Maximum Entropy Theory Research Articles

Searching for long timescales without fine tuning.

Animal behavior occurs on timescales much longer than the response times of individual neurons. In many cases, it is plausible that these long timescales emerge from the recurrent dynamics of electrical activity in networks of neurons. In linear models, timescales are set by the eigenvalues of a dynamical matrix whose elements measure the strengths of synaptic connections between neurons. It is not clear to what extent these matrix elements need to be tuned to generate long timescales; in some cases, one needs not just a single long timescale but a whole range. Starting from the simplest case of random symmetric connections, we combine maximum entropy and random matrix theory methods to construct ensembles of networks, exploring the constraints required for long timescales to become generic. We argue that a single long timescale can emerge generically from realistic constraints, but a full spectrum of slow modes requires more tuning. Langevin dynamics that generates patterns of synaptic connections drawn from these ensembles involves a combination of Hebbian learning and activity-dependent synaptic scaling.

Generalized Core Functions of Maximum Entropy Theory of Ecology

Core distributions of Maximum Entropy Theory of Ecology (METE) are the Spatial Structure Function (SSF) and the Ecosystem Structure Function (ESF). SSF is a by-species prediction of the clustering of individuals over space. ESF is a kind of container function that describes the probability space of how abundances are assigned to species and how metabolic energy is parti-tioned over individuals in a community. In this study, these core functions of METE are generalized by deriving the corresponding functions in the Tsallis q-entropy. Derivation used the method of Lagrange multipliers. The generalized SSF and ESF are expressed in terms of the q-exponential function. Numerical examples are provided to illustrate the generalized SSF.

Efficient catalysis and products regulation of methane dry reforming under mild temperature conditions using novel high-entropy catalyst

Dry reforming of methane to syngas (H2/CO) is the most dominant upstream reaction in chemical production line, which also helps capture greenhouse gases. In this work, we report a novel CoxNi0.8-xLa0.2Ca0.5Ce0.5@Al2O3 high-entropy catalyst applied to CH4-CO2 reforming reaction, which can widen the reaction-temperature window and achieve over 40 % methane conversion and 220 mmol·gcat−1·h−1 hydrogen yield at 500 °C. Compared with other studies, the activity of proposed CoxNi0.8-xLa0.2Ca0.5Ce0.5@Al2O3 high-entropy catalyst exhibits absolute advantage in low-medium temperature environments (500–650 °C). Due to the regulation of structure–activity relationship among various active metal elements, the proposed catalysts present synergistic effect within catalytic system, which can also suppress carbon deposition and maintain stable activity during a 12-hour continuous operation. Importantly, this research utilizes the remarkable characteristics of high-entropy alloys to induce the orderly transformation of reactants. The thermodynamic regulation of the reaction process is also improved by regulating the catalyst structure and thermal properties through intermetallic lattice distortion and “Maximum Entropy Theory”. The experimental results show that the product H2/CO ratio can be stably maintained over 0.9 for temperature ranging from 500 to 850 °C. This provides a reference for the application of high-entropy alloys in the field of carbon capture and hydrogen production.

Shared manufacturing service evaluation based on intuitionistic fuzzy VIKOR

With the rise of the concept of sharing economy, the shared manufacturing model has gained widespread attention. The VIKOR shared manufacturing service evaluation approach is presented based on an intuitionistic fuzzy environment, which enables users to filter out acceptable shared manufacturing services from a wide pool of shared manufacturing services with similar functional qualities. Firstly, considering the QOS multi-indicator comprehensive evaluation of services by multiple stakeholders under the fundamental characteristics of shared manufacturing, the QOS evaluation index system is built from the two aspects of online and offline, which includes 2 first-level indicators and 10 second-level indicators. The paper also constructs a service recommendation model considering supply and demand constraints. Secondly, the intuitionistic fuzzy numbers are introduced to define the non-quantitative indexes, and the G1-method and variable-precision rough set theory are used for the assignment, and the maximum entropy theory is utilized to integrate the assignment method to obtain the combination weights. Thirdly, the VIKOR method based on intuitionistic fuzzy sets is used to evaluate and rank the shared manufacturing candidate services, in which the combined benefits and minimum regret values of the groups are solved based on the intuitionistic fuzzy number similarity. Finally, the reliability and feasibility of the algorithm are verified with a real case.

