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Dynamic phenomena in electric power systems require fast and accurate algorithms for processing signals. The processing results include synchrophasor parameters, e.g., varying amplitude, phase or frequency of sinusoidal voltage or current signals. This paper presents a novel estimation method of synchrophasor parameters that comply with the requirements of IEEE/IEC standards. The authors analyzed an algorithm for measuring the phasor magnitude by means of a selected artificial neural network (ANN), an algorithm for estimating the phasor phase and frequency that makes use of the zero-crossing method. The original components of the presented approach are: the method of the synchrophasor magnitude estimation by means of a suitably trained and applied radial basic function (RBF), the idea of using two algorithms operating simultaneously to estimate the synchrophasor magnitude, phase and frequency that apply identical calculation methods are different in that the first one filters the input signal using the FIR filter and the second one operates without any filter, and the algorithm calculating corrections of the phase shift between the input and output signal and the algorithm calculating corrections of the magnitude estimation. The error results obtained from the applied algorithms were compared with those of the quadrature filter method and the ones presented in literature, as well as with the permissible values of the errors. In all cases, these results were lower than the permissible values and at least equal to the values found in the literature.

This brief proposes a new unbiased finite impulse response (FIR) filter with improved robustness for state-space models in continuous time. The FIR filter proposed in this brief is called the unbiased FIR filter based on the Frobenius norm and exponential weight (UFFFNE). A new integral cost function based on the Frobenius norm for the filter gain function with exponential weight is introduced to improve its robustness. It is shown that the UFFFNE design problem can be cast into the constrained minimum-energy optimal control problem. A new analytic expression for the gain function of the UFFFNE is also proposed. The higher robustness of the proposed UFFFNE is demonstrated through a comparison with the existing minimum variance unbiased FIR filter and the conventional Kalman-Bucy filter based on a numerical example.

A novel robust filter referred as maximum correntropy sparse Gauss–Hermite quadrature filter (MCSGHQF) is proposed. The novel algorithm makes use of the sparse Gauss–Hermite quadrature (SGHQ) rule to numerically compute Gaussian-weighted integrals, which are propagated through non-linear state equation, and then a weighted means and covariance is taken. As the sensor measurements are always corrupted by non-Gaussian noise which is typically glint noise or mixed Gaussian-impulsive noise, the measurement update is redesigned based on the maximum correntropy criterion instead of minimum mean square error. Therefore, the MCSGHQF could exhibit robustness to the non-Gaussian measurement noise, especially impulsive noise. In addition, the study proposes the use of MCSGHQF for ballistic missile tracking during midcourse phase to deal with the non-Gaussian noise. The tracking performance is compared with that of SGHQ filter (SGHQF), Huber-based filter and extended Kalman filter by Monte-Carlo simulations. The simulation results demonstrate that the MCSGHQF is effective in glint noise case and exhibits superior to Huber-based filter in mixed Gaussian-impulsive noise case.

This study presents denoising of phases signal by comb filter. Signal phase is widely used in biomedical and communications engineering, and has become increasingly important over the past few years. In particular, steady-state visual evoked potential (SSVEP) of electroencephalogram (EEG) and quadrature amplitude modulation (QAM) uses phase to distinguish channel and data. For signal processing, the filter is usually adopted. In this study, the usefulness of comb and bandpass filters in detecting the phase of a signal is compared by using simulated and real signals to verify phase signal denoising. Experimental data show that comb filters had a higher signal to noise ratio (SNR) of phase signal. However, even if a comb filter performs well, the delay time of a digital comb filter will be limited by the sampling rate. It is possible to solve this problem, but doing so is inconvenient within the context of real-time applications. Using a variable delay (VD) approached to fractional delay for digital comb filter, it is both simple and easy to use.

In this paper, a novel fuzzy quadrature particle filter (FQPF) based on maximum entropy fuzzy clustering for maneuvering target tracking is proposed. The novelties of the fuzzy quadrature particle filter are in the update step in which the predicted and posterior probability density functions are approximated by introducing a set of quadrature point probability densities based on the Gauss–Hermite quadrature rule as a Gaussian. The particle and quadrature point weights can be adaptively estimated based on the weighting exponent and fuzzy membership degrees provided by a modified version of maximum entropy fuzzy clustering algorithm. Unlike the Gaussian particle filter (GPF) using the prior distribution as the proposal distribution, the new FQPF uses a set of modified quadrature point probability densities as the proposal distribution that can effectively enhance the diversity of samples and improve the approximate performance. Finally, simulation results are presented to demonstrate the versatility and improved performance of the fuzzy quadrature particle filter over other nonlinear filtering approaches, namely the unscented Kalman filter, quadrature Kalman filter, particle filter, and GPF, to solve maneuvering target tracking problems.

