Questions tagged [state-space]
The state-space tag has no usage guidance.
17
questions with no upvoted or accepted answers
3
votes
0answers
123 views
Converting an FIR Filter Model to a State Space Model for Kalman Filtering
I want to try and determine the true value of a quantity $\alpha[k]$ from observations of a related quantity $\vartheta[k]$ using a Kalman filter. The observations are of the following FIR filter form:...
3
votes
0answers
2k views
Difference between state space and transfer function model response (in Simulink)
Why I get a different response from the same system (e.g. three phase inverter with LC filter) in state space form and in transfer function (Laplace) form when using the same PI controller values ($...
3
votes
0answers
144 views
What is right and full Frobenius canonical form?
I'm having a trouble here. I'm supposed to learn Frobenius canonical representation form for finding statespace matrices, but I found many different forms.
Let's suppose we have a system with this ...
2
votes
1answer
63 views
KalmanFilter EM estimation of covariances
The question might be very simple, but I get a strange result from Kalman Filter. Let us consider the simplest state-space model, the random walk plus noise:
$$
y_{t} = x_{t} + \varepsilon_{t}\\
x_{t} ...
2
votes
0answers
103 views
Derivation of ZOH Discretization
I'm trying to understand the derivation of the zero order hold discretization method, and I have a couple of questions about some of the steps.
I think I understand the first part, this is just the ...
2
votes
0answers
42 views
Calculating pre-history of recursive filter from state space representation when optimising for initial z
For a recursive filter, suppose a set of $b$ and $a$ coefficients have been calculated. Assume a state-space representation for which an initial set of $z$-values have also been calculated as in ...
2
votes
0answers
218 views
Identifiability of a state space model (Dynamic Linear Model)
Take a general linear Gaussian state space model (SSM)(aka Dynamic Linear Model DLM):
\begin{align}
X_{t+1}&=FX_t + V_t\\
Y&=HX_t+W_t\\
V_t &\sim \mathcal N(0,Q)\\
W_t &\sim \...
1
vote
1answer
41 views
Equations for particle filter
The particle filter is based on the state and observation model equations
$x_{t+1}=f_t(x_t, v_t)$
$y_t=h_t(x_t, u_t)$
The idea is to randomly generate some particles then propagate them through the ...
1
vote
0answers
66 views
identifying overshoots in given state space system with step inputs
Suppose I have the following state space system:
$$
\dot{x}(t) = Ax(t) + Bu, \quad y(t) = Lx(t), \quad x(0) = x_0
$$
where $A$, $B$ and $L$ are real matrices, $u$ is a constant real vector (so that ...
1
vote
0answers
29 views
Kalman Filtering and space parametrization
I am familiar with Kalman filtering given a linear (time-invariant) state space model.
However, the state space parametrization is not unique. Given a controllable and observable state space model (A,...
1
vote
0answers
8 views
State Space model of a differential eqn. for use in Least Squares
The code in this page solves the Least Squares problem for the following dynamic model:
$\dot{y}=ay+bu$
where $a$ and $b$ are constants, $u$ is an input. The code is as follow:
...
1
vote
0answers
62 views
Identifiability for Time Invariant State Space Models
Kevin Murphy's Kalman Filter toolbox (for Matlab) contains an example where it's the fact that the state space system in not identifiable causes problems. I include the example in it's entirety but ...
1
vote
0answers
77 views
Simulating a state space model
I want to simulate data from the following model:
$\textbf{z}_k=\textbf{H}\textbf{x}_k+\textbf{v}_k$ $\textbf{v}_k \sim N(\textbf{0},\textbf{R})$
$\textbf{H}$ does not change over time
$\textbf{x}$ ...
0
votes
1answer
30 views
Continuous time double exponential filtering in state space form?
I'm trying to determine the continuous time formulation of the double exponential filter so that I can adapt it more flexibly for my particular problem.
Typically, this model is expressed as a pair ...
0
votes
0answers
38 views
How do I derive complicated robotic motion models easily?
I have a filter that tracks a robot. I want it to use a 2D coordinated turn polar velocity motion model (from page 15 here):
But I want to expand on this motion model: I want an additional velocity ...
0
votes
0answers
122 views
State Space conversion of Sinusoidal model
i would like to learn how to convert sinusoidal model into state space form which has following equation
our model consist of sum of periodic components with additive of white noise, given by ...
-1
votes
2answers
158 views
How to find derivative of 2-D elliptical Gaussian function with different standard deviations along $x$ and $y$ directions?
I am trying to find the 2-D derivative of an elongated Gaussian density.
The Gaussian has standard deviations $\sigma_x$ and $\sigma_y$. How can I get the scale-normalized 2-D Gaussian derivative in ...
