Sum Of Squares Research Articles

Prediction and MDL for infinite sequences

AbstractWe combine Solomonoff’s approach to universal prediction with algorithmic statistics and suggest to use the computable measure that provides the best “explanation” for the observed data (in the sense of algorithmic statistics) for prediction. In this way we keep the expected sum of squares of prediction errors bounded (as it was for the Solomonoff’s predictor) and, moreover, guarantee that the sum of squares of prediction errors is bounded along any Martin-Löf random sequence. An extended abstract of this paper was presented at the 16th International Computer Science Symposium in Russia (CSR 2021) (Milovanov 2021).

Symmetry and asymmetry between positive and negative square energies of graphs

The positive and negative square energies of a graph, $s^+(G)$ and $s^-(G)$, are the sums of squares of the positive and negative eigenvalues of the adjacency matrix, respectively. The first results on square energies revealed symmetry between $s^+(G)$ and $s^-(G)$. This paper reviews examples of asymmetry between these parameters, for example using large random graphs and the ratios $s^+/s^-$ and $s^-/s^+$, as well as new examples of symmetry. Some questions previously asked about $s^{+}$ and $s^{-}$ are answered and several further avenues of research are suggested.

Diurnal and day-to-day biological variation of salivary cortisol and cortisone.

There is a growing interest in the relevance of salivary cortisol and cortisone concentrations in stress-related research. To correctly attribute the magnitude of salivary cortisol and cortisone variation as an effect of a stressful event, a coherent understanding of the day-to-day intra-individual and inter-individual variability across the diurnal cycle of the two steroids is required. However, such information is currently lacking. This study aimed to overcome these existing limitations by performing an investigation of the biological variation (BV) of salivary cortisol and cortisone within one day and between five days using an LC-MS/MS method. Saliva samples were collected from 20 healthy volunteers immediately after waking up, at 8:00, 12:00, 15:00, 19:00 and 23:00 on each day over five days. All samples were analyzed in duplicate in one run. Nested ANOVA was used to calculate the sums of squares for analytical and biological components of variation. The within-subject BV of salivary cortisol and cortisone (CVI) ranged from a minimum of 29.3 and 19.0 % to a maximum of 56.5 and 49.1 %, respectively, while the between-subject biological variation (CVG) ranged from 29.7 and 29.0 % to 51.6 and 43.6 %. The reference change values (RCVs) ranged from 96 to 245 % for cortisol and from 55 to 194 % for cortisone. A medium index of individuality was observed for both compounds at all time points. This study provides updated BV estimates and RCVs for different times of day that can be used to assess the magnitude of change in biomarkers in future stress-related research.

Dispersion Analysis of Perpendicular Modes Using a Hybrid Two-Trace Two-Dimensional (2T2D) Smart Error Sum.

Using linear dichroism theory, one would assume that a z-cut of a uniaxial crystal is equivalent to an x-cut to determine the perpendicular component of the dielectric tensor and the corresponding oscillator parameters. However, Fresnel's equations show that the effect of interfaces in the form of the continuity relations of the different components of the electric field must be considered. A consequence of the continuity relations is that perpendicular modes increase less significantly in strength with increasing angle of incidence than expected. This is a consequence of the fact that it is the inverse of the perpendicular component of the dielectric function that increasingly becomes important with a growing angle of incidence. An inverse dielectric function, however, has typically much smaller values than the dielectric function. An additional consequence is that perpendicular modes are blueshifted and coupled in such a way that oscillator strength is transferred to the higher wavenumber mode. Thus, the spectral signatures of perpendicular modes are often weak and masked by the parallel modes when two modes overlap. Accordingly, to enable dispersion analysis, it is suggested to use a hybrid of the conventional residual sum of squares and the two-trace two-dimensional (2T2D) smart error sum, which can correct systematic multiplicable errors in the experimental spectrum. As demonstrated for fresnoite (Ba2TiSi2O8), this is an important step toward determining the perpendicular component of the dielectric tensor and the corresponding oscillator parameters using dispersion analysis, since asynchronous 2T2D correlation spectra are, in particular, sensitive to perpendicular modes.

