Minimum Estimation Research Articles

Two-stage and purely sequential minimum risk point estimation of the scale parameter of a family of distributions under modified LINEX loss plus sampling cost

Two-stage and purely sequential minimum risk point estimation of the scale parameter of a family of distributions under modified LINEX loss plus sampling cost

A Comparing Robust Wilks’ statistics in Multivariate Multiple Linear Regression

In multivariate linear regression, the classical Wilks’ statistic is the most used method to test hypotheses, which is extremely responsive to the effect of outliers. Many authors have examined the non-robust test statistic established on normal theories for various cases. In this study, we constructed a robust version of Wilks’ statistic relying on a reweighed minimum covariance determinant estimator, that relies on the weight of the observations, with the weights being determined by using the Hampel weight function and Huber weight function. A comparison of the suggested statistics with the regular Wilks’ statistic has been discussed. Monte Carlo studies are used to evaluate how well test statistics work with different datasets. So, this study looked at how two different test statistics perform under a normal distribution. The first is the classical Wilks’ statistic, and the second is a proposed new one. For both of them, the rate of type I errors and the power of the tests were close to the expected significance levels. In situations where the distribution is contaminated, the proposed statistical method works best. If the data has been corrupted or affected somehow, this approach seems to perform the best out of the options

Minimum Profile Hellinger Distance Estimation of General Covariate Models

Covariate models, such as polynomial regression models, generalized linear models, and heteroscedastic models, are widely used in statistical applications. The importance of such models in statistical analysis is abundantly clear by the ever-increasing rate at which articles on covariate models are appearing in the statistical literature. Because of their flexibility, covariate models are increasingly being exploited as a convenient way to model data that consist of both a response variable and one or more covariate variables that affect the outcome of the response variable. Efficient and robust estimates for broadly defined semiparametric covariate models are investigated, and for this purpose the minimum distance approach is employed. In general, minimum distance estimators are automatically robust with respect to the stability of the quantity being estimated. In particular, minimum Hellinger distance estimation for parametric models produces estimators that are asymptotically efficient at the model density and simultaneously possess excellent robustness properties. For semiparametric covariate models, the minimum Hellinger distance method is extended and a minimum profile Hellinger distance estimator is proposed. Its asymptotic properties such as consistency are studied, and its finite-sample performance and robustness are examined by using Monte Carlo simulations and three real data analyses. Additionally, a computing algorithm is developed to ease the computation of the estimator.

Saturated load forecasting based on improved logistic regression and affinity propagation

Saturated load forecasting (SLF) is a crucial guarantee for stable operation of power grid. However, insufficient data makes SLF collapse. Although logistic regression (LR) can be employed to tackle this problem, its non-linearity may lead to analytically unsolvable maximum likelihood (ML) function. Due to this dilemma, this paper proposes a sequential LR estimator. It depends on minimum variance unbiased estimator (MVUE) and maximum likelihood estimator (MLE) to form an iterative method: in which a linearized statistical model is established by inverse substitution to reduce complexity. Moreover, a new forecasting framework combining LR estimator with clustering algorithms is constructed. In this framework, load data are clustered based on affinity propagation (AP) before LR. Subsequently, SLF result is obtained from corresponding categories by iteration. Simulation results show that the method proposed in this paper has lower computational complexity and higher prediction accuracy.

Preservation of probable MIS 7 deglacial and nonglacial deposits near the edge of the Hudson Bay Lowland in Manitoba, Canada

The stratigraphic principle of superposition assumes that sediments at surface are youngest. And yet, patches of older preserved landscapes continue to be identified in the regions formerly covered by the Laurentide Ice Sheet. Two gravel pits, at the edge of the western Hudson Bay Lowland near the geographic centre of the North American Ice Sheet Complex, reveal additional patches where older glacial and nonglacial sediment is preserved. These sites expose 1–4 m of a darker, highly overconsolidated, clayier till, and 0–2 m of a lighter, less consolidated, sandier till over glaciofluvial and post-glacial gravels and sands; the waning stages of deposition occurred at 214 ± 22 ka (1σ minimum age model quartz grain optical age estimates, n = 2). This was during the latter end of the cool Marine Isotope Stage (MIS) 7-d (within 1σ range) or near the end of MIS-8 (within 2σ range). Next followed a warmer period similar to, or warmer than, present day with higher precipitation; inferred from pollen and macrofossils deposited in nonglacial low-energy floodplain or pond sediments. Our study highlights the need to accurately date Quaternary sediments, given that the shallowest nonglacial sediments at both gravel pits were deposited during an old (MIS 7) interglacial; there is likely no record of the youngest interglacial (MIS 5). Preservation of older sediment also means that in Quaternary stratigraphy, disjoint regional nonglacial “organic marker beds” should not automatically be considered correlative. Identification of similar “old” patches, together with till stratigraphy and composition, is essential to accurately model glacial sediment transport over time.

