Alternative Nonlinear Filtering Techniques in Geodesy for Dual State and Adaptive Parameter Estimation

Abstract

In many fields of geodesy applications, state and parameter estimation are of major importance within modeling of on-line processes. The fundamental block of such processes is a filter for recursive estimation. Kalman Filter is the well known filter, a simple and efficient algorithm, as an optimal recursive Bayesian estimator for a somewhat restricted class of linear Gaussian problems. However, in the case that state and/or measurement functions are highly non-linear and the density function of process and/or measurement noise are non-Gaussian, classical filters do not yield satisfying estimates. So it is necessary to adopt alternative filtering techniques in order to provide almost optimal results. A number of such filtering techniques will be reviewed in this contribution, but the main focus lays on the sequential Monte Carlo (SMC) estimation. The SMC filter (well known as particle filter) allows to reach this goal numerically, and works properly with nonlinear, non-Gaussian state estimation. The main idea behind the SMC filter is to approximate the posterior PDF by a set of random particles, which can be generated from a known PDF. These particles are propagated through the nonlinear dynamic model. They are then weighted according to the likelihood of the observations. By means of the particles the true mean and the covariance of the state vector are estimated. However, the computational cost of particle filters has often been considered as their main disadvantage. This occur due to the large, sufficient number of particles to be drawn. Therefore a more efficient approach will be presented, which is based on the combination of SMC filter and the Kalman Filter. The efficiency of the developed filters will be demonstrated through application to a method for direct georeferencing tasks for a multi-sensor system (MSS).