Analytic Minimum Mean-Square Error Bounds in Linear Dynamic Systems With Gaussian Mixture Noise Statistics
For linear dynamic systems with Gaussian noise, the Kalman filter provides the Minimum Mean-Square Error (MMSE) state estimation by tracking the posterior. Similarly, for systems with Gaussian Mixture (GM) noise distributions, a bank of Kalman filters or the Gaussian Sum Filter (GSF), can provide th...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9058631/ |
| _version_ | 1818854841488769024 |
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| author | Leila Pishdad Fabrice Labeau |
| author_facet | Leila Pishdad Fabrice Labeau |
| author_sort | Leila Pishdad |
| collection | DOAJ |
| description | For linear dynamic systems with Gaussian noise, the Kalman filter provides the Minimum Mean-Square Error (MMSE) state estimation by tracking the posterior. Similarly, for systems with Gaussian Mixture (GM) noise distributions, a bank of Kalman filters or the Gaussian Sum Filter (GSF), can provide the MMSE state estimation. However, the MMSE itself is not analytically tractable. Moreover, the general analytic bounds proposed in the literature are not tractable for GM noise statistics. Hence, in this work, we evaluate the MMSE of linear dynamic systems with GM noise statistics and propose its analytic lower and upper bounds. We provide two analytic upper bounds which are the Mean-Square Errors (MSE) of implementable filters, and we show that based on the shape of the GM noise distributions, the tighter upper bound can be selected. We also show that for highly multimodal GM noise distributions, the bounds and the MMSE converge. Simulation results support the validity of the proposed bounds and their behavior in limits. |
| first_indexed | 2024-12-19T07:59:07Z |
| format | Article |
| id | doaj.art-aad3ce78b03a41bab33eabc8c0bcac79 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-19T07:59:07Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-aad3ce78b03a41bab33eabc8c0bcac792022-12-21T20:29:55ZengIEEEIEEE Access2169-35362020-01-018679906799910.1109/ACCESS.2020.29864209058631Analytic Minimum Mean-Square Error Bounds in Linear Dynamic Systems With Gaussian Mixture Noise StatisticsLeila Pishdad0https://orcid.org/0000-0001-7825-5757Fabrice Labeau1https://orcid.org/0000-0001-5814-9156Department of Electrical and Computer Engineering, McGill University, Montreal, QC, CanadaDepartment of Electrical and Computer Engineering, McGill University, Montreal, QC, CanadaFor linear dynamic systems with Gaussian noise, the Kalman filter provides the Minimum Mean-Square Error (MMSE) state estimation by tracking the posterior. Similarly, for systems with Gaussian Mixture (GM) noise distributions, a bank of Kalman filters or the Gaussian Sum Filter (GSF), can provide the MMSE state estimation. However, the MMSE itself is not analytically tractable. Moreover, the general analytic bounds proposed in the literature are not tractable for GM noise statistics. Hence, in this work, we evaluate the MMSE of linear dynamic systems with GM noise statistics and propose its analytic lower and upper bounds. We provide two analytic upper bounds which are the Mean-Square Errors (MSE) of implementable filters, and we show that based on the shape of the GM noise distributions, the tighter upper bound can be selected. We also show that for highly multimodal GM noise distributions, the bounds and the MMSE converge. Simulation results support the validity of the proposed bounds and their behavior in limits.https://ieeexplore.ieee.org/document/9058631/Analytic bounds on minimum mean-square errorGaussian mixture noiseonline Bayesian filteringGaussian sum filterminimum mean-square error estimator |
| spellingShingle | Leila Pishdad Fabrice Labeau Analytic Minimum Mean-Square Error Bounds in Linear Dynamic Systems With Gaussian Mixture Noise Statistics IEEE Access Analytic bounds on minimum mean-square error Gaussian mixture noise online Bayesian filtering Gaussian sum filter minimum mean-square error estimator |
| title | Analytic Minimum Mean-Square Error Bounds in Linear Dynamic Systems With Gaussian Mixture Noise Statistics |
| title_full | Analytic Minimum Mean-Square Error Bounds in Linear Dynamic Systems With Gaussian Mixture Noise Statistics |
| title_fullStr | Analytic Minimum Mean-Square Error Bounds in Linear Dynamic Systems With Gaussian Mixture Noise Statistics |
| title_full_unstemmed | Analytic Minimum Mean-Square Error Bounds in Linear Dynamic Systems With Gaussian Mixture Noise Statistics |
| title_short | Analytic Minimum Mean-Square Error Bounds in Linear Dynamic Systems With Gaussian Mixture Noise Statistics |
| title_sort | analytic minimum mean square error bounds in linear dynamic systems with gaussian mixture noise statistics |
| topic | Analytic bounds on minimum mean-square error Gaussian mixture noise online Bayesian filtering Gaussian sum filter minimum mean-square error estimator |
| url | https://ieeexplore.ieee.org/document/9058631/ |
| work_keys_str_mv | AT leilapishdad analyticminimummeansquareerrorboundsinlineardynamicsystemswithgaussianmixturenoisestatistics AT fabricelabeau analyticminimummeansquareerrorboundsinlineardynamicsystemswithgaussianmixturenoisestatistics |