Local functional connectivity abnormalities in mild cognitive impairment and Alzheimer's disease: A meta-analytic investigation using minimum Bayes factor activation likelihood estimation

Functional magnetic resonance imaging research employing regional homogeneity (ReHo) analysis has uncovered aberrant local brain connectivity in individuals with mild cognitive impairment (MCI) and Alzheimer's disease (AD) in comparison with healthy controls. However, the precise localization, extent, and possible overlap of these aberrations are still not fully understood. To bridge this gap, we applied a novel meta-analytic and Bayesian method (minimum Bayes Factor Activation Likelihood Estimation, mBF-ALE) for a systematic exploration of local functional connectivity alterations in MCI and AD brains. We extracted ReHo data via a standardized MEDLINE database search, which included 35 peer-reviewed experiments, 1,256 individuals with AD or MCI, 1,118 healthy controls, and 205 x-y-z coordinates of ReHo variation. We then separated the data into two distinct datasets: one for MCI and the other for AD. Two mBF-ALE analyses were conducted, thresholded at “very strong evidence” (mBF ≥ 150), with a minimum cluster size of 200 mm³. We also assessed the spatial consistency and sensitivity of our Bayesian results using the canonical version of the ALE algorithm. For MCI, we observed two clusters of ReHo decrease and one of ReHo increase. Decreased local connectivity was notable in the left precuneus (Brodmann area – BA 7) and left inferior temporal gyrus (BA 20), while increased connectivity was evident in the right parahippocampal gyrus (BA 36). The canonical ALE confirmed these locations, except for the inferior temporal gyrus. In AD, one cluster each of ReHo decrease and increase were found, with decreased connectivity in the right posterior cingulate cortex (BA 30 extending to BA 23) and increased connectivity in the left posterior cingulate cortex (BA 31). These locations were confirmed by the canonical ALE. The identification of these distinct functional connectivity patterns sheds new light on the complex pathophysiology of MCI and AD, offering promising directions for future neuroimaging-based interventions. Additionally, the use of a Bayesian framework for statistical thresholding enhances the robustness of neuroimaging meta-analyses, broadening its applicability to small datasets.

Improving source estimation of retinotopic MEG responses by combining data from multiple subjects

Abstract Magnetoencephalography (MEG) is a functional brain imaging modality, which measures the weak magnetic field arising from neuronal activity. The source amplitudes and locations are estimated from the sensor data by solving an ill-posed inverse problem. Commonly used solutions for these problems operate on data from individual subjects. Combining the measurements of multiple subjects has been suggested to increase the spatial resolution of MEG by leveraging the intersubject differences for increased information. In this article, we compare 3 multisubject analysis methods on a retinotopic mapping dataset recorded from 20 subjects. The compared methods are eLORETA with source-space averaging, minimum Wasserstein estimates (MWE), and MWE with source-space averaging. The results were quantified by the geodesic distances between early (60–100 ms) MEG peak activations and fMRI-based retinotopic target points in the primary visual cortex (V1). By increasing the subject count from 1 to 10, the median distances decreased by 6.6–9.4 mm (33–46%) compared with the single-subject median distances of around 20 mm. The observed peak activation locations with multisubject analysis also comply better with the established retinotopic maps of the primary visual cortex. Our results suggest that higher spatial accuracy can be achieved by pooling data from multiple subjects. The strength of MWE lies in individualized and sparse source estimates, but in our data, averaging eLORETA estimates across individuals in source space outperformed MWE in spatial accuracy.

A two-phase sequential algorithm for global optimization of the standard quadratic programming problem

AbstractWe introduce a new sequential algorithm for the Standard Quadratic Programming Problem (StQP), which exploits a formulation of StQP as a Linear Program with Linear Complementarity Constraints (LPLCC). The algorithm is finite and guarantees at least in theory a $$\delta $$ δ -approximate global minimum for an arbitrary small $$\delta $$ δ , which is a global minimum in practice. The sequential algorithm has two phases. In Phase 1, Stationary Points (SP) with strictly decreasing objective function values are computed. Phase 2 is designed for giving a certificate of global optimality for the last SP computed in Phase 1. Two different Nonlinear Programming Formulations for LPLCC are proposed for each one of these phases, which are solved by efficient enumerative algorithms. New procedures for computing a lower bound for StQP are also proposed, which are easy to implement and give tight bounds in general. Computational experiments with a number of test problems from known sources indicate that the two-phase sequential algorithm is, in general, efficient in practice. Furthermore, the algorithm seems to be an efficient way to study the copositivity of a matrix by exploiting an StQP with this matrix.

