensi- tivit y threshold are notoriously dicult to handle, as the true signal can b e hard to extract. Moreo v er, maxim um curren t v alues around this threshold often o ccur in tandem with in- ated energy v alues. As energy has a direct relationship with spacecraft p otential (see 8 Equation( 2 )), very high energy v alues result in clearly erroneous spacecraft p otential v al- ues, far ab ov e the automatic disc harge threshold of the ISS (spacecraft p otential of 40 v olts) ( Sw enson et al. 2003 ). Initial thresholding eorts considered these p oints “un trust w orthy” and remo v ed them from subsequent analyses, creating a notable amount of missing data, particularly during the 7-hour ov erlap p erio d used in cross-calibration eorts with FPMU. Figure 4 shows the o verlap perio d for Julian da ys 271-272 in 2023 for EPEE maxim um curren t (   ) and energy (   ) v alues. Energy v alues are on the y-axis with time on the x-axis (month-da y:hour) and colors p ertaining to current v alues. All current v alues at or b elo w the instrument noise o or (0.15 nA) are colored in dark grey , and the remaining curren t v alues (ranging from 0.15-5 nA) are represented with dark er blues indicating low er v alues and y ello ws indicating higher v alues. Current v alues at or b elow the noise o or predominan tly o ccur in tandem with v ery high energy v alues, as exemplied in Figure 3 . Note that the initial resp ective energy v alue for the raw current maximum w ould b e 169.9 e V, a clearly unphysical v alue. F urthermore, when these data are aligned with sensors pro viding spacecraft p otential ob- serv ations from the FPMU instrumen t (Wide-Sweeping Langmuir Prob e (WLP), Floating P oten tial Prob e (FPP); please see Sw enson et al. ( 2003 ) for more information on these sen- sors), more instances of missingness o ccur. Due to mismatc hing time stamps and missing data from FPMU, the already short window of time a v ailable for cross-calibration b ecomes further disjointed, limiting our ability to extract as muc h information as p ossible from the data. T ypically , these v alues would b e dropp ed from analysis but ev en seemingly erroneous observ ations ma y provide motiv ation for future explorations, th us we seek to preser v e as man y observ ations as p ossible. F or the remainder of the pap er w e consider an illustrative subset of data that o v erlaps with FPMU av ailabilit y (Sept 28, 2023 22:00:00 UTC - Sept 29, 2023 05:00:00 UTC) to 9 Figure 4: Maxim um current v alues (y-axis) across time (x-axis), with colors indicating resp ectiv e curren t v alues. Co oler colors indicate lo w er curren t v alues and w armer colors indicate higher curren t v alues (range 0-5 nA). All observ ations with current v alues at or b elo w the instrument noise o or (0.15 nA) are colored in dark grey . These current v alues often - although not alw a ys - o ccur in tandem with very high energy v alues. explore an alternativ e approac h to handling noisy current input v alues, emplo ying a series of tec hniques to capture data p oints previously considered un usable and smo oth input v alues for use in the calculation of spacecraft p oten tial. W e show ho w this approac h facilitates b etter cross-calibration with FPMU data and estimation of parameters crucial to mission safet y and success. 2 Metho ds 2.1 Ov erview As previously describ ed, the instrument noise o or ho v ers around 0.15 nA, leading to mis- iden tication of the appropriate p eak energy bin. An alternative approach to handling 10 these v alues is outlined in the follo wing steps: 1. Learn the smo oth current surface: Fit Gaussian pro cess (GP) mo dels to the current data I , producing smooth estimates I S of the current surface as a function of time and energy . 2. Identify “minimal signal” timestamps: Using I , iden tify a subset of times that are bac kground-dominated t                   with          indexing the selected timestamps. 3. Iteratively t and rene an instrumen t baseline prole, i.e. the shap e around which pure-noise observ ations at eac h energy bin app ear: Consider the smo oth curren t prole      asso ciated with time    across energy bins       . W e mo del this prole as the sum of tw o main comp onents: a Ric hards curve with a parab olic adjustment, which is our baseline prole      or “bac kground”, plus a Gaussian impulse to capture “signal” . W e do this for each prole, then select from these individual proles to iden tify a conserv ative underlying baseline prole    . 