Weak in the NEES?: Auto-tuning Kalman Filters with Bayesian Optimization
Department of Computer Science（计算机科学系）；University of Colorado Boulder（科罗拉多大学博尔德分校）；University College London（伦敦大学学院）；Smead Aerospace Engineering Sciences（Smead航空航天工程科学系）
Zhaozhong Chen, Christoffer Heckman, Simon Julier, Nisar Ahmed
备注：
Final version presented at FUSION 2018 Conference, Cambridge, UK, July 2018 (submitted June 1, 2018)
Kalman filters are routinely used for many data fusion applications including navigation, tracking, and simultaneous localization and mapping problems. However, significant time and effort is frequently required to tune various Kalman filter model parameters, e.g. process noise covariance, pre-whitening filter models for non-white noise, etc. Conventional optimization techniques for tuning can get stuck in poor local minima and can be expensive to implement with real sensor data. To address these issues, a new "black box" Bayesian optimization strategy is developed for automatically tuning Kalman filters. In this approach, performance is characterized by one of two stochastic objective functions: normalized estimation error squared (NEES) when ground truth state models are available, or the normalized innovation error squared (NIS) when only sensor data is available. By intelligently sampling the parameter space to both learn and exploit a nonparametric Gaussian process surrogate function for the NEES/NIS costs, Bayesian optimization can efficiently identify multiple local minima and provide uncertainty quantification on its results.
Real-world measurement noise in applications like robotics is often correlated in time, but we typically assume i.i.d. Gaussian noise for filtering. We propose general Gaussian Processes as a non-parametric model for correlated measurement noise that is flexible enough to accurately reflect correlation in time, yet simple enough to enable efficient computation. We show that this model accurately reflects the measurement noise resulting from vision-based Simultaneous Localization and Mapping (SLAM), and argue that it provides a flexible means of modeling measurement noise for a wide variety of …
In this paper, we consider the task of designing a Kalman Filter (KF) for an unknown and partially observed autonomous linear time invariant system driven by process and sensor noise. To do so, we propose studying the following two step process: first, using system identification tools rooted in subspace methods, we obtain coarse finite-data estimates of the state-space parameters and Kalman gain describing the autonomous system; and second, we use these approximate parameters to design a filter which produces estimates of the system state. We show that when the system identification step prod…
University of Technology Sydney（悉尼科技大学）；Zhejiang University（浙江大学）
With the recent advance of deep learning based object recognition and estimation, it is possible to consider object level SLAM where the pose of each object is estimated in the SLAM process. In this paper, based on a novel Lie group structure, a right invariant extended Kalman filter (RI-EKF) for object based SLAM is proposed. The observability analysis shows that the proposed algorithm automatically maintains the correct unobservable subspace, while standard EKF (Std-EKF) based SLAM algorithm does not. This results in a better consistency for the proposed algorithm comparing to Std-EKF. Final…
Markov chain Monte Carlo (MCMC) methods are powerful computational tools for analysis of complex statistical problems. However, their computational efficiency is highly dependent on the chosen proposal distribution, which is generally difficult to find. One way to solve this problem is to use adaptive MCMC algorithms which automatically tune the statistics of a proposal distribution during the MCMC run. A new adaptive MCMC algorithm, called the variational Bayesian adaptive Metropolis (VBAM) algorithm, is developed. The VBAM algorithm updates the proposal covariance matrix using the variationa…
I2EKF-LO: A Dual-Iteration Extended Kalman Filter Based LiDAR Odometry
Harbin Institute of Technology（哈尔滨工业大学）；Nanyang Technological University（南洋理工大学）；Hangzhou Guochen Robot Technology Company Limited（杭州国辰机器人科技有限公司）；Zhejiang University（浙江大学）
The Covid-19 pandemic has resulted in a variety of approaches for managing infection outbreaks in international populations. One example is mobile phone applications, which attempt to alert infected individuals and their contacts by automatically inferring two key components of infection risk: the proximity to an individual who may be infected, and the duration of proximity. The former component, proximity, relies on Bluetooth Low Energy (BLE) Received Signal Strength Indicator(RSSI) as a distance sensor, and this has been shown to be problematic; not least because of unpredictable variations …
Department of Electronic Engineering, Tsinghua University（清华大学电子工程系）；State Key Laboratory of Space Network and Communications（空间网络与通信国家重点实验室）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）
LIO-EKF: High Frequency LiDAR-Inertial Odometry using Extended Kalman Filters
Institute of Geodesy and Geoinformation, University of Bonn（波恩大学大地测量与地理信息研究所）；Department of Engineering Science at the University of Oxford（牛津大学工程科学系）；Lamarr Institute for Machine Learning and Artificial Intelligence（拉马尔机器学习与人工智能研究所）
Data assimilation is concerned with sequentially estimating a temporally-evolving state. This task, which arises in a wide range of scientific and engineering applications, is particularly challenging when the state is high-dimensional and the state-space dynamics are unknown. This paper introduces a machine learning framework for learning dynamical systems in data assimilation. Our auto-differentiable ensemble Kalman filters (AD-EnKFs) blend ensemble Kalman filters for state recovery with machine learning tools for learning the dynamics. In doing so, AD-EnKFs leverage the ability of ensemble …
This paper introduces a computational framework to reconstruct and forecast a partially observed state that evolves according to an unknown or expensive-to-simulate dynamical system. Our reduced-order autodifferentiable ensemble Kalman filters (ROAD-EnKFs) learn a latent low-dimensional surrogate model for the dynamics and a decoder that maps from the latent space to the state space. The learned dynamics and decoder are then used within an ensemble Kalman filter to reconstruct and forecast the state. Numerical experiments show that if the state dynamics exhibit a hidden low-dimensional structu…
