Covariance Recovery from a Square Root Information Matrix for Data Association

Abstract

Data association is one of the core problems of simultaneous localization and mapping (SLAM), and it requires knowledge about the uncertainties of the estimation problem in the form of marginal covariances. However, it is often difficult to access these quantities without calculating the full and dense covariance matrix, which is prohibitively expensive. We present a dynamic programming algorithm for efficient recovery of the marginal covariances needed for data association. As input we use a square root information matrix as maintained by our incremental smoothing and mapping (iSAM) al- gorithm. The contributions beyond our previous work are an improved algorithm for recovering the marginal covariances and a more thorough treatment of data association now including the joint compatibility branch and bound (JCBB) algorithm. We further show how to make information theoretic decisions about measurements before actually taking the measurement, therefore allowing a reduction in estimation complexity by omitting uninformative measurements. We evaluate our work on simulated and real-world data.