PSVI-3 Effects of dried distillers grains on performance of suckling beef calves in a creep-feeding system

Abstract Dried distiller’s grains (DDG) have been successfully used in beef cattle diets due to their high protein content and increasing availability around the world. However, the chemical composition of DDG varies according to the type of fermented grain and processing methods, and its increased sulfur content can compromise animal performance. There are few studies evaluating DDG in supplements for beef calves in creep-feeding systems. Hence, our objective was to assess the effects of DDG on performance of suckling beef calves in a creep-feeding system. Nellore×Red Angus male calves (n = 37), weighing 162 ± 4.06 kg at 120 d of age, along with their respective dams (n =37 Nellore cows) were used. The cow-calf pairs were randomly assigned into eight paddocks formed by Urochloa decumbens pastures. Animals were subjected to a 14-dadaptation period and an additional 108-d period for performance evaluation. All animals had access to water and mineral mixture ad libitum. Four treatments were evaluated, as follows: control (mixture mineral only), supplement without DDG, or supplements including 375 and 750 g/kg DDG [dry matter (DM) basis]. The supplements were composed of ground corn, soybean meal, urea, and DDG, planned to contain 300 g CP/kg DM, and provided daily at 7.0 g/kg body weight (BW; as fed). Treatments were assigned to experimental units (i.e., calf) in a completely randomized design. Calves were weighed at the beginning and end of the experiment, as well as every 15 d, to adjust the amount of supplement to be provided. Comparisons between treatments were performed by decomposing its sum of squares into orthogonal effects as follows: 1) control (mineral mixture only) versus supplemented calves; 2) evaluation of the linear and quadratic effects of the inclusion of DDG in the supplements. Data were analyzed using the MIXED procedure of SAS 9.4 (α = 0.05). Supplementation enhanced (P < 0.05) average daily gain (ADG) and final body weight (FBW) when compared with control. On average, ADG was increased from 0.94 kg/d to 1.08 kg/d for control and supplemented calves, respectively. On the other hand, ADG and FBW decreased linearly as the DDG inclusion in the supplement increased (P < 0.05). The differential ADG of calves that received supplements with 375 and 750 g/kg DDG compared with calves that did not receive DDG was -0.046 and -0.096 kg, respectively. It is worth emphasizing that calves fed supplements with 375 g/kg and 750 g/kg DDG had a 14% and 46% less supplement intake, respectively, than animals that were not fed DDG. Supplementing beef calves in a creep-feeding system enhances animal performance. However, the inclusion of high DDG levels in supplements decreases the performance of suckling beef calves.

A novel approach to assessing the anaerobic bio-accessibility of straw using fractal dimension

Traditional methods for evaluating the bioconversion capacity of organic solid waste are known for time-consuming property and often exhibit low prediction accuracy. However, leveraging fractal dimensions offers a more precise characterization of the complexity, irregularity, and spatial structure of organic solid waste. In this study, a novel and efficient method for evaluating the bio-accessibility of straw's anaerobic transformation, based on fractal dimensions, was introduced. To comprehensively compare the structural differences, this research encompasses the measurement of nine different varieties of straw under ten distinct pretreatment conditions. The regression sum of squares for these correlations consistently exceeds 0.83, highlighting the robustness of our findings. The results unequivocally demonstrate the close relationship between the fractal dimension and the structural characteristics of straw. This relationship underscores the utility of fractal dimension analysis as a reliable tool for evaluating the anaerobic bio-accessibility of organic solid waste.

Custom Bell inequalities from formal sums of squares

Bell inequalities play a key role in certifying quantum properties for device-independent quantum information protocols. It is still a major challenge, however, to devise Bell inequalities tailored for an arbitrary given quantum state. Existing approaches based on sums of squares provide results in this direction, but they are restricted by the necessity of first choosing measurement settings suited to the state. Here, we show how the sum of square property can be enforced for an arbitrary target state by making an appropriate choice of nullifiers, which is made possible by leaving freedom in the choice of measurement. Using our method, we construct simple Bell inequalities for several families of quantum states, including partially entangled multipartite GHZ states and qutrit states. In most cases we are able to prove that the constructed Bell inequalities achieve self-testing of the target state. We also use the freedom in the choice of measurement to self-test partially entangled two-qubit states with a family of settings with two parameters. Finally, we show that some statistics can be self-tested with distinct Bell inequalities, hence obtaining new insight on the shape of the set of quantum correlations.