4. Subtract the baseline prole, p ost-pro cess to remov e an y remaining noisy artifacts, and calculate downstream metrics: Let                denote the set of all smo othed, baseline-subtracted, cleaned curren t v alues. Using these   v alues in place of  , w e can compute the maxim um curren t v alue at timestamp  as    in order to retain more usable observ ations. Figure 5 sho ws a dierent persp ective of these steps, with inputs (teal blue rectangles), outputs (burnt orange rectangles) and processes (plum circles) showing mo vemen t from observ ation-based input to the deriv ed v ariables of interest (white b ox with black outline). Although sp ecic decisions ha v e b een made at v arious steps that were b est-suited to these data and application, the ov erall metho dology represen ts a general denoising approac h. F or 11 Figure 5: Flow chart depicting the metho dology for handling v alues near the instrumen t baseline. Inputs are in blue and outputs in burn t orange, both are rectangular shap es. Outputs that then b ecome inputs in subsequen t steps hav e a dashed outline. Processes are in purple circles with a solid line representing input to a pro cess and an arrow representing output of a pro cess. The nal, desired v ariables of interest are iden tied with a white b ox outlined in blac k. example, in Step 1 w e implement a V ecc hia GP in order to learn the smo oth curren t surface; a dierent underlying mo del could b e chosen, a dieren t GP appro ximation metho d could replace scaled V ecc hia, or - dep ending on the size of the data - an exact GP could b e implemen ted. The baseline itself could b e describ ed with a known shap e (e.g. a constan t oset), if this w ere appropriate, instead of learning this prole from the data. 2.2 Step 1: Fit a smo oth surface using a GP approximation The data are partitioned into quarter-day interv als and a GP is used to learn the underly- ing smo oth current surface as a function of time and energy for each 6-hour c h unk. GPs are exible statistical mo dels that allo w for surfaces to b e t to data without requiring man y assumptions to b e made ab out the surface structure. GPs can b e conceptualized as distributions o ver functions (or surfaces) or as innite-dimensional generalizations of the m ultiv ariate Gaussian distribution. GPs are fully sp ecied b y t w o functions, a mean 12 function (   X   ) and a cov ariance function (   X  X   ). The mean function is commonly set to zero for centered data, leaving the dep endence structure b et w een obser- v ations to driv e the mo del’s behavior. The curren t surface ov er time and energy is then dened:            󰄐           󰄐     󰄝   (3) Let          denote the time/energy combination asso ciated with observ ation  . Then, the v ector I            of observ ed curren ts at inputs        follo ws an  - v ariate Gaussian distribution with cov ariance matrix   󰄝    , where the   th en try of  is given by           . Th us, the kernel    sp ecies the cov ariance b etw een laten t current surface v alues at t w o time–energy combinations ( Betancourt 2020 , Lawrence et al. 2022 ). W e dene    as a Matérn  kernel ( Rasmussen & Williams 2006 ) with separate range parameters for time and energy (see App endix 6 ). These range parameters, the pro cess v ariance, and the noise v ariance 󰄝  are optimized via maxim um likelihoo d. In v erting the co v ariance matrix in the lik eliho o d computation b ecomes infeasible as  increases due to the required    op erations. Many approaches ha v e b een developed to circum v en t this issue. One such approximation, the V ecchia approximation ( V ecc hia 1988 ), w as originally developed in spatial statistics and has b een substantially extended in recent w ork. F ollo wing the metho dology of Lawrence et al. ( 2022 ), and for a xed ordering of the inputs        , the joint density of the latent current surface ev aluated at those inputs is appro ximated as                             (4) where          denotes a xed-size neigh bor set for observ ation  . Details 13 regarding V ecc hia design c hoices are pro vided in App endix 6 . Because the underlying pro cess is Gaussian, an y conditional distribution of the observ ations is Gaussian; thus eac h term in ( 4 ) is Gaussian with mean and v ariance determined by the corresp onding submatrices of the Matérn co v ariance kernel. 