A Geometric Approach to Conditioning and the Search for Minimum Variance Unbiased Estimators

Our purpose is twofold: to present a prototypical example of the conditioning technique to obtain the best estimator of a parameter and to show that this technique resides in the structure of an inner product space. The technique uses conditioning of an unbiased estimator on a sufficient statistic. This procedure is founded upon the conditional variance formula, which leads to an inner product space and a geometric interpretation. The example clearly illustrates the dependence on the sampling methodology. These advantages show the power and centrality of this process.

Improved minimum variance distortionless response spectrum method for efficient and robust non-uniform undersampled frequency identification in blade tip timing

The noncontact blade tip timing(BTT)measurement has been an attractive technology for blade health monitoring(BHM).However,the severe undersampled BTT signal causes a significant challenge for blade vibration parameter identification and fault feature extraction.This study proposes a novel method based on the minimum variance distortionless response(MVDR)of the direction of arrival(DoA)estimation for blade natural frequency estimation from the non-uniformly undersampled BTT signals.First,based on the similarity between the general data acquisition model for BTT and the antenna array model in DoA estimation,the circumferentially arranged probes on the casing can be regarded as a non-uniform linear array.Thus,BTT signal reconstruction is converted into the DoA estimation problem of the non-uniform linear array signal.Second,MVDR is employed to address the severe undersampling issue and recover the BTT undersampled signal.In particular,spatial smoothing is innovatively utilized to enhance the estimation of covariance matrix of the BTT signal to avoid ill-condition or singularity,while improving efficiency and robustness.Lastly,numerical simulation and experimental testing are employed to verify the validity of the proposed method.Monte Carlo simulation results suggest that the proposed method behaves better than conventional methods,especially under a lower signal-to-noise ratio condition.Experimental results indicate that the proposed method can effectively overcome the severe undersampling problem of BTT signal induced by physical limitations,and has a strong potential in the field of BHM.

A novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise,minimum mean square variance criterion and least mean square adaptive filter

Underwater acoustic signal processing is one of the research hotspots in underwater acoustics.Noise reduction of underwater acoustic signals is the key to underwater acoustic signal processing.Owing to the complexity of marine environment and the particularity of underwater acoustic channel,noise reduction of underwater acoustic signals has always been a difficult challenge in the field of underwater acoustic signal processing.In order to solve the dilemma,we proposed a novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN),minimum mean square variance criterion(MMSVC) and least mean square adaptive filter(LMSAF).This noise reduction technique,named CEEMDAN-MMSVC-LMSAF,has three main advantages:(i) as an improved algorithm of empirical mode decomposition(EMD) and ensemble EMD(EEMD),CEEMDAN can better suppress mode mixing,and can avoid selecting the number of decomposition in variational mode decomposition(VMD);(ii) MMSVC can identify noisy intrinsic mode function(IMF),and can avoid selecting thresholds of different permutation entropies;(iii) for noise reduction of noisy IMFs,LMSAF overcomes the selection of deco mposition number and basis function for wavelet noise reduction.Firstly,CEEMDAN decomposes the original signal into IMFs,which can be divided into noisy IMFs and real IMFs.Then,MMSVC and LMSAF are used to detect identify noisy IMFs and remove noise components from noisy IMFs.Finally,both denoised noisy IMFs and real IMFs are reconstructed and the final denoised signal is obtained.Compared with other noise reduction techniques,the validity of CEEMDAN-MMSVC-LMSAF can be proved by the analysis of simulation signals and real underwater acoustic signals,which has the better noise reduction effect and has practical application value.CEEMDAN-MMSVC-LMSAF also provides a reliable basis for the detection,feature extraction,classification and recognition of underwater acoustic signals.

Beamforming analysis based on CSB sin-FDA

This paper studies the adaptive beamforming algorithm based on the frequency diverse array(FDA)array where the interference is located at the same angle(but different range)with the target.We take the cross subarray-based FDA with sinusoidal frequency offset(CSB sin-FDA)as the receiving array instead of the basic FDA.The sampling covariance matrix under insufficient snapshot can be corrected by the automatic diagonal loading method.On the basis of decomposing the mismatched steering vector error into a vertical component and a parallel one,this paper searches the vertical component of the error by the quadratic constraint method.The numerical simulation verifies that the beamformer based on the CSB sin-FDA can effectively hold the mainlobe at the target position when the snapshot is insufficient or the steering vector is mismatched.

