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This paper attempts to establish the grey GM(0,N) estimation model of the soil organic matter content spectral inversion under the uncertainties between soil organic matter contents and spectral characteristics and the theory of grey system.

At first, based on the uncertainty of the relationship between the soil organic matter content and spectral characteristics, using the ordered grey accumulation generation and grey GM(0, N) model to establish hyper‐spectral grey estimation model of soil organic matter content. Second, the presented model is used to estimate soil organic matter of Hengshan County in Shanxi province in the last part of the paper.

The results are convincing: not only that soil organic matter content spectral inversion grey GM(0, N) model based on the ordered grey accumulation generation theory is valid, but also the model's prediction accuracy is higher, with the sample's average prediction accuracy being 93.662 per cent.

The method exposed in the paper can be used on soil organic matter content hyper‐spectral inversion and even for other similar forecast problems.

The paper succeeds in realising both prediction pattern and application of soil organic matter content hyper‐spectral inversion by using the newest developed theories: grey GM(0, N) model based on the ordered grey accumulation generation.

The purpose of this paper is to establish the grey‐weighted relationship prediction pattern of the soil organic matter content spectral inversion under the uncertainties between soil organic matter contents and spectral characteristics and the theory of grey system.

At first, according to grey‐weighted distance, a new grey relationship model is presented. Second, in order to make full use of the information of grey relationship sequences, the maximum grey relationship discrimination principle is improved and then the soil organic matter content spectral inversion pattern is put forward based on weighted grey recognition theory. A numeric example of Hengshan County in Shanxi Province is also computed in the last part of the paper.

The results are convincing: not only that soil organic matter content spectral inversion pattern based on the weighted grey recognition theory is valid, but also the model's prediction accuracy is higher; the sample's average prediction accuracy is 94.917 per cent.

The method exposed in the paper can be used at soil organic matter content hyper‐spectral inversion and even for other similar forecast problems.

The paper succeeds in realising both prediction pattern and application of soil organic matter content hyper‐spectral inversion by using the newest developed theories: weighted grey recognition theory.

The purpose of this paper is to establish the grey relational estimating model of soil pH value based on hyper-spectral data.

As to the uncertainty of the factors affecting the soil pH value estimation based on hyper-spectral, the grey weighted relation estimation model was set up according to the grey system theory. Then the linear regression correction model is established according to the difference and grey relation degree information between the estimated samples and their corresponding pattern. At the same time, the model was applied to Hengshan county of Shanxi province.

The results are convincing: not only that the linear regression correction model of grey relation estimating pattern of soil pH value based on hyper-spectral data is valid, but also the model’s estimating accuracy is higher, which the corrected average relative error is 0.2578 per cent, and the decision coefficient R²=0.9876.

The method proposed in the paper can be used at soil pH value hyper-spectral inversion and even for other similar forecast problem.

The paper succeeds in realising both the soil pH value hyper-spectral grey relation estimating pattern based on the grey relational theory and the correction model of the estimating pattern by using the linear regression.

This paper presents an overview of three information‐theoretic methods, which have been used extensively in many areas such as signal/image processing, pattern recognition and statistical inference. These are: the maximum entropy (ME), minimum cross‐entropy (MCE) and mutual information (MI) methods. The development history of these techniques is reviewed, their essential philosophy is explained, and typical applications, supported by simulation results, are discussed.

In order to overcome the uncertainty and improve the accuracy of spectral estimation, this paper aims to establish a grey fuzzy prediction model of soil organic matter content by using grey theory and fuzzy theory.

Based on the data of 121 soil samples from Zhangqiu district and Jiyang district of Jinan City, Shandong Province, firstly, the soil spectral data are transformed by spectral transformation methods, and the spectral estimation factors are selected according to the principle of maximum correlation. Then, the generalized greyness of interval grey number is used to modify the estimation factors of modeling samples and test samples to improve the correlation. Finally, the hyper-spectral prediction model of soil organic matter is established by using the fuzzy recognition theory, and the model is optimized by adjusting the fuzzy classification number, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

The results show that the generalized greyness of interval grey number can effectively improve the correlation between soil organic matter content and estimation factors, and the accuracy of the proposed model and test samples are significantly improved, where the determination coefficient R² = 0.9213 and the mean relative error (MRE) = 6.3630% of 20 test samples. The research shows that the grey fuzzy prediction model proposed in this paper is feasible and effective, and provides a new way for hyper-spectral estimation of soil organic matter content.

The research shows that the grey fuzzy prediction model proposed in this paper can not only effectively deal with the three types of uncertainties in spectral estimation, but also realize the correction of estimation factors, which is helpful to improve the accuracy of modeling estimation. The research result enriches the theory and method of soil spectral estimation, and it also provides a new idea to deal with the three kinds of uncertainty in the prediction problem by using the three kinds of uncertainty theory.

The paper succeeds in realizing both the grey fuzzy prediction model for hyper-spectral estimating soil organic matter content and effectively dealing with the randomness, fuzziness and grey uncertainty in spectral estimation.

In order to improve the estimation accuracy of soil organic matter, this paper aims to establish a modified model for hyperspectral estimation of soil organic matter content based on the positive and inverse grey relational degrees.