2.3 Step 2: Iden tify bac kground regions and create a baseline prole T o identify timestamps that are bac kground-dominated (i.e., those whose global maxima o ccur aw ay from a lo cal p eak, see Figure 3 ), we leveraged the understanding that maxima iden tied in energy bins ab ov e a certain threshold result in non-physical spacecraft p oten- tial v alues (see Section 1.2 ). Conserv atively , maximum currents identied in bins 50–100 are treated as lik ely bac kground-dominated maxima. After agging likely background- dominated timestamps, the next step is to isolate those that represent low est-signal con- ditions. T o ac hieve this, the algorithm leverages the clustering of likely bac kground- dominated times, visually eviden t in Figure 7 as dense groups of observ ations at higher energy v alues. This heuristic approach fo cuses on identifying the ”heart” of these obser- v ations, targeting the cen tral regions where background dominance is most pronounced. F or these candidate noise timestamps, w e computed the total decrease in current across the rst 20 energy bins, whic h is expected to b e zero for a background-only prole. T o fa v or timestamps lying in the center of sustained bac kground-dominated p erio ds rather than at their edges, we applied a cen tered rolling window to this quan tit y ov er the ordered candidate background timestamps. Starting with a window spanning 3 timestamps and in- creasing it in o dd-sized incremen ts (3, 5, 7, …), a timestamp was retained only if the rolling sum within its window was zero. The windo w was expanded un til the num b er of retained timestamps w ould fall b elow a prespecied target prop ortion of candidate bac kground- 14 dominated times (default 10%), and the retained set from the previous step was used. Larger windows enforce this zero-decrease condition ov er a broader neighborho o d, pro duc- ing a smaller but more conserv ative set of background-only timestamps, whereas smaller windo ws retain more timestamps but are less stringent. This pro cedure isolates the most stable, minimal-signal in terv als and enables accurate characterization of the instrument’s baseline bac kground-dominated b eha vior. After iden tifying background timestamps, w e mo del eac h bac kground-dominated current prole      as the sum of an instrument baseline and a p ossible ionospheric signal con tri- bution via a prole-tting pro cedure that mo dels      as the sum of three comp onents: a Ric hards curve, a parab olic curve, and a Gaussian p eak.           R 󰄓        P 󰄓        instrumen t baseline      G 󰄓        ionospheric signal (5) where the instrumen t baseline is comp osed of the Richards curve t (     R 󰄓   ) and parab olic comp onen t (     P 󰄓   ), parameterized by 󰄓         󰄙     and 󰄓       , resp ectively .Any remaining lo calized structure is identied using a Gaussian p eak     G 󰄓   with parameters 󰄓   󰄌 󰄘 󰄝  (see App endix 6.1 for full mathematical forms). The Richards curve is a generalization of the logistic function that in tro duces a shap e parameter 󰄙 to allo w for asymmetry in the sigmoidal form. Although originally developed for gro wth mo deling in biology , epidemiology , and ecology ( Richards 1959 ), it is w ell suited to mo deling the stabilizing behavior of instrumen t bac kground across energy bins, capturing smo oth rises and plateaus with exibilit y in slop e and curv ature. As suc h, the Ric hards comp onen t is alw a ys included as the base mo del in our background prole estimate. After subtracting the Richards t, a Gaussian comp onen t is t to the residuals to capture an y remaining localized structure. This structure is presumed to represen t true signal 15 rather than bac kground, so the Gaussian is used only during tting and not added to the nal bac kground prole. Once parameter estimates for the Richards and Gaussian comp onen ts ha ve stabilized, a parabolic term is in tro duced to mo del lo w-order curv ature not captured by the sigmoid. Thus our rened bac kground prole for each timestamp b ecomes           󰄓        󰄓   (see App endix 6.1 for further details and visualizations). Although written as an additiv e mo del, the three comp onents are not t sim ultaneously . Instead, all parameters are estimated by constrained nonlinear least squares in a sequential pro cedure designed to prev en t lo calized enhancemen ts from biasing the smo oth baseline estimate. Sp ecically , the