Non-Parametric Bayesian State Space Estimator for Negative Information

Abstract

Simultaneous Localisation and Mapping (SLAM) is concerned with the development of filters to accurately and efficiently infer the state parameters (position, orientation,...) of an agent and aspects of its environment, commonly referred to as the map. A mapping system is necessary for the agent to achieve situatedness which is a precondition for planning and reasoning. In this work, we consider an agent who is given the task of finding a set of objects. The agent has limited perception and can only sense the presence of objects if a direct contact is made, as a result most of the sensing is negative information. In the absence of recurrent sightings or direct measurements of objects, there are no correlations from the measurement errors which can be exploited. This renders SLAM estimators, for which this fact is their backbone such as EKF-SLAM, ineffective. In addition for our setting, no assumptions are taken with respect to the marginals (beliefs) of both the agent and objects (map). From the loose assumptions we stipulate regarding the marginals and measurements, we adopt a histogram parametrisation. We introduce a Bayesian State Space Estimator (BSSE), which we name Measurement Likelihood Memory Filter (MLMF), in which the values of the joint distribution are not parametrised but instead we directly apply changes from the measurement integration step to the marginals. This is achieved by keeping track of the history of likelihood functions’ parameters. We demonstrate that the MLMF gives the same filtered marginals as a histogram filter and show two implementations: MLMF and scalable-MLMF which both have a linear space complexity. The original MLMF retains an exponential time complexity (although an order of magnitude smaller than the histogram filter) whilst the scalable-MLMF introduced independence assumption such to have a linear time complexity. We further quantitatively demonstrate the scalability of our algorithm with 25 beliefs having up to 10’000’000 states each. In an Active-SLAM setting we evaluate the impact that the size of the memory’s history has on the decision-theoretic process in a search scenario for a one-step look-ahead information gain planner. We report on both 1D and 2D experiments.