[formula omitted] output tracking control for polynomial parameter-varying systems via homogeneous Lyapunov methods

This paper investigates the H∞ output tracking control for polynomial parameter-varying systems—a class of nonlinear parameter-varying systems. Based on the homogeneous polynomial Lyapunov function (HPLF), a state feedback controller is presented to make the augmented system (composed of the original system and the tracking error system) robust exponentially stable, so that the output of the original system can track the reference signal and satisfy the H∞ output tracking performance. The conservativeness of the theoretical results is reduced due to the following facts: (1) the HPLF can depend on the full states and time-varying parameters; and (2) there are no constraints on the input coefficient matrix and the inverse of the Lyapunov matrix. In particular, when the system states and time-varying parameters are confined to a compact set, local results are obtained based on the generalized S-procedure. The solvable conditions are given in terms of state-and-parameter-dependent linear matrix inequalities, which can be solved by sum of squares (SOS) techniques. Finally, the feasibility and effectiveness of the proposed method are verified by a numerical example and the heading control of unmanned surface vehicle.

Exploring the role of spending on malaria incidence in Uganda using the auto-regressive distributed lag approach.

Malaria has remained a persistent global health problem. Despite multiple government and donor initiatives to eradicate malaria and its detrimental effects on Uganda's health outcomes, the incidence of malaria is worrying as it appears higher than the average of 219 cases per 1000 for sub-Saharan Africa for the period 2017-2018. This study investigated the effect of public and private healthcare spending on the incidence of malaria in Uganda. Employing time series data spanning over 20years from the first quarter of 2000 to the last quarter of 2019, the study builds a model based on the Grossman framework for analysing demand for health. The estimation technique used was the ARDL approach that takes into account reverse causality and incidental relationships. Prior to the adoption of the technique, a bounds test was performed to determine whether the variables contained in the model have a long-term relationship. Several diagnostic tests for serial correlation, functional normality, and heteroskedastic specification error were carried out to verify the ARDL model's goodness of fit. Additionally, the cumulative sum of recursive (CUSUM) and cumulative sum of squares of recursive residuals (CUSUMSQ) were used to test model stability. The results indicate that in the long run, an increase in public spending of one percent significantly reduces malaria incidence by 0.196 at the 10 percent level of significance. On the other hand, there is no significant evidence of private health expenditure's effect on malaria incidence. However, in the short run, public spending reduces malaria incidence by a smaller magnitude of 0.158 percent relative to the long-run. Still, private expenditure is found to exhibit no significant effect. Additional findings point to the importance of GDP per capita and urban population growth in reducing malaria incidence, whereas female unemployment, income inequality, as well as female-headed household. In the short run, however, the female-headed households and urban population growth are found to significantly reduce malaria incidence while an improvement in regulatory quality decreases malaria incidence by 0.129 percent. There is need for further government interventions to reduce malaria incidence in the country via budget allocation, as well as the strengthening of programmes to raise household income to support private health spending, in addition to the development of strategies to promote well-planned and organized urban centres.

Augmenting locomotor perception by remapping tactile foot sensation to the back

BackgroundSensory reafferents are crucial to correct our posture and movements, both reflexively and in a cognitively driven manner. They are also integral to developing and maintaining a sense of agency for our actions. In cases of compromised reafferents, such as for persons with amputated or congenitally missing limbs, or diseases of the peripheral and central nervous systems, augmented sensory feedback therefore has the potential for a strong, neurorehabilitative impact. We here developed an untethered vibrotactile garment that provides walking-related sensory feedback remapped non-invasively to the wearer’s back. Using the so-called FeetBack system, we investigated if healthy individuals perceive synchronous remapped feedback as corresponding to their own movement (motor awareness) and how temporal delays in tactile locomotor feedback affect both motor awareness and walking characteristics (adaptation).MethodsWe designed the system to remap somatosensory information from the foot-soles of healthy participants (N = 29), using vibrotactile apparent movement, to two linear arrays of vibrators mounted ipsilaterally on the back. This mimics the translation of the centre-of-mass over each foot during stance-phase. The intervention included trials with real-time or delayed feedback, resulting in a total of 120 trials and approximately 750 step-cycles, i.e. 1500 steps, per participant. Based on previous work, experimental delays ranged from 0ms to 1500ms to include up to a full step-cycle (baseline stride-time: µ = 1144 ± 9ms, range 986-1379ms). After each trial participants were asked to report their motor awareness.ResultsParticipants reported high correspondence between their movement and the remapped feedback for real-time trials (85 ± 3%, µ ± σ), and lowest correspondence for trials with left-right reversed feedback (22 ± 6% at 600ms delay). Participants further reported high correspondence of trials delayed by a full gait-cycle (78 ± 4% at 1200ms delay), such that the modulation of motor awareness is best expressed as a sinusoidal relationship reflecting the phase-shifts between actual and remapped tactile feedback (cos model: 38% reduction of residual sum of squares (RSS) compared to linear fit, p < 0.001). The temporal delay systematically but only moderately modulated participant stride-time in a sinusoidal fashion (3% reduction of RSS compared a linear fit, p < 0.01).ConclusionsWe here demonstrate that lateralized, remapped haptic feedback modulates motor awareness in a systematic, gait-cycle dependent manner. Based on this approach, the FeetBack system was used to provide augmented sensory information pertinent to the user’s on-going movement such that they reported high motor awareness for (re)synchronized feedback of their movements. While motor adaptation was limited in the current cohort of healthy participants, the next step will be to evaluate if individuals with a compromised peripheral nervous system, as well as those with conditions of the central nervous system such as Parkinson’s Disease, may benefit from the FeetBack system, both for maintaining a sense of agency over their movements as well as for systematic gait-adaptation in response to the remapped, self-paced, rhythmic feedback.