Richards comp onent is t rst, a Gaussian term is then t to the residuals o v er low energy bins to capture lo calized signal, and once those t w o comp onents ha v e stabilized, a parab olic term is t to the remaining residual structure. The Gaussian comp onen t is used only to protect the baseline t from ionospheric signal and is not included in the nal background prole estimate. This sequential strategy a v oids joint-t behavior in whic h the exible Ric hards curve can partially absorb lo calized p eaks, thereby inating the estimated baseline and suppressing true ionospheric signal. The resulting baseline estimate for eac h candidate bac kground prole is           R 󰄓        P 󰄓   . Among all candidate bac kground proles, we selected as the nal background prole estimate the tted baseline with the smallest integrated magnitude ov er bins 2 through 20, corresp onding to the most stable lo w-energy background regime. Figure 6 sho ws results for the rst and fourth quarters of Julian day 271 (both with n=10799) with GP-smo othed curren t v alues (y-axis) for each timestamp plotted across energy bins (x-axis) and color indicating energy v alue. There are 100 timestamps iden- tied as ’lik ely minimal signal’ from eac h p erio d. After each timestamp undergo es the tting process individually , the tted background prole with the smallest integral is se- lected (highlighted in red). The rst quarter (top facet) candidate selection do es a fairly 16 go o d job and little Gaussian shap e is left in the residuals to t and remov e. In contrast, the initial candidate selection in the fourth quarter (b ottom facet) pic ks up signal in the earlier bins, which we successfully capture through the iterative tting pro cess and preserve b y subtracting this shap e from the nal tted bac kground prole. Figure 6: Results of the bac kground prole tting pro cess for the rst (top facet) and fourth quarter (b ottom facet) of Julian da y 271 (b oth with n=10799). Candidate bac kground- dominan t timestamps (those identied as likely minimal signal) are plotted across energy bins (x-axis) and GP-smo othed current v alues (y-axis) with raw energy identied b y color- ing (blues lightening with increasing v alues). The nal tted bac kground prole, comprised of Ric hards and parab olic comp onen t shap es, is highligh ted in red. 2.4 Step 3: Learn the smo oth curren t prole Because the instrument baseline is omnipresent, we subtract it from our predicted GP t to yield a learned current surface that is smo other (due to the GP) and less dominated b y instrumen tal eects in low-curren t times (due to the bac kground iden tication and subtraction). The background-subtracted, smo oth current surface is then used to select 17 the maximum current v alue by timestamp and the respective energy v alue from the raw energy v alues is identied. These maxima represent the inferred p eak signal lo cations and are the only non-constan ts that enter in to the equation for calculating our main downstream metric of in terest, spacecraft p oten tial (Equation ( 2 )). 2.5 Step 4: P ost-pro cessing Although the bac kground-tting and remo v al pro cess mitigates many of the previously- deemed un trust w orth y times across the 13-month dataset, several post-pro cessing lters are applied to address outlier cases and ensure robust signal identication. Sp ecically , w e remov e time in terv als that exhibit prolonged sequences of high-energy maxima, which often indicate instrumental anomalies or solar interference. W e also exclude observ ations in which the p eak bin undergo es a sudden and drastic down ward shift, suggesting an arti- fact in tro duced during background prole subtraction, particularly after timeline merging. Finally , any maxima asso ciated with energy v alues exceeding 45 e V are discarded, as these are considered physically implausible in the context of this analysis. All remov ed entries are agged and retained in the nal dataset to preserve transparency and supp ort further algorithmic impro v emen ts. 3 V erications 3.1 Bac kground Iden tication and Instrument Baseline Mo deling Figure 7 shows maximum energy v alue (   ) results for the 7-hour p erio d spanning Ju- lian da ys 271-272. Smo othed, noise-subtracted curren t v alues are depicted with darker blues indicating lo w er v alues and yello ws indicating higher v alues. Time is on the x-axis. Observ ations identied as un trust w orthy and dropp