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Proceedings ArticleDOI

Signal tracking approach for simultaneous estimation of phase and instantaneous frequency

01 Feb 2015-pp 1-5

TL;DR: This paper addresses the problem of simultaneous phase and instantaneous frequency estimation from polynomial phase signals embedded in Gaussian noise by introducing the modified signal tracking approach which is then realized using unscented Kalman filter.

AbstractPhase estimation plays an important role in various signal processing areas like Radar, Sonar, power systems, speech analysis, communications and many others. The phase of the analytic form of the non stationary signals can be used to find instantaneous frequency. This paper addresses the problem of simultaneous phase and instantaneous frequency estimation from polynomial phase signals embedded in Gaussian noise. Here we have introduced the modified signal tracking approach which is then realized using unscented Kalman filter. The state space model is derived using Taylor series expansion of the phase of polynomial phase signal as process model while Polar to Cartesian conversion as measurement model. Proposed method, compared with state-of-the-art, performs better for signals with higher order polynomial phase variations at lower Signal-to-Noise-Ratio (0-5dB). We also present the simulation results for phase estimation.

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Citations
More filters
01 Aug 2002
TL;DR: The letter defines an IFR estimation algorithm and theoretically analyzes it and is seen to be asymptotically optimal at the center of the data record for high signal-to-noise ratios.
Abstract: This letter introduces a two-dimensional bilinear mapping operator referred to as the cubic phase (CP) function. For first-, second-, or third-order polynomial phase signals, the energy of the CP function is concentrated along the frequency rate law of the signal. The function, thus, has an interpretation as a time-frequency rate representation. The peaks of the CP function yield unbiased estimates of the instantaneous (angular) frequency rate (IFR) and, hence, can be used as the basis for an IFR estimation algorithm. The letter defines an IFR estimation algorithm and theoretically analyzes it. The estimation is seen to be asymptotically optimal at the center of the data record for high signal-to-noise ratios. Simulations are provided to verify the theoretical claims.

175 citations

Proceedings ArticleDOI
01 Aug 2015
TL;DR: This paper discusses a Fourier transform based phase unwrapping method that is highly robust to noise and performs better even at lower SNR values (5-10dB) with a very less value of RMS error.
Abstract: Phase information recovered through interferometric techniques is mathematically wrapped in the interval (−π, π). Obtaining the original unwrapped phase is very important in numerous number of applications. This paper discusses a Fourier transform based phase unwrapping method. Kalman filter is proposed for denoising in post processing step to restore the unwrapped phase without any noise. The proposed method is highly robust to noise and performs better even at lower SNR values (5–10dB) with a very less value of RMS error. Also, the time taken for execution is very less compared to the many available methods in the literature.

7 citations


Additional excerpts

  • ...The piecewise polynomial approximation approach [12] and signal tracking approach [15], [16] provides unwrapped phase directly, but the non-linear measurement model limits the performance of those methods....

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References
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Book
01 Jan 1964
Abstract: Chapter 1: The Real and Complex Number Systems Introduction Ordered Sets Fields The Real Field The Extended Real Number System The Complex Field Euclidean Spaces Appendix Exercises Chapter 2: Basic Topology Finite, Countable, and Uncountable Sets Metric Spaces Compact Sets Perfect Sets Connected Sets Exercises Chapter 3: Numerical Sequences and Series Convergent Sequences Subsequences Cauchy Sequences Upper and Lower Limits Some Special Sequences Series Series of Nonnegative Terms The Number e The Root and Ratio Tests Power Series Summation by Parts Absolute Convergence Addition and Multiplication of Series Rearrangements Exercises Chapter 4: Continuity Limits of Functions Continuous Functions Continuity and Compactness Continuity and Connectedness Discontinuities Monotonic Functions Infinite Limits and Limits at Infinity Exercises Chapter 5: Differentiation The Derivative of a Real Function Mean Value Theorems The Continuity of Derivatives L'Hospital's Rule Derivatives of Higher-Order Taylor's Theorem Differentiation of Vector-valued Functions Exercises Chapter 6: The Riemann-Stieltjes Integral Definition and Existence of the Integral Properties of the Integral Integration and Differentiation Integration of Vector-valued Functions Rectifiable Curves Exercises Chapter 7: Sequences and Series of Functions Discussion of Main Problem Uniform Convergence Uniform Convergence and Continuity Uniform Convergence and Integration Uniform Convergence and Differentiation Equicontinuous Families of Functions The Stone-Weierstrass Theorem Exercises Chapter 8: Some Special Functions Power Series The Exponential and Logarithmic Functions The Trigonometric Functions The Algebraic Completeness of the Complex Field Fourier Series The Gamma Function Exercises Chapter 9: Functions of Several Variables Linear Transformations Differentiation The Contraction Principle The Inverse Function Theorem The Implicit Function Theorem The Rank Theorem Determinants Derivatives of Higher Order Differentiation of Integrals Exercises Chapter 10: Integration of Differential Forms Integration Primitive Mappings Partitions of Unity Change of Variables Differential Forms Simplexes and Chains Stokes' Theorem Closed Forms and Exact Forms Vector Analysis Exercises Chapter 11: The Lebesgue Theory Set Functions Construction of the Lebesgue Measure Measure Spaces Measurable Functions Simple Functions Integration Comparison with the Riemann Integral Integration of Complex Functions Functions of Class L2 Exercises Bibliography List of Special Symbols Index

