Kalman smoothing with persistent nuisance parameters

Abstract

Kalman filtering and smoothing methods are key to a broad range of applications, including navigation, financial tracking, and weather prediction. Many such applications contain nuisance parameters, such as persistent bias, and classic approaches estimate these parameters by augmenting the state and posing appropriate constraints on their dynamics. These approaches work in practice, but they are difficult to interpret, and can result in poor conditioning. In this paper, we propose a variant of Kalman smoothing models that includes both dynamic state variables and static biases, but estimate only a single value for each static bias variable. We incorporate both kinds of variables into an augmented optimization framework, and design efficient algorithms for estimation, providing computational complexity and numerical stability guarantees, and a straightforward method to estimate the variance of the bias estimates. We illustrate the efficacy of the proposed method in two examples, including the classic navigation problem of estimating attitude from biased gyro measurements.