Effective removal of microplastics by filamentous algae and its magnetic biochar: Performance and mechanism

In recent years, filamentous algae blooms and microplastics (MPs) pollution have become two major ecological and environmental problems in urban water systems. In order to solve these two problems at the same time, this study explored the loading capacity of MPs on fresh filamentous algae, and successfully synthesized magnetic filamentous algae biochar loading with Fe3O4 by hydrothermal method, with the purpose of removing MPs from water. The magnetic filamentous algal biochar was characterized by scanning electron microscopy (SEM), Fourier transform infrared (FTIR), X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), and so on. Experiments on adsorption kinetics, adsorption isotherms and optimum pH were carried out to explore the adsorption mechanism of MPs on magnetic filamentous algal biochar. The adsorption kinetics and adsorption isotherm models were evaluated, and the selection criterion for the appropriate model was determined by using the residual sum of squares (RSS) and Bayesian information criterion (BIC). Microscope images revealed that fresh filamentous algae could interact with MPs in the form of entanglement, adhesion and encapsulation. The average load of MPs in filamentous algae samples was 14.1 ± 5 items/g dry weight. The theoretical maximum adsorption capacities of polystyrene MPs (PS-MPs) by raw biochar (A500) and magnetic biochar with Fe3O4 (M2A500) were 176.99 mg/g and 215.58 mg/g, respectively. The adsorbent materials gave better reusability because they could be reused up to five times. Overall, these findings have provided new insights into the use of filamentous algae for in situ remediation of fluvial MPs pollution, as well as feasible strategies for the recycling of algal waste.

Robust 3D coordinate transformation based on genetic algorithm intelligent weighting

In order to improve the solution quality of 3D coordinate transformation parameters, a robust optimization model is obtained by integrating the 3D coordinate transformation model within the overall framework of the genetic algorithm in this paper. The minimum of the weighted sum of squares of the point residuals of the common points is taken as the objective function for optimization, and the parallel search is started from the initial population, and the updating process of the solution set is used to generate new and better individuals, and the adaptive weight combination corresponding to the optimum of the fitness function is obtained at the end of the generation iteration. The generated simulated data and measured data were analyzed using the Hefei Light Source tunnel control network as an application scenario. The results show that the method in this paper can automatically reduce the influence of low-quality data on the model, and compared with the two robust conversion models of IGG III iterative weighting, the method in this paper is not affected by the empirical parameters in determining the weight combinations and the weighted sum of squares of the residuals of the solved points are smaller, so it can effectively improve the quality of the solved conversion parameters.

Variable parameters memory-type control charts for simultaneous monitoring of the mean and variability of multivariate multiple linear regression profiles

Variable parameters (VP) schemes are the most effective adaptive schemes in increasing control charts' sensitivity to detect small to moderate shift sizes. In this paper, we develop four VP adaptive memory-type control charts to monitor multivariate multiple linear regression profiles. All the proposed control charts are single-chart (single-statistic) control charts, two use a Max operator and two use an SS (squared sum) operator to create the final statistic. Moreover, two of the charts monitor the regression parameters, and the other two monitor the residuals. After developing the VP control charts, we developed a computer algorithm with which the charts' time-to-signal and run-length-based performances can be measured. Then, we perform extensive numerical analysis and simulation studies to evaluate the charts’ performance and the result shows significant improvements by using the VP schemes. Finally, we use real data from the national quality register for stroke care in Sweden, Riksstroke, to illustrate how the proposed control charts can be implemented in practice.

