• Title/Summary/Keyword: Least Squares Algorithm

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Performance Comparison of the Batch Filter Based on the Unscented Transformation and Other Batch Filters for Satellite Orbit Determination (인공위성 궤도결정을 위한 Unscented 변환 기반의 배치필터와 다른 배치필터들과의 성능비교)

  • Park, Eun-Seo;Park, Sang-Young;Choi, Kyu-Hong
    • Journal of Astronomy and Space Sciences
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    • v.26 no.1
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    • pp.75-88
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    • 2009
  • The main purpose of the current research is to introduce the alternative algorithm of the non-recursive batch filter based on the unscented transformation in which the linearization process is unnecessary. The presented algorithm is applied to the orbit determination of a low earth orbiting satellite and compared its results with those of the well-known Bayesian batch least squares estimation and the iterative UKF smoother (IUKS). The system dynamic equations consist of the Earth's geo-potential, the atmospheric drag, solar radiation pressure and the lunar/solar gravitational perturbations. The range, azimuth and elevation angles of the satellite measured from ground stations are used for orbit determination. The characteristics of the non recursive unscented batch filter are analyzed for various aspects, including accuracy of the determined orbit, sensitivity to the initial uncertainty, measurement noise and stability performance in a realistic dynamic system and measurement model. As a result, under large non-linear conditions, the presented non-recursive batch filter yields more accurate results than the other batch filters about 5% for initial uncertainty test and 12% for measurement noise test. Moreover, the presented filter exhibits better convergence reliability than the Bayesian least squares. Hence, it is concluded that the non-recursive batch filter based on the unscented transformation is effectively applicable for highly nonlinear batch estimation problems.

An Efficient Adaptive Digital Filtering Algorithm for Identification of Second Order Volterra Systems (이차 볼테라 시스템 인식을 위한 효율적인 적응 디지탈 필터링 알고리즘)

  • Hwang, Y.S.;Mathews, V.J.;Cha, I.W.;Youn, D.H.
    • The Journal of the Acoustical Society of Korea
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    • v.7 no.4
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    • pp.98-109
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    • 1988
  • This paper introduces an adaptive nonlinear filtering algorithm that uses the sequential regression(SER) method to update the second order Volterra filter coefficients in a recursive way. Conventionally, the SER method has been used to invert large matrices which result from direct application of Wiener filter theory to the Volterra filter. However, the algorithm proposed in this paper uses the SER approach to update the least squares solution which is derived for Gaussian input signals. In such an algorithm, the size of the matrix to be inverted is smaller than that of conventional approaches, and hence the proposed method is computationally simpler than conventional nonlinear system identification techniques. Simulation results are presented to demonstrate the performance of the proposed algorithm.

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Fuzzy Inference Systems Based on FCM Clustering Algorithm for Nonlinear Process (비선형 공정을 위한 FCM 클러스터링 알고리즘 기반 퍼지 추론 시스템)

  • Park, Keon-Jun;Kang, Hyung-Kil;Kim, Yong-Kab
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.5 no.4
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    • pp.224-231
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    • 2012
  • In this paper, we introduce a fuzzy inference systems based on fuzzy c-means clustering algorithm for fuzzy modeling of nonlinear process. Typically, the generation of fuzzy rules for nonlinear processes have the problem that the number of fuzzy rules exponentially increases. To solve this problem, the fuzzy rules of fuzzy model are generated by partitioning the input space in the scatter form using FCM clustering algorithm. The premise parameters of the fuzzy rules are determined by membership matrix by means of FCM clustering algorithm. The consequence part of the rules is expressed in the form of polynomial functions and the coefficient parameters of each rule are determined by the standard least-squares method. And lastly, we evaluate the performance and the nonlinear characteristics using the data widely used in nonlinear process.

Nonlinear Process Modeling Using Hard Partition-based Inference System (Hard 분산 분할 기반 추론 시스템을 이용한 비선형 공정 모델링)

  • Park, Keon-Jun;Kim, Yong-Kab
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.7 no.4
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    • pp.151-158
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    • 2014
  • In this paper, we introduce an inference system using hard scatter partition method and model the nonlinear process. To do this, we use the hard scatter partition method that partition the input space in the scatter form with the value of the membership degree of 0 or 1. The proposed method is implemented by C-Means clustering algorithm. and is used for the initial center values by means of binary split. by applying the LBG algorithm to compensate for shortcomings in the sensitive initial center value. Hard-scatter-partitioned input space forms the rules in the rule-based system modeling. The premise parameters of the rules are determined by membership matrix by means of C-Means clustering algorithm. The consequence part of the rules is expressed in the form of polynomial functions and the coefficient parameters of each rule are determined by the standard least-squares method. The data widely used in nonlinear process is used to model the nonlinear process and evaluate the characteristics of nonlinear process.