ed through the original thresholding 18 metho dology are colored in gray . The blac k p oints represen t observ ations that were statis- tically indistinguishable from zero (at 󰄌   condence level) through the alternative metho dology that are th us considered ‘truly untrust worth y’ . The revised approach results in a 98.2% decrease in the n um b er of p oints classied as un trustw orthy (38 versus 2,144 with the original metho d), substantially increasing the amoun t of usable data for charac- terizing plasma b eha vior. F urthermore, the observ ations iden tied as un trust w orthy no w predominantly o ccur in a small windo w of time, latitude and longitude (further describ ed in Figure 9 ). Although careful consideration o v er the en tire 13 mon ths is still needed, observ ations agged as un trust w orthy through the new metho dology may serve as a starting p oint for iden tication of the lo cation of the Equatorial Ionization Anomaly . This is an exciting p ossible direction of future researc h. Figure 7: Comparison of original and new metho dologies for pro cessing the data. Energies at p eak curren ts found under the new metho dology are colored by the baseline-subtracted, smo othed current v alue with p oints identied as un trust w orth y in black. Original metho d- ology results for observ ations that w ere previously dropp ed from analyses are in grey . 19 Empirical V alidation of Learned Maxima A fully sp ecied generative mo del for raw EPEE current measuremen ts—including all in- strumen tal artifact mechanisms at sub-minute resolution—is not a v ailable. As a result, constructing a realistic sim ulation framework for v alidating trust worthiness classication w ould require strong and un v eriable assumptions ab out the data-generating pro cess. In- stead, we assess the reliabilit y of the prop osed p eak identication procedure empirically using indep enden t measuremen ts from the FPMU instrument. Figure 8 demonstrates the increased data a v ailabilit y for calibration with FPMU instru- men t data (FPP and WLP) after implemen ting the new metho dology . In the sev en-hour in terv al sho wn, the original approac h pro duces notable gaps in usable data (top panel), limiting in terp olation b et w een calibration windo ws. In contrast, the smo othed current esti- mates (b ottom panel) preserve the exp ected p erio dic structure of spacecraft charging while substan tially increasing the num b er of usable calibration p oin ts. Quan titativ ely , the cleaned EPEE curren ts exhibit improv ed coherence with FPMU mea- suremen ts, including increased correlation and reduced calibration residual v ariance relative to the original data. This improv ed cross-instrument consistency pro vides real-w orld v ali- dation that p oin ts retained b y the prop osed pro cedure reect physically meaningful signal rather than residual artifact. The resulting increase in calibration co v erage establishes a stronger foundation for estimating the more complex plasma density v ariable, which relies on join t interpretation of FPMU and EPEE measurements. 20 Figure 8: Spacecraft p oten tial estimation results for b oth the original (top panel) and alternativ e (b ottom panel) metho ds compared to estimates from the WLP (mulberry) and FPP (c hartreuse) sensors on the FPMU instrument. Both original and smo othed results are in dandelion; the x-axis shows the sev en hours b etw een Julian days 271-272 shared by the t w o sensors in 2023. 21 4 Conclusion 4.1 P oten tial applications This metho dology , although sp ecic to these data and scenario, pro vides a general frame- w ork applicable to other sensor interpretation tasks. Both the pip eline and the resulting smo othed energy and current surfaces can be used in the next steps of our work, whic h include plasma densit y estimation, exploration of the EIA in relation to spacecraft charging and densit y v alues, and analysis of the uctuation of these v ariables in relation to the ISS orbit. These estimates also hav e the p otential for integration to output from the Inter- national Reference Ionsophere (IRI) mo del. The IRI is considered the source of truth for data describing the physical parameters of the ionosphere and as of 2014 is the Interna- tional Standardization Organization standard for the ionosphere ( Bilitza et al. 2022 ). As the IRI is an empirical, data-based mo del, p ossible disadv an tages arise during nov el condi- tions. F