Questions tagged [state-space]

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Are there any State Space Control C libraries?

I'm searching for a C library which implements methods needed for state space control (e.g. state feedback controller and state observer equations). Googling various terms only brought up a non-C (C# ?...
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1answer
1k 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 ...
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1answer
181 views

Kalman Filter 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} ...
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1answer
70 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 ...
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23 views

Kalman Filter - combining data from sensors with different measurement rates, does one have a good source where i can get more information about it?

someone already wrote a question about the topic, and thats exactly what i am looking for but i need a source to get more information and to cite from in my work i combine 2 kalman-filter for ...
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12 views

Very stiff state space matrices after linearizing my Simscape model

I want to simulate and build a furuta pendulum from scratch as a project. Currently I´m having some difficulties with the simulation of my model in Simscape and I can´t figure out what´s wrong with it....
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1answer
34 views

Why is my MATLAB's bode plot wildly off?

I will give out all the details in case it is relevant. I have a MIMO state space system. I find its bode plot using MATLAB and separately using Mathematica. The plot from MATLAB is wildly off ...
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1answer
71 views

Is there any difference in Implementing sigma delta modulator using filters and state space model in FPGA?

Sigma delta modulation is extensively used in quantization to reduce quantization noise. In the literature one can see different architecture for example python-deltasigma to implement a modulator. ...
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1answer
102 views

How does Overlap-Add work for IIR filter?

So let's say I'm trying to implement something like an LPC vocoder. I analyse a speech signal by breaking it up in small chunks and determining their LPC coefficients, which are by design, the ...
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1answer
39 views

Application of UKF on quaternions

I'm trying to perform a state estimation on quaternions to predict the future orientation of a human head. The only sensor data I can obtain (from the AR headset) is the current orientation of the ...
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1answer
830 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 ...
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1answer
126 views

Fundamental questions about state-space and Kalman filters

I am a dsp guy, I only did a minimum of control theory back in university. While trying to grok state space analysis and (discrete time) regular Kalman filters, I am hitting a few questions that ...
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3answers
178 views

Discrete State Space Model - Why Are We Calculating $ x \left[ k + 1 \right] $ Instead of $ \dot{\boldsymbol{x}} \left( t \right) $?

A continuous state space model is defined as follows. $$ \dot{\boldsymbol{x}}(t) = A \boldsymbol{x}(t)+ B \boldsymbol{u}(t) \\ \boldsymbol{y}(t)= C \boldsymbol{x}(t)+ D \boldsymbol{u}(t) $$ If we ...
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3answers
51 views

System classification: unit-time delay

I'm reading a book on linear systems and I can't understand why the unit-time delay is a distributed system. This is the example given in the book: I understand that the initial state of the system ...
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32 views

Using trignonometric functions in system matrix

I am currently trying to create a kinematic model based on the single-track model for vehicles. The following equations are given: $$ \dot{x} = v * cos(\theta) \\ \dot{y} = v * sin(\theta) \\ \dot{\...
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2answers
53 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 ...
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1answer
54 views

Got stack in calculating state-space representation

I got stack in the process of deriving a state-space representation of the following system: There is an electrical oven described as follows: control of the power supply $u$, heating efficiency ...
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9k 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: Why use a Kalman filter instead of keeping a running average? there's no ...
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177 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:...
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545 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 ...
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2answers
154 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 ...
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39 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 ...
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55 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 ...
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1answer
1k 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 ...
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1answer
200 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 ...
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163 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 ...
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2answers
308 views

State space representation in s-domain

I was supposed to find state space representation and its matrices of this system: and I have no idea, how to do this. We were told not to transfer the system to time domain, but I can only do state ...
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1answer
93 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:...
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1answer
274 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 ...
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1answer
308 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 ...
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2answers
3k 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 $u(t)$ ...
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1answer
242 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 ...
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2answers
136 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....
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2answers
746 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., ...
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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 ...
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1answer
87 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 ...
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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 ...
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1answer
375 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 ...
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1answer
345 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 ...
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260 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 ...
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1answer
466 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{...
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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 ($...
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2answers
176 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 ...
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30 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,...
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222 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 \...
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2answers
474 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 ...
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2answers
435 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 ( $n_x$ , $n_v$ , ...
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1answer
138 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, $$...
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1answer
187 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. ...
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1answer
8k 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 ...