Advertisement

Suboptimal Filter Stability

  • Juan Andrade-Cetto
  • Alberto Sanfeliu
Chapter
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 23)

Abstract

When a stochastic system is partially controllable, such as in the case of SLAM, the Gaussian noise sources v k do not affect all of the elements of the state space. The diagonal elements of P corresponding to these incorruptible states will be driven to zero by the Kalman filter, and once this happens, these estimates will remain fixed and no further observations will alter their values. The dynamics of the model assume the landmarks are fixed elements, for which no process noise is considered. Therefore, their associated noise covariance (its determinant) will asymptotically tend to zero [31]. The filter gain for the landmark states will also tend to zero. Figure 3.1 shows two new simulations for a linear SLAM case, a monobot under Brownian motion with one and two landmarks. The simulations show the evolution of the localization errors for both the monobot and the landmarks, and the reduction of the landmark part of the Kalman gain, due to the uncontrollability of the system. The only way to remedy this situation is to add a positive definite pseudo-noise covariance to those incorruptible states [18].

Keywords

Covariance Estimate Kalman Gain Landmark State State Error Covariance Nonlinear Vehicle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Authors and Affiliations

  • Juan Andrade-Cetto
    • 1
  • Alberto Sanfeliu
    • 1
  1. 1.Institut de Robòtica i Informàtica Industrial Universitat Politècnica de Catalunya – Consejo Superior de Investigaciones Científicas Llorens Artigas 4–6 08028 BarcelonaSpain

Personalised recommendations