Masaya Murata

BM25 With Exponential IDF for Instance Search

This paper deals with a novel concept of an exponential IDF in the BM25 formulation and compares the search accuracy with that of the BM25 with the original IDF in a content-based video retrieval (CBVR) task. Our video retrieval method is based on a bag of keypoints (local visual features) and the exponential IDF estimates the keypoint importance weights more accurately than the original IDF. The exponential IDF is capable of suppressing the keypoints from frequently occurring background objects in videos, and we found that this effect is essential for achieving improved search accuracy in CBVR. Our proposed method is especially designed to tackle instance video search, one of the CBVR tasks, and we demonstrate its effectiveness in significantly enhancing the instance search accuracy using the TRECVID2012 video retrieval dataset.

Unscented statistical linearization and robustified Kalman filter for nonlinear systems with parameter uncertainties

Kalman filter (KF) design is well established for perfectly known linear system and observation models. Real-world phenomena, however, have significant associated uncertainties, and the tuning of the KF is not so straightforward for tackling them. In this paper, we present a method of designing a robust filter for nonlinear systems with model parameter uncertainties. The uncertainties are imposed on the temporal changes in system parameters, which corresponds to the conditions that most real-world problems exhibit. Our proposed filter is based on a robustified KF, which assumes Gaussian distributed states and is designed to be robust to significant changes in the system parameters. The uncertain nonlinear systems are handled by using the linearized approximation models to guarantee the Gaussianity of states. This is achieved by using a statistical linearization in conjunction with unscented transformations and we thus call the linearization technique unscented statistical linearization (USL). The USL is employed for the prediction step of nonlinearly transformed state and the subsequent filtering is executed by using the robustified KF to make the filter robust to upcoming observations. We call our proposed filter for the uncertain nonlinear systems a robustified nonlinear KF (robustified NKF) and confirm the effectiveness by experiments using artificially generated data.

Monte Carlo filter particle filter

We propose a new realization method of the sequential importance sampling (SIS) algorithm to derive a new particle filter. The new filter constructs the importance distribution by the Monte Carlo filter (MCF) using sub-particles, therefore, its non-Gaussianity nature can be adequately considered while the other type of particle filter such as unscented Kalman filter particle filter (UKF-PF) assumes a Gaussianity on the importance distribution. Since the state estimation accuracy of the SIS algorithm theoretically improves as the estimated importance distribution becomes closer to the true posterior probability density function of state, the new filter is expected to outperform the existing, state-of-the-art particle filters. We call the new filter Monte Carlo filter particle filter (MCF-PF) and confirm its effectiveness through the numerical simulations.

Robustifying Kalman filter to rapidly adapt to significant changes in system model parameters of state-space models

A Kalman filter (KF) is state-of-the-art for estimating states of linear-Gaussian state-space models. The KF selects an expectation of a posterior probability density function of state and the expectation is an analytic solution for minimizing the square estimation error. The estimate of KF is therefore optimal, however, simultaneously inherits the problem of the variance/covariance matrix of the estimation error becoming too small as the filtering proceeds to some extent. In this paper, we tackle this problem by deliberately making a KF suboptimal in case of detecting a significantly large prediction error, which implies that the state estimate at this moment is no longer an expectation of the posterior probability density function. By this suboptimization, the resulting square estimation error becomes larger than that of the KF and we make the KF more responsive to upcoming observations. We call the new filter a robustified Kalman filter and demonstrate the revived ability to adapt to significant changes in system model parameters in a series of numerical experiments.

Normalized unscented Kalman filter and normalized unscented RTS smoother for nonlinear state-space model identification

A Kalman filter (KF) and Rauch-Tung-Striebel smoother (RTSS) provide the minimum mean square estimates of states for linear state-space models with additive Gaussian system and observation noises given a series of the past, current, and future observations. When the noise statistics such as the variances are unknown, initially normalizing the KF and RTSS algorithms by the total of the unknown variances provides new state estimation algorithms. We call these algorithms the normalized KF and normalized RTSS and on the basis of the log-likelihoods scored by the multiple trials with varied parameters, we can effectively identify the unknown system and observation noise variances. In this paper, we present the same normalization technique for nonlinear KF and RTSS algorithms named the unscented KF and unscented RTSS. In the same way as the normalized KF and normalized RTSS, these new normalized unscented KF and normalized unscented RTSS algorithms make it possible to estimate the unknown noise variances of nonlinear state-space models. Because it often happens that the noise variances are unknown in actual analysis cases, these algorithms are considerably effective from the aspect of the application viewpoints. The performance was confirmed by experiments using artificially generated data.

