Supervisory Measurement-Guided Noise Covariance Estimation: Discussing Forward and Reverse Differentiation
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909946211205120 |
|---|---|
| author | Li, Haoying Peng, Yifan Wu, Yuchi Wu, Junfeng |
| author_facet | Li, Haoying Peng, Yifan Wu, Yuchi Wu, Junfeng |
| contents | Reliable state estimation depends on accurately modeled noise covariances, which are difficult to determine in practice. This paper formulates the noise covariance estimation as a bilevel optimization problem that factorizes the joint likelihood of primary and supervisory measurements to reconcile information exploitation with computational tractability. The factorization converts the nested Bayesian dependency into a Markov-chain structure, allowing efficient computation. At the lower level, a Kalman filter with state augmentation performs such computation. Meanwhile, closed-form forward and reverse differentiation provide efficient gradients for the upper-level updates, and we compare the two models' space and time complexities to inform their practical selection. The upper level subsequently refines the noise covariances to guide the lower-level estimation. Taken together, the proposed algorithms offer a systematic and computationally efficient approach to noise covariance estimation in linear Gaussian systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05604 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Supervisory Measurement-Guided Noise Covariance Estimation: Discussing Forward and Reverse Differentiation Li, Haoying Peng, Yifan Wu, Yuchi Wu, Junfeng Systems and Control Reliable state estimation depends on accurately modeled noise covariances, which are difficult to determine in practice. This paper formulates the noise covariance estimation as a bilevel optimization problem that factorizes the joint likelihood of primary and supervisory measurements to reconcile information exploitation with computational tractability. The factorization converts the nested Bayesian dependency into a Markov-chain structure, allowing efficient computation. At the lower level, a Kalman filter with state augmentation performs such computation. Meanwhile, closed-form forward and reverse differentiation provide efficient gradients for the upper-level updates, and we compare the two models' space and time complexities to inform their practical selection. The upper level subsequently refines the noise covariances to guide the lower-level estimation. Taken together, the proposed algorithms offer a systematic and computationally efficient approach to noise covariance estimation in linear Gaussian systems. |
| title | Supervisory Measurement-Guided Noise Covariance Estimation: Discussing Forward and Reverse Differentiation |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2512.05604 |