Estimating a State-Space Model from Point Process Observations: A Note on Convergence

2010 ◽  
Vol 22 (8) ◽  
pp. 1993-2001 ◽  
Author(s):  
Ke Yuan ◽  
Mahesan Niranjan
Keyword(s):  
State Space ◽  
Point Process ◽  
Expectation Maximization ◽  
State Space Model ◽  
Optimal Solution ◽  
Discrete Events ◽  
Convergence Properties ◽  
Unknown Parameters ◽  
Neural Spikes ◽  
Space Model

Physiological signals such as neural spikes and heartbeats are discrete events in time, driven by continuous underlying systems. A recently introduced data-driven model to analyze such a system is a state-space model with point process observations, parameters of which and the underlying state sequence are simultaneously identified in a maximum likelihood setting using the expectation-maximization (EM) algorithm. In this note, we observe some simple convergence properties of such a setting, previously un-noticed. Simulations show that the likelihood is unimodal in the unknown parameters, and hence the EM iterations are always able to find the globally optimal solution.

scholarly journals Gauss process state-space model optimization algorithm with expectation maximization

2019 ◽  
Vol 15 (7) ◽  
pp. 155014771986221
Author(s):  
Hongqiang Liu ◽  
Haiyan Yang ◽  
Tao Zhang ◽  
Bo Pan
Keyword(s):  
State Space ◽  
Optimization Algorithm ◽  
Expectation Maximization ◽  
Conditional Expectation ◽  
State Space Model ◽  
Expectation Maximization Algorithm ◽  
Model Optimization ◽  
Laboratory Environment ◽  
Space Model ◽  
Gauss Process

A Gauss process state-space model trained in a laboratory cannot accurately simulate a nonlinear system in a non-laboratory environment. To solve this problem, a novel Gauss process state-space model optimization algorithm is proposed by combining the expectation–maximization algorithm with the Gauss process Rauch–Tung–Striebel smoother algorithm, that is, the EM-GP-RTSS algorithm. First, a theoretical formulation of the Gauss process state-space model is proposed, which is not found in previous references. Second, a Gauss process state-space model optimization framework with the expectation–maximization algorithm is proposed. In the expectation–maximization algorithm, the unknown system state is considered as the lost data, and the maximization of measurement likelihood function is transformed into that of a conditional expectation function. Then, the Gauss process–assumed density filter algorithm and the Gauss process Rauch–Tung–Striebel smoother algorithm are proposed with the Gauss process state-space model defined in this article, in order to calculate the smoothed distribution in the conditional expectation function. Finally, the Monte Carlo numerical integral method is used to obtain the approximate expression of the conditional expectation function. The simulation results demonstrate that the Gauss process state-space model optimized by the EM-GP-RTSS can simulate the system in the non-laboratory environment better than the Gauss process state-space model trained in the laboratory, and can reach or exceed the estimation accuracy of the traditional state-space model.

Estimating a State-Space Model from Point Process Observations

2003 ◽  
Vol 15 (5) ◽  
pp. 965-991 ◽  
Author(s):  
Anne C. Smith ◽  
Emery N. Brown
Keyword(s):  
State Space ◽  
Point Process ◽  
State Space Model ◽  
The State ◽  
Conditional Intensity ◽  
Space Model ◽  
Neural Spiking ◽  
Latent Process ◽  
Conditional Intensity Function ◽  
Spiking Activity

A widely used signal processing paradigm is the state-space model. The state-space model is defined by two equations: an observation equation that describes how the hidden state or latent process is observed and a state equation that defines the evolution of the process through time. Inspired by neurophysiology experiments in which neural spiking activity is induced by an implicit (latent) stimulus, we develop an algorithm to estimate a state-space model observed through point process measurements. We represent the latent process modulating the neural spiking activity as a gaussian autoregressive model driven by an external stimulus. Given the latent process, neural spiking activity is characterized as a general point process defined by its conditional intensity function. We develop an approximate expectation-maximization (EM) algorithm to estimate the unobservable state-space process, its parameters, and the parameters of the point process. The EM algorithm combines a point process recursive nonlinear filter algorithm, the fixed interval smoothing algorithm, and the state-space covariance algorithm to compute the complete data log likelihood efficiently. We use a Kolmogorov-Smirnov test based on the time-rescaling theorem to evaluate agreement between the model and point process data. We illustrate the model with two simulated data examples: an ensemble of Poisson neurons driven by a common stimulus and a single neuron whose conditional intensity function is approximated as a local Bernoulli process.