Calculation of probabilistic harmonic power flow based on improved three-point estimation method and maximum entropy as distributed generators access to distribution network

Uncertainty and volatility are the features of distributed generation (DG), which can impact greatly on the operational status of distribution network. Thus, an improved three-point estimation method and maximum entropy theory (ITPEM&ME) for calculating the probabilistic harmonic power flow in distribution network is proposed in this study. Firstly, the probabilistic model is constructed according to the uncertainty of input variables and the improved three-point estimate method is utilized to convert a probabilistic problem into a deterministic problem. Secondly, in order to obtain the distribution of the random harmonics in distribution network, the maximum entropy theory is adopted to reconstruct the statistical characteristics after the deterministic calculation is realized for each harmonic voltages. The case of an IEEE-33 system under various conditions is conducted. The results by the different algorithms indicate that the proposed method ITPEM&ME has a smaller error than the traditional method, as well as the fitting effect of the probability density function (PDF) is much closer to the practical engineering. It is feasible and accurate in dealing with probabilistic harmonic power flow problems.

Probabilistic Small Signal Stability Analysis with Wind Power Based on Maximum Entropy Theory

The probability parameters for the small signal stability in a system are studied to quantify the impact of uncertain wind power on system stability. With the increase in the scale of wind power access systems, how to more efficiently and accurately obtain the probability of small signal stability is worthy of further investigation. Therefore, this work proposes an analysis method of probabilistic small signal stability (PSSS) based on maximum entropy (ME) theory for studying power systems with uncertain wind power from doubly fed induction generators (DFIGs). Firstly, the sensitivity of the eigenvalues to the variable power is obtained by linearization. Then, when the probability characteristic for wind is known, the probability characteristic for the system critical eigenvalues is approximated using the ME method and the derived sensitivity. The proposed ME method is used in the analysis of the PSSS for power systems with different wind power penetration scales in case studies. Compared to the probability function for the eigenvalue obtained by the conventional series expansion method, the proposed method has excellent accuracy and sufficient efficiency in analysing the PSSS for a system with uncertain wind power.

Chaotic signal denoising based on energy selection TQWT and adaptive SVD.

Aiming at the problem of denoising chaotic signals with low signal-to-noise ratio and unknown dynamic system parameters, a new chaotic signal denoising algorithm is proposed, which combines adjustable Q-factor wavelet transform (TQWT) and adaptive singular value decomposition (ASVD). This method uses TQWT to decompose the noisy chaotic signal. According to the maximum wavelet entropy theory and energy threshold rule, the subband of TQWT is accurately divided into signal subband and noise subband. For noise subbands, adaptive SVD is used to denoise them, to achieve preliminary denoising. In ASVD, the standard deviation of the singular value subset is used to determine the effective reconstruction order to improve the noise suppression effect. To further remove noise in the signal subband, TQWT reconstruction is performed on the preliminarily denoised signal, and ASVD is used to denoise the reconstructed signal again to obtain the chaotic signal after secondary denoising. Chua's simulated signal and four kinds of underwater radiated noise measured by TQWT-ASVD were denoised, and compared with the SVD denoising method, TQWT denoising method, complete ensemble empirical mode decomposition with adaptive noise and threshold denoising method (CEEMDAN-WT) and modified ensemble empirical mode decomposition combined with least squares denoising method (MEEMD-LMS), The experimental results show that the TQWT-ASVD method can reduce the noise of chaotic signals more effectively. Compared with SVD, TQWT, CEEMDAN-WT, MEEMD-LMS, and Chua's signal denoising method, the signal-to-noise ratio (SNR) of this method increased by 23.22%, 26.46%, 18.79%, 16.11% the root mean square error (RMSE) decreased by 32.53%,39.48%, 30.96%, 27.94%, and the row entropy (PE) decreased by 40.44%, 41.96%, 22.78%, 20.59%; After reducing the radiation noise of cargo ships, the PE value of this method is reduced by 13.91%, 10.18%, 10.88%, 8.68% respectively, and the FE value is reduced by 33.66%, 31.42%, 26.98%, 21.32% respectively.