P-Singular characters and normal Sylow p-subgroups

Let [Formula: see text] be a finite group and [Formula: see text] a prime. We denote by [Formula: see text] the set of irreducible complex characters of [Formula: see text] whose degrees are linear or divisible by [Formula: see text], and we write [Formula: see text] to denote the ratio of the sum of squares of irreducible character degrees in [Formula: see text] to the sum of irreducible character degrees in [Formula: see text]. The Itô–Michler Theorem on character degrees states that [Formula: see text] if and only if [Formula: see text] has a normal abelian Sylow [Formula: see text]-subgroup. We generalize this theorem as follows: if [Formula: see text], then [Formula: see text] has a normal Sylow [Formula: see text]-subgroup.

Impact of a free trade agreement on unemployment and productivity growth in Nigeria

This research investigates the impact of a free trade agreement on unemployment and productivity growth in Nigeria over the period 1981–2019. Data was collected from the World Bank Development Indicators (WDI) online database as of 2020. The study employed various analytical methods, including unit root tests, autoregressive distributed lag (ARDL) bound tests, error correction models (ECM), and cumulative sum (CUSUM) and cumulative sum of squares (CUSUMSQ) tests to assess data stability. The ARDL bound test statistics (F-statistics) of 4.26914 and 7.680624 exceeded the critical values for both I(0) and I(1) bounds, indicating a meaningful relationship between the variables. In the long run, physical capital, human capital development, and economic growth were found to have a negative impact on unemployment, with statistical significance. Additionally, sectoral productivity growth negatively influenced aggregate productivity growth. The error correction model (ECM) indicated a weak speed of adjustment, suggesting that the disequilibrium takes around 13% of the time to return to equilibrium annually. Based on these findings, the study recommends the implementation of safeguards to protect vulnerable industries, particularly in manufacturing and agriculture. Additionally, the government should focus on fostering human capital development by ensuring the availability of suitable support measures.

Gradient Weakly Sensitive Multi-Source Sensor Image Registration Method

Aiming at the nonlinear radiometric differences between multi-source sensor images and coherent spot noise and other factors that lead to alignment difficulties, the registration method of gradient weakly sensitive multi-source sensor images is proposed, which does not need to extract the image gradient in the whole process and has rotational invariance. In the feature point detection stage, the maximum moment map is obtained by using the phase consistency transform to replace the gradient edge map for chunked Harris feature point detection, thus increasing the number of repeated feature points in the heterogeneous image. To have rotational invariance of the subsequent descriptors, a method to determine the main phase angle is proposed. The phase angle of the region near the feature point is counted, and the parabolic interpolation method is used to estimate the more accurate main phase angle under the determined interval. In the feature description stage, the Log-Gabor convolution sequence is used to construct the index map with the maximum phase amplitude, the heterogeneous image is converted to an isomorphic image, and the isomorphic image of the region around the feature point is rotated by using the main phase angle, which is in turn used to construct the feature vector with the feature point as the center by the quadratic interpolation method. In the feature matching stage, feature matching is performed by using the sum of squares of Euclidean distances as a similarity metric. Finally, after qualitative and quantitative experiments of six groups of five pairs of different multi-source sensor image alignment correct matching rates, root mean square errors, and the number of correctly matched points statistics, this algorithm is verified to have the advantage of robust accuracy compared with the current algorithms.

Energy-Based Design of Buckling-Restrained Steel Braced Frames for Concurrent Occurrences of Earthquake and Wind

This paper describes the development of a dual hazard spectrum for use in the dynamic analysis of steel frames subject to the combined effects of earthquakes and wind. The proposed spectrum is obtained by combining the power spectra of earthquakes and wind using the square root of the sum of squares (SRSS) combination method. An equivalent time excitation function is then computed using an inverse fast Fourier transform (IFFT) and serves as input for the dynamic analysis. Using time-history analysis on the OpenSees platform, the dynamic responses expressed in terms of peak and residual inter-story and roof drifts for two multistory steel frames located in two US cities (Los Angeles and Charleston) are obtained to demonstrate that designing these buildings based on just one hazard may not be adequate. For frames that are considered under-designed, an energy-based design procedure that uses buckling-restrained braces (BRBs) to dissipate the excess energy imparted to these frames is proposed so they will satisfy the FEMA 356 recommended drift limits for the performance levels of immediate occupancy and life safety.