or example, during anomalous p erio ds in the solar cycle that may not ha v e b een previously recorded, such as the very low solar cycle minim um in 2008-2009, the IRI can sometimes o v er- or underestimate physical parameters. In this instance, this misalignment w as identied by several research groups and the IRI mo del w as corrected ( Bilitza et al. 2022 ). As the EPEE instrumen t provides data during part of Solar Cycle 25 as it heads to w ards the solar maximum ( Maldonado et al. 2023 ), observ ations could serve to v alidate - and if necessary - p ossibly calibrate the IRI mo del in service to the scientic comm unit y . Due in large part to this nov el application of statistical metho ds to signal pro cessing, we ha v e iden tied the p otential for trust w orthiness to b e used as an indicator of physical phe- nomena. Figure 9 displays spacecraft p otential estimates for the original data (grey) and with implementation of the new metho d (black) against the bac kdrop of latitude (y-axis) and longitude (x-axis) taken from GPS ab oard the ISS. Previously , observ ations iden tied 22 as falling b elow the instrument noise o or show ed some scattering across lo cations. No w, all observ ations iden tied as un trust w orth y (n=38) are concen trated within a very small latitude range, suggesting these observ ations ma y not b e random. Although not pictured here, initial exploration across the entire dataset sho w ed truly un trust w orth y observ ations o ccurring in a similar spatial range. F urther exploration o v er a longer timeline with con- founding factors tak en into consideration is needed. Figure 9: Spacecraft p oten tial (V) in blue fading to y ellow with increasing v alues are plotted across longitude (x-axis) and latitude (y-axis) for the 7-hour case study time p erio d. The relatively small num b er of untrust worth y v alues (n=38) o ccur in a very concentrated latitude range and are colored in black. Previous thresholding of curren t v alues under the noise o or are in gra y and sho w muc h more considerable spatial spread. 4.2 F uture Directions and Considerations Co de used to pro cess the 7-hour time p erio d used as an example throughout this pap er has b een formatted to allow for batch pro cessing across the 13-mon th dataset. Excitingly , our team has no w implemented the non-trivial co de alterations necessary to allo w for 23 heterosk edastic noise consideration within the scaled V ecchia GP approximation. Although the pap er explaining these metho ds and subsequen t ramications is in preparation ( P otter et al. 2025 ), w e are ready to explore implemen tation for EPEE data and to compare to homosk edastic noise assumptions. Cross calibration to the FPMU data is ongoing as part of a full data release eort by the team. This w ork includes a thorough review of the mo died algorithms recen tly presen ted for the WLP instrumen t, intended ”to yield improv ements in the quality of the plasma densit y , temp erature, and p otential parameters extracted from the probe data” ( Minow et al. 2023 ). 5 Disclosure statemen t The authors declare that no conicts of interest exist. Research presen ted in this man uscript w as supp orted by the Laboratory Directed Researc h and Developmen t (LDRD) program of Los Alamos National Lab oratory (LANL) under project No. 20240045DR. W ork at LANL is conducted under the auspices of the United States Departmen t of Energy . The authors also ackno wledge the supp ort of the Department of Defense (DoD) Space T est Program which provides mission design, spacecraft acquisition, in tegration, launch and on-orbit op erations supp ort for DoD’s science and tec hnology (S&T) exp erimen ts, and manages all DoD payloads on the International Space Station. Approv ed for public release: LA-UR-25-29600. 6 Data A v ailabilit y Statemen t The data and co de used in this pap er ha v e b een made av ailable at the following URL: XX. **Note: Data hav e b een reviewed b y our organization and released for public access. The 24 co de release is in progress. As so on as it is approv ed we can make public the git rep ository con taining b oth.