Efficient spatial prediction using gaussian markov random fields under uncertain localization

Mahdi Jadaliha, Yunfei Xu, Jongeun Choi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

In this paper, we develop efficient spatial prediction algorithms using Gaussian Markov random fields (GMRFs) under uncertain localization and sequential observations. We first review a GMRF as a discretized Gaussian process (GP) on a lattice, and justify the usage of maximum a posteriori (MAP) estimates of noisy sampling positions in making inferences. We show that the proposed approximation can be viewed as a discrete version of Laplace's approximation for GP regression under localization uncertainty. We then formulate our problem of computing prediction and propose an approximate Bayesian solution, taking into account observations, measurement noise, uncertain hyperparameters, and uncertain localization in a fully Bayesian point of view. In particular, we present an efficient scalable approximation using MAP estimates of noisy sampling positions with a controllable tradeoff between approximation error and complexity. The effectiveness of the proposed algorithms is illustrated using simulated and real-world data.

Original languageEnglish
Title of host publicationASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012
Pages253-262
Number of pages10
DOIs
Publication statusPublished - 2012 Dec 1
EventASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012 - Fort Lauderdale, FL, United States
Duration: 2012 Oct 172012 Oct 19

Publication series

NameASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012
Volume3

Other

OtherASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012
CountryUnited States
CityFort Lauderdale, FL
Period12/10/1712/10/19

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Sampling
Uncertainty

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

Cite this

Jadaliha, M., Xu, Y., & Choi, J. (2012). Efficient spatial prediction using gaussian markov random fields under uncertain localization. In ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012 (pp. 253-262). (ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012; Vol. 3). https://doi.org/10.1115/DSCC2012-MOVIC2012-8596
Jadaliha, Mahdi ; Xu, Yunfei ; Choi, Jongeun. / Efficient spatial prediction using gaussian markov random fields under uncertain localization. ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012. 2012. pp. 253-262 (ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012).
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Jadaliha, M, Xu, Y & Choi, J 2012, Efficient spatial prediction using gaussian markov random fields under uncertain localization. in ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012. ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012, vol. 3, pp. 253-262, ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012, Fort Lauderdale, FL, United States, 12/10/17. https://doi.org/10.1115/DSCC2012-MOVIC2012-8596

Efficient spatial prediction using gaussian markov random fields under uncertain localization. / Jadaliha, Mahdi; Xu, Yunfei; Choi, Jongeun.

ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012. 2012. p. 253-262 (ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012; Vol. 3).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - In this paper, we develop efficient spatial prediction algorithms using Gaussian Markov random fields (GMRFs) under uncertain localization and sequential observations. We first review a GMRF as a discretized Gaussian process (GP) on a lattice, and justify the usage of maximum a posteriori (MAP) estimates of noisy sampling positions in making inferences. We show that the proposed approximation can be viewed as a discrete version of Laplace's approximation for GP regression under localization uncertainty. We then formulate our problem of computing prediction and propose an approximate Bayesian solution, taking into account observations, measurement noise, uncertain hyperparameters, and uncertain localization in a fully Bayesian point of view. In particular, we present an efficient scalable approximation using MAP estimates of noisy sampling positions with a controllable tradeoff between approximation error and complexity. The effectiveness of the proposed algorithms is illustrated using simulated and real-world data.

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Jadaliha M, Xu Y, Choi J. Efficient spatial prediction using gaussian markov random fields under uncertain localization. In ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012. 2012. p. 253-262. (ASME 2012 5th Annual Dynamic Systems and Control Conference Joint with the JSME 2012 11th Motion and Vibration Conference, DSCC 2012-MOVIC 2012). https://doi.org/10.1115/DSCC2012-MOVIC2012-8596