The design of two-channel quadrature mirror filter banks can be constructed based on real infinite impulse response (IIR) all-pass digital filters without yielding magnitude distortion. The design problem is first formulated as a phase optimization using IIR all-pass filters in the least-squares sense. Then the nonlinear phase optimization is further converted into solving an eigenproblem of an appropriate real, symmetric, and positive-definite matrix. In this paper, the minor component analysis algorithm based on the neural learning rule is exploited to the design of eigenfilter. When the learning algorithm achieves convergence, the weights of the neural system approximate the smallest eigenvector, which are the optimal filter coefficients of the IIR all-pass filters. The simulation results confirm that the proposed neural-based method can achieve accurate performance by incorporating the simple neural model.

We propose general methodology of deterministic single-mode quantum interaction nonlinearly modifying single quadrature variable of a continuous variable system. The methodology is based on linear coupling of the system to ancillary systems subsequently measured by quadrature detectors. The nonlinear interaction is obtained by using the data from the quadrature detection for dynamical manipulation of the coupling parameters. This measurement-induced methodology enables direct realization of arbitrary nonlinear quadrature interactions without the need to construct them from the lowest-order gates. Such nonlinear interactions are crucial for more practical and efficient manipulation of continuous quadrature variables as well as qubits encoded in continuous variable systems., Comment: 6 pages, 2 figures

An improved quadrature nonlinear filter named delayed Genz-Keister sequences-based sparse-grid quadrature filter (DGKSGQF) is developed for the target tracking problems. The filter changes the non-nested Gaussian quadrature points of the quadrature filters to the nested Genz-Keister points for selecting the unvariate points, which are the basis point sets extended to form a multidimensional grid using the sparse-grid theory. As a result, the points used for lower accuracy levels DGKSGQF can be reused for any higher accuracy level. Thus, it can further reduce the number of total points used for the conventional Gauss-Hermite SGQF without sacrificing performance. The proposed filter is applied to the reentry ballistic target tracking problem. The simulation results show that the DGKSGQF achieves higher accuracy than the EKF and the UKF. In addition, it can more flexibly control the performance in terms of the number of points and accuracy level.

In this paper, a new CMOS current-mode single input and multi-output (SIMO) universal filter and quadrature oscillator (QO) based on current differencing transconductance amplifiers (CDTA) are proposed. The SIMO filter can realize low-pass, high-pass, band-pass band-stop and all-pass filter functions simultaneously without any component matching conditions and the angular frequency (ω o) and the quality factor of the proposed filter can be electronically controlled and tuned orthogonal. By some modifications of the filter, a new current-mode four-phase QO can be obtained easily. The condition of oscillation and frequency of oscillation of the QO can be controlled electronically and independently through the bias current of the CDTAs, and it is suitable for variable frequency oscillator. Moreover, all the passive and active sensitivities of the circuits are low. SPICE simulation results are included to confirm the theory.

Battery state of charge (SOC) can directly reflect its sustainable power supply capacity and health. It is important basis to formulate balance and energy management strategy for battery management system (BMS). In this paper, a second-order RC battery model with factors affected battery characteristics was established based on the Gauss-Hermite quadrature filter (GHQF) theory. According to Kirchhoffs law a state space model was established and the parameters in the model were identified. The GHQF algorithm and model were verified, and comparison was made to an extended Kalman filter (EKF) algorithm on the Matlab and Simulink simulation platform.

In this paper, vision-based relative navigation of two spacecraft is addressed using the sparse-grid quadrature filter. The relative navigation provides the estimates of the relative orbit and relative attitude as well as the gyro biases. It is a challenging problem because of its high nonlinearity and dimensionality. The extended Kalman filter (EKF) and the unscented Kalman filter (UKF) have been used in the past to solve this problem. However, these filters are not accurate enough in the presence of large initial uncertainties or high nonlinearities. Moreover, although other filters, such as the Gauss-Hermite quadrature filter and the particle filter, can be more accurate than the EKF and UKF, they are hard to use in this high-dimensional estimation problem since a large number of quadrature points or particles are required and therefore the computation complexity is prohibitive. It is shown in this paper that the new sparse-grid quadrature filter can achieve much higher estimation accuracy than EKF, UKF, and the cubature Kalman filter without excessive computation load.