Variations in cuticular hydrocarbons of Calliphora vicina (Diptera: Calliphoridae) empty puparia: Insights for estimating late postmortem intervals.

Necrophagous flies, particularly blowflies, serve as vital indicators in forensic entomology and ecological studies, contributing to minimum postmortem interval estimations and environmental monitoring. The study investigates variations in the predominant cuticular hydrocarbons (CHCs) viz. n-C25, n-C27, n-C28, and n-C29 of empty puparia of Calliphora vicina Robineau-Desvoidy, 1830, (Diptera: Calliphoridae) across diverse environmental conditions, including burial, above-ground and indoor settings, over 90 days. Notable trends include a significant decrease in n-C25 concentrations in buried and above-ground conditions over time, while n-C27 concentrations decline in buried and above-ground conditions but remain stable indoors. Burial conditions show significant declines in n-C27 and n-C29 concentrations over time, indicating environmental influences. Conversely, above-ground conditions exhibit uniform declines in all hydrocarbons. Indoor conditions remain relatively stable, with weak correlations between weathering time and CHC concentrations. Additionally, machine learning techniques, specifically Extreme Gradient Boosting (XGBoost), are employed for age estimation of empty puparia, yielding accurate predictions across different outdoor and indoor conditions. These findings highlight the subtle responses of CHC profiles to environmental stimuli, underscoring the importance of considering environmental factors in forensic entomology and ecological research. The study advances the understanding of insect remnant degradation processes and their forensic implications. Furthermore, integrating machine learning with entomological expertise offers standardized methodologies for age determination, enhancing the reliability of entomological evidence in legal contexts and paving the way for future research and development.

Solving the project scheduling problem with dependent resource constraints

ABSTRACT Most resource-constrained project scheduling problems consider resources that are independent of the job processing sequence. However, solving project scheduling problems in some industrial manufacturing is challenging because the required resources depend on the job processing sequence in existing scheduling approaches. To address this issue, this paper proposes a dependent resource-constrained project scheduling problem formulated with two types of models: a conceptual model and a binary integer programming model. The performance of four proposed algorithms – binary integer programming, reduced subproblem of the binary integer programming, job sequence assignment, and job as early as possible – is tested on 68 combinations of numerical simulation experiments. The computational results show that the job as early as possible algorithm can find a better approximate solution for solving real-world problems. This achievement aids project managers in generating activity schedules and finding the approximate minimum makespan for a project with dependent resource constraints.

Body mass estimate and in-vivo reconstruction of Hippopotamus antiquus from Figline, Upper Valdarno (Tuscany)

ABSTRACT Hippopotamus antiquus was an extinct semiaquatic megaherbivore foraging mainly on aquatic vegetation, with a biochronological range in the Italian peninsula spanning from around 2.2 to 0.4 Ma. Considering its large body size, and its lifestyle considered to be more aquatic than the current form H. amphibius, a correct estimate of the body mass is interesting to correctly interpret various biological aspects of this extinct megaherbivore. In this contribution, we propose an estimate of the body mass of H. antiquus by comparing the results obtained with classical regression formulae with the values obtained through a new 3D volumetric approach. For both approaches, we used the mounted specimen on display at the Museum of Geology and Palaeontology of the University of Florence. As already found in recent contributions, the estimates obtained with the regression methods provide very high ranges compared to the volumetric approach, with minimum estimates of 200 kg and maximum estimates of over 6 tons, completely incompatible with a tetrapod of this size. The new volumetric estimate provides an average value for the BM in H. antiquus of approximately 3170 tons, thus confirming a body weight approximately double compared to the average values in the extant species H. amphibius.

EEG/MEG source imaging of deep brain activity within the maximum entropy on the mean framework: Simulations and validation in epilepsy.

