2013 Fiscal Year Final Research Report
A Unified Approach to Nonlinear Filtering by Statistical Equivalent Linearization
| Project/Area Number |
24656264
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Control engineering
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| Research Institution | Ritsumeikan University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
SUGIMOTO Sueo 立命館大学, 理工学部, 教授 (70093424)
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| Project Period (FY) |
2012-04-01 – 2014-03-31
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| Keywords | 非線形フィルタ / 等価線形化フィルタ / ガウシアンフィルタ / ガウス和フィルタ / ガウス和等価線形化フィルタ / GPS信号処理 / 連続‐離散非線形フィルタ |
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| Research Abstract |
From the point of view of statistical equivalent linearization, we analyze algorithms of the equivalent linealization Kalman filter (EqKF), the extended Kalman filter (EKF), the Gaussian filter (GF) and the unscented Kalman filter (UKF). For a cubic sensor problem, we show that EqKF is close to GF, and UKF is in-between EqKF and GF, but the EKF is quite different from other filters. Also, with the aim to GPS applications, a new Gaussian sum equivalent linearization filter is derived by applying the Gauss-Hermite integral formula for evaluating the conditional expectations, under the assumption that the conditional probability density function of the state is a Gaussian sum. Moreover, we obtain two continuous-discrete (CD) filters, i.e. CD-EqKF and CD-GF, showing that both filters have the same time update equations, and a difference is in the observation update equations. Heun scheme-based simulations show that CD-EqKF and CD-GF are superior to the classical CD-EKF.
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Research Products
(11 results)