Modelling the dynamics of microbial populations and Salmonella spp. in milk kefir

Kefir is a fermented dairy product based on the fermentation of milk by bacteria and yeasts. It is produced by adding kefir grains, consisting of a consortium of microorganisms, to milk in order to start a natural fermentation (Garofalo et al., 2020). Kefir is well recognized for its potential health value as a source of probiotics, however, there have been concerns about the potential growth of pathogenic microorganisms in kefir and the potential health hazards associated (Leite et al., 2013) A mathematical model was developed to describe the evolution of microbes present during kefir fermentation and the potential growth of Salmonella spp. as one example of a potential food safety hazard. For this, equations previously described in the scientific literature were combined and adapted to the milk kefir matrix. To assess the safety of the product, the growth of Salmonella was predicted considering its interaction with the medium and the other species. The drop in pH; generation of yeasts metabolites such as ethanol; and buffer capacity was described and considered when modelling Salmonellas’ kinetics. Interaction between the pathogenic species and the background microflora was included in the model. Parameters of some well-described systems were taken from literature. Alongside, some other parameters describing specific assets from the system were estimated using experimental data of microbial population kinetics during kefir fermentation. The growth of yeasts, lactic acid bacteria, Salmonella together with the pH were experimentally collected at critical processing times and fitted to the mathematical model by minimizing the residual sum of squares (RSS). Confidence intervals of 95 % were calculated. For further validation, the output of the model was contrasted with an independent data set. It was concluded that Salmonella is able to increase its population during the first hours of the kefir fermentation process. Inactivation can be apportioned to the drop of pH as a consequence of the LAB metabolism, once the pH reaches values below 4. After this no growth of Salmonella seems to be found in milk kefir as confirmed by the model. No residual population of the pathogen is observed. This suggests that by controlling the growth and metabolism of the background microflora, safety can be assured in milk kefir. This process was successfully described by a novel mathematical model and the estimation of its´parameters.

Policy iteration for H∞ control of polynomial time‐varying systems

AbstractThis paper studies the H∞ control problem for polynomial time‐varying systems. The H∞ control problem has been much less investigated for time‐varying systems in comparison to the time‐invariant systems. Approximate dynamic programming (ADP) is an optimal method to solve the control problems. Therefore, it is valuable to solve the polynomial time‐varying H∞ control problem with the ADP approach. Considering the time as an independent variable for sum‐of‐squares (SOS) optimization problems, an SOS‐based ADP method is proposed to solve this problem. A policy iteration algorithm is presented, where in its policy evaluation step it is sufficient to solve an optimization problem. Some constraints are added to this optimization problem to guarantee the closed‐loop exponential stability. The convergence and stability properties of the proposed algorithm are stated and proven. Moreover, in order to design an H∞ controller with a smaller disturbance attenuation coefficient, a two‐loop algorithm is suggested. Finally, the effectiveness of the proposed method is demonstrated by simulation examples.

Improved ellipsoid fitting aided geomagnetic sensor calibration algorithm

Aiming at the problems that the traditional single ellipsoid fitting fails to eliminate the errors of the geomagnetic sensor and does not consider the geomagnetic anomaly information, etc., this paper proposes a robust least squares combined with the Levenberg–Marquardt (LM-RLS) algorithm to fit an accurate ellipsoid to achieve accurate data calibration. According to the geomagnetic sensor error model, the total amount of geomagnetism is used as the constraint, the fitted ellipsoid coefficients of RLS are used as the initial values, and the LM algorithm is used to calculate the magnetic field dispersion points to the nearest point of the fitted ellipsoid surface. Then, the initial calibration value is solved by the criterion of the minimum weighted sum of squares of the closest point distance. Finally, the accurate ellipsoid is obtained to realize data calibration. The results of the dynamic experiment show that after the ellipsoid is precisely fitted by the LM-RLS algorithm, the sum of the absolute values of the distance from the magnetic field discrete data to the ellipsoid surface is reduced by 48.33% (RLS) and 43.10% (RWTLS). The relative errors of the magnetic field in the X, Y, and Z axes are reduced from 0.48%, 0.78%, 1.48% (RLS) and 0.30%, 0.58%, 1.14% (RWTLS) to 0.10%, 0.04% 0.16 %, respectively. The accuracy of geomagnetic calibration is improved by 68.06% (RLS) and 61.02% (RWTLS) in the dynamic experiment. The algorithm improves the accuracy of geomagnetic measurement, which provides a new idea for the calibration of three-axis geomagnetic sensors.