Gaussian Process Gauss-Newton: Non-Parametric State Estimation

There is uncertainty in the neuromusculoskeletal system, and deterministic models cannot describe this significant presence of uncertainty, affecting the accuracy of model predictions. In this paper, a knee joint angle prediction model based on surface electromyography (sEMG) signals is proposed. To address the instability of EMG signals and the uncertainty of the neuromusculoskeletal system, a non-parametric probabilistic model is developed using a Gaussian process model combined with the physiological properties of muscle activation. Since the neuromusculoskeletal system is a dynamic system, the Gaussian process model is further combined with a non-linear autoregressive with eXogenous inputs (NARX) model to create a Gaussian process autoregression model. In this paper, the normalized root mean square error (NRMSE) and the correlation coefficient (CC) are compared between the joint angle prediction results of the Gaussian process autoregressive model prediction and the actual joint angle under three test scenarios: speed-dependent, multi-speed and speed-independent. The mean of NRMSE and the mean of CC for all test scenarios in the healthy subjects dataset and the hemiplegic patients dataset outperform the results of the Gaussian process model, with significant differences (p < 0.05 and p < 0.05, p < 0.05 and p < 0.05). From the perspective of uncertainty, a non-parametric probabilistic model for joint angle prediction is established by using Gaussian process autoregressive model to achieve accurate prediction of human movement.

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A Gaussian process latent force model for joint input-state estimation in linear structural systems

Mechanical Systems and Signal Processing ◽

10.1016/j.ymssp.2019.03.048 ◽

2019 ◽

Vol 128 ◽

pp. 497-530 ◽

Cited By ~ 15

Author(s):

Rajdip Nayek ◽

Souvik Chakraborty ◽

Sriram Narasimhan

Keyword(s):

Gaussian Process ◽

State Estimation ◽

Structural Systems ◽

Input State ◽

Force Model

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Bayesian Joint Input-State Estimation for Nonlinear Systems

Vibration ◽

10.3390/vibration3030020 ◽

2020 ◽

Vol 3 (3) ◽

pp. 281-303

Author(s):

Timothy J. Rogers ◽

Keith Worden ◽

Elizabeth J. Cross

Keyword(s):

Nonlinear Systems ◽

Gaussian Process ◽

State Estimation ◽

State Space ◽

Mean Squared Error ◽

Duffing Oscillator ◽

State Space Model ◽

Input State ◽

Force Model ◽

Internal States

This work suggests a solution for joint input-state estimation for nonlinear systems. The task is to recover the internal states of a nonlinear oscillator, the displacement and velocity of the system, and the unmeasured external forces applied. To do this, a Gaussian process latent force model is developed for nonlinear systems. The model places a Gaussian process prior over the unknown input forces for the system, converts this into a state-space form and then augments the nonlinear system with these additional hidden states. To perform inference over this nonlinear state-space model a particle Gibbs approach is used combining a “Particle Gibbs with Ancestor Sampling” Markov kernel for the states and a Metropolis-Hastings update for the hyperparameters of the Gaussian process. This approach is shown to be effective in a numerical case study on a Duffing oscillator where the internal states and the unknown forcing are recovered, each with a normalised mean-squared error less than 0.5%. It is also shown how this Bayesian approach allows uncertainty quantification of the estimates of the states and inputs which can be invaluable in further engineering analyses.

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Gaussian process based state estimation for a gyroscope-free IMU

2010 IEEE Sensors ◽

10.1109/icsens.2010.5690871 ◽

2010 ◽

Cited By ~ 3

Author(s):

Patrick Schopp ◽

Axel Rottmann ◽

Lasse Klingbeil ◽

Wolfram Burgard ◽

Yiannos Manoli

Keyword(s):

Gaussian Process ◽

State Estimation

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Multi-kernel Gaussian process regression and Bayesian model averaging based nonlinear state estimation and quality prediction of multiphase batch processes

2013 American Control Conference ◽

10.1109/acc.2013.6580690 ◽

2013 ◽

Author(s):

Jie Yu ◽

Kuilin Chen ◽

Junichi Mori ◽

Mudassir M. Rashid

Keyword(s):

Gaussian Process ◽

State Estimation ◽

Bayesian Model ◽

Bayesian Model Averaging ◽

Model Averaging ◽

Gaussian Process Regression ◽

Batch Processes ◽

Quality Prediction ◽

Nonlinear State Estimation ◽

Nonlinear State

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Variational Inference for Sparse Gaussian Process Modulated Hawkes Process

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i04.6160 ◽

2020 ◽

Vol 34 (04) ◽

pp. 6803-6810

Author(s):

Rui Zhang ◽

Christian Walder ◽

Marian-Andrei Rizoiu

Keyword(s):

Model Selection ◽

Gaussian Process ◽

Linear Time ◽

Expectation Maximization Algorithm ◽

Synthetic Data ◽

Variational Inference ◽

Hawkes Process ◽

Prediction Confidence ◽

Inference Schema ◽

Non Parametric

The Hawkes process (HP) has been widely applied to modeling self-exciting events including neuron spikes, earthquakes and tweets. To avoid designing parametric triggering kernel and to be able to quantify the prediction confidence, the non-parametric Bayesian HP has been proposed. However, the inference of such models suffers from unscalability or slow convergence. In this paper, we aim to solve both problems. Specifically, first, we propose a new non-parametric Bayesian HP in which the triggering kernel is modeled as a squared sparse Gaussian process. Then, we propose a novel variational inference schema for model optimization. We employ the branching structure of the HP so that maximization of evidence lower bound (ELBO) is tractable by the expectation-maximization algorithm. We propose a tighter ELBO which improves the fitting performance. Further, we accelerate the novel variational inference schema to linear time complexity by leveraging the stationarity of the triggering kernel. Different from prior acceleration methods, ours enjoys higher efficiency. Finally, we exploit synthetic data and two large social media datasets to evaluate our method. We show that our approach outperforms state-of-the-art non-parametric frequentist and Bayesian methods. We validate the efficiency of our accelerated variational inference schema and practical utility of our tighter ELBO for model selection. We observe that the tighter ELBO exceeds the common one in model selection.

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