This paper deals with a state-space approach for adaptive second-order IIR notch digital filters with constrained poles and zeros. A simplified iterative algorithm is derived from the gradient-descent method to minimize the mean-squared output of an adaptive notch digital filter. Then, stability and parameter-estimation bias are analyzed for the simplified iterative algorithm. A numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive state-space notch digital filter and parameter-estimation bias analysis.

Recently, more and more people start investing. Understanding the factors affecting financial products is important for making investment decisions. However, it is difficult to understand factors for novices because various factors affect each other. Various technique has been studied, but conventional factor analysis methods focus on revealing the impact of factors over a certain period locally, and it is not easy to predict net asset values. As a reasonable solution for the prediction of net asset values, in this paper, we propose a trend shift model for the global analysis of factors by introducing trend change points as shift interference variables into state space models. In addition, to realize the trend shift model efficiently, we propose an effective trend detection method, TP-TBSM (two-phase TBSM), by extending TBSM (trend-based segmentation method). Comparing with TBSM, TP-TBSM could detect trends flexibly by reducing the dependence on parameters. We conduct experiments with eleven investment trust products and reveal the usefulness and effectiveness of the proposed model and method.

In this paper, we propose a CTRIL (Common Trend and Regression with Independent Loss) model to infer latent traffic demand in overloaded links as well as how much it is reduced due to QoS (Quality of Service) degradation. To appropriately provision link bandwidth for such overloaded links, we need to infer how much traffic will increase without QoS degradation. Because original latent traffic demand cannot be observed, we propose a method that compares the other traffic time series of an underloaded link, and by assuming that the latent traffic demands in both overloaded and underloaded are common, and actualized traffic demand in the overloaded link is decreased from common pattern due to the effect of QoS degradation. To realize the method, we developed a CTRIL model on the basis of a state-space model where observed traffic is generated from a latent trend but is decreased by the QoS degradation. By applying the CTRIL model to actual HTTP (Hypertext transfer protocol) traffic and QoS time series data, we reveal that 1% packet loss decreases traffic demand by 12.3%, and the estimated latent traffic demand is larger than the observed one by 23.0%.

This paper proposes a novel scheme for sequential orthogonal frequency division multiplexing channel estimation on the receiver side.The scheme comprises two methods: one improves estimation accuracy and the other reduces computational complexity. Based on a state-space model, the first method appropriately considers frequency correlation in an approach that derives a narrow-band channel gain for multiple pilot subcarriers; such consideration of frequency correlation leads to an averaging effect in the frequency domain. The second method is based on the first one and forces the observation matrix into a sparse bidiagonal matrix in order to decrease the number of mathematical processes. The proposed scheme is verified by numerical analysis.

We propose a noise suppression algorithm with the Kalman filter theory. The algorithm aims to achieve robust noise suppression for the additive white and colored disturbance from the canonical state space models with (i) a state equation composed of the speech signal and (ii) an observation equation composed of the speech signal and additive noise. The remarkable features of the proposed algorithm are (1) applied to adaptive white and colored noises where the additive colored noise uses babble noise, (2) realization of high performance noise suppression without sacrificing high quality of the speech signal despite simple noise suppression using only the Kalman filter algorithm, while many conventional methods based on the Kalman filter theory usually perform the noise suppression using the parameter estimation algorithm of AR (auto-regressive) system and the Kalman filter algorithm. We show the effectiveness of the proposed method, which utilizes the Kalman filter theory for the proposed canonical state space model with the colored driving source, using numerical results and subjective evaluation results.

Filtering and smoothing using a non-Gaussian state space model are proposed for motion trajectory of feature point in image sequence. A heavy-tailed non-Gaussian distribution is used for measurement noise to reduce the effect of outliers in motion trajectory. Experimental results are presented to show the usefulness of the proposed method.

A hierarchical structure of the statistical models involving the parametric, state space, generalized state space, and self-organizing state space models is explained. It is shown that by considering higher level modeling, it is possible to develop models quite freely and then to extract essential information from data which has been difficult to obtain due to the use of restricted models. It is also shown that by rising the level of the model, the model selection procedure which has been realized with human expertise can be performed automatically and thus the automatic processing of huge time series data becomes realistic. In other words, the hierarchical statistical modeling facilitates both automatic processing of massive time series data and a new method for knowledge discovery.

In this paper, we present a new state space-based approach for the two-dimensional (2-D) frequency estimation problem which occurs in various areas of signal processing and communication problems. The proposed method begins with the construction of a state space model associated with the noiseless data which contains a summation of 2-D harmonics. Two auxiliary Hankel-block-Hankel-like matrices are then introduced and from which the two frequency components can be derived via matrix factorizations along with frequency shifting properties. Although the algorithm can render high resolution frequency estimates, it also calls for lots of computations. To alleviate the high computational overhead required, a highly parallelizable implementation of it via the principle subband component (PSC) of some appropriately chosen transforms have been addressed as well. Such a PSC-based transform domain implementation not only reduces the size of data needed to be processed, but it also suppresses the contaminated noise outside the subband of interest. To reduce the computational complexity induced in the transformation process, we also suggest that either the transform of the discrete Fourier transform (DFT) or the Haar wavelet transform (HWT) be employed. As a consequence, such an approach of implementation can achieve substantial computational savings; meanwhile, as demonstrated by the provided simulation results, it still retains roughly the same performance as that of the original algorithm.

A simple inequality that guarantees stability of perturbed linear state space models is proposed. It is shown that the result is superior to some existing result in sharpness and possesses some advantageous aspects.