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.

A new technique for instantaneous frequency rate estimation

Newton algorithms are commonly used in the final “refinement” stage of parameter estimation for sinusoids and higher order phase polynomial signals Such parameter estimation scenarios arise commonly in radar applications where the radial target velocity (which is possibly time-varying) must be estimated The author and coworkers have previously proposed an elegant and efficient alternative to a Newton gradient search type algorithm based on filtering and phase unwrapping A statistical and computational analysis of this filtering/phase unwrapping method is presented here The analysis shows the algorithm to be computationally efficient and much less sensitive to the accuracy of the initial guesses for the parameters than a Newton algorithm A first-order statistical analysis of the filtering/phase unwrapping algorithm is performed, and guidelines are derived for the required accuracy of the initial estimates Simulations are presented to confirm the analysis

On refining polynomial phase signal parameter estimates

Cubic phase function

Review of the quasi-maximum likelihood estimator for polynomial phase signals

Effective quasi maximum likelihood – random samples consensus algorithm is proposed for the instantaneous frequency (IF) estimation of overlapping signals in the time-frequency (TF) plane. The proposed algorithm is tested on signal with five overlapping components. The IF estimation accuracy is excellent with signal-to-noise ratio threshold below 0 dB.

QML-RANSAC Instantaneous Frequency Estimator for Overlapping Multicomponent Signals in the Time-Frequency Plane

This paper considers parameter estimation of a hybrid sinusoidal frequency modulated (FM) and polynomial phase signal (PPS) from a finite number of samples. We first show limitations of an existing method, the high-order ambiguity function (HAF), and then propose a new method by adopting the high-order phase function which was originally designed for the pure PPS. The proposed method estimates parameters of interest from peak locations in the time-frequency rate domain, which are less perturbed by the noise than peak values used by the HAF-based method. Numerical evaluation shows the proposed method can handle the hybrid FM-PPS signal with low sinusoidal frequency and improve estimation accuracy in terms of mean squared error for several orders of magnitude.

Parameter Estimation of Hybrid Sinusoidal FM-Polynomial Phase Signal

THz encoders have distinct advantages for position sensing compared with other types of encoders, such as those based on optical and inductive sensors. A polarization-dependent metamaterial absorber reflects one polarization while absorbs the other, which makes it an ideal building block for the barcode of a THz encoder system. In this paper, we present the design, fabrication, and experiments of a THz polarization-dependent metamaterial absorber, and its application to a polarimetric sensing system.

Metamaterial absorber for THz polarimetric sensing

This letter introduces a new coupled mixture of polynomial phase signal (PPS) and sinusoidal frequency modulated (FM) signal, motivated by real-world applications, for example, contactless linear encoders. Specifically, the coupling is introduced to express the sinusoidal FM frequency as a function of the PPS-related parameters. Given the coupling mixture, it generalizes two existing models: the pure PPS model and the independent mixture model. Performance bounds of parameter estimation for the coupled mixture model are established in terms of the Cramer–Rao bound (CRB). Unlike the pure PPS case, the derived CRB shows its dependence on the PPS-related and sinusoidal FM-related parameters due to the coupling mixture. On the other hand, the derived CRBs for the PPS-related parameters are lower than their counterparts of the independent mixture model, as the sinusoidal FM frequency provides additional information on the PPS parameters.

Cramér–Rao Bounds for a Coupled Mixture of Polynomial Phase and Sinusoidal FM Signals

We propose a linear encoder which utilizes Terahertz (THz) wave and polarization information. The encoder consists of a polarization angle reader as a read head and a periodic polarizer linear array as a scale. The read head determines its position based on polarization angle on the scale. This technology has possibility to have resistance to fine particles and gap fluctuation between the read head and scale. We experimentally demonstrated that the linear encoder based on the terahertz polarimetric sensing is useful for the industrial applications.

Terahertz Polarimetric Sensing for Linear Encoder

This paper considers speed estimation for contactless electromagnetic (EM) encoder system with a moving read-head and spatially periodic placed reflectors. We first introduce a new signal model to capture reflected signals from these spatially periodic placed reflectors. Then an instantaneous phase-based speed estimator is proposed by using the phase unwrapping technique followed by a nonlinear least square method for motion-related parameters. The proposed speed estimator is verified by 1) Monte-Carlo simulations to confirm its statistical efficiency as the numerical mean squared errors approach to corresponding Cramer-Rao bounds and 2) a semi-analytical dataset by accounting for real system specificaltions such as the antenna beampattern, 3-dB beamwidth, and noise.

Kota Sadamoto

Papers

Parameter Estimation of Hybrid Sinusoidal FM-Polynomial Phase Signal

Metamaterial absorber for THz polarimetric sensing

Cramér–Rao Bounds for a Coupled Mixture of Polynomial Phase and Sinusoidal FM Signals

Terahertz Polarimetric Sensing for Linear Encoder

Speed estimation for contactless electromagnetic encoders