Effective sample size for importance sampling based on discrepancy measures

This paper presents a particle filter, called Log-PF, based on particle weights represented on a logarithmic scale. In practical systems, particle weights may approach numbers close to zero which can cause numerical problems. Therefore, calculations using particle weights and probability densities in the logarithmic domain provide more accurate results. Additionally, calculations in logarithmic domain improve the computational efficiency for distributions containing exponentials or products of functions. To provide efficient calculations, the Log-PF exploits the Jacobian logarithm that is used to compute sums of exponentials. We introduce the weight calculation, weight normalization, resampling, and point estimations in logarithmic domain. For point estimations, we derive the calculation of the minimum mean square error (MMSE) and maximum a posteriori (MAP) estimate. In particular, in situations where sensors are very accurate the Log-PF achieves a substantial performance gain. We show the performance of the derived Log-PF by three simulations, where the Log-PF is more robust than its standard particle filter counterpart. Particularly, we show the benefits of computing all steps in logarithmic domain by an example based on Rao-Blackwellization.

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“…By using (14), the SIS PF can be described in log-domain as shown in Algorithm 2 by a pseudocode. Algorithm 2 is…”

Section: Algorithm Derivationmentioning

confidence: 99%

“…Alternative effective sample size approximations as introduced in [14] can also be represented in log-domain. Table 1 summarizes four generalized alternative effective sample size approximations in lin-domain and log-domain which depend on the parameter .…”

Section: Algorithm Derivationmentioning

confidence: 99%

Log-PF: Particle Filtering in Logarithm Domain

Gentner

Zhang

Jost

2018

Journal of Electrical and Computer Engineering

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“…A resampling step is applied at each iteration that the Effective Sample Size (ESS) is smaller than a threshold value ( N where | | ≤ 1). We adapt some approximations of ESS proposed in literature [13,20,27,26] to the MAPF context, hence for instance the possible conditions are…”

Section: Model Averaging Particle Filtersmentioning

confidence: 99%

“…Within the SIS framework, there are two possible formulations of the estimator of Z, i.e., Z in Eq. (27) and Z given in Eq. (28).…”

Section: A Recursive Formulas For Sequential Inferencementioning

confidence: 99%

Cooperative parallel particle filters for online model selection and applications to urban mobility

Martino

Read

Elvira

et al. 2017

Digital Signal Processing

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132

112

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We design a sequential Monte Carlo scheme for the dual purpose of Bayesian inference and model selection. We consider the application context of urban mobility, where several modalities of transport and different measurement devices can be employed. Therefore, we address the joint problem of online tracking and detection of the current modality. For this purpose, we use interacting parallel particle filters, each one addressing a different model. They cooperate for providing a global estimator of the variable of interest and, at the same time, an approximation of the posterior density of each model given the data. The interaction occurs by a parsimonious distribution of the computational effort, with online adaptation for the number of particles of each filter according to the posterior probability of the corresponding model. The resulting scheme is simple and flexible. We have tested the novel technique in different numerical experiments with artificial and real data, which confirm the robustness of the proposed scheme.

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“…One prevents the quick deterioration of the SMC method by resorting to resampling methods (see [40] for an overview of the most common techniques). These are often triggered based on the effective sample size of the SMC approximation at every time instant [41].…”

Section: Sequential Monte Carlomentioning

confidence: 99%

Sequential Monte Carlo for inference of latent ARMA time-series with innovations correlated in time

Urteaga

Bugallo

Djurić

2017

EURASIP J. Adv. Signal Process.

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We consider the problem of sequential inference of latent time-series with innovations correlated in time and observed via nonlinear functions. We accommodate time-varying phenomena with diverse properties by means of a flexible mathematical representation of the data. We characterize statistically such time-series by a Bayesian analysis of their densities. The density that describes the transition of the state from time t to the next time instant t + 1 is used for implementation of novel sequential Monte Carlo (SMC) methods. We present a set of SMC methods for inference of latent ARMA time-series with innovations correlated in time for different assumptions in knowledge of parameters. The methods operate in a unified and consistent manner for data with diverse memory properties. We show the validity of the proposed approach by comprehensive simulations of the challenging stochastic volatility model.

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Effective sample size for importance sampling based on discrepancy measures

Cited by 158 publications

References 30 publications

Log-PF: Particle Filtering in Logarithm Domain

Log-PF: Particle Filtering in Logarithm Domain

Cooperative parallel particle filters for online model selection and applications to urban mobility

Sequential Monte Carlo for inference of latent ARMA time-series with innovations correlated in time

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