Potential geographical distribution and its multi-factor analysis of Pinus massoniana in China based on the maxent model

Pinus massoniana, an important timber, producing, and silvicultural species in southern China, exhibits high adaptability and wide distribution. This study utilizes the Maximum Entropy Model (MaxEnt), a species distribution model based on the theory of maximum entropy, to forecast the potential suitable distribution areas of P. massoniana in China under four climate change scenarios (SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5) for both present and future (2080) conditions. The research integrates and analyzes the effects of various environmental factors, including topography, soil, and population, on the distribution of P. massoniana. Additionally, a geographical detector is employed to assess the interaction between different environmental factors and their contribution to the variation in suitability zones.The findings indicate that the MaxEnt model accurately predicts the potential distribution areas of P. massoniana, with AUC values exceeding 0.94. Precipitation in the driest month (BIO14), population density (POP), and annual precipitation (BIO12) emerge as the main factors influencing the current distribution of P. massoniana. Notably, BIO14 has the greatest impact on the species' distribution (43%), followed by POP (32.7%). Furthermore, lower BIO14 values correspond to higher probabilities of pine distribution, while higher POP values correlate with increased pine distribution probabilities. The potential distribution of P. massoniana is primarily concentrated in southern China under current climatic conditions, encompassing a total suitable survival zone of 25.24 × 105 km2, accounting for 26.29% of China's total area. Among the regions, Guangxi exhibits the largest suitable area for survival, reaching 28.9 × 104 km2, implying that the environmental characteristics of Guangxi are conducive to P. massoniana's survival. Under future climate scenarios, the overall distribution pattern of the potential range of P. massoniana remains similar to the present one, with an increasing trend in area. Notably, the SSP3-7.0 emissions scenario shows the most significant increase in area, totaling 4.71 × 104 km2, suggesting that this particular scenario is more favorable for the distribution of P. massoniana. This study provides valuable scientific insights for the management, conservation, and rational site selection of P. massoniana.

Detecting the damage of concrete subjected to fatigue load coupled with freeze-thaw cycles using alternating current electric impedance spectroscopy

The coupled effect of fatigue load and freeze-thaw cycles may cause damage to concrete structures. This paper explores the potential of alternating current (AC) electric impedance spectroscopy (EIS) technology to characterize the micro-damage of concrete under the mentioned coupled effect. Firstly, the mass loss rate (ML) and the relative dynamic elastic modulus (RDEM) evolution were employed to evaluate damage of concrete subjected to freeze-thaw cycles coupled with fatigue load. Comparatively, the degradation was also described in terms of ACEIS. The functional correlations between impedance parameters and concrete damage under the coupled effect were identified using the maximum entropy theory. The results show that the impedance parameters, RCCP and RCP, follow a consistent three-stage trend with ML and RDEM as the number of freeze-thaw cycles and fatigue load time increase. RCCP and RCP, however, are more vulnerable to early damage and can be used to faster recognize concrete damage caused by the coupled effect. Compared to RCP, RCCP is a more stable indicator for characterizing concrete damage, as it is less affected by external factors. The relationships between impedance parameters (RCCP and RCP) and traditional indicators (ML and RDEM) at stage II can be quantified as a third-order power function.

Multi-UAV Cooperative Air Combat Decision-Making Based on Multi-Agent Double-Soft Actor-Critic

Multiple unmanned aerial vehicle (multi-UAV) cooperative air combat, which is an important form of future air combat, has high requirements for the autonomy and cooperation of unmanned aerial vehicles. Therefore, it is of great significance to study the decision-making method of multi-UAV cooperative air combat since the conventional methods are challenging to solve the high complexity and highly dynamic cooperative air combat problems. This paper proposes a multi-agent double-soft actor-critic (MADSAC) algorithm for solving the cooperative decision-making problem of multi-UAV. The MADSAC achieves multi-UAV cooperative air combat by treating the problem as a fully cooperative game using a decentralized partially observable Markov decision process and a centrally trained distributed execution framework. The use of maximum entropy theory in the update process makes the method more exploratory. Meanwhile, MADSAC uses double-centralized critics, target networks, and delayed policy updates to solve the overestimation and error accumulation problems effectively. In addition, the double-centralized critics based on the attention mechanism improve the scalability and learning efficiency of MADSAC. Finally, multi-UAV cooperative air combat experiments validate the effectiveness of MADSAC.