Based on 82 soil sample data collected in Daiyue District, Tai'an City, Shandong Province, firstly, the spectral data of soil samples are transformed by the first order differential and logarithmic reciprocal first order differential and so on, the correlation coefficients between the transformed spectral data and soil organic matter content are calculated, and the estimation factors are selected according to the principle of maximum correlation. Secondly, the positive and inverse grey relational degree model is used to identify the samples to be identified, and the initial estimated values of the organic matter content are obtained. Finally, based on the difference information between the samples to be identified and their corresponding known patterns, a modified model for the initial estimation of soil organic matter content is established, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

The results show that the methods of logarithmic reciprocal first order differential and the first-order differential of the square root for transforming the original spectral data are more effective, which could significantly improve the correlation between soil organic matter content and spectral data. The modified model for hyperspectral estimation of soil organic matter has high estimation accuracy, the average relative error (MRE) of 11 test samples is 4.091%, and the determination coefficient (R²) is 0.936. The estimation precision is higher than that of linear regression model, BP neural network and support vector machine model. The application examples show that the modified model for hyperspectral estimation of soil organic matter content based on positive and inverse grey relational degree proposed in this article is feasible and effective.

The model in this paper has clear mathematical and physics meaning, simple calculation and easy programming. The model not only fully excavates and utilizes the internal information of known pattern samples with “insufficient and incomplete information”, but also effectively overcomes the randomness and grey uncertainty in the spectral estimation of soil organic matter. The research results not only enrich the grey system theory and methods, but also provide a new approach for hyperspectral estimation of soil properties such as soil organic matter content, water content and so on.

The paper succeeds in realizing both a modified model for hyperspectral estimation of soil organic matter based on the positive and inverse grey relational degrees and effectively dealing with the randomness and grey uncertainty in spectral estimation.

This study aims to improve the accuracy of hyperspectral estimation of soil organic matter content.

Based on the uncertainty in spectral estimation, 76 soil samples collected in Zhangqiu District, Jinan City, Shandong Province, were studied in this paper. First, the spectral transformation of the spectral data after denoising was carried out by means of 11 transformation methods such as reciprocal and square, and the estimation factor was selected according to the principle of maximum correlation. Secondly, the grey weighted distance was used to calculate the grey relational degree between the samples to be estimated and the known patterns, and the local linear regression estimation model of soil organic matter content was established by using the pattern samples closest to the samples to be identified. Thirdly, the models were optimized by gradually increasing the number of modeling samples and adjusting the decision coefficient, and a comprehensive index was constructed to determine the optimal predicted value. Finally, the determination coefficient and average relative error are used to evaluate the validity of the model.

The results show that the maximum correlation coefficient of the seven estimated factors selected is 0.82; the estimation results of 14 test samples are of high accuracy, among which the determination coefficient R² = 0.924, and the average relative error is 6.608%.

Studies have shown that it is feasible and effective to estimate the content of soil organic matter by using grey correlation local linear regression model.

The paper succeeds in realizing both the soil organic matter hyperspectral grey relation estimating pattern based on the grey relational theory and the estimating pattern by using the local linear regression.

The low Mach number approximation of the Navier—Stokes equations is of similar nature to the equations for incompressible flow. A major difference, however, is the appearance of a space‐ and time‐varying density that introduces a supplementary non‐linearity. In order to solve these equations with spectral space discretization, an iterative solution method has been constructed and successfully applied in former work to two‐dimensional natural convection and isobaric combustion with one direction of periodicity. For the extension to other geometries efficiency is an important point, and it is therefore desirable to devise a direct method which would have, in the best case, the same stability properties as the iterative method. The present paper discusses in a systematic way different approaches to this aim. It turns out that direct methods avoiding the diffusive time step limit are possible, indeed. Although we focus for discussion and numerical investigation on natural convection flows, the results carry over for other problems such as variable viscosity flows, isobaric combustion, or non‐homogeneous flows.

The importance of thoroughly monitoring the state of the environment in Mediterranean ecosystems has long been recognised. With regard to the spatial extension of large areas threatened by various degradation processes it becomes obvious that terrestrial observation alone is hardly able to cope with this task. Remote sensing with air‐ or spaceborne sensor systems provides a comprehensive spatial coverage, is intrinsically synoptic, and collects objective, repetitive data and is thus ideally suited for monitoring environmentally sensitive areas. The major problem associated with its use is to quantitatively interpret a measured signal that has interacted with remote objects in terms of the properties of these objects. In parallel to the advances in remote sensing geographical information systems (GIS) have emerged as a fully functional support for resource management tasks. As an example for tracing and analysing environmental change with coupled remote sensing and GIS approaches we present a case study on the island of Crete which was carried out in the framework of research programmes supported by the European Union. Although it is known that grazing in Crete dramatically increased during the last two decades, it was not well understood how grazing pressure differs spatially and in how far it altered the landscape of Crete. One of the major rangeland areas of central Crete, the Psiloritis Mountains, have been selected to serve as a test site for answering these questions. On the basis of an extended Landsat‐TM and ‐MSS data set acquired between 1977 and 1996 it has been shown that time series analysis techniques based on vegetation fractions derived from spectral unmixing can substantiate a spatio‐temporal interpretation of degradation processes. In areas under massive grazing pressure such processes can be linked to the respective driving forces by GIS‐based analyses of natural and socio‐economic boundary conditions.

Multiple-input multiple-output (MIMO) combined with multi-user massive MIMO has been a well-known approach for high spectral efficiency in wideband systems, and it was targeted to detect the MIMO signals. The increasing data rates with multiple antennas and multiple users that share the communication channel simultaneously lead to higher capacity requirements and increased complexity. Thus, different detection algorithms were developed for the Massive MIMO.

This paper focuses on the various literature analyzes on various detection algorithms and techniques for MIMO detectors. Here, it reviews several research papers and exhibits the significance of each detection method.

This paper provides the details of the performance analysis of the MIMO detectors and reveals the best value in the case of each performance measure. Finally, it widens the research issues that can be useful for future researchers to be accomplished in MIMO massive detectors

This paper has presented a detailed review of the detection of massive MIMO on different algorithms and techniques. The survey mainly focuses on different types of channels used in MIMO detections, the number of antennas used in transmitting signals from the source to destination, and vice-versa. The performance measures and the best performance of each of the detectors are described.