Electro/Magneto-EncephaloGraphy (EEG/MEG) source imaging (EMSI) of epileptic activity from deep generators is often challenging due to the higher sensitivity of EEG/MEG to superficial regions and to the spatial configuration of subcortical structures. We previously demonstrated the ability of the coherent Maximum Entropy on the Mean (cMEM) method to accurately localize the superficial cortical generators and their spatial extent. Here, we propose a depth-weighted adaptation of cMEM to localize deep generators more accurately. These methods were evaluated using realistic MEG/high-density EEG (HD-EEG) simulations of epileptic activity and actual MEG/HD-EEG recordings from patients with focal epilepsy. We incorporated depth-weighting within the MEM framework to compensate for its preference for superficial generators. We also included a mesh of both hippocampi, as an additional deep structure in the source model. We generated 5400 realistic simulations of interictal epileptic discharges for MEG and HD-EEG involving a wide range of spatial extents and signal-to-noise ratio (SNR) levels, before investigating EMSI on clinical HD-EEG in 16 patients and MEG in 14 patients. Clinical interictal epileptic discharges were marked by visual inspection. We applied three EMSI methods: cMEM, depth-weighted cMEM and depth-weighted minimum norm estimate (MNE). The ground truth was defined as the true simulated generator or as a drawn region based on clinical information available for patients. For deep sources, depth-weighted cMEM improved the localization when compared to cMEM and depth-weighted MNE, whereas depth-weighted cMEM did not deteriorate localization accuracy for superficial regions. For patients' data, we observed improvement in localization for deep sources, especially for the patients with mesial temporal epilepsy, for which cMEM failed to reconstruct the initial generator in the hippocampus. Depth weighting was more crucial for MEG (gradiometers) than for HD-EEG. Similar findings were found when considering depth weighting for the wavelet extension of MEM. In conclusion, depth-weighted cMEM improved the localization of deep sources without or with minimal deterioration of the localization of the superficial sources. This was demonstrated using extensive simulations with MEG and HD-EEG and clinical MEG and HD-EEG for epilepsy patients.

Genetic parameter estimates for growth traits in Texel sheep of Brazil

The present study aimed to estimate the genetic parameters for direct and maternal influences on birth weight (BW), weaning weight (WW) and postweaning weight (PW) of Texel sheep, raised in an extensive system from Brazil. Data file used in this study consisted of 834 body weight records of 834 Texel lambs (376 males and 458 females) born from 2020 to 2021, offspring of 475 ewes and 45 rams. Multivariate animal model was conducted to estimate the variance components, heritability and genetic correlations using the restricted maximum likelihood method in ASReml-R software, while the effects of fixed factors were analyzed by the general linear model procedure of statistical analysis system. Five different animal models, with or without maternal genetic effect, maternal permanent environment effect and covariance between additive genetic and maternal genetic effects, were fitted on the growth traits data of the Texel sheep population. AIC and BIC test results were used to evaluate the best fit models for growth traits. The effect of lamb's sex was significant on BW, WW and PW while birth type and year of lambing effects were on all traits (P < 0.05). Model 4, incorporating direct additive genetic, maternal additive genetic and maternal permanent environmental effects showed the minimum AIC estimate for all growth traits. The direct additive genetic heritability for BW, WW and PW were 0.11 ± 0.03, 0.37 ± 0.05 and 0.31 ± 0.08, respectively and maternal heritability for these traits were 0.00 ± 0.00, 0.04 ± 0.02 and 0.00 ± 0.00, respectively. The total heritability estimates for BW, WW and PW were 0.11 ± 0.03, 0.39 ± 0.05 and 0.31 ± 0.08, respectively. The estimates of the direct additive genetic correlation between BW-WW, BW-PW and WW-PW were 0.68 ± 0.12, 0.66 ± 0.12 and 0.78 ± 0.07, respectively. The maternal permanent environmental correlation between BW-WW, BW-PW and WW-PW were 0.38 ± 0.27, 0.29 ± 0.20 and 0.74 ± 0.16, respectively. Phenotypic correlation ranged from 0.43 ± 0.03 to 0.75 ± 0.02. It is concluded that due to the existence of genetic variation for BB, WW and PW and strong genetic correlation among them, genetic progress for these traits is possible by selection in Texel sheep from Brazil.

Does urban construction land in China achieve sustainable allocation and utilization?

