Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [linear-dynamical-system]

Dynamic linear models refers to modeling problems where coefficients (as in regression) are allowed to vary with time. This is the so called state-space approach.

0
votes
0answers
10 views

How to model this as a POMDP?

I would like to fit a DLM to a dataset in R but I don't know the underlying transition matrices between states nor do I have a guess for the emission matrix (given a state, what responses should I see)...
0
votes
0answers
38 views

Understanding the DLM

The DLM model in my notes is described as: $f_k(\theta,u)=F_k\theta+u$ and $h_k(\theta,v)=H_k\theta+v$, where $F_k$ is a $d\times d$ matrix and $H_k$ is a $d'\times d$ matrix, respectively called ...
1
vote
0answers
28 views

How to numerically solve a matrix differential equation in R?

I have interest in using the R language and environment to numerically solve a system of linear ordinary differential equations. The numerical solver, deSolve, ...
0
votes
0answers
20 views

How important is research on model selection methods in Statistics?

My question is nothing technical. I just wanted your opinion on how important is the model selection problem in the field of Statistics considering the age of big data. Are the current methods such as ...
0
votes
1answer
110 views

Convert a state-space model with exogenous input to one without

I have a state space model of the form \begin{align} x_{t+1} &= Ax_t + Bu_t + w_t\\ y_t &= Cx_t + Du_t + v_t \end{align} where $u$ is the exogenous input. Also, $ w_t \sim N(0, Q)$ and $v_t \...
1
vote
0answers
63 views

R dynr: Having trouble setting up state-space model [closed]

I was looking around to flexibly implement state space models in R. I found dynr, but I am being frustrated to no end by its tad vague documentation and lack of ...
0
votes
0answers
63 views

How does one approximate $\mu$ and $\sigma$ in an arithmetic Brownian motion using a Kalman filter?

My concern arises from the fact that in the following system: $x_k = (\mu, \sigma)^T = x_{k-1}$ $Y_k = Y_{k-1} + \mu + \sigma Z_k \quad Z_k \sim N(0,1)$ that I cannot separate the states I want to ...
2
votes
0answers
320 views

How to ensure covariance matrix is positive semi definite in linear dynamical model learning?

I am trying to learn a linear dynamical model for a data using expectation-maximization algorithm. The model is defined as follows: $$x_0 \sim \mathcal{N}(\mu_0 ,\Sigma_0)$$ $$ x_{t+1} = Fx_t + w_t, \...
4
votes
1answer
51 views

Help on statistical modeling of pedestrian flow in subways

I'm a New Yorker and take the subways every day. I have a growing interest in understanding the distribution of paths people take on the subways to work every day. I.e. if there are $n$ subway ...
1
vote
0answers
33 views

Determining state space for a dynamic linear model

Are there any techniques for determining a good state space to use for a dynamic linear model? I'm trying to model ad-clicks with observed values being whether a user clicked on an ad and I'm curious ...
1
vote
0answers
55 views

What should be the termination criteria for my problem with a closed loop system identification?

I have modelled a dynamic system which needs to be validated against test data. A closed loop system identification process is used for the validation. In this process, the time domain simulation of ...
3
votes
0answers
154 views

How to add stochastic drift in dynamic linear model?

As I'm not able to comment (yet), my question follows the one raised by @mzuba here I would like to use the DLM R package to model the local linear trend model, which unlike mzuba specified, has a ...
1
vote
0answers
35 views

Predictions in a control loop like airconditions

I wonder if there are special things to consider with predictions in a control loop, e.g. An airconditioner trys to hold the target temperature at 20 degrees. I want to predict the energy consumption,...
0
votes
1answer
345 views

How to estimate coefficients of a state space when relevant data is provided?

I have a state space system $\dot{x}$ = $Ax$ + $Bu$ $y$ = $Cx$ I know C matrix exactly. And A matrix looks something like this, and some of the $x_{ij}$ in A are known as well. Same goes with B. \...
1
vote
1answer
111 views

Help in CRLB for linear model

The model is an FIR (MA) filter $$x(t) = h_1 u(t-1) + h_2 u(t-2) + u(t) \tag{1}$$ $$ y(t) = h^T x(t) + v(t) \tag{2}$$ $u(t)$ is a pseudo-random binary signal (PRBS) that excites/ drives the ...
0
votes
1answer
81 views

Simulating a dynamical system

Basically I need to replicate Hartley's 'A User's Guide to Solving Real Business Cycle Models' . Specifically (to make question relevant to stats.stackexchange), I want to simulate the dynamical ...
2
votes
0answers
146 views

State Space model question [closed]

I am looking for some help with estimating Space state model of this form: $r_{t} = r^{*}_{t} + \pi + \varepsilon_{1}$ $R_{t}= r^{*}_{t} + \alpha + \pi + \varepsilon_{2}$ $r^{*}_{t} = r^{*}_{t-...
6
votes
2answers
2k views

Forward Filtering Backwards Sampling (FFBS) and Look-Ahead Bias

Assumptions / Context: Let's assume that I have data that can be modeled as a dynamic linear model. To estimate the parameters (e.g., covariance matrix of the state/system equation), I use a Gibbs ...
2
votes
1answer
334 views

Model selection and parameter estimation in forecasting with a Dynamic Linear Model

I am implementing a general purpose prediction tool for time series. I want to tolerate missing values, so I decided to settle for DLMs. To make it as relevant as possible on a large number of ...
2
votes
0answers
49 views

Estimation from two observations [closed]

Suppose there are two vector signals $x$, $z$. The observer 1 receives a linear version of $x$ plus Gaussian noise. Observer 2 receives a linear sum of both $x$ and $z$ plus Gaussian noise as shown ...
3
votes
0answers
69 views

How to include prior knowledge that a model might be able to figure out itself

I have a problem where I want to predict the outcome of a sequence given another sequence online. Let $(x_1, x_2, ... x_T)$ be denoted by $x_{1:T}$, then I am estimating: $$ p(y_T|x_{1:T}) $$ where $...
2
votes
2answers
282 views

Learning a mapping from one time series to another with a Kalman Filter

I am interested in finding the relation between two (possibly multi dimensional) time series $x_{1:T}$ and $y_{1:T}$. I wonder how I can do that with a linear dynamical system/Kalman filter. My ...
1
vote
1answer
374 views

Assumption of Gaussian distribution of acceleration

I have a data set consisting of noisy position values of a trajectory of a human hand. I want to estimate a generative model of these trajectories, and the obvious choice is a Kalman Filter/linear ...