## Details

Originalsprache | Englisch |
---|---|

Seiten (von - bis) | 766-780 |

Seitenumfang | 15 |

Fachzeitschrift | IEEE Transactions on Aerospace and Electronic Systems |

Jahrgang | 58 |

Ausgabenummer | 2 |

Publikationsstatus | Veröffentlicht - 24 Aug. 2021 |

## Abstract

Observations from high rate sensors are known to be time-correlated. When processed in a Kalman filter (KF) without accounting for correlations, i) a discrepancy with the true solution occurs, up to a divergence of the filter and ii) the covariance estimates are overestimated, which is equally problematic. Two main solutions exist to account for correlations in a KF: The time differenced and the state augmentation approach. They both model the correlated noise corresponding to an autoregressive process of the first order (AR(1), also called the Gauss Markov process) as it has a short memory, is linear and can be easily implemented. In this contribution, we propose a new method to account for measurement correlations by means of a variance inflation factor (VIF). The latter is derived from an AR(1) assumption for the measurement noise, and its parameters can be estimated by whitening the KF residuals. Our proposal, called the KF_VIF, is further extended to an AR(p) model to account for finer correlation structures. We compare the different approaches and address the impact of noise mismodeling. We use simulations to test the sensitivity of the KF solution to misspecifications and show that the KF_VIF proposed is a powerful answer to account for correlated measurement noise. A real case analysis corresponding to a precomputed flight trajectory with a constant velocity validates the results of the simulations.

## ASJC Scopus Sachgebiete

- Ingenieurwesen (insg.)
**Luft- und Raumfahrttechnik**- Ingenieurwesen (insg.)
**Elektrotechnik und Elektronik**

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- BibTex
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**Kalman filter and correlated measurement noise: the Variance inflation factor.**/ Kermarrec, Gael; Jain, Ankit; Schon, Steffen.

in: IEEE Transactions on Aerospace and Electronic Systems, Jahrgang 58, Nr. 2, 24.08.2021, S. 766-780.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

*IEEE Transactions on Aerospace and Electronic Systems*, Jg. 58, Nr. 2, S. 766-780. https://doi.org/10.1109/taes.2021.3103564

*IEEE Transactions on Aerospace and Electronic Systems*,

*58*(2), 766-780. https://doi.org/10.1109/taes.2021.3103564

}

TY - JOUR

T1 - Kalman filter and correlated measurement noise

T2 - the Variance inflation factor

AU - Kermarrec, Gael

AU - Jain, Ankit

AU - Schon, Steffen

PY - 2021/8/24

Y1 - 2021/8/24

N2 - Observations from high rate sensors are known to be time-correlated. When processed in a Kalman filter (KF) without accounting for correlations, i) a discrepancy with the true solution occurs, up to a divergence of the filter and ii) the covariance estimates are overestimated, which is equally problematic. Two main solutions exist to account for correlations in a KF: The time differenced and the state augmentation approach. They both model the correlated noise corresponding to an autoregressive process of the first order (AR(1), also called the Gauss Markov process) as it has a short memory, is linear and can be easily implemented. In this contribution, we propose a new method to account for measurement correlations by means of a variance inflation factor (VIF). The latter is derived from an AR(1) assumption for the measurement noise, and its parameters can be estimated by whitening the KF residuals. Our proposal, called the KF_VIF, is further extended to an AR(p) model to account for finer correlation structures. We compare the different approaches and address the impact of noise mismodeling. We use simulations to test the sensitivity of the KF solution to misspecifications and show that the KF_VIF proposed is a powerful answer to account for correlated measurement noise. A real case analysis corresponding to a precomputed flight trajectory with a constant velocity validates the results of the simulations.

AB - Observations from high rate sensors are known to be time-correlated. When processed in a Kalman filter (KF) without accounting for correlations, i) a discrepancy with the true solution occurs, up to a divergence of the filter and ii) the covariance estimates are overestimated, which is equally problematic. Two main solutions exist to account for correlations in a KF: The time differenced and the state augmentation approach. They both model the correlated noise corresponding to an autoregressive process of the first order (AR(1), also called the Gauss Markov process) as it has a short memory, is linear and can be easily implemented. In this contribution, we propose a new method to account for measurement correlations by means of a variance inflation factor (VIF). The latter is derived from an AR(1) assumption for the measurement noise, and its parameters can be estimated by whitening the KF residuals. Our proposal, called the KF_VIF, is further extended to an AR(p) model to account for finer correlation structures. We compare the different approaches and address the impact of noise mismodeling. We use simulations to test the sensitivity of the KF solution to misspecifications and show that the KF_VIF proposed is a powerful answer to account for correlated measurement noise. A real case analysis corresponding to a precomputed flight trajectory with a constant velocity validates the results of the simulations.

KW - Autoregressive (AR) process

KW - correlated measurement noise

KW - Correlation

KW - Covariance matrices

KW - Filtering

KW - Kalman filter

KW - Kalman filters

KW - Mathematical model

KW - Noise measurement

KW - power law noise

KW - Standards

KW - state augmentation method

KW - variance inflation factor

UR - http://www.scopus.com/inward/record.url?scp=85113840316&partnerID=8YFLogxK

U2 - 10.1109/taes.2021.3103564

DO - 10.1109/taes.2021.3103564

M3 - Article

AN - SCOPUS:85113840316

VL - 58

SP - 766

EP - 780

JO - IEEE Transactions on Aerospace and Electronic Systems

JF - IEEE Transactions on Aerospace and Electronic Systems

SN - 0018-9251

IS - 2

ER -