# Signal tracking approach for simultaneous estimation of phase and instantaneous frequency

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.

Abstract: Phase 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

175 citations

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

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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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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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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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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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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