Building sustainable cities and communities is a key priority of the Sustainable Development Goals. However, the spatial mismatch of construction land (SMCL) poses a significant challenge to sustainable urban development. This paper presents a new framework for measuring the SMCL from the dual perspectives of planning deviation (PD) and economic mismatch (EM). Using a minimum deviation estimation model, a land-comparable correction method, and the extended HK model, this study focused on 285 cities in China from 2002 to 2021. The results revealed that the PD exhibited an “N”-shaped fluctuating trend, reaching a peak of 27.63 km2 in 2011, with the deviation direction generally characterized by over-planning allocation followed by lack of planning allocation. The eastern region had the highest PD, with an annual average of 35.06 km2, followed by the western region. In contrast, the central and northeast regions had relatively low PD. The EM fluctuated in a “W” shape, with an annual average of 0.37. The direction was always dominated by economic over-allocation and complemented by economic under-allocation. There was also heterogeneity in EM across regions. Furthermore, both PD and EM differed considerably between cities by size. In 2021, most cities in China still existed PD or EM, but EM was more widespread and severe. This indicated that SMCL was still a serious issue in China, and there was still a long way to go to achieve the vision of sustainable allocation of construction land. This paper enriches the relevant literature on SMCL and provides a decision-making reference for governments to implement optimal land allocation.

Estimating separable matching models

SummaryMost recent empirical applications of matching with transferable utility have imposed a natural restriction: that the joint surplus be separable in the sources of unobserved heterogeneity. We propose here two simple methods to estimate models in this class. The first method is a minimum distance estimator that relies on the generalized entropy of matching. The second applies to the more special but popular Choo and Siow model, which reformulates as a generalized linear model with two‐way fixed effects. Neither method requires solving for the stable matching. Both methods are easy to apply and perform very well.

Dead mammal walking: A month‐long march by a bison (Bison bison) after an ungulate–vehicle collision

AbstractGlobally, ungulate–vehicle collisions (UVCs) are a major human safety concern and may also represent a significant source of mortality for some ungulate populations. However, records of UVC based on counts of roadside carcasses or reports by drivers involved in these incidents are assuredly underestimated because not all ungulates struck die immediately or at the roadside or are reported by drivers or authorities. Here, we provide an observation and analysis of the movements of a GPS‐collared bison (Bison bison) that was involved in a UVC on the Alaska Highway and died in a thick boreal forest 29 days later. During that time, she moved 49.7 km from where she was hit. Her daily movement rate (in kilometers per hour) and daily net displacement (in kilometers per day) were significantly greater in the 29‐day period before she was struck compared with 29 days afterward. This vivid example illustrates that individuals injured in a UVC can die several weeks later and at a considerable distance from where they were initially struck. Moreover, when they eventually die, it may be where their carcass would not be found or associated with a UVC. Bison are the largest land mammal in North America and perhaps more robust to some lower impact UVC than smaller bodied species. Even so, if not for the GPS collar on this bison, we would have never known the fate of this individual, and the carcass likely never found. Taken together, the movements and final resting place of this bison illuminate how estimates of mortality as a result of UVC can be underestimated when the animal does not die immediately and in a location where it can be found. Given our data, we further urge managers to consider roadside counts of animals killed in UVC as a minimum estimate when considering options for mitigation.

The effect of an intervention to promote isoniazid preventive therapy on leadership and management abilities

&lt;sec&gt;&lt;title&gt;BACKGROUND&lt;/title&gt;Across sub-Saharan Africa, mid-level healthcare managers oversee implementation of national guidelines. It remains unclear whether leadership and management training can improve population health outcomes.&lt;/sec&gt;&lt;sec&gt;&lt;title&gt;METHODS&lt;/title&gt;We sought to evaluate leadership/management skills among district-level health managers in Uganda participating in the SEARCH-IPT randomised trial to promote isoniazid preventive therapy (IPT) for persons with HIV (PWH). The intervention, which led to higher IPT rates, included annual leadership/management training of managers. We conducted a cross-sectional survey assessing leadership/management skills among managers at trial completion. The survey evaluated self-reported use of leadership/management tools and general leadership/management. We conducted a survey among a sample of providers to understand the intervention’s impact. Targeted minimum loss-based estimation (TMLE) was used to compare responses between trial arms.&lt;/sec&gt;&lt;sec&gt;&lt;title&gt;RESULTS&lt;/title&gt;Of 163 managers participating in the SEARCH-IPT trial, 119 (73%) completed the survey. Intervention managers reported more frequent use of leadership/management tools taught in the intervention curriculum than control managers (+3.64, 95% CI 1.98–5.30, P &lt; 0.001). There were no significant differences in self-reported leadership skills in the intervention as compared to the control group. Among providers, the average reported quality of guidance and supervision was significantly higher in intervention vs control districts (+1.08, 95% CI 0.63–1.53, P = 0.001).&lt;/sec&gt;&lt;sec&gt;&lt;title&gt;CONCLUSIONS&lt;/title&gt;A leadership and management training intervention increased the use of leadership/management tools among mid-level managers and resulted in higher perceived quality of supervision among providers in intervention vs control districts in Uganda. These findings suggest improved leadership/management among managers contributed to increased IPT use among PWH in the intervention districts of the SEARCH-IPT trial.&lt;/sec&gt;