Hedge effectiveness of put replication, gold, and oil on ASEAN-5 equities

The previous studies have shown that capital market integration has increased in the ASEAN-5,implying that investors making investment diversification across ASEAN capital markets could only earn limited diversification advantages.To diversify their portfolios,equity investors must find other assets.The main focus of this research is to analyze the effectiveness of put replication,gold,and oil on hedge equities in the ASEAN-5(Indonesia,Malaysia,Singapore,Thailand,and the Philippines).Protective put strategy,DCC-GARCH,and Markowitz optimization are used to measure hedge effectiveness,risk-adjusted-performance such as Sharpe ratio,drawdown,and Omega ratio.The result reveals that gold is a cheaper hedge than oil and oil-hedged strategy is more expensive in ASEAN-5 compared to oil exporting nations.Also,investors with big exposure to the oil-related portfolio should diversify to Philippine equity.From hedging effectiveness and risk-adjusted-performance perspectives,oil is less attractive than money market instruments and gold.This study also implies that risk-averse investors should prefer to put replication or guaranteed financial products compared to commodities-hedged strategy.

Dynamic Hedging Based on Markov Regime-Switching Dynamic Correlation Multivariate Stochastic Volatility Model

It is important to consider the changing states in hedging.The Markov regime-switching dynamic correlation multivariate stochastic volatility( MRS-DC-MSV) model was proposed to solve this issue. DC-MSV model and MRS-DC-MSV model were used to calculate the time-varying hedging ratios and compare the hedging performance. The Markov chain Monte Carlo( MCMC) method was used to estimate the parameters. The results showed that,there were obviously two economic states in Chinese financial market. Two models all did well in hedging,but the performance of MRS-DCMSV model was better. It could reduce risk by nearly 90%. Thus,in the hedging period,changing states is a factor that cannot be neglected.

Block Iterative STMV Algorithm and Its Application in Multi-Targets Detection

STMV beamforming algorithm needs inversion operation of matrix, and its engineering application is limited due to its huge computational cost. This paper proposed block iterative STMV algorithm based on one-phase regressive filter, matrix inversion lemma and inversion of block matrix. The computational cost is reduced approximately as 1/4 M times as original algorithm when array number is M. The simulation results show that this algorithm maintains high azimuth resolution and good performance of detecting multi-targets. Within 1 - 2 dB directional index and higher azimuth discrimination of block iterative STMV algorithm are achieved than STMV algorithm for sea trial data processing. And its good robustness lays the foundation of its engineering application.

Model-free adaptive robust control method for high-speed trains

Aiming at the robustness issue in high-speed trains(HSTs)operation control,this article proposes a model-free adaptive control(MFAC)scheme to suppress disturbance.Firstly,the dynamic linearization data model of train system under the action of measurement disturbance is given,and the Kalman filter(KF)based on this model is derived under the minimum variance estimation criterion.Then,according to the KF,an anti-interference MFAC scheme is designed.This scheme only needs the input and output data of the controlled system to realize the MFAC of the train under strong disturbance.Finally,the simulation experiment of CRH380A HSTs is carried out and compared with the traditional MFAC and the MFAC with attenuation factor.The proposed control algorithm can effectively suppress the measurement disturbance,and obtain smaller tracking error and larger signal to noise ratio with better applicability.

Performance analysis of SBAS ephemeris corrections and integrity algorithms in China region

Satellite Based Augmentation Systems(SBASs)improve the positioning accuracy and integrity by broadcasting to the civil aviation community the corrections and integrity parameters.A snapshot algorithm based on the minimum variance estimation is investigated in this study to calculate the satellite clock and orbit corrections.A chi-square test is performed on the remaining errors in the corrected ephemeris to guarantee the integrity.User Differential Range Error(UDRE)and scaling matrix contained in Message Type 28 are derived using the covariance information based on the assumption that one of the reference stations failed.A software package is developed and applied in the real data collected at 26 stations.International GNSS(Global Navigation Satellite System)Service(IGS)precise clock and orbit products are taken as the references to assess the accuracy of corrections.For both Global Positioning System(GPS)and BeiDou Navigation Satellite System(BDS),the range accuracy of 0.10 m can be achieved with the employment of the derived corrections.No obvious performance difference between GPS and BDS is found.UDREs for all visible satellites are generated with the maximum index of 12 and minimum index of 3.The geometric range differences calculated with IGS precise products and broadcast ephemeris are employed to assess the integrity of UDRE.It is found that the UDRE is able to bound the residuals with 99.9%confidence which meet the requirement of aviation users.With ionospheric delay corrected by Global Ionosphere Map(GIM),the positioning accuracy of 0.98 m with GPS corrections and 0.80 m with multi-constellation augmentation can be achieved which indicates a significant improvement of GPS standalone results.