scholarly journals A Kalman particle filter for online parameter estimation with applications to affine models

2021 ◽  
Author(s):  
Jian He ◽  
Asma Khedher ◽  
Peter Spreij
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
State Space ◽  
Outer Layer ◽  
Posterior Distribution ◽  
State Space Model ◽  
The State ◽  
State Variables ◽  
Unknown Parameters ◽  
Space Model

AbstractIn this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous-time state space model with discrete-time observations by an algorithm that combines the Kalman filter and a particle filter. The proposed algorithm is semi-recursive and has a two layer structure, in which the outer layer provides the estimation of the posterior distribution of the unknown parameters and the inner layer provides the estimation of the posterior distribution of the state variables. This algorithm has a similar structure as the so-called recursive nested particle filter, but unlike the latter filter, in which both layers use a particle filter, our algorithm introduces a dynamic kernel to sample the parameter particles in the outer layer to obtain a higher convergence speed. Moreover, this algorithm also implements the Kalman filter in the inner layer to reduce the computational time. This algorithm can also be used to estimate the parameters that suddenly change value. We prove that, for a state space model with a certain structure, the estimated posterior distribution of the unknown parameters and the state variables converge to the actual distribution in $$L^p$$ L p with rate of order $${\mathcal {O}}(N^{-\frac{1}{2}}+\varDelta ^{\frac{1}{2}})$$ O ( N - 1 2 + Δ 1 2 ) , where N is the number of particles for the parameters in the outer layer and $$\varDelta $$ Δ is the maximum time step between two consecutive observations. We present numerical results of the implementation of this algorithm, in particularly we implement this algorithm for affine interest models, possibly with stochastic volatility, although the algorithm can be applied to a much broader class of models.

Development of L1-norm sliding mode observer for sensor fault diagnosis of an industrial gas turbine

2021 ◽  
pp. 095965182199617
Author(s):  
Mahyar Akbari ◽  
Abdol Majid Khoshnood ◽  
Saied Irani
Keyword(s):  
Fault Detection ◽  
State Space ◽  
Gas Turbine ◽  
Sliding Mode ◽  
State Space Model ◽  
Sensor Fault ◽  
Space Model ◽  
Decision Logic ◽  
Sensor Fault Detection ◽  
Industrial Gas Turbine

In this article, a novel approach for model-based sensor fault detection and estimation of gas turbine is presented. The proposed method includes driving a state-space model of gas turbine, designing a novel L1-norm Lyapunov-based observer, and a decision logic which is based on bank of observers. The novel observer is designed using multiple Lyapunov functions based on L1-norm, reducing the estimation noise while increasing the accuracy. The L1-norm observer is similar to sliding mode observer in switching time. The proposed observer also acts as a low-pass filter, subsequently reducing estimation chattering. Since a bank of observers is required in model-based sensor fault detection, a bank of L1-norm observers is designed in this article. Corresponding to the use of the bank of observers, a two-step fault detection decision logic is developed. Furthermore, the proposed state-space model is a hybrid data-driven model which is divided into two models for steady-state and transient conditions, according to the nature of the gas turbine. The model is developed by applying a subspace algorithm to the real field data of SGT-600 (an industrial gas turbine). The proposed model was validated by applying to two other similar gas turbines with different ambient and operational conditions. The results of the proposed approach implementation demonstrate precise gas turbine sensor fault detection and estimation.

Modeling of CCLP in koryo extract production

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ji Chol ◽  
Ri Jun Il
Keyword(s):  
Process Control ◽  
Medical Care ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Space Model ◽  
Effective Components ◽  
Counter Current

Abstract The modeling of counter-current leaching plant (CCLP) in Koryo Extract Production is presented in this paper. Koryo medicine is a natural physic to be used for a diet and the medical care. The counter-current leaching method is mainly used for producing Koryo medicine. The purpose of the modeling in the previous works is to indicate the concentration distributions, and not to describe the model for the process control. In literature, there are no nearly the papers for modeling CCLP and especially not the presence of papers that have described the issue for extracting the effective components from the Koryo medicinal materials. First, this paper presents that CCLP can be shown like the equivalent process consisting of two tanks, where there is a shaking apparatus, respectively. It allows leachate to flow between two tanks. Then, this paper presents the principle model for CCLP and the state space model on based it. The accuracy of the model has been verified from experiments made at CCLP in the Koryo Extract Production at the Gang Gyi Koryo Manufacture Factory.

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