Questions tagged [state-space]
The state-space tag has no usage guidance.
60
questions
1
vote
2answers
35 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 ...
2
votes
0answers
30 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 ...
0
votes
1answer
23 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
37 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 ...
2
votes
0answers
31 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 ...
0
votes
1answer
335 views
How to model state space for complex valued system correctly in SIMULINK (MATLAB)?
When trying to use the default state-space model block, if there is a complex number valued in the matrices, there will be an error
To resolve that, firstly I need to look at pseudo reference model ...
2
votes
1answer
90 views
What is wrong with my residue partial expansion method? (Transfer Function into State-Space Modal/Diagonal Form)
I'm using reference from here and here.
This is Laplace transfer function of DC Control Speed System:
$$\frac{\omega(s)}{V(s)}=\frac{K}{(Js+b)(Ls+R)+K^2}$$
Where,
$\omega$ is the motor angular ...
2
votes
1answer
450 views
Python toolboxes for state-space estimation via subspace estimation
Is there (open-source) toolboxes for state-space estimation via subspace estimation in Python?
I know this is used in Matlab's n4sid function, but I didn't found any Python's implementation (even in ...
0
votes
3answers
102 views
Discrete state space model - Why are we calculating $x[k+1]$ instead of $\dot{\textbf{x}}(t)$?
A continuous state space model is defined as follows.
$$
\dot{\textbf{x}}(t)=\textbf{A}\textbf{x}(t)+\textbf{B}\textbf{u}(t) \\
\textbf{y}(t)=\textbf{C}\textbf{x}(t)+\textbf{D}\textbf{u}(t)
$$
If we ...
0
votes
0answers
107 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 ...
0
votes
1answer
186 views
A State space model for discrete Sine wave Using kalma filter
I'm looking to apply an optimal LQR filter to a discrete signal of the form
$$
x[n]=A\sin(\omega_0n+\phi)+v[n]
$$
The amplitude $A$ and the phase $\phi$ are unknown variables I want to estimate using ...
3
votes
1answer
205 views
State-Space Representation of Forward and Backward Filters
In [1], the author shows an efficient way of implementing the forward and backward filter using matrices. One can also implement this using filtfilt command in ...
7
votes
2answers
2k views
Initial conditions for systems described in state space - LTI or not?
Suppose we have some system given by
$$\begin{aligned}
\dot{x}(t) &= Ax(t) +Bu(t) \\
y(t) &= Cx(t)+Du(t)
\end{aligned}$$
where $x(t)$ are the state variables, $y(t)$ is the output and $u(t)$ ...
1
vote
1answer
651 views
Bilinear transformation of continuous time state space system
I'm trying to understand the derivation of the bilinear transform for a set of continuous time state-space matrices. I've found plenty of websites which list steps to perform the conversion (here 1 or ...
1
vote
1answer
79 views
Learner level information on Kalman filtering for different input kinds
I am learning Kalman filters and have seen example on data as state varaibles that have real values / numeric. However, in digital communication the information is in digital - bits. So, can Kalman ...
1
vote
2answers
108 views
MATLAB: Implementing Least Squares Estimator for a Given Model
The formula to estimate $\mathbf{h}$ is then
$$\hat{\mathbf{h}} = (X^T X)^{-1} X^T \vec{y}\tag{2}$$
I think this can be implemented in Matlab using ...
0
votes
2answers
133 views
Effect of sampling
I have this continuos-time system
$$\dot{x}=Ax+Bu$$
where
\begin{equation}A=\begin{bmatrix}0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & \phantom{0}2.8040 & -\phantom{0}5....
3
votes
2answers
493 views
Control design: under what conditions can closed-loop poles be placed arbitrarily?
Say we have a single-input linear system $\dot{\mathbf{x}} = A\mathbf{x}+Bu$. With full-state feedback ($u=-G\mathbf{x}$), it is straightforward to arbitrarily place the $n$ closed-loop poles (i.e., ...
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 ...
0
votes
1answer
212 views
Discrete time non-linear time invariant system dynamics descriptions (state-space or input-output relationship)
For the sake of simplicity the following notation $a_k := a[k]$ is assumed for time sequences.
A completely general discrete-time (DT) non-linear(NL) time-invariant (TI) dynamical system can be ...
0
votes
1answer
215 views
Conceptual Question on equalization technique in rayleigh fading channel based on a paper
Question Link http://www.raymaps.com/index.php/theoretical-ber-of-m-qam-in-rayleigh-fading/
gives theoretical expressions for BER in Rayleigh fading channel. Can I use the expression for 64-QAM in ...
0
votes
1answer
284 views
$N$ point moving average filters in state space
I am new to this filter, I did read about them, but could find out a state space notation of these:
$$y(n)=\frac{1}{N}\sum_{m=0}^{N-1}x(n-m)$$
Are moving average filters an LTI systems?
And how do ...
2
votes
0answers
222 views
Scipy.signal.dimpulse(system): how to translate a StateSpace to a “system”? [closed]
The command scipy.signal.dimpulse(system, x0=None, t=None, n=None) does not seem to accept a scipy StateSpace as an input to its ...
0
votes
1answer
327 views
Designing observer with non-observable system
I have this state-space system
\begin{align}
\dot{x}&=\begin{bmatrix}1 & 0\\3 & -2\end{bmatrix}x+\begin{bmatrix}10\\0 \end{bmatrix}u\\
y&=\begin{bmatrix}1 & 0\end{bmatrix}x
\end{...