6,363 citations


"Signal tracking approach for simult..." refers methods in this paper

  • ...The phase of these signals are then modelled as polynomial approximation of appropriate order according to Weirstrass theorem [5]....

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Journal ArticleDOI
08 Nov 2004
TL;DR: The motivation, development, use, and implications of the UT are reviewed, which show it to be more accurate, easier to implement, and uses the same order of calculations as linearization.
Abstract: The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT.

5,559 citations


"Signal tracking approach for simult..." refers methods in this paper

  • ...UKF uses a deterministic sampling technique known as the unscented transform to pick a minimal set of sample points (called sigma points) around the mean such that these points capture mean and covariance of a prior random variable exactly, while approximating the mean and covariance of the transformed random variable up to the third order in Taylor series [19]....

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  • ...[19], the unscented transform performs better than linearization and close to the Monte Carlo method....

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Journal ArticleDOI
TL;DR: The estimation of the parameters of a sinusoid from observations of signal samples corrupted by additive noise is investigated, suggesting frequency and phase estimation by linear regression on the signal phase.
Abstract: The estimation of the parameters of a sinusoid from observations of signal samples corrupted by additive noise is investigated. At high signal-to-noise ratios the additive noise is viewed as an equivalent phase noise, suggesting frequency and phase estimation by linear regression on the signal phase. The variances of the regression estimates are shown to achieve the Cramer-Rao bounds. A formula for the variance of the regression frequency estimator is derived in terms of the noise power spectrum. A simple formula for the variance with 1/f^{2} phase noise is presented.

448 citations


"Signal tracking approach for simult..." refers methods in this paper

  • ...Whereas later approach is also discussed extensively in literature like Kalman-Tretter Filter [14], Kalman filter for chirp signal parameter estimation [15], robust EKF [16], [17]....

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Journal ArticleDOI
TL;DR: The authors define the discrete polynomial-phase transform, derive its basic properties, and use it to develop computationally efficient estimation and detection algorithms.
Abstract: The discrete polynomial-phase transform (DPT) is a new tool for analyzing constant-amplitude polynomial-phase signals. The main properties of the DPT are its ability to identify the degree of the phase polynomial and to estimate its coefficients. The transform is robust to deviations from the ideal signal model, such as slowly-varying amplitude, additive noise and nonpolynomial phase. The authors define the DPT, derive its basic properties, and use it to develop computationally efficient estimation and detection algorithms. A statistical accuracy analysis of the estimated parameters is also presented. >

361 citations


"Signal tracking approach for simult..." refers methods in this paper

  • ...Former approach is realized using various methods such as Maximum Likelihood Estimation (MLE), High-order Ambiguity function (HAF) [7], Cubic polynomial phase function (CPF) [8], Discrete Chirp-Fourier Transform (DCFT) [9], Discrete Polynomial Phase Transform (DPT) [10], [11] and others [12], [13]....

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Journal ArticleDOI
TL;DR: A novel new integral transform that is adapted for signals of this type is introduced and used to derive estimation and classification algorithms that are simple to implement and that exhibit good performance.
Abstract: The measurement of the parameters of complex signals with constant amplitude and polynomial phase, measured in additive noise, is considered. A novel new integral transform that is adapted for signals of this type is introduced. This transform is used to derive estimation and classification algorithms that are simple to implement and that exhibit good performance. The algorithms are extended to constant amplitude and continuous nonpolynomial phase signals. >

331 citations


"Signal tracking approach for simult..." refers methods in this paper

  • ...Former approach is realized using various methods such as Maximum Likelihood Estimation (MLE), High-order Ambiguity function (HAF) [7], Cubic polynomial phase function (CPF) [8], Discrete Chirp-Fourier Transform (DCFT) [9], Discrete Polynomial Phase Transform (DPT) [10], [11] and others [12], [13]....

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