Asymptotic properties of linear filter for deterministic processes

Reddy, Anugu Sumith; Apte, Amit; Vadlamani, Sreekar

doi:10.1016/j.sysconle.2020.104676

Cited by 4 publications

(5 citation statements)

References 15 publications

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“…(2017), Grudzien et al . (2018a; 2018b), Frank and Zhuk (2018), Reddy et al . (2020), and Tranninger et al . (2020) are all, at least in part, devoted to discussing the necessary and/or sufficient criteria for filter stability in terms of the projection of the observations in unstable/neutral/weakly stable directions, and this is directly related to the choice of adaptive observation operators in Law et al .…”

Section: Introductionmentioning

confidence: 94%

“…Albeit empirical, that choice already signified using only data projected on to an approximation of the unstable subspace, which was obtained by breeding on the data assimilation cycle (BDAS). Furthermore, González-Tokman and Hunt (2013), , Grudzien et al (2018a;2018b), Frank and Zhuk (2018), Reddy et al (2020), andTranninger et al (2020) are all, at least in part, devoted to discussing the necessary and/or sufficient criteria for filter stability in terms of the projection of the observations in unstable/neutral/weakly stable directions, and this is directly related to the choice of adaptive observation operators in Law et al (2016).…”

Section: Introductionmentioning

confidence: 99%

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Particle filters for data assimilation based on reduced‐order data models

Maclean

Vleck

2021

Quart J Royal Meteoro Soc

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We introduce a framework for data assimilation (DA) in which the data is split into multiple sets corresponding to low-rank projections of the state space. Algorithms are developed that assimilate some or all of the projected data, including an algorithm compatible with any generic DA method. The major application explored here is PROJ-PF, a projected particle filter. The PROJ-PF implementation assimilates highly informative but low-dimensional observations. The implementation considered here is based on using projections corresponding to assimilation in the unstable subspace (AUS). In the context of particle filtering, the projected approach mitigates the collapse of particle ensembles in high-dimensional DA problems, while preserving as much relevant information as possible, as the unstable and neutral modes correspond to the most uncertain model predictions. In particular, we formulate and implement numerically a projected optimal proposal particle filter (PROJ-OP-PF) and compare this with the standard optimal proposal and the ensemble transform Kalman filter.

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Particle filters for data assimilation based on reduced‐order data models

Maclean

Vleck

2021

Quart J Royal Meteoro Soc

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“…4. Relation to observability -the information loss by the dynamics is compensated by information gained from observations: Assumption 2.2 resembles closely the well-known observability condition [1], [37,Definition 1] in the linear case except for the dependence of ρ t on t satisfying certain conditions. These additional conditions on ρ t can be understood intuitively in the following way.…”

Section: It Follows From Assumption 22 Thatmentioning

confidence: 93%

“…(and an analogous Theorem 4.7 in discrete time). Previous results of stability with linear deterministic dynamics and linear observations can be found in [23,10] in the case of discrete time and in [33,37] in the case of continuous time. The problem of accuracy (which is a measure of deviation of the filter from the signal) of the filter for deterministic dynamics is studied in [16], and we rely heavily on the techniques used in that study.…”

Section: Stability Of Non-linear Filter For Deterministic Dynamicsmentioning

confidence: 94%

“…Theorems 3.7 and 4.7 do not give any rate of convergence, because of the use of Martingale convergence theorem, and it would be interesting to find finer methods that may give the rate of convergence, such as those [10,Section 4.3] available for the convergence of covariance of the filter for linear models. Further, partly because of the use of convergence of the smoother to prove filter stability, our results do not give much information about the structure of the asymptotic filtering distribution, such as that which is available [10,Sections 4.3,5], [37,Remark 3.2] for the linear filter. We hope that further investigations in this direction will lead to efficient numerical implementations of the filter for deterministic dynamics, especially for high dimensional systems.…”

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confidence: 96%

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Stability of non-linear filter for deterministic dynamics

Reddy¹,

Apte²

2021

FoDS

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<p style='text-indent:20px;'>This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time filters. Earlier works on the stability of the nonlinear filters are in the context of stochastic dynamics and assume conditions like compact state space or time independent observation model, whereas we prove filter stability for deterministic dynamics with more general assumptions on the state space and observation process. We give several examples of systems that satisfy these assumptions. We also show that the asymptotic structure of the filtering distribution is related to the dynamical properties of the signal.</p>

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