This paper explores a novel adaptive sparse grid quadrature filter. The sparse grid quadrature approach has been recently developed for nonlinear estimation problems to alleviate the curse-of-dimensionality issue of the Gauss–Hermite quadrature filter. Accuracy level of the sparse grid quadrature filter is an important tuning factor that affects desired performance. The proposed filter autonomously adjusts the accuracy level of the sparse grid quadrature rule in both prediction and update steps by increasing the level gradually until an adaptation criterion is satisfied. The adaptation criterion is derived based on a quadrature error estimator. The nestedness property of sparse grid quadrature rule enables efficient computation in adaptation by reusing quadrature points of the previous level sparse grid quadrature. An application to spacecraft relative navigation has been made to demonstrate the adaptive spare grid quadrature filter outperforming the extended Kalman filter and the unscented Kalman filter.

The problem of robust transmitted waveform and received filter design for cognitive radar in a signal-dependent interference environment is considered. When estimate errors of the target impulse response (TIR) and clutter impulse response (CIR) exist, in order to improve the worst signal-to-clutter ratio (SCR) and signal-to-interference-and-noise ratio (SINR), a robust transmitted waveform and received filter are designed based on the minimax criterion by using the information fed back from the receiver. Using deterministic and random models, the waveform and filter design problem is divided into three optimization problems. The robust waveform and filter are then obtained by solving these problems. In the deterministic model, we prove that the robust waveform and filter impulse response can be generated by a pseudorandom code. In the random model, the robust waveform and filter impulse response can be obtained by an alternative projection algorithm. Numerical results indicate that the worst SINR of the robust waveform and filter is higher than that of the traditional waveform and filter.

The cubature Kalman filter (CKF), which is based on the third degree spherical-radial cubature rule, is numerically more stable than the unscented Kalman filter (UKF) but less accurate than the Gauss-Hermite quadrature filter (GHQF). To improve the performance of the CKF, a new class of CKFs with arbitrary degrees of accuracy in computing the spherical and radial integrals is proposed. The third-degree CKF is a special case of the class. The high-degree CKFs of the class can achieve the accuracy and stability performances close to those of the GHQF but at lower computational cost. A numerical integration problem and a target tracking problem are utilized to demonstrate the necessity of using the high-degree cubature rules to improve the performance. The target tracking simulation shows that the fifth-degree CKF can achieve higher accuracy than the extended Kalman filter, the UKF, the third-degree CKF, and the particle filter, and is computationally much more efficient than the GHQF.

In this study, a closed-form equation is derived which relates the mean-squared error (MSE) to the frequency response of the interpolation filter. Effects of additive white Gaussian noise and timing jitter on the MSE are accounted for in the equation. By using properties of the Nyquist signalling pulse, a simple approximation to the MSE equation is obtained, which is found to be accurate over the range of excess bandwidths commonly used in quadrature amplitude modulation receivers.

In this work, a hybrid method in frequency domain for design of a linear-phase quadrature mirror filter bank is proposed. The nonlinear least square hybrid method based on Levenberg-Marquardt (LM) and Quasi-Newton (QN) is developed for the design of a low-pass prototype filter whose responses in the passband and stopband are ideal, and the filter bank response at quadrature frequency is 0.707. The proposed method is employed to optimize the quadratic measure of ideal characteristics of the prototype filter and filter bank at quadrature frequency. Performance and effectiveness of the proposed method in terms of peak reconstruction error (PRE), mean squares error in passband and stopband regions, and error in transition band at quadrature frequency are shown through numerical examples and comparison of the results with other existing method. It was found that the proposed method is very simple and easy to implement for QMF bank design problem.

