Fuzzy logic for digital phase-locked loop filter design

Simon, Daniel J.; El-Sherief, H.

doi:10.1109/91.388174

Cited by 49 publications

(29 citation statements)

References 19 publications

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“…In general, we will use lower-case letters to refer to scalars, bold-faced lower case letters to refer to column vectors, and upper case let ters to refer to matrices. We use the convention that the derivative of an m-element vector a with respect to a p-element vector b is defined as (11) Consider a nonlinear finite dimensional discrete time system of the form (12) where the vector Xn is the state of the system at time n, Wn and Vn are noise, d n is the observation vector, and f(·) and hO are nonlinear vector functions of the state.…”

Section: Extended Kalman Filteringmentioning

confidence: 99%

Sum Normal Optimization of Fuzzy Membership Functions

Simon

2002

Int. J. Unc. Fuzz. Knowl. Based Syst.

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Given a fuzzy logic system, how can we determine the membership functions that will result in the best performance? If we constrain the membership functions to a certain shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a small number of variables and the membership optimization problem can be reduced to a parameter optimization problem. This is the approach that is typically taken, but it results in membership functions that are not (in general) sum normal. That is, the resulting membership function values do not add up to one at each point in the domain. This optimization approach is modified in this paper so that the resulting membership functions are sum normal. Sum normality is desirable not only for its intuitive appeal but also for computational reasons in the real time implementation of fuzzy logic systems. The sum normal constraint is applied in this paper to both gradient descent optimization and Kalman filter optimization of fuzzy membership functions. The methods are illustrated on a fuzzy automotive cruise controller.

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Section: Extended Kalman Filteringmentioning

confidence: 99%

Sum Normal Optimization of Fuzzy Membership Functions

Simon

2002

Int. J. Unc. Fuzz. Knowl. Based Syst.

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“…For example, many results have been presented in the literature of the use of genetic algorithms for fuzzy membership function optimization [23,31,38]. Other derivative-free methods that have been used include neural networks [5,10], evolutionary programming [12], cell mapping (a geometric method) [35], fuzzy equivalence relations [43], and heuristic methods [39].…”

Section: Introductionmentioning

confidence: 99%

“…Other derivative-free methods that have been used include neural networks [5,10], evolutionary programming [12], cell mapping (a geometric method) [35], fuzzy equivalence relations [43], and heuristic methods [39]. Gradient descent is one of the derivative-based methods that has been used for shaping a fuzzy system's membership functions [7,31]. Other derivative-based methods that have been used to * Tel.…”

Section: Introductionmentioning

confidence: 99%

Training fuzzy systems with the extended Kalman filter

Simon

2002

Fuzzy Sets and Systems

132

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The generation of membership functions for fuzzy systems is a challenging problem. We show that for Mamdani-type fuzzy systems with correlation-product inference, centroid defuzziÿcation, and triangular membership functions, optimizing the membership functions can be viewed as an identiÿcation problem for a nonlinear dynamic system. This identiÿcation problem can be solved with an extended Kalman ÿlter. We describe the algorithm and compare it with gradient descent and with adaptive neuro-fuzzy inference system (ANFIS) based optimization of fuzzy membership functions. The methods discussed in this paper are illustrated on a fuzzy ÿlter for motor winding current estimation, and are compared with Butterworth ÿltering. We demonstrate that the Kalman ÿlter can be an e ective tool for improving the performance of a fuzzy system.

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“…Simon and El-Sherief [5] proposed a fuzzy PLL estimation filter for missile navigation. The gradient descent (GD) algorithm and genetic algorithm (GA) were used for optimization of the fuzzy estimators.…”

Section: Introductionmentioning

confidence: 99%

“…However, this target tracking model applies a simplified PLL architecture, which is not an adequate solution of implementation for practical receiver design. Jwo [5] presented an optimal estimator for bandwidth determination in dynamic environments based on a linear Kalman filter. The optimal noise bandwidths were obtained for the first-, second-, and third-order linear PLLs in the steady state.…”

Section: Introductionmentioning

confidence: 99%

Applications of New Fuzzy Inference-Based Tracking Loops for Kinematic GPS Receiver

Mao

2007

Circuits Syst Signal Process

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Abstract. Carrier phase measurement is essential for high-accuracy measurement in kinematic global positioning system (GPS) applications. For GPS receiver design, a narrow noise bandwidth is desired to decrease phase jitter due to thermal noise. However, this bandwidth will deteriorate the capability of the tracking loop and result in cycle slipping. Based on bandwidth adjustment criteria, a novel intelligent GPS receiver is proposed for solving the carrier phase tracking problem in the presence of high dynamic environments. A phase error estimator is developed in the carrier loop to conduct the phase error signals; i.e., frequency and frequency ramp errors. Two kinds of fuzzy inference (FI)-based approaches, fuzzy logic control and adaptive neuro-fuzzy control methods, that are simple and have easy realization properties are designed to perform rapid and accurate control of the digital frequency phase-locked loop (FPLL). A new design procedure for kinematic GPS receiver development is also presented. The computer results show that the FI-based receivers achieve faster settling time and wider pull-in range than the conventional tracking loops while also preventing the occurrence of cycle slips.

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Fuzzy logic for digital phase-locked loop filter design

Cited by 49 publications

References 19 publications

Sum Normal Optimization of Fuzzy Membership Functions

Sum Normal Optimization of Fuzzy Membership Functions

Training fuzzy systems with the extended Kalman filter

Applications of New Fuzzy Inference-Based Tracking Loops for Kinematic GPS Receiver

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