Earthquake disturbance shifts metabolic energy use and partitioning in a monodominant forest

AbstractAimBoth macroecology and disturbance ecology have long been used to characterize population‐ and community‐level patterns across scales, but the integration of both approaches in characterizing disturbed ecosystems is rare. Here, we use the maximum entropy theory of ecology (METE) to model the individual size distribution (ISD) of trees in pre‐ and post‐disturbance tree populations and estimate the corresponding metabolic scaling exponents.LocationNew Zealand.Time Period1987–1999.Major Taxa StudiedMountain beech (Fuscospora cliffortioides Nothofagaceae).MethodsMETE uses information entropy and empirical macro‐state variables to constrain predictions of ecological distributions related to biodiversity. METE has successfully predicted a range of biodiversity metrics in static or relatively undisturbed conditions. However, METE can fail to accurately model ecological patterns in disturbed ecosystems. We extend existing theoretical predictions to a highly disturbed ecosystem by treating the metabolic scaling exponent and Lagrange multipliers as free parameters in METE.ResultsWe showed that the fully parameterized METE (FP‐METE) model reasonably predicted the ISD of mountain beech populations in a monodominant forest after a strong earthquake, which restructured the forest. Furthermore, the FP‐METE model revealed that decreasing metabolic scaling exponent drove the substantial decline of total metabolic rate energy and the redistribution of energy towards smaller trees after the earthquake. Increased number of small trees was not sufficient to capture the full impact of disturbance on forest energy use.Main ConclusionsOur FP‐METE model applies an informatics approach to estimate the metabolic scaling relationship. We find that instead of maintaining a fixed value, the metabolic scaling exponent is variable among populations, and declines significantly after an earthquake disturbance. This leads to major shifts in the total population metabolic energy and energy distribution. With this approach, we now have the opportunity to advance beyond categorizing forms of mathematical distributions that describe biodiversity patterns and move into a predictive framework where the true constraints on ecosystems and their dynamics emerge.

Maximum entropy models reveal spatial variation of metabolic scaling in stream fish communities.

Metabolic scaling provides valuable information about the physiological and ecological functions of organisms, although few studies have quantified the metabolic scaling exponent (b) of communities under natural conditions. Maximum entropy theory of ecology (METE) is a constraint-based unified theory with the potential to empirically assess the spatial variation of the metabolic scaling. Our main goal is to develop a novel method of estimating b within a community by integrating metabolic scaling and METE. We also aim to study the relationships between the estimated b and environmental variables across communities. We developed a new METE framework to estimate b in 118 stream fish communities in the north-eastern Iberian Peninsula. We first extended the original maximum entropy model by parameterizing b in the model prediction of the community-level individual size distributions and compared our results with empirical and theoretical predictions. We then tested the effects of abiotic conditions, species composition and human disturbance on the spatial variation of community-level b. We found that community-level b of the best maximum entropy models showed great spatial variability, ranging from 0.25 to 2.38. The mean exponent (b = 0.93) resembled the community-aggregated mean values from three previous metabolic scaling meta-analyses, all of which were greater than the theoretical predictions of 0.67 and 0.75. Furthermore, the generalized additive model showed that b reached maximum at the intermediate mean annual precipitation level and declined significantly as human disturbance intensified. The parameterized METE is proposed here as a novel framework for estimating the metabolic pace of life of stream fish communities. The large spatial variation of b may reflect the combined effects of environmental constraints and species interactions, which likely have important feedback on the structure and function of natural communities. Our newly developed framework can also be applied to study the impact of global environmental pressures on metabolic scaling and energy use in other ecosystems.

Pollution threshold assessment and risk area delineation of heavy metals in soils through the finite mixture distribution model and Bayesian maximum entropy theory

Pollution threshold and high-risk area determination for heavy metals is important for effectively developing pollution control strategies. Based on heavy metal contents in 3627 dense samples, an integrated framework combining the finite mixture distribution model and Bayesian maximum entropy (BME) theory was proposed to assess pollution thresholds, contamination levels and risk areas in an uncertain environment for soil heavy metals. The results showed that the average heavy metal contents were in the order Zn > Cr > Pb > Cu > Ni > As > Cd > Hg, with strong/moderate variation, and the corresponding pollution thresholds were 158.39, 84.29, 47.84, 49.75, 28.95, 18.01, 0.49 and 0.16 mg/kg, respectively. The thresholds were consistently greater than the Zhejiang Province backgrounds but lower than the national risk screening values, except for Cd. Approximately 27.9% of the samples were classified as contaminated at various levels, and they were distributed in the northern, northwestern and eastern regions of the study area. Additionally, 3.73%, 5.34% and 8.22% of the total area were classified as at-risk areas under confidence levels of 95%, 90% and 75%, respectively, through BME theory. The findings provide a reasonable classification system and suggestions for heavy metal pollution management and control.