In this paper, a novel nonlinear filter named Sparse-grid Quadrature Filter (SGQF) is proposed. The filter utilizes weighted sparse-grid quadrature points to approximate the multi-dimensional integrals in the nonlinear Bayesian estimation algorithm. The locations and weights of the univariate quadrature points with a range of accuracy levels are determined by the moment matching method. Then the univariate quadrature point sets are extended to form a multi-dimensional grid using the sparse-grid theory. Compared with the conventional point-based methods, the estimation accuracy level of the SGQF can be flexibly controlled and the number of sparse-grid quadrature points for the SGQF is a polynomial of the dimension of the system, which alleviates the curse of dimensionality for high dimensional problems. The Unscented Kalman Filter (UKF) is proven to be a subset of the SGQF at the level-2 accuracy. The performance of this filter is demonstrated by an orbit estimation problem. The simulation results show that the SGQF achieves higher accuracy than the Extended Kalman Filter (EKF), the UKF, and the Cubature Kalman Filter (CKF). In addition, the SGQF is computationally much more efficient than the multi-dimensional Gauss-Hermite Quadrature Filter (GHQF) with the same performance.

A novel sparse Gauss―Hermite quadrature filter is proposed using a sparse-grid method for multidimensional numerical integration in the Bayesian estimation framework. The conventional Gauss―Hermite quadrature filter is computationally expensive for multidimensional problems, because the number of Gauss―Hermite quadrature points increases exponentially with the dimension. The number of sparse-grid points of the computationally efficient sparse Gauss―Hermite quadrature filter, however, increases only polynomially with the dimension. In addition, it is proven in this paper that the unscented Kalman filter using the suggested optimal parameter is a subset of the sparse Gauss―Hermite quadrature filter. The sparse Gauss-Hermite quadrature filter is therefore more flexible to use than the unscented Kalman filter in terms of the number of points and accuracy level, and it is more efficient than the conventional Gauss―Hermite quadrature filter. The application to the spacecraft attitude estimation problem demonstrates better performance of the sparse Gauss―Hermite quadrature filter in comparison with the extended Kalman filter, the cubature Kalman filter, and the unscented Kalman filter.

This paper presents a novel quadrature compensation scheme for vibratory rate gyroscopes in closed-loop electro- mechanical sigma-delta-modulators (ΣΔM). The proposed technique is able to detect and compensate quadrature errors beyond the full-scale limits of the ΣΔM with a minimal analog hardware effort. The quadrature detection is based on a pure digital pattern recognition algorithm, the quadrature compensation is done using DC bias voltages. An appropriate quadrature compensation is reached within a few iterations of the proposed algorithm.

In this paper, a particle swarm optimization (PSO) is used to design the quadrature mirror filter (QMF) banks with linear phase in frequency domain. A unique PSO is developed to optimize filter bank coefficients to match the ideal system response. The three main attributes used in assessing the performance of filter are reconstruction error, mean square error in pass band and mean square error in stop band. The proposed PSO based method produces almost the same result as that of the existing methods. As compared to the existing methods this method is very simple to implement for the QMF bank optimization. To implement the proposed PSO algorithm, a Matlab program is developed and three examples have been presented to illustrate the performance of the proposed method.

This paper proposes an algorithm to design a two-channel linear phase quadrature mirror filter (QMF) bank. The design problem is presented systematically as an unconstrained optimization that minimizes the weighted sum of error of transfer function of the filter bank at quadrature frequency, stopband energy and the passband error of a prototype filter (PF). A new method is developed for the design of a low pass prototype filter for QMF banks. For solving given optimization problem, Quasi-Newton optimization technique is used. Numerical examples and comparisons with several existing methods are included to show the performances and effectiveness of this method. An application of the proposed method is considered in the area of subband coding of the images.

An output effect of a quadrature correlation receiver with an input band-pass filter at reception of a phase-keyed wideband signal is considered. Analytical expressions for output effect of a receiver proportional to the absolute value of a complex envelope of a cross-correlation function for received and reference signals are obtained. Dependences of cross-correlation function absolute value on a time delay, frequency mismatch of a received and reference signals, and passband width of input filter are analyzed. It is shown, that cross-correlation function’s maximum is reached in case of non-zero time delay of a received signal when there is no frequency mismatch between input and reference signals. The time delay value corresponding to cross-correlation function’s maximum depends on passband width of input filter.

The recently emerging sparse-grid quadrature filter (SGQF) has been shown to outperform the unscented Kalman filter owing to its higher levels of estimation accuracy It can achieve the close performance to the Gauss Hermite quadrature filter without suffering the curse-of-dimensionality problem. However, the computation efficiency of the SGQF can be further improved by exploring the inherent system structure. In this paper, a new adaptive sparse-grid quadrature filter (ASGQF) is proposed. The accuracy levels of the sparse-grid quadrature (SGQ) are adaptively selected based on the nonlinearity of the stochastic system such that a higher level of SGQ is used only when the nonlinearity measure is high, which reduces the unnecessary computation complexity. A global measure and a local measure of nonlinearity are used and compared. In a target tracking example, the ASGQF with the adaptive mixture of low level SGQ and high level SGQ is shown to achieve close performance to the sole higher level SGQF and demands much less computation load.

