scholarly journals Approximate Smoothing and Parameter Estimation in High-Dimensional State-Space Models

2017 ◽  
Vol 65 (22) ◽  
pp. 5982-5994 ◽  
Author(s):  
Axel Finke ◽  
Sumeetpal S. Singh
Keyword(s):  
Parameter Estimation ◽  
State Space ◽  
State Space Models ◽  
High Dimensional ◽  
Dimensional State Space

scholarly journals Spatiotemporal blocking of the bouncy particle sampler for efficient inference in state-space models

2021 ◽  
Vol 31 (5) ◽  
Author(s):  
Jacob Vorstrup Goldman ◽  
Sumeetpal S. Singh
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Simulated Data ◽  
State Space Models ◽  
High Dimensional ◽  
Effective Sample Size ◽  
Stat Assoc ◽  
Dimensional State Space ◽  
State Inference ◽  
New Algorithms

AbstractWe propose a novel blocked version of the continuous-time bouncy particle sampler of Bouchard-Côté et al. (J Am Stat Assoc 113(522):855–867, 2018) which is applicable to any differentiable probability density. This alternative implementation is motivated by blocked Gibbs sampling for state-space models (Singh et al. in Biometrika 104(4):953–969, 2017) and leads to significant improvement in terms of effective sample size per second, and furthermore, allows for significant parallelization of the resulting algorithm. The new algorithms are particularly efficient for latent state inference in high-dimensional state-space models, where blocking in both space and time is necessary to avoid degeneracy of MCMC. The efficiency of our blocked bouncy particle sampler, in comparison with both the standard implementation of the bouncy particle sampler and the particle Gibbs algorithm of Andrieu et al. (J R Stat Soc Ser B Stat Methodol 72(3):269–342, 2010), is illustrated numerically for both simulated data and a challenging real-world financial dataset.

Parameter Estimation Using a Modified Version of SPSA Algorithm Applied to State Space Models

2009 ◽  
Vol 129 (12) ◽  
pp. 1187-1194 ◽  
Author(s):  
Jorge Ivan Medina Martinez ◽  
Kazushi Nakano ◽  
Kohji Higuchi
Keyword(s):  
Parameter Estimation ◽  
State Space ◽  
State Space Models

scholarly journals Bounding on rough terrain with the LittleDog robot

2010 ◽  
Vol 30 (2) ◽  
pp. 192-215 ◽  
Author(s):  
Alexander Shkolnik ◽  
Michael Levashov ◽  
Ian R. Manchester ◽  
Russ Tedrake
Keyword(s):  
State Space ◽  
Open Loop ◽  
Random Trees ◽  
Configuration Spaces ◽  
High Dimensional ◽  
Rough Terrain ◽  
Task Space ◽  
Motion Primitive ◽  
Dimensional State Space ◽  
Planning Algorithm

A motion planning algorithm is described for bounding over rough terrain with the LittleDog robot. Unlike walking gaits, bounding is highly dynamic and cannot be planned with quasi-steady approximations. LittleDog is modeled as a planar five-link system, with a 16-dimensional state space; computing a plan over rough terrain in this high-dimensional state space that respects the kinodynamic constraints due to underactuation and motor limits is extremely challenging. Rapidly Exploring Random Trees (RRTs) are known for fast kinematic path planning in high-dimensional configuration spaces in the presence of obstacles, but search efficiency degrades rapidly with the addition of challenging dynamics. A computationally tractable planner for bounding was developed by modifying the RRT algorithm by using: (1) motion primitives to reduce the dimensionality of the problem; (2) Reachability Guidance, which dynamically changes the sampling distribution and distance metric to address differential constraints and discontinuous motion primitive dynamics; and (3) sampling with a Voronoi bias in a lower-dimensional “task space” for bounding. Short trajectories were demonstrated to work on the robot, however open-loop bounding is inherently unstable. A feedback controller based on transverse linearization was implemented, and shown in simulation to stabilize perturbations in the presence of noise and time delays.

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