Information Retrieval Model using Generalized Pareto Distribution and Its Application to Instance Search

We adopt the generalized Pareto distribution for the information-based model and show that the parameters can be estimated based on the mean excess function. The proposed information retrieval model corresponds to the extension of the divergence from independence and is designed to be data-driven. The proposed model is then applied to the specific object search called the instance search and the effectiveness is experimentally confirmed.

Filter design based on multiple model estimation

We show that famous filtering algorithms such as Gaussian sum filter (GSF) and particle filter (PF) are derived from the multiple model estimation (MME). Based on the MME, we propose a new filter called particle Gaussian sum filter (PGSF) to overcome the problems of GSF and PF. To realize the algorithm of PGSF, we also show that ensemble Kalman filter (EnKF) asymptotically approaches Gaussian filter (GF) when using sufficiently large ensemble number. The PGSF employing the EnKF achieves higher estimation accuracy than that using the extended Kalman filter (EKF), while the latter approach is much faster in terms of processing time. We compare the proposed filter with several existing filters and demonstrate its effectiveness through a numerical simulation.

Gaussian sum resampling filter

In this paper we propose the Gaussian sum resampling filter (GSRF) in which the predicted state distribution is approximated by the sum of the sub-Gaussian components whose variances are designed to be smaller than the Gaussian components used for the standard Gaussian sum filter (GSF). These sub-Gaussian components contribute for the improvement in the subsequent Gaussian sum approximation of the filtered state distribution and the diversity produced in the sub components also work for the enhancement of the state estimation accuracy. The resampling of the sub components makes the number of the Gaussian components constant throughout the filter execution. Numerical examples show the superior filtering accuracy of the GSRF over the other existing filters including the GSF.

Iterative unscented statistically linearized filter for nonlinear Gaussian observation models

State filtering for nonlinear Gaussian observation models still remains as one of the challenging problems in the estimation and control research field. It is mainly due to the non-existence of the realizable optimal filter and for addressing to this problem, the following two approaches are often taken. The first approach is based on the Gaussian assumed density filter (Gaussian filter) and the most well-known realization is the Unscented Kalman filter. The second approach is based on the series expansion based filter and the most widely-used algorithm is the extended Kalman filter or iterative extended Kalman filter. Note that both approaches are the approximation to the optimal filter and thus a room is still left for the further exploration into the effective filters in terms of both filtering accuracy and speed. In this paper, we focus on the unscented statistical linearization (USL) which is a realization method of the statistical linearization whose linearization accuracy is theoretically better than that of the truncated Taylor series. The filter employing the USL is called the unscented statistically linearized filter (USLF). We newly propose the iterative type algorithm to tackle the filtering problem of the nonlinear Gaussian observation models and numerically show the superior state filtering performance over the aforementioned state-of-the-art filtering approaches.

Suboptimal Kalman Filter for Dual Estimation under Dynamical Uncertainties

This paper presents a method of designing a suboptimal Kalman filter (SKF) for nonlinear systems, including uncertainties on the system parameter dynamics. In general, governing dynamics behind real-world phenomena has significant associated uncertainties and all we can presume is the approximation to system models. We thus need a robust filter that is capable of rapidly following up the unknown system model parameters while adequately estimating the system states as well. The SKF is suboptimal in terms of standard square errors that the KF minimizes at each time step and this suboptimization results in the enhancement of filters parameter adaptation ability. The nonlinearity of system models is handled by using an unscented transforming statistical linearization without losing the Gaussianity of states to be estimated. We confirm the effectiveness of the proposed filter by numerical simulations.