The design of two channel Quadrature Mirror Filter (QMF) banks is considered with constraints on the peaks of the reconstruction error and that of the subband filter ripple sizes. In this paper a design method of the optimum quadrature mirror filters (QMF), by using grouped B-spline functions in each transition band, is presented. It was shown that linear phase FIR filters cannot exactly satisfy the condition that the squared amplitude frequency responses are mirror images of each other about the line ω = π / 2, which has led to the name quadrature mirror flters. It is important to have a flat frequency response for the filters. The solution is to approximate the response of each frequency band by using grouped B-spline functions, that insures continuous superior order derivatives.

Grid synchronization has always been a great challenge for single-phase gird-connected converters since only one signal is provided and it is beneficial for the control system if grid information is obtained rapidly and accurately. In this paper, a novel quadrature signal generation algorithm and a phase-locked loop based on it are proposed and analyzed. The proposed algorithm functions as two finite impulse response filters that can eliminate most harmonics in the input signal and the introduced phase-locked loop shows great harmonic cancellation ability with transient response less than half a cycle. Analysis, along with simulation and experimental results are presented to verify the feasibility and effectiveness of the proposed quadrature signal generation method and phase-locked loop structure.

This paper proposes an efficient method for the design of two-channel, quadrature mirror filter (QMF) bank. The design problem is formulated to minimize an objective function, which is a linear combination of pass-band error and stop-band residual energy of the low-pass analysis filter of the filter bank, and the square error of the overall transfer function of the QMF bank at the quadrature frequency. A new algorithm has been developed to minimize the objective function by optimizing the filter tap weights by using Marquardt optimization method. Simulation results of the algorithm show that the performance of the proposed method is better than that of the already existing methods.

This paper proposes a new technique for the design of quadrature mirror filter (QMF) banks by exploiting steepest descent method. The design problem is formulated to minimize an objective function, which is a weighted sum of the pass band error and stop band residual energy of the low pass analysis filter of the QMF bank. The minimization has been carried out gradually by respective optimum step lengths in the corresponding steepest descent directions of a linear combination of the objective function and square of the reconstruction error of the QMF bank at the quadrature frequency by optimizing the filter tap weights. The design results show that the proposed method gives a comparable performance to the already existing methods.

A quadrature method for frequency modulation (FM) detection popular in continuous-time (analog) FM receiver designs involves operating on one of the quadrature components with a frequency-to-phase filter and then multiplying the result by the other quadrature component. This article describes an efficient discrete implementation of this technique as presented in D. Farrell and A. Oakley (2004).

Quadrature bandpass filters take a real-valued signal and output an analytic signal from which the instantaneous amplitude and phase can be computed. For this reason, they represent a useful tool to extract time-varying, narrow-band information from electrophysiological signals such as electroencephalogram (EEG) or electrocardiogram. One of the defining characteristics of quadrature filters is its null response to negative frequencies. However, when the frequency band of interest is close to 0 Hz, a careless filter design could let through negative frequencies, producing distortions in the amplitude and phase of the output. In this work, three types of quadrature filters (Ideal, Gabor and Sinusoidal) have been evaluated using both artificial and real EEG signals. For the artificial signals, the performance of each filter was measured in terms of the distortion in amplitude and phase, and sensitivity to noise and bandwidth selection. For the real EEG signals, a qualitative evaluation of the dynamics of the synchronization between two EEG channels was performed. The results suggest that, while all filters under study behave similarly under noise, they differ in terms of their sensitivity to bandwidth choice. In this study, the Sinusoidal filter showed clear advantages for the estimation of low-frequency EEG synchronization.

This paper introduces a current-mode first-order all-pass filter (APF) and its application in quadrature oscillator (QO) based on CCCII. The proposed filter can provide inverting and noninverting all-pass functions with a same circuit topology, it uses two CCCIIs and one grounded capacitor. Moreover, the first-order all-pass filter was applied in current-mode sinusoidal quadrature oscillators with the design based on block diagrams. The introduced oscillators can provide four phase-quadrature signals which independently control the condition of oscillation (CO) and frequency of oscillation (FO). The proposed oscillators consist of three CCCIIs and two grounded capacitors. The proposed APF and QOs have high output impedance which can directly drive load without additional current buffer. In addition, they use only grounded capacitors which are very appropriate to future development into an integrated circuit. The results of PSPICE simulation program correspond to the theoretical analysis.