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
1answer
79 views
State space equation from differential equation
I have very general system. I don't know whether it is electrical or mechanical or whatever. This system can be modeled by the following differential equation
$$\dot q = \frac{Tf_1-f_2}{T+1}$$
where:...
2
votes
2answers
299 views
Why is it necessary to have two state variables
I am learning about control theory.
Let's consider this system.
$$
m a(t) + b v(t) + k x(t) = f(t)
$$
$a$ is acceleration
$v$ is velocity
$x$ is displacement
$f$ is external force
In my ...
4
votes
1answer
149 views
How can the order of a transfer function be derived from its equivalent state space representation?
Suppose I have a discrete state space model:
\begin{align}
\theta[k+1] &= A \theta[k] + B u[k]\\
y[k] &= C \theta[k]
\end{align}
I know that the equivalent transfer function can be found by ...
2
votes
1answer
132 views
How to represent the nonlinear model as a state space in Unscented Kalman Filter
There is an Autoregressive model of order 1 (AR(1)) that is excited by a non-linear signal as the input:
$$x_t = \rho x_{t-1} + u_t \tag{1}$$
The time series $u_t$ is generated from a nonlinear map,
$$...
2
votes
0answers
216 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 \...
5
votes
1answer
186 views
Expectation maximization of moving average with binary source input
I am trying to do blind system identification of a univariate linear FIR model:
I am unsure if the approach is correct or not and any help to further proceed with the maximization will be great. ...
6
votes
1answer
5k views
Why eigen values and poles of a system are equivalent?
In control systems engineering, the stability of a system (modeled in the form of Transfer Function) is determined by the poles of the system in the right or left hand sides.
When the model is ...
0
votes
1answer
222 views
Is this model nonlinear?
I have this state-space model:
Is this state space model nonlinear? If it is, why is that?
0
votes
2answers
254 views
How to form Kalman filtering matrices for a problem with variable acceleration?
Assuming we have
time vector $T$ with constant time step $dt$
position vector $X$
velocity vector $V$
acceleration vector $A$
All vectors $X, V, A$ have noise on their measurement ( $n_x$ , $n_v$ , ...
1
vote
1answer
67 views
State Space representation
I'm trying to change this filter transfer function to state space representation
$ y_t=\frac{1+b_1 z^{-1}}{1+a_1 z^{-1} +a_2 z^{-2}}u_t $
I tried writing it as time series
$ y_t+a_1 y_{t-1}+...
1
vote
1answer
674 views
The two types of stability and “Why exponential”
When I was learning about LTI systems,
I noticed that
LTI system is said to be BIBO stable
if and only if its square sum of impulse response is finite.
This expression is found on many textbook of ...
1
vote
1answer
145 views
Doubt in state space representation
$y$ is scalar observations and so C will be a 1x2 matrix.
I want to represent the following model as a state space representation so as to estimate the hidden states from the noisy observations $y$ ...
5
votes
3answers
7k views
when is a kalman filter different from a moving average?
this thread asks when a discrete-time Kalman filter is better/different from a simple moving average of the observations:
https://math.stackexchange.com/questions/173901/why-use-a-kalman-filter-...
1
vote
1answer
1k views
kalman filter with time-varying noise?
in regular discrete-time (1 dimensional) kalman filter, it is assumed that we have white gaussian noise affecting the transitions and the observations:
$x(t+1) = Ax + w$
$y(t) = Cx(t) + v$
...
3
votes
2answers
568 views
How to intuitively understand the state space formulation of discrete time system?
The SS formulation of DT system is given by
$$x[(k+1)T] = Ax(kT) + Bu(kT)$$
$$y(kT) = Cx(kT) + Du(kT)$$
Note: T is the sampling period and often omited
Can someone explain to me why the state ...
asked Jan 30 '15 at 2:46
Carlos - the Mongoose - Danger
3112 gold badges6 silver badges22 bronze badges
3
votes
2answers
94 views
How to find the output signal of a filter using state space matrices?
I have a filter.
It has two poles and two zeros.
I found the state space equations and the matrices A, B, C, and D
Now. I have 9 samples that I need to process with my filter.
How do I use A,B,C,D ...
1
vote
2answers
625 views
Does the system matrix being singular tell us anything about the system?
If we have a linear system, represented in State Space and the A matrix is singular (det(A) == 0), can we expect any special properties from the system?
1
vote
2answers
2k views
Why is my discretized transfer function unstable when my discretized state-space model is stable?
I am working with a 30-state, 14-input linear model that is described by a state-space model:
model_state_space = ss(A, B, C, D);
The model is extremely slow (it ...
-1
votes
2answers
146 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 ...
0
votes
1answer
1k views
state space formulation of a sinusoidal system
Let $f=A\sin{\omega t}=x_1$ and $\dot{f}=A\omega\cos{\omega t}=\dot{x}_1=x_2$. Let the output be $y=cA\omega$, where $c=1$ is a constant. I want to represent this in a state space formulation:
$\dot{...
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
61 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
75 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
95 views
Logarithm in state space equations
I want to linearize a system to this form
$$\begin{bmatrix}
\Delta\dot{x}_1\\
\Delta\dot{x}_2\\
\Delta\dot{x}_3
\end{bmatrix} = A\begin{bmatrix}\Delta x_1\\ \Delta x_2\\ \Delta x_3\end{...
0
votes
1answer
279 views
How to find transfer function by state space representation matrices
A state space representation is given by:
$$\dot{x}= \begin{bmatrix}0 & 0 & 0 & 0\\ 1 & 0 & 0 & 0 \\ 0&0&-2&-4\\0&0&1&0\end{bmatrix}x+\begin{bmatrix} 1\\...
