Geometrically Intrinsic Nonlinear Recursive Filters I: Algorithms
| dc.creator | Darling, R. W. R. | |
| dc.date | 1998-09-06 | |
| dc.date.accessioned | 2026-07-07T05:25:54Z | |
| dc.date.available | 2026-07-07T05:25:54Z | |
| dc.description | The Geometrically Intrinsic Nonlinear Recursive Filter, or GI Filter, is designed to estimate an arbitrary continuous-time Markov diffusion process X subject to nonlinear discrete-time observations. The GI Filter is fundamentally different from the much-used Extended Kalman Filter (EKF), and its second-order variants, even in the simplest nonlinear case, in that: (i) It uses a quadratic function of a vector observation to update the state, instead of the linear function used by the EKF. (ii) It is based on deeper geometric principles, which make the GI Filter coordinate-invariant. This implies, for example, that if a linear system were subjected to a nonlinear transformation f of the state-space and analyzed using the GI Filter, the resulting state estimates and conditional variances would be the push-forward under f of the Kalman Filter estimates for the untransformed system - a property which is not shared by the EKF or its second-order variants. The noise covariance of X and the observation covariance themselves induce geometries on state space and observation space, respectively, and associated canonical connections. A sequel to this paper develops stochastic differential geometry results - based on "intrinsic location parameters", a notion derived from the heat flow of harmonic mappings - from which we derive the coordinate-free filter update formula. The present article presents the algorithm with reference to a specific example - the problem of tracking and intercepting a target, using sensors based on a moving missile. Computational experiments show that, when the observation function is highly nonlinear, there exist choices of the noise parameters at which the GI Filter significantly outperforms the EKF. | |
| dc.description | 22 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/9809028 | |
| dc.identifier | http://arxiv.org/abs/math/9809028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77359 | |
| dc.subject | Optimization and Control | |
| dc.subject | Probability | |
| dc.subject | 93E11, 60G35, 58G32 | |
| dc.title | Geometrically Intrinsic Nonlinear Recursive Filters I: Algorithms | |
| dc.type | text |