International audience; This paper proposes a method that simultaneously builds the analytic signal from non-uniform samples of a bandpass signal and rejects interferences. The analytic signal is required for many onboard operations in communication satellites. This method operates in the time domain and without preliminary demodulation, using Periodic Non-uniform Sampling of order 2 (PNS2). This non-uniform sampling scheme can be easily implemented with available devices. Exact formulas for the analytic signal construction are derived for an infinite observation window (an infinite number of samples). For practical applications, the formulas should also demonstrate a high convergence rate due to the finite observation window. Formulas with increasing convergence rates are thus derived. The proposed method has been tested through simulations according to the number of available samples, the interference parameters and the filter transfer function regularity.

The past over the years, single or multi-dimensional signal processing applications, communication systems, biomedical signal processing, word coding, sub-band coding in applications such as efficient use filter banks; single filter instead of multiple custom filters come together with being designed. In this study, two-channel filter banks a special case known as the QMF (Quadrature Mirror Filter - Quarter-mirror filter) bank for the design of Kaiser, Chebyshev and Hanning windowing methods with the filter's cutoff frequency frequency on the optimization of a design based were made. QMF bank design, failure to peak reconstruction error (Peak Reconstruction Error-PRA) is based. As a result of the ongoing applications designed filter banks belonging to the numerical results and comparisons are given.

This paper we present a new computational scheme to derive the impulse response of p-step UFIR filter. We use a set of polynomials that can be expressed in terms of their kth moment to derive the same impulse response obtained by other methods. Furthermore, we apply the p-step UFIR filter in two cases: enhanced of a square signal and the denoisy image processing. Finally, some quantitative and qualitative evaluations are carried out to verify filter's efficiency based on RMSE analysis.

Diabetes mellitus is a serious chronic condition of the human metabolism. The development of an automated treatment has reached clinical phase in the last few years. The goal is to keep the blood glucose concentration within a certain region with minimal interaction required by the patient or medical personnel. However, there are still several practical problems to solve. One of these would be that the available sensors have significant noise and drift. The latter is rather difficult to manage, because the deviating signal can cause the controller to drive the glucose concentration out of the safe region even in the case of frequent calibration. In this study a linear-quadratic-Gaussian (LQG) controller is employed on a widely used diabetes model and enhanced with an advanced Sparse-grid quadratic filter and a fuzzy interference system-based calibration supervisor.

An integrable quadrature oscillator circuit is given which uses only transconductance elements and grounded capacitors in its realization. The circuit provides four quadrature outputs of equal magnitude. It uses a low component count and is compatible for monolithic implementation in MOS technology. The simulation results on the quadrature oscillator verify the theory.

This paper considers design of L ∞ - and L 2 -optimal CQF bank which reduces the influence of the additive noise on the output in an optimal fashion. To deal with this design problem, we first give a glance at the characterization of solutions set of the so-called Smith–Barnwell equation, whereby we derive the explicit expression of all optimum solutions for the deterministic-but-unknown disturbance. We also treat the stochastic noise case, and show that the average power of the output due to the channel noise cannot be controlled by the choice of filters. Numerical examples are given to illustrate the results developed in the paper.

A new quadrature sampling technique for arbitrary bandpass signal within baseband sampling rate is presented. The input bandpass signal whose carrier frequency lies in the A/D baseband sampling rate is first decimated by factor 2 and modulated by (−1) n , and then is interpolated by a linear phase FIR all-pass filter, finally the modulated complex envelope of bandpass signal can be produced.

This paper introduces an alternative form of analytic signal that is formed using homomorphic signal processing techniques. It may be generated for signals that demonstrate redundancy in their pole-zero distributions, such as phase signals and real signals. The analytic signal is formed by manipulating the positions of the signal's nonminimum phase poles and zeros to create a minimum phase signal. A factorization of real signals is presented that demonstrates the properties of the homomorphic analytic signal, and a new definition of instantaneous frequency is developed. Examples are given to verify the theory and comparisons with the linear analytic signal, and instantaneous frequency are made.