Enhancing the predictability of ecology in a changing world: A call for an organism-based approach

Ecology is usually very good in making descriptive explanations of what is observed, but is often unable to make predictions of the response of ecosystems to change. This has implications in a human-dominated world where a suite of anthropogenic stresses are threatening the resilience and functioning of ecosystems that sustain mankind through a range of critical regulating and supporting services. In ecosystems, cause-and-effect relationships are difficult to elucidate because of complex networks of negative and positive feedbacks. Therefore, being able to effectively predict when and where ecosystems could pass into different (and potentially unstable) new states is vitally important under rapid global change. Here, we argue that such better predictions may be reached if we focus on organisms instead of species, because organisms are the principal biotic agents in ecosystems that react directly on changes in their environment. Several studies show that changes in ecosystems may be accurately described as the result of changes in organisms and their interactions. Organism-based theories are available that are simple and derived from first principles, but allow many predictions. Of these we discuss Trait-based Ecology, Agent Based Models, and Maximum Entropy Theory of Ecology and show that together they form a logical sequence of approaches that allow organism-based studies of ecological communities. Combining and extending them makes it possible to predict the spatiotemporal distribution of groups of organisms in terms of how metabolic energy is distributed over areas, time, and resources. We expect that this “Organism-based Ecology” (OE) ultimately will improve our ability to predict ecosystem dynamics.

Bayesian maximum entropy method for stochastic model updating using measurement data and statistical information

The presence of summarized statistical information, such as some statistics of the system response, is not rare in practical engineering as the acquisition of precisely measured point data is expensive and may not be always accessible. In this paper, we integrate the Bayesian framework with the maximum entropy theory and develop a Bayesian Maximum Entropy (BME) approach for model updating in a scenario where measurement data and statistical information are simultaneously available. Within the scope of this contribution, it is assumed that measurement data denote direct observations, e.g. point data, representing system response measurements while statistical information involves summarized information, e.g. moment and/or reliability information, of the system response. The basic principle of our approach is to convert point data and various statistical information into constraints under the BME framework and use the method of Lagrange multipliers to find the optimal posterior distributions. We then extend this approach to imprecise probabilistic models which have not been addressed so far. The approximate Bayesian computation is employed to facilitate the estimation of cumbersome likelihood functions which results from the involvement of entropy terms accounting for statistical information. Furthermore, a Wasserstein distance-based metric is proposed and embedded into the framework to capture the divergence information in an effective and efficient way. The effectiveness of the proposed approach is verified by a numerical case of simply supported beam and an engineering problem of fatigue crack growth. It shows some promising aspects of this research as better calibration results are produced with less uncertainty, and hence potential of our approach for engineering applications.

An equation of state unifies diversity, productivity, abundance and biomass

To advance understanding of biodiversity and ecosystem function, ecologists seek widely applicable relationships among species diversity and other ecosystem characteristics such as species productivity, biomass, and abundance. These metrics vary widely across ecosystems and no relationship among any combination of them that is valid across habitats, taxa, and spatial scales, has heretofore been found. Here we derive such a relationship, an equation of state, among species richness, energy flow, biomass, and abundance by combining results from the Maximum Entropy Theory of Ecology and the Metabolic Theory of Ecology. It accurately captures the relationship among these state variables in 42 data sets, including vegetation and arthropod communities, that span a wide variety of spatial scales and habitats. The success of our ecological equation of state opens opportunities for estimating difficult-to-measure state variables from measurements of others, adds support for two current theories in ecology, and is a step toward unification in ecology.

Land use change through the lens of macroecology: insights from Azorean arthropods and the maximum entropy theory of ecology

Human activity and land management practices, in particular land use change, have resulted in the global loss of biodiversity. These types of disturbance affect the shape of macroecological patterns, and therefore analyzing these patterns can provide insights into how ecosystems are affected by land use change. We here use arthropod census data from 96 sites at Terceira Island in the Azores archipelago across four different land uses of increasing management intensity: native forest, exotic forest, semi‐natural pasture and intensive pasture, to examine the effects of land use type on three macroecological patterns: the species abundance distribution, the metabolic rate distribution of individuals and the species–area relationship. The maximum entropy theory of ecology (METE) has successfully predicted these patterns across habitats and taxa in undisturbed ecosystems, and thus provides a null expectation for their shapes. Across these patterns, we find that the forest habitats are the best fit by METE predictions, while the semi‐natural pasture is consistently the worst fit, and the intensive pasture is intermediately well fit. We show that the direction of failure of the METE predictions at the pasture sites is likely due to the hyper‐dominance of introduced spider species present there. We hypothesize that the particularly poor fit for the semi‐natural pasture is due to the mix of arthropod communities out of equilibrium, leading to greater heterogeneity in composition and complex dynamics that violate METE's assumption of static state variables. The comparative better fit for the intensive pasture plausibly results from more homogeneous arthropod communities that are well adapted to intensive management, and thus whose state variables are less in flux. Analyzing deviations from theoretical predictions across land use type provides useful information about how land use and disturbance affect ecosystems, and such comparisons could be useful across other habitats and taxa.

