Metaheuristic algorithms have been widely used in determining the optimum Rational polynomial coefficients (RPCs). By eliminating a number of unnecessary RPCs, these algorithms increase the accuracy of geometric correction of highresolution satellite images. To this end, these algorithms use ordinary least squares and a number of ground control points (GCPs) to determine RPCs' values. Due to the cost of GCPs collection, using limited GCPs has become an attractive topic in various researches. In this study, a new reformulation of particle swarm optimization (PSO) algorithm, namely, Discrete-Binary PSO for Rational Function Model (DBPSORFM), is presented to find the optimal number and combination of RPCs in the case of limited GCPs. Based on the fact that the maximum number of RPCs, the values of which are obtained through least squares, is twice the number of GCPs, the particle of the proposed algorithm is composed of two binary and discrete parts. The discrete part contains the number of Rational coefficients that can vary from 1 to 78. In the binary section, which contains 0 and 1 values, the absence or presence of the corresponding coefficient in the discrete section is investigated. This method is not only compatible with the nature of the metaheuristic algorithms but also significantly reduces the search space. The proposed method has been tested on various types of high-resolution data. The results of the experiments indicate the superiority of the proposed method in comparison with the conventional approach in metaheuristic algorithms.

In the absence of satellite ephemeris data and inner geometry of satellite’ s sensor, utilization of Rational Function Models ((RFMs)) is one of the best approaches to georeferencing satellite images and extracting spatial information from them. However, since (RFMs) have high number of coefficients, then usually high number of control points is needed for their estimation. In the other hand, RFM terms are uninterpretable and all of them causes over-parametrization error which count as the most important weakness of the terrain-dependent (RFMs). Utilization of optimization algorithms is one of the best approaches to eliminate these weaknesses. Therefore, various optimization algorithms have been used to discover the optimal composition of RFM’ s terms. Since the mechanism of these algorithms is different, the performance and feature characteristics of these algorithms differ in the discovery of the optimal composition train-dependent RFM’ s terms. But the existing differences not comprehensively analyzed. In this paper, in order to comprehensive assessment the abilities of Genetic Optimization Algorithm (GA), Genetic modified Algorithm (GM), and a modified Particle Swarm Optimization (PSO) in terms of accuracy, quickness, number of control points required, and reliability of results, are evaluated. These methods are evaluated using for different datasets including a GeoEye-1, an IKONOS-2, a SPOT-3-1A, and a SPOT-3-1B satellite images. In terms of accuracy achieved, difference between these methods was less than 0. 4 pixel. In terms of speed of evaluation of parameters, GM was 10 to 12 time more quickly in comparison with two other algorithms. In terms of control points required, degree of freedom of modified PSO was 45. 25 percent and 27 percent more than GM and GA respectively, and finally in terms of reliability, the dispersion of RMSE obtained in 10 runs of three algorithms are relatively same. These results indicated that accuracy and reliability of all three methods are almost the same, speed of GM is higher and modified PSO needs less control points to optimize terrain-dependent RFM.

The existence of both ill-posedness and overparameterization phenomena in the Rational Function model (RFM), makes it difficult to determine Rational polynomial coefficients (RPCs). In this regard, Metaheuristic algorithms have been widely used. Despite the extensive efforts in this field, it is still challenging to find optimum structures of RFM due to the above-mentioned phenomena. The existing meta-heuristic methods focus on overparameterization and try to remove some unnecessary RPCs using binary particles. Although solving overparameterization can automatically address the ill-posedness phenomenon, metaheuristics do not achieve desired results by solely focusing on overparameterization. Therefore, it seems necessary to consider both ill-posedness and overparameterization phenomena to achieve an optimum structure of the RFM. Accordingly, in this study, a bi-objective particle swarm optimization (PSO) algorithm, namely BOPSO-RFM, is proposed to determine the optimum RFM structure. This method has two objective Functions that should be minimized: 1) the Root Mean Square Error (RMSE) over some of the ground control points (GCPs), and 2) the maximum Pearson correlation coefficient between the columns of the design matrix, each of which corresponding to one of RPCs. While binary meta-heuristic algorithms mostly address the overparameterization phenomenon by considering binary particles and calculating the RMSE over some GCPs, the added objective Function tries to address ill-posedness. Experiments conducted on three high-resolution datasets show that the proposed method has led to average improvements of 95% and 29% in terms of accuracy and RMSE values and 99% and 76% improvements in terms of stability, over well-known PSORFO and the state-of-the-art PSO-KFCV method, respectively. Moreover, the analysis of the final design matrix obtained from the final RFM structure revealed that the average of condition numbers corresponding to the BOPSO-RFM results had been 1. 14e+9 and 7. 39e+4 times lower than those of PSORFO and PSO-KFCV.

