A stochastic two dimensional Fornasini Marchesini’s Model Ⅱ (2 D FMM Ⅱ) with multiplicative noise is given, and a filtering algorithm for this model, which is optimal in the sense of linear minimum variance, is dev...A stochastic two dimensional Fornasini Marchesini’s Model Ⅱ (2 D FMM Ⅱ) with multiplicative noise is given, and a filtering algorithm for this model, which is optimal in the sense of linear minimum variance, is developed. The stochastic 2 D FMM Ⅱ with multiplicative noise can be reduced to a 1 D model, and the proposed optimal filtering algorithm for the stochastic 2 D FMM Ⅱ with multiplicative noise is obtained by using the state estimation theory of 1 D systems. An example is given to illustrate the validity of this algorithm.展开更多
Traditional beamformers need to know the incident angle of the desired signal leading while its abili-ty to handle interference is limited.In this paper,the constrained steer vector of linearly constrained min-imum-va...Traditional beamformers need to know the incident angle of the desired signal leading while its abili-ty to handle interference is limited.In this paper,the constrained steer vector of linearly constrained min-imum-variance(LCMV)beamformer is modified to make sidelobe null to direction of powerful jammer.Inaddition,the state-space concept is used to describe the anti-jammer filter,and Kalman filter algorithm isdeduced by building the observation model and measurement equation.The new method is more efficient oncomputation and more robust to survive environment with large scale variation in interference strength.Fi-nally,simulation results shows that the new approach can form the null with its depth in proportion to powerin direction of jammer,and has steady convergence process.The novel method can effectively improve thesignal-to-jammer-plus-noise power ratio(SJNR)of GPS signals to make the correlation peak easy to track.展开更多
Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiase...Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiased estimation of this risk under specific model assumptions. Norm constrained portfolios have recently been studied to keep the effective dimension low. In this paper we consider three sets of high dimensional data, the stock market prices for three countries, namely US, UK and India. We compare the Markowitz efficient frontier to those obtained by unbiasedness corrections and imposing norm-constraints in these real data scenarios. We also study the out-of-sample performance of the different procedures. We find that the 2-norm constrained portfolio has best overall performance.展开更多
基金supported by NSFS Project for Tianyuan Mathematical Fund(No.A0324676)the Science&Technology Research Key Projects of the Ministry of Education of China(No.02131).
文摘A stochastic two dimensional Fornasini Marchesini’s Model Ⅱ (2 D FMM Ⅱ) with multiplicative noise is given, and a filtering algorithm for this model, which is optimal in the sense of linear minimum variance, is developed. The stochastic 2 D FMM Ⅱ with multiplicative noise can be reduced to a 1 D model, and the proposed optimal filtering algorithm for the stochastic 2 D FMM Ⅱ with multiplicative noise is obtained by using the state estimation theory of 1 D systems. An example is given to illustrate the validity of this algorithm.
基金Supported by the National High Technology Research and Development Programme of China (No. 2006AA701108)
文摘Traditional beamformers need to know the incident angle of the desired signal leading while its abili-ty to handle interference is limited.In this paper,the constrained steer vector of linearly constrained min-imum-variance(LCMV)beamformer is modified to make sidelobe null to direction of powerful jammer.Inaddition,the state-space concept is used to describe the anti-jammer filter,and Kalman filter algorithm isdeduced by building the observation model and measurement equation.The new method is more efficient oncomputation and more robust to survive environment with large scale variation in interference strength.Fi-nally,simulation results shows that the new approach can form the null with its depth in proportion to powerin direction of jammer,and has steady convergence process.The novel method can effectively improve thesignal-to-jammer-plus-noise power ratio(SJNR)of GPS signals to make the correlation peak easy to track.
文摘Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiased estimation of this risk under specific model assumptions. Norm constrained portfolios have recently been studied to keep the effective dimension low. In this paper we consider three sets of high dimensional data, the stock market prices for three countries, namely US, UK and India. We compare the Markowitz efficient frontier to those obtained by unbiasedness corrections and imposing norm-constraints in these real data scenarios. We also study the out-of-sample performance of the different procedures. We find that the 2-norm constrained portfolio has best overall performance.