Gauss-Newton Based Emitter Location Method Using Successive TDOA and FDOA Measurements (연속 측정된 TDOA와 FDOA를 이용한 Gauss-Newton 기법 기반의 신호원 위치추정 방법)

  • Kim, Yong-Hee;Kim, Dong-Gyu;Han, Jin-Woo;Song, Kyu-Ha;Kim, Hyoung-Nam
    • Journal of the Institute of Electronics and Information Engineers
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    • v.50 no.7
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    • pp.76-84
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    • 2013
  • In the passive emitter localization using instantaneous TDOA (time difference of arrival) and FDOA (frequency difference of arrival) measurements, the estimation accuracy can be improved by collecting additional measurements. To achieve this goal, it is required to increase the number of the sensors. However, in electronic warfare environment, a large number of sensors cause the loss of military strength due to high probability of intercept. Also, the additional processes should be considered such as the data link and the clock synchronization between the sensors. Hence, in this paper, the passive localization of a stationary emitter is presented by using the successive TDOA and FDOA measurements from two moving sensors. In this case, since an independent pair of sensors is added in the data set at every instant of measurement, each pair of sensors does not share the common reference sensor. Therefore, the QCLS (quadratic correction least squares) methods cannot be applied, in which all pairs of sensor should include the common reference sensor. For this reason, a Gauss-Newton algorithm is adopted to solve the non-linear least square problem. In addition, to show the performance of the proposed method, we compare the RMSE (root mean square error) of the estimates with CRLB (Cramer-Rao lower bound) and derived the CEP (circular error probable) planes to analyze the expected estimation performance on the 2-dimensional space.

Performance Comparison of Wave Information Retrieval Algorithms Based on 3D Image Analysis Using VTS Sensor (VTS 센서를 이용한 3D영상 분석에 기초한 파랑 정보 추출 알고리즘 성능 비교)

  • Ryu, Joong-seon;Lim, Dong-hee;Kim, Jin-soo;Lee, Byung-Gil
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.20 no.3
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    • pp.519-526
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    • 2016
  • As marine accidents happen frequently, it is required to establish a marine traffic monitoring system, which is designed to improve the safety and efficiency of navigation in VTS (Vessel Traffic Service). For this aim, recently, X-band marine radar is used for extracting the sea surface information and, it is necessary to retrieve wave information correctly and provide for the safe and efficient movement of vessel traffic within the VTS area. In this paper, three different current estimation algorithms including the classical least-squares (LS) fitting, a modified iterative least-square fitting routine and a normalized scalar product of variable current velocities are compared with buoy data and then, the iterative least-square method is modified to estimate wave information by improving the initial current velocity. Through several simulations with radar signals, it is shown that the proposed method is effective in retrieving the wave information compared to the conventional methods.

Improvement of LMS Algorithm Convergence Speed with Updating Adaptive Weight in Data-Recycling Scheme (데이터-재순환 구조에서 적응 가중치 갱신을 통한 LMS 알고리즘 수렴 속 도 개선)

  • Kim, Gwang-Jun;Jang, Hyok;Suk, Kyung-Hyu;Na, Sang-Dong
    • Journal of the Korea Institute of Information Security & Cryptology
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    • v.9 no.4
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    • pp.11-22
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    • 1999
  • Least-mean-square(LMS) adaptive filters have proven to be extremely useful in a number of signal processing tasks. However LMS adaptive filter suffer from a slow rate of convergence for a given steady-state mean square error as compared to the behavior of recursive least squares adaptive filter. In this paper an efficient signal interference control technique is introduced to improve the convergence speed of LMS algorithm with tap weighted vectors updating which were controled by reusing data which was abandoned data in the Adaptive transversal filter in the scheme with data recycling buffers. The computer simulation show that the character of convergence and the value of MSE of proposed algorithm are faster and lower than the existing LMS according to increasing the step-size parameter $\mu$ in the experimentally computed. learning curve. Also we find that convergence speed of proposed algorithm is increased by (B+1) time proportional to B which B is the number of recycled data buffer without complexity of computation. Adaptive transversal filter with proposed data recycling buffer algorithm could efficiently reject ISI of channel and increase speed of convergence in avoidance burden of computational complexity in reality when it was experimented having the same condition of LMS algorithm.