Sparse and low-dimensional representation with maximum entropy adaptive graph for feature selection

Traditional feature selection algorithms usually explore the relationship between data and cluster structure in a single space, so the internal relationship obtained is not very rich, and it is not enough to select more valuable features. To solve the above problems, in order to fully mine the intrinsic correlation information in different spaces, so that the relationship between data, features and clustering structure can be explored at the same time, this paper proposes a feature selection method based on sparse and low-dimensional representation with maximum entropy adaptive graph (SLMEA). Firstly, the SLMEA combines the sparse transform representation with pseudo-label matrix learning to optimize, and uses the pseudo-label matrix to guide the learning of sparse low-dimensional space. It can not only explore the relationship between data and pseudo-labels in data space, but also mine the association between features and pseudo-labels in feature space, so as to select more discriminative features. Secondly, based on the maximum entropy theory, the similarity matrix is constructed adaptively, so that the two different manifold structures corresponding to sparse transform representation and pseudo label matrix learning can be adaptively learned and retained in the iterative process. In addition, in order to ensure the sparsity of the transformation matrix, the constraint of ℓ2,1/2-norm is applied to the matrix, which can better deal with the redundant features and obtain more sparse solutions. Finally, the SLMEA uses an alternate iterative update method to optimize the objective function, and carries out extensive experiments on eight mainstream datasets. Compared with seven state-of-the-art algorithms, SLMEA can have higher clustering accuracy and normalized mutual information.

Feature selection based on non-negative spectral feature learning and adaptive rank constraint

Unsupervised feature selection plays a significant role in data classification and clustering. General regression models cannot directly exploit the information on the feature space and fail to accurately describe the local geometric structure of data during feature selection. To address these problems, this paper proposes the feature selection algorithm, which is based on non-negative spectral feature learning and adaptive rank constraint (NNSAFS). First, the algorithm utilizes the residual term in sparse regression to ensure that the learned low-dimensional subspaces have greater fault tolerance and introduces a feature graph on the sparse transformation matrix to reveal the manifold information on the feature space. This sparse transformation matrix is the projection matrix because the introduction of feature graphs on this matrix can connect manifold learning to feature selection. In addition, traditional spectral clustering algorithms usually construct fixed similarity graphs for clustering analysis. The NNSAFS algorithm imposes a rank constraint on the clustering indicator matrix, which is equivalent to the graph regularization that can recover accurate local structure information. Moreover, the similarity matrix in the regularization term is constructed by using the maximum entropy theory, which can increase the adaptability of manifold learning. Finally, the algorithm imposes the l1-norm constraint on the projection matrix, which makes the selected features more conducive to clustering performance. The clustering performance of the NNSAFS algorithm is evaluated against seven other unsupervised feature selection algorithms on nine benchmark datasets. The experimental results show that the features selected by the proposed algorithm are more discriminative and outperform other algorithms in the clustering task.11The code of the proposed algorithm has been uploaded and available at the following link: https://github.com/Vita427/NNSAFS.git.

2D Fingerprinting-Based Localization for mmWave Cell-Free Massive MIMO Systems

In this letter, fingerprinting-based cooperative localization for millimeter-wave (mmWave) cell-free massive multiple-input multiple-output (MIMO) systems is investigated. For the purpose of robust localization in line-of-sight (LOS) or non-LOS (NLOS) environments, a dynamic two-dimensional (2D) fingerprint training scheme employing maximum likelihood (ML) estimation and information entropy theory is proposed. This scheme regularly extracts link state matrix and confidence factor-aided AOA vectors from uplink channels. Then, a dynamic AP select scheme along with an anchor node (AN) filtering scheme is used to rapidly lock the range of the user location. Based on this, a weighted mean square error (WMSE)-based AOA fingerprinting scheme is developed to estimate the user location. Numerical results are provided to validate the localization accuracy of the proposed scheme.