This paper considers the linear-phase quadrature mirror filters (LP-QMFs) with coefficients constrained to the values of −1, 0 and + 1. A new filter structure and a design technique based on a recently developed weighted least-squares (WLS) algorithm are presented. First, we design an LP-QMF with continuous coefficients using the WLS algorithm. This design process provides two favourable design results that the prototype LP analysis filter has least-squares stopband response and the resulting QMF bank shows quasi-equiripple reconstruction error behavior. In conjunction with the new proposed filter structure, we then present an efficient method to obtain a design solution with coefficients restricted to −1, 0 and + 1 in the minimax sense. Several design examples demonstrating the effectiveness of the proposed technique are provided.

Attitude Determination Subsystem (ADS) is essential to the spacecraft pointing control and highly relies on the onboard sensors’ quality and filtering techniques. For high quality gyros, it is quite doable to achieve precision ADS using the 6 state EKF. However, for low grade low cost Micro-Electro-Mechanical System (MEMS) gyros and Complementary Metal-Oxide Semiconductor (CMOS) star tracker (ST), especially in higher slew rates type of missions, the 6 state EKF may not be the right or adequate structure to achieve precision attitude estimation capability because MEMS Scale Factor Errors (SFE) and Mis-Alignment Errors (MAE) at high rate will become a dominant error source contaminating gyros' measured rate vector. As a result, SFE and MAE errors may need to be estimated on-line along with the gyro bias errors for real-time error removal and correction to address the high rate slew operating conditions. This paper looks into the emerging Sparse Grid Quadrature Filter (SGQF), a nonlinear point-based Gaussian approximation filtering technique, as an alternative to potentially replace the EKF from the accuracy and robustness standpoints. The study is intended to determine the pros and cons of each filtering scheme and perform a simulation based evaluation of both filters for a possible precision ADS solution using low cost MEMS gyros and CMOS star tracker.

In this paper a design method of the optimum quadrature mirror filters (QMF), by using symmetric B-spline functions, is presented. It was shown that linear phase FIR filters cannot exactly satisfy the condition that the squared amplitude frequency responses are mirror images of each other about the line ω= π /2 which has led to the name quadrature mirror flters. It is important to have a flat frequency response for the filters. The solution is to approximate the response of each frequency band by using B-spline functions, that insures continuous superior order derivatives. In the proposed method, the prototype filter is optimized with the novelty of using spline functions in the transition band.

In this paper a two channel Quadrature Mirror Filter (QMF) bank is designed using Genetic Algorithm (GA) and coefficients of filters are represented in Canonical Signed Digit (CSD). A fresh Genetic operator is used that combines crossover and adaptive mutation to improve the convergence rate and solution quality of GA. Prototype filter is constructed using GA and the coefficients of the filter are converted to nearest signed power of two terms which reduces hardware complexity of the overall system. The proposed design of QMF is also achieved least value of Reconstruction error. The technique improves the performance of QMF with respect to its peak reconstruction error, transition bandwidth and hardware required to realize FIR digital filter to less than the complexity of 2's complement representation. During the optimization of prototype filter coefficients only nonzero CSD digits are used so that better performance is achieved.

In the navigation system, the accurate measurement of key indicators of the payload modulation signal can help identify the problems in system design. The phase quadrature is one of the important indicators. In this paper, analyzed the main reason of the phase quadrature measurement error, and established the phase quadrature measurement formulas under a constant envelope modulation mode. This paper solved the problem of the navigation signal cross-correlation for the phase quadrature measurement error. In the end, the validity of the correction method is verified in different simulation conditions.

This chapter contains sections titled: Analytic Signal Generation Approach Defining the Frequency Response Impulse Response Derivations Rotating Filter Impulse Responses Computing Fir Filter Coefficients Conclusion References

In this paper, vision-based relative navigation of two spacecraft is addressed using the sparse Gauss-Hermite quadrature filter. The relative navigation provides the estimation of the relative attitude and relative orbit between spacecraft, which is a challenging filtering problem since it is a highly nonlinear and high dimensional estimation problem. Many filters have been used to solve this problem, such as, the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). However, these filters are not accurate enough when the initial uncertainty is large or the nonlinearity is significant. Moreover, although the conventional Gauss-Hermite quadrature filter is more accurate than the UKF, it cannot be used since a huge number of points is required. It is shown in this paper that the sparse Gauss-Hermite quadrature filter can achieve better estimation accuracy than the EKF, the UKF, and the cubature Kalman filter without excessive computation load.