** SUPPLEMENT AR Y MA TERIAL The supplementary material contains further details describing the GP tting, Scaled V ec- c hia approximation, and iterative noise prole tting pro cess. App endix: GP and Scaled V ecc hia Appro ximation De- tails Gaussian Pro cess P arameters Although the GP is dened on joint co ordinates          , we do not assume identical correlation structure in time and energy . W e use an anisotropic Matérn  k ernel with separate range (length-scale) parameters for time and energy ,       , estimated from the data via maxim um likelihoo d. In particular, correlation dep ends on the scaled distance                           allo wing correlation to decay at dierent rates along the temp oral and sp ectral dimensions. 6.1 Scaled V ecc hia Appro ximation The primary design parameter of the V ecchia approximation is the conditioning set size  , whic h determines the num b er of previously ordered neigh b ors in   used in eac h conditional densit y in ( 4 ). Larger v alues of  improv e approximation accuracy at in- creased computational cost. F ollowing recommendations in La wrence et al. ( 2022 ), we xed    . In exploratory analyses, increasing  to 40 produced no material change 25 in parameter estimates or predicted current surfaces, indicating that    pro vided a stable appro ximation for the data considered here. Inputs w ere ordered using max–min ordering with parameter-based scaling, as recom- mended b y La wrence et al. ( 2022 ). Gaussian pro cess cov ariance parameters (v ariance and range parameters of the Matérn  k ernel) were estimated by maxim um likelihoo d under the V ecc hia approximation. App endix: Mathematical F orms of the Noise Prole Comp onen ts W e mo del eac h bac kground-dominated curren t prole    as the sum of three com- p onen ts: a Ric hards curv e, a parab olic baseline correction, and a Gaussian peak. This app endix provides the explicit mathematical forms of these comp onen ts and their parame- terizations. In the main text, the dep endence of each mo del comp onent on the energy-bin index  is suppressed for clarity . Here, we pro vide the explicit functional forms of   ,   , and   as functions of  and their resp ective parameter vectors. Ric hards Curv e The dominan t comp onent of the instrument baseline is mo deled using a Richards curve, a generalization of the logistic function dened as    󰄓          󰄙 exp      󰅭  (6) where the parameter v ector 󰄓         󰄙     (7) 26 consists of the amplitude at the inection p oint (  ), gro wth rate (  ), inection lo cation (   ), shap e parameter ( 󰄙 ), and v ertical oset (   ). This comp onen t captures the dominant monotonic structure of the instrumen t baseline prole. P arab olic Comp onen t Residual lo w-order curv ature in the instrument baseline is captured using a second-order p olynomial,    󰄓           (8) with parameter v ector 󰄓        (9) where  controls quadratic curv ature,  controls linear slop e, and  is the intercept. These parameters t ypically remain small in magnitude, indicating that the parab olic term pro vides only a minor correction to the Ric hards curv e. Gaussian Comp onen t An y remaining lo calized structure after remov al of the instrument baseline is mo deled as a Gaussian p eak,    󰄓    󰄌 exp    󰄘  󰄝    (10) with parameter v ector 󰄓   󰄌 󰄘 󰄝  (11) where 󰄌 is the amplitude of the remaining signal, 󰄘 is the p eak lo cation in energy-bin space, and 󰄝 con trols the width of the p eak. 27 Com bined Mo del The full tted prole is therefore giv en b y         󰄓       󰄓       󰄓   (12) where the Richards and parab olic comp onen ts together constitute the instrument baseline and the Gaussian comp onen t represen ts the true signal. Figures 10 and 11 both describ e the selected noise prole with the smallest in tegral out of the candidate noise proles for the rst quarter of Julian da y 272. Figure 10 plots the individual comp onents that constitute the rened instrument baseline prole (Ric hards and parab olic curv es) and identied true signal (Gaussian shap e). Ra w initial input and the nal tted prole (Richards and parab olic input com bined) are also display ed. Figure 11 displa ys the resp ective parameter estimates for each of these comp onen ts (Richards, parab olic, Gaussian shap es) in table form. Parameters for each shap e that conv ey the most information ab out the imp ortance of the shap e in the nal prole t are highligh ted in colors matching the plot. These include Richards A (p oin t of inection), Gaussian amplitude, and the three parab olic comp onen ts (quadratic term (p), slop e (q), in tercept (r)). Baseline decomp osition with raw signal. 