# Questions tagged [state-space]

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### How does sampling jitter affect state estimation?

Suppose I have some process which is governed by: $$\vec{x_{k+1}} = A\vec{x_k} + B\vec{u_k} + w_k$$ where $u_k$ is the input, and $w_k$ is process disturbance. This process is continuous time in ...
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### Mismatch between the frequency response of a transfer function and bode plot

I generate a state space model as follows (The details are not important. This part is used to get matrix A_xi and B_xi and the state space model is xi(k+1) = A_xi*xi(k)+B1_xi*u0(k); y(k) = x(k)): <...
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### How to linearize this state space model and write it in discrete form?

This might not be trivial nor short so in advance thank you all who read this in attempt to help. I'm building a Kalman filter in matlab and I'm fairly certain the software itself is working correctly ...
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### State-space model and/or TF for a $K$-th order linear system given the signal sequence

The discrete-time signal $x_n$ is a sum of $K$ discrete-time complex damped exponential: x_n = \sum_{k=1}^{K} \underbrace{(a_k e^{j\phi_k})}_{c_k} {\underbrace{e^{\{(- \...
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### How to get state-space equations form from a block diagram?

This is the block diagram that I'd like to transform into a state-space representation, where u1 and u2 are inputs and y1 and y2 are the outputs of the system I tried to place state variables on the ...
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### Methods for time series estimation in time domain

I am trying to estimate the clean form of a time series, $u(t)$ that is corrupted by additive White Gaussian noise $w(t)$ at a particular SNR. The received signal is: $$y(t) = u(t) + w(t)$$ My first ...
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### States transformation of the bilinear transform

I have used the bilinear (or tustin) transform for a while, have been though the derivation of it and also through the concept of frequency warping. Something that I still not understand that is ...
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### What does it mean for a transfer function to have multiple sets of zeros in the numerator?

I was looking at the source code for Matlab's tf2ss function and I noticed that it parses the numerator assuming that it is a matrix, not a vector. So I looked at ...
I want to build a question on state space using a given, nilpotent matrix, $A$. $$q[n+1]=Aq[n]+Bx[n]$$ $$y[n]=Cq[n]+Dx[n]$$ Usually, I am using the canonical form so there is no problem extracting $A,... 1answer 58 views ### Offline State Estimation Imagine I have a nonlinear system: $$\frac{\text{d} x}{\text{d} t} = f(x,t)\\ y = g(x).$$ I can design a nonlinear observer to estimate the state$x$based on the measurements$y$. However, this ... 0answers 43 views ### Augment State Space Model with Derivative of State Problem How do you augment a state space model with the derivative of a state? I know how to augment a state space model with the integral of a state by doing the following. Given a linear system $$\... 1answer 105 views ### Simulate butterworth filter with initial condition of state vector in R I'm working in R with the packages signal and control (don't know wether these are even the best for my use case). I have a high ... 2answers 534 views ### State space physical meaning Let T(s) be a transfer function that describes a mechanical system, where the input is force and the output is position. And let [A,B,C,D] be the equivalent state-space representation of T(s), ... 1answer 52 views ### Why can't this system be adequately represented using a z-domain transfer function? According to this question and answer the following system cannot be adequately captured by a z-transform transfer function.$$y[n] = y[n-1] + F_{\psi}(y[n-1)) + F_{\phi}(x[n-1])$$where F_{\alpha}(z)... 1answer 74 views ### State-space filters in fixed-point? I am having difficulties implementing state-space filters in (32-bit) fixed-point. This is because the coefficients have a huge dynamic range, for example (MATLAB code): ... 0answers 55 views ### 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# ?... 1answer 39 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 ... 1answer 218 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 ... 1answer 141 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 ... 1answer 296 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 ... 3answers 151 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 ... 1answer 62 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 ... 1answer 89 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. ... 1answer 544 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} ... 0answers 273 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:... 2answers 67 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 ... 0answers 591 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 ... 1answer 126 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 ... 0answers 46 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 ... 0answers 65 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 ... 1answer 2k 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 ... 1answer 390 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 ... 1answer 1k 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 ... 3answers 376 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 ... 0answers 290 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 ... 1answer 363 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$\phiare unknown variables I want to estimate using ... 1answer 421 views ### State-Space Representation of Forward and Backward Filters In [1], the author shows an efficient way of implementing the forward and backward filter using matrices. One can also implement this using filtfilt command in ... 2answers 4k views ### Initial conditions for systems described in state space - LTI or not? Suppose we have some system given by \begin{aligned} \dot{x}(t) &= Ax(t) +Bu(t) \\ y(t) &= Cx(t)+Du(t) \end{aligned} wherex(t)$are the state variables,$y(t)$is the output and$u(t)$... 1answer 2k 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 ... 1answer 98 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 ... 2answers 226 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 ... 2answers 140 views ### Effect of sampling I have this continuos-time system $$\dot{x}=Ax+Bu$$ where A=\begin{bmatrix}0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & \phantom{0}2.8040 & -\phantom{0}5.... 2answers 1k 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., ... 0answers 69 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 ... 1answer 458 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 ... 1answer 255 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 ... 1answer 468 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 ...