Airfall volume of the 15 January 2022 eruption of Hunga volcano estimated from ocean color changes

On 15 January 2022, Hunga volcano erupted, creating an extensive and high-reaching umbrella cloud over the open ocean, hindering traditional isopach mapping and fallout volume estimation. In MODIS satellite imagery, ocean surface water was discolored around Hunga following the eruption, which we attribute to ash fallout from the umbrella cloud. By relating intensity of ocean discoloration to fall deposit thicknesses in the Kingdom of Tonga, we develop a methodology for estimating airfall volume over the open ocean. Ash thickness measurements from 41 locations are used to fit a linear relationship between ash thickness and ocean reflectance. This produces a minimum airfall volume estimate of 1.8-0.4+0.3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${1.8}_{-0.4}^{+0.3}$$\\end{document} km3. The whole eruption produced > 6.3 km3 of uncompacted pyroclastic material on the seafloor and a caldera volume change of 6 km3 DRE. Our fall estimates are consistent with the interpretation that most of the seafloor deposits were emplaced by gravity currents rather than fall deposits. Our proposed method does not account for the largest grain sizes, so is thus a minimum estimate. However, this new ocean-discoloration method provides an airfall volume estimate consistent with other independent measures of the plume and is thus effective for rapidly estimating fallout volumes in future volcanic eruptions over oceans.

Optimal Joint Defense and Monitoring for Networks Security under Uncertainty: A POMDP-Based Approach

The increasing interconnectivity in our infrastructure poses a significant security challenge, with external threats having the potential to penetrate and propagate throughout the network. Bayesian attack graphs have proven to be effective in capturing the propagation of attacks in complex interconnected networks. However, most existing security approaches fail to systematically account for the limitation of resources and uncertainty arising from the complexity of attacks and possible undetected compromises. To address these challenges, this paper proposes a partially observable Markov decision process (POMDP) model for network security under uncertainty. The POMDP model accounts for uncertainty in monitoring and defense processes, as well as the probabilistic attack propagation. This paper develops two security policies based on the optimal stationary defense policy for the underlying POMDP state process (i.e., a network with known compromises): the estimation-based policy that performs the defense actions corresponding to the optimal minimum mean square error state estimation and the distribution-based policy that utilizes the posterior distribution of network compromises to make defense decisions. Optimal monitoring policies are designed to specifically support each of the defense policies, allowing dynamic allocation of monitoring resources to capture network vulnerabilities/compromises. The performance of the proposed policies is examined in terms of robustness, accuracy, and uncertainty using various numerical experiments.

Kalman filter for radio source power and direction of arrival estimation

Images are an important source of information for spacecraft navigation. Based on an image and a known attitude, triangulation techniques (intersection or resection) are often used for positioning and navigation. In the resection problem, an observer estimate its unknown location by using angle measurements to points at known locations (i.e., landmarks), the localization performance depending on the accuracy of the angle measurements. As a contribution to resection for spacecraft navigation, we considers the dynamic image estimation problem based on radio interferometry, i.e., image of radio source power, where the measurements are sample covariance matrices (SCMs). Considering the case where several measurements are available as well as a known dynamic linear model of image evolution, a.k.a a linear state model, the minimum mean-squared error image estimator (MMSE) is given by the Kalman filter (KF) or one of its variants. However standard Kalman-like filters are not a priori suitable for the problem at hand since the measurements (i.e., SCMs) cannot be formulated analytically as a function of state parameters to be estimated (i.e., radio source power). In fact, this lack of analytical formulation can be circumvented by a statistical linear fitting allowing the SCMs to be expressed in terms of the state. This linear fitting introduces an additive residual noise, equivalent to a measurement noise, whose covariance matrix depends on the current state, a non-standard case for a measurement model. The covariance matrix of the residual noise is derived whatever the distributions of the radio sources and of the additive noise at the samples level, unveiling the contribution of their multivariate kurtosis. The proposed method is evaluated on simulated data representative of a dynamic radio interferometry framework. The results show that the proposed method is capable of effectively tracking moving radio sources in complex scenes with theoretical guaranties when the signal multivariate kurtosis is known.