28 Figure 10: Comp onents of the noise prole tting pro cess for the rst quarter of Julian da y 272 (n=10799). The selected noise prole from all candidate noise timestamps is decomp osed in to Ric hard’s t (steel blue), parab olic (magen ta) and remaining Gaussian signal (m ustard). Raw signal is in dotted black and the nal tted noise prole is in corno w er blue. Energy bin is on the x-axis and current (nA) is on the y-axis. P arameter estimates for baseline components. 29 Figure 11: Parameter estimates of the noise prole tting pro cess for the rst quarter of Julian day 272 (n=10799) after conv ergence. The main parameter estimates of interest are highlighted in colors corresp onding to 10 . Ric hard’s A (steel blue) describ es the max heigh t at the inection p oint. A relativ ely large v alue suggests that this shap e dominates in the noise tting pro cess. The parabolic parameters (magen ta) are ho vering near zero, suggesting that they do not manipulate the t m uc h. Remaining Gaussian signal (mustard) is mainly describ ed by amplitude, with small v alues indicating that little true signal remains after the Ric hards and parab olic iterativ e tting. 30 References Betancourt, M. (2020), ‘Mic hael b etancourt, phd’ . URL: https://b etanalpha.github.io/ Bilitza, D., P ezzopane, M., T ruhlik, V., Altadill, D., Reinisc h, B. W. & Pignalb eri, A. (2022), ‘The international reference ionosphere mo del: A review and description of an ionospheric b enc hmark’, R eviews of Ge ophysics 60 (4), e2022RG000792. URL: https://doi.or g/10.1029/2022R G000792 Hastings, D. E. (1995), ‘A review of plasma interactions with spacecraft in low earth orbit’, Journal of Ge ophysic al R ese ar ch: Sp ac e Physics 100 (A8), 14457–14483. URL: https://doi.or g/10.1029/94JA03358 Ho w ard, J. (2002), Kinetic theory , in ‘In tro duction to Plasma Ph ysics’, Australian National Univ ersit y , Canberra, Australia, chapter 2. A ccessed on: Decem b er 4, 2024. URL: https://p e ople.physics.anu.e du.au/ jnh112/AIIM/c17/chap02.p df La wrence, E., Guinness, J. & Katzfuss, M. (2022), ‘Scaled v ecchia approximation for fast computer-model emulation’, SIAM/ASA Journal on Unc ertainty Quantic ation 10 (2), 537–554. Maldonado, C. A., Ketsdever, A. D., Balthazor, R. D., Neal, P . C., Wilson, G. R., Williams, J. D. & McHarg, M. G. (2023), ‘Automated plume sen try observ ations during interna- tional space station thermal con trol system v en ting’, Journal of Sp ac e cr aft and R o ckets 60 (1), 339–350. URL: https://doi.or g/10.2514/1.A34995 Maldonado, C. A., Ulric h, R., Moran, K., P otter, K., Castro, L., Lira, P . A. R., Eddy , T., Klem, S. M., Janhunen, J., Delzanno, G. L., McGlo wn, J., W eav er, B., Balthazor, R., Williams, J. D. & McHarg, M. G. (2025), Initial on-orbit results from the electric 31 propulsion electrostatic analyzer exp erimen t (ÈpÈe), in ‘AIAA SciT ec h 2025 F orum’ . URL: https://ar c.aiaa.or g/doi/10.2514/6.2025-2547 Mino w, J. I., Deb choudh ury , S., Barjaty a, A., Coey , V. & P ark er, L. N. (2023), Floating p oten tial measurement unit (fpmu) data pro cessing algorithm developmen t and analysis assessmen t, T ec hnical Memorandum NASA/TM-20230013386, NASA Engineering and Safet y Center. Accessed on: December 4, 2024. URL: https://ntrs.nasa.gov/api/citations/20230013386/downlo ads/20230013386.p df Mino w, J. I., Jordano v a, V. K., Pitc hford, D., Gan ushkina, N. Y., Zheng, Y., Luca Delzanno, G., Jun, I. & Kim, W. (2024), ‘ISW A T spacecraft surface c harging review’, A dvanc es in Sp ac e R ese ar ch . URL: https://www.scienc e dir e ct.c om/scienc e/article/pii/S0273117724008822 P otter, K., Moran, K., Ulric h, R., Castro, L., Stenning, D., Bingham, D. & Maldonado, C. (2025), ‘Scalable heterosk edastic gaussian pro cess mo dels for large inhomogeneous data’, Man uscript in preparation. Rasm ussen, C. E. & Williams, C. K. I. (2006), Gaussian Pr o c esses for Machine L e arning , MIT Press, Cam bridge, MA. URL: https://gaussianpr o c ess.or g/gpml/ Ric hards, F. J. (1959), ‘A exible growth function for empirical use’, Journal of Exp eri- mental Botany 10 (2), 290–301. Sw enson, C. M., Fish, C. S. & Thompson, D. C. (2003), Calibrating the oating p otential measuremen t unit, in ‘Proceedings of the 8th Spacecraft Charging T echnology Confer- ence’, Hun tsville, Alabama. V ecc hia, A. V. (1988), ‘Estimation and mo del iden tication for con tin uous spatial pro- 32 cesses’, Journal of the R oyal Statistic al So ciety: Series B (Metho dolo gic al) 50 (2), 297– 312. 33