Nonlinear Characteristics of Non-Fuzzy Inference Systems Based on HCM Clustering Algorithm (HCM 클러스터링 알고리즘 기반 비퍼지 추론 시스템의 비선형 특성)

  • Park, Keon-Jun;Lee, Dong-Yoon
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.13 no.11
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    • pp.5379-5388
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    • 2012
  • In fuzzy modeling for nonlinear process, the fuzzy rules are typically formed by selection of the input variables, the number of space division and membership functions. The Generation of fuzzy rules for nonlinear processes have the problem that the number of fuzzy rules exponentially increases. To solve this problem, complex nonlinear process can be modeled by generating the fuzzy rules by means of fuzzy division of input space. Therefore, in this paper, rules of non-fuzzy inference systems are generated by partitioning the input space in the scatter form using HCM clustering algorithm. The premise parameters of the rules are determined by membership matrix by means of HCM clustering algorithm. The consequence part of the rules is represented in the form of polynomial functions and the consequence parameters of each rule are identified by the standard least-squares method. And lastly, we evaluate the performance and the nonlinear characteristics using the data widely used in nonlinear process. Through this experiment, we showed that high-dimensional nonlinear systems can be modeled by a very small number of rules.

Sparsity Adaptive Expectation Maximization Algorithm for Estimating Channels in MIMO Cooperation systems

  • Zhang, Aihua;Yang, Shouyi;Li, Jianjun;Li, Chunlei;Liu, Zhoufeng
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.10 no.8
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    • pp.3498-3511
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    • 2016
  • We investigate the channel state information (CSI) in multi-input multi-output (MIMO) cooperative networks that employ the amplify-and-forward transmission scheme. Least squares and expectation conditional maximization have been proposed in the system. However, neither of these two approaches takes advantage of channel sparsity, and they cause estimation performance loss. Unlike linear channel estimation methods, several compressed channel estimation methods are proposed in this study to exploit the sparsity of the MIMO cooperative channels based on the theory of compressed sensing. First, the channel estimation problem is formulated as a compressed sensing problem by using sparse decomposition theory. Second, the lower bound is derived for the estimation, and the MIMO relay channel is reconstructed via compressive sampling matching pursuit algorithms. Finally, based on this model, we propose a novel algorithm so called sparsity adaptive expectation maximization (SAEM) by using Kalman filter and expectation maximization algorithm so that it can exploit channel sparsity alternatively and also track the true support set of time-varying channel. Kalman filter is used to provide soft information of transmitted signals to the EM-based algorithm. Various numerical simulation results indicate that the proposed sparse channel estimation technique outperforms the previous estimation schemes.

A 3D Magnetic Inversion Software Based on Algebraic Reconstruction Technique and Assemblage of the 2D Forward Modeling and Inversion (대수적 재구성법과 2차원 수치모델링 및 역산 집합에 기반한 3차원 자력역산 소프트웨어)

  • Ko, Kwang-Beom;Jung, Sang-Won;Han, Kyeong-Soo
    • Geophysics and Geophysical Exploration
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    • v.16 no.1
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    • pp.27-35
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    • 2013
  • In this study, we developed the trial product on 3D magnetic inversion tentatively named 'KMag3D'. Also, we briefly introduced its own function and graphic user interface on which especially focused through the development in the form of user manual. KMag3D is consisted of two fundamental frame for the 3D magnetic inversion. First, algebraic reconstruction technique was selected as a 3D inversion algorithm instead of least square method conventionally used in various magnetic inversion. By comparison, it was turned out that algebraic reconstruction algorithm was more effective and economic than that of least squares in aspect of both computation time and memory. Second, for the effective determination of the 3D initial and a-priori information model required in the execution of our algorithm, we proposed the practical technique based on the assemblage of 2D forward modeling and inversion results for individual user-selected 2D profiles. And in succession, initial and a-priori information model were constructed by appropriate interpolation along the strke direction. From this, we concluded that our technique is both suitable and very practical for the application of 3D magentic inversion problem.