Identification with stochastic sampling time jitter

Abstract

This work investigates how stochastic unmeasurable sampling jitter noise affects the result of system identification, and proposes a modification of known approaches to mitigate the effects of sampling jitter. By just assuming conventional additive measurement noise, the analysis shows that the identified model will get a bias in the transfer function amplitude that increases for higher frequencies. A frequency domain approach with a continuous time system model allows an analysis framework for sampling jitter noise. The bias and covariance in the frequency domain model are derived. This is used in bias compensated (weighted) least squares algorithms, and by asymptotic arguments this leads to a maximum likelihood algorithm. Continuous time output error models are used for numerical illustrations.Keywords: system identification, stochastic systems, least-squares estimation, maximum likelihood, frequency domain Identification with Stochastic Sampling Time Jitter ⋆ Frida Eng1 , Fredrik Gustafsson. Dept of EE, Linköpings universitet, SE-58183 Linköping, Sweden AbstractThis work investigates how stochastic unmeasureable sampling jitter noise affects the result of system identification, and proposes a modification of known approaches to mitigate the effects of sampling jitter. By just assuming conventional additive measurement noise, the analysis shows that the identified model will get a bias in the transfer function amplitude that increases for higher frequencies. A frequency domain approach with a continuous time system model allows an analysis framework for sampling jitter noise. The bias and covariance in the frequency domain model are derived. This is used in bias compensated (weighted) least squares algorithms, and by asymptotic arguments this leads to a maximum likelihood algorithm. Continuous time output error models are used for numerical illustrations.

Interactive parameter estimation for output error moving average systems

“…In the past few decades, a large number of important achievements have been made in the literature (Eng and Gustafsson 2008;Ding et al 2009bLiu and Lu 2010;Liu et al 2010a), e.g. the filtering-based recursive least squares algorithms ), the auxiliary model-based identification algorithms (Ding andChen 2004, 2005a;Ding and Ding 2010), the multi-innovation identification algorithms Ding et al 2009aDing et al , 2010bHan and Ding 2009a;Liu et al 2009Liu et al , 2010cDing 2010;Zhang et al 2009), the hierarchical identification algorithms (Ding and Chen 2005b,c;Han et al 2010;Xiang et al 2010), and the iterative identification algorithms Liu et al 2010b;Wang et al 2010c).…”

Tracking of Animals Using Airborne Cameras

“…The model in (2.43) can then be extended with an additional measurement having the conditional distribution 46) where the conditional distribution is modelled to fit the application. Given the current mode δ k , the distribution is assumed to be conditionally independent from the states X 1:k , the measurements Y 1:k and Z 1:k−1 = {z i } i∈{1:k−1}∩I , and all previous modes…”

“…Sampling jitter is one exception, see for instance [46], where estimation problems are formulated based on parametric models mixed with prior distributions of the One attempt would be to consider the uncertain timestamps as latent variables and use for example the expectation-maximization (em) algorithm [40]. For instance, [102] discusses missing data in an ssm, using the em algorithm, and this is further developed in, e.g., [68] and [92].…”

Co-prime sampling jitter analysis

“…Covariance estimation from discrete time observations under jitter and delay conditions is studied in [3], and consistency and asymptotic normality of the estimators are established. System identification under the influence of stochastic sampling jitter noise is considered in [4]. It also provides ways to mitigate this effect for the case when the jitter is unknown and not measurable.…”