Two-dimensional Kalman Filter Research Articles

Two-dimensional Kalman filter approach to airborne vector gravimetry

Abstract The paper presents a new approach to the airborne vector gravimetry problem. The idea of the approach is to take into account spatial correlation of the gravity field to improve observability of horizontal components of the gravity disturbance vector (GDV). We consider the GDV determination problem given airborne data at a set of parallel survey lines assuming that lines are flown in the same direction at a constant height above the reference ellipsoid. We use a 2-D random field model for the gravity field at the flight height. The random field is governed by two autoregressive equations (one in the direction along the lines, the other across the lines). Then we pose the estimation problem simultaneously for the GDV horizontal components and systematic errors of an inertial navigation system at all the lines simultaneously. The developed estimation algorithm is based on 2D Kalman filtering and smoothing techniques. Numerical results obtained from simulated data processing showed improved accuracy of the gravity horizontal component determination.

On robust Kalman filter for two-dimensional uncertain linear discrete time-varying systems: A least squares method

The robust Kalman filter design problem for two-dimensional uncertain linear discrete time-varying systems with stochastic noises is investigated in this study. First, we prove that the solution to a certain deterministic regularized least squares problem constrained by the nominal two-dimensional system model is equivalent to the generalized two-dimensional Kalman filter. Then, based on this relationship, the robust state estimation problem for two-dimensional uncertain systems with stochastic noises is interpreted as a deterministic robust regularized least squares problem subject to two-dimensional dynamic constraint. Finally, by solving the robust regularized least squares problem and using a simple approximation, a recursive robust two-dimensional Kalman filter is determined. A heat transfer process serves as an example to show the properties and efficacy of the proposed filter.

New results in two-dimensional Kalman filtering with applications to image restoration

This paper describes the application of 2-D Kalman filtering to the restoration of images degraded by linear space invariant (LSI) blur and additive white Gaussian noise (WGN). The image restoration problem is formulated in the framework of the well-known Kalman strip filter. However, the Kalman filtering scheme assumes the availability of a statespace dynamic model for the image process as well as the blur. In the past, most researchers have sought to track the problem of image modeling by making the sometimes unrealistic assumption of separability of the image correlation. A new technique for image modeling which does not make this assumption is proposed. On-line, recursive methods for implementing the modeling algorithm are also presented. We then introduce a novel technique for the state-space realization of separable blurs, since separable 2-D blurs are often encountered in practice and constitute an important subset of 2-D blurs. This state-space model is rendered compatible with strip filtering by using a new recursive scheme which we call as pseudorecursion. An extension for estimating the blur when it is unknown, but can be parameterized, has also been indicated. Simulated experimental results using natural scenery are presented.