In this manuscript, we proposed a new scheme in communication signal detection which is respect to the curve shape of received signal and based on the extraction of curve fitting (CF) features. This feature extraction technique is proposed for signal data classification in receiver. The proposed scheme is based on curve fitting and approximation of Rational fraction coefficients. For each symbol of received signal, a specific Rational Function approximation is developed to fit with received signal curve and the coefficients of the numerator and denominator polynomials of this Function are considered as new extracted features. Then it will be shown that the coefficients of this polynomials have the potential for using as new features in a statistical classifier and have better performance in competition with other solutions such as linear and even nonlinear feature extraction methods in classification. The criteria used in performance evaluation are probability of error and signal to noise ratio in FSK and ASK modulations. For each symbol of received signal, a specific Rational Function approximation is developed to fit with received signal curve and the coefficients of the numerator and denominator polynomials of this Function are considered as new extracted features. In the proposed method, there are two phases train and test, which are described in the following two steps. First, in the train phase, the algorithm starts by using binary FSK and ASK modulations, so first, a system generate a number of random symbols then signal is modulated by binary ASK and FSK. The Modulated FSK and ASK signals are corrupted in the channel with noise. The noise-corrupted signal enters the receiver at the corresponding transmitted interval. Then, the samples are extracted from the modulated signals based on predetermined sample rates. Then, we fit a Rational fraction curve with degrees of L and M to each set of N samples. Afterward, we apply all the numerator (L+1) and denominator (M) coefficients to 0 and 1 classes in the binary FSK and ASK modulations. We store all the specific coefficients of the deterministic symbols at different M and L values to create the corresponding histogram in each class. In each histogram (i. e., the coefficients of a class), we extract and store specific coefficients that completely discriminate between the two classes. Therefore, we determine all the histograms where there is a good approximation of discrimination and create the related table. Note that the data used in histograms are the training data. Then, in order to analyze and evaluate the performance of the proposed curve fitting method, we send the testing data through the channel corresponding to the related modulator. The results of the proposed classification method show that it provides smaller error rate regarding to the theoretical error rate probability in AWGN channel.

Rational Functions are of great interest to engineers and geoscientists. The Rational polynomial coefficient (RPC) model as a generalized sensor model has been introduced as an alternative for the rigorous sensor model of the satellite imaging.umerical instability of normal equations is the only single obstacle to the implementation of these Functions. Practically, estimating Rational Function coefficients using available control points is mostly an ill-posed problem. Condition number of the normal matrix in the linear parametric model is relatively large. Therefore, a regularization method has to be employed in order to stabilize the equations.Implementation of the regularization technique improves the solution in the linear parametric model. The optimum value of the regularization parameter is estimated using the generalized cross validiation technique.Moreover, simplification of the observation equations leads to a linear observation model which is the most frequently utilized approach for estimation of the unknown coefficients. However, rigorous modeling is recast in a combined adjustment model. Due to nonlinearity of the combined model, the initial values of unknown parameters are needed. The initialization process can be done using the estimated parameters from the linear parametric model.Here, Rational Function coefficients are estimated using a combined model.Furthermore, the Tikhonov regularization method is employed for regularization of the problem in the combined model. Five different methods are implemented and their performances are compared.Comparison of the root mean squared errors shows that the implementation of the combined model with an appropriate regularization parameter significantly improves the accuracy of the estimated coefficients. The regularized combined model gives the minimum root mean squared errors which is about half the value of the linear parametric model. The proposed method outperforms the already existing ones from an accuracy and computational point of view.