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Questions tagged [state-space]

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IMU gravity tracking

I'm interested in tracking the gravity vector for a UAV supposing we don't have external input or GPS. I think a solution to the problem is as a follows: We have a past gravity direction vector which ...
FourierFlux's user avatar
2 votes
0 answers
49 views

Direct and numerically robust conversion from zero-pole to state-space representation

Note: this question was initially asked in a different community. Encouraged by the comments, I decided to cross-post here too. Given (z,p,k) my goal is to convert to a state-space representation (A, ...
DaveC's user avatar
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2 votes
1 answer
79 views

Why do they say that complex exponentials are eigenfunctions of LTI systems, when there are still transient responses?

Let $$\dot{x} = Ax+Bu$$ $$y = Cx + Du$$ be a linear ODE with $x(0)=0$. Here, I am assume $A$ is invertible. As you can see, the relation $$H:u(.) \mapsto y(.),$$ where $(u(.),y(.))$ is a solution to ...
Spencer Kraisler's user avatar
2 votes
1 answer
135 views

State space transformation

I have some governing equations of the form: $$\begin{align} \ddot \theta(t) &= \frac{MgL + mgl}{J} \theta(t) + \frac B J \dot x(t) - \frac \alpha J V + \frac {mg}{J} d - \frac{c_1}{J} \dot \theta(...
skylinev2's user avatar
1 vote
1 answer
96 views

Controllability matrix is full rank identity matrix

What does it mean, when my system has controllability matrix that is full rank and identity matrix? Having full rank means that the system is controllable, but does the Identity feature of my ...
Neuling's user avatar
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1 vote
1 answer
235 views

What exactly are the assumptions behind Tustin's formula? Application on state space models

I was parsing the forum when I saw this post surging out of the depths of this forum like an old Kraken. The problem is quite simple. You have a continuous time state space model : $$ \begin{split} \...
NokiYola's user avatar
  • 507
2 votes
0 answers
183 views

Initial conditions of state-space realization

In a discrete-time difference equation (ARX model), the output $y[k]$ is dependent on its past values and inputs, expressed as: $y[k] = -a_1 y[k-1] - ... - a_N y[k-N] + b_1 u[k-1] + ... + b_M u[k-M]$, ...
lilio's user avatar
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2 votes
0 answers
61 views

How is the transfer function of a state space representation computed in practice?

I know that if you have a linear time invariant system defined by $$ \dot{X} = AX+BU $$ $$Y = CX$$ by "Laplacing" the previous equations, you get the following transfer function in the ...
NokiYola's user avatar
  • 507
0 votes
1 answer
180 views

How to discretize the continuous time domain state space model?

I have a dsp algorithm which is based on the below given state space model in the continuous-time domain $$ \begin{bmatrix} \frac{\mathrm{d}\hat{\psi}_{r_{\alpha}}}{\mathrm{d}t} \\ \frac{\mathrm{d}\...
Steve's user avatar
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1 answer
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Finite Difference Estimation for error propagation

For a complex system where symbolic computation of the jacobian is challenging, is estimating the jacobian via finite difference a viable option? To be explicit I'm mostly interested in playing around ...
FourierFlux's user avatar
2 votes
1 answer
86 views

Simulation of the discrete linear Kalman filter

I have been working on a Scilab simulation of the discrete Kalman filter which is used as a state observer of the linear dynamic system. The Scilab script for the discrete Kalman filter is as follows <...
Steve's user avatar
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1 vote
1 answer
70 views

What are the Kalman filter capabilities for the state estimation in presence of the uncertainties in the system input?

I have a question regarding the capabilities of the discrete Kalman filter for estimation of the unmeasurable state variables of a dynamic system. In the time being I have been using a discrete ...
Steve's user avatar
  • 397
1 vote
2 answers
219 views

First Order State Space Question

I am trying to understand the state space equation for a simple first-order LTI system. Suppose I have a system with impulse response $$h(t) = \frac{1}{\tau}e^{\frac{-t}{\tau}} \ \theta(t)$$ In this ...
solo's user avatar
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2 votes
2 answers
236 views

Does every continuous-time filter have a state-space representation?

Given a continuous-time filter with impulse response $h(t)$, is it possible to represent any $h(t)$ in state-space form? More precisely, given the state-space representation of a single-input single-...
mhdadk's user avatar
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2 votes
1 answer
1k views

Why does sequential update of Kalman Filter work when you have multiple sensors?

If you are using a kalman filter with multiple sensing sensors there are two ways to fuse them. One way is doing a single observation step where you include all the sensors in a single vector and a ...
FourierFlux's user avatar
1 vote
1 answer
157 views

IMU state estimation Covariance updating

EKF filter normally has a predict + update step, I am curious - how do you evolve the covariance of the state without one of the steps? In essence I want to evolve the state of an object using an IMU ...
FourierFlux's user avatar
1 vote
0 answers
104 views

Converting a SISO LTI System to a MIMO LTI System

I have a SIMO IIR filter represented as a state space system. I'm wondering if there is a canonical way of converting a IIR filter into a MIMO system, so I can calculate $N$ terms as input at once and ...
Torkoal's user avatar
  • 115
1 vote
1 answer
327 views

Intuition for $\mathbf{P} = \mathbf{0}$ in steady-state when $\mathbf{Q} = \mathbf{0}$ (Kalman filter)

Consider the following discrete-time system: \begin{equation} \mathbf{x}(k+1) = \mathbf{A}_d \mathbf{x}(k) + \mathbf{B}_d \mathbf{u}(k) \end{equation} \begin{equation} y(k) = \mathbf{C}_d \mathbf{x}(k)...
Gab's user avatar
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1 vote
0 answers
29 views

Stability analysis of hybrid discrete-continuous systems

I'm trying to derive the overall state-space system model for a hybrid system, in order to plot its eigenvalues. The system is shown as follows: Which is originally from this paper: Modeling and ...
Derek Topovski's user avatar
2 votes
2 answers
114 views

For continuous systems that in Quasi-static / Static Equilibrium are Memoryless?

A. BACKGROUND: Apparently this question’s answer says this some static systems have memory especially those that hysteresis: Confusion about 'memoryless' meaning So the word static to me ...
L92MD14's user avatar
  • 21
8 votes
2 answers
1k views

What sensors can be fused using the Kalman Filter framework

I was recently introduced to the concept of Kalman filtering in the context of projectile tracking. A classmate recommended this to me, and what intrigued me most was its ability to fuse different ...
batlike's user avatar
  • 213
3 votes
1 answer
85 views

Linear Time-Invariant system without State-space form

I would like to know whether there is any LTI system that does not have state-space representation, but do have a convolution representation. and vice-versa. Can you name some examples for me to ...
Neuling's user avatar
  • 103
1 vote
1 answer
86 views

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 ...
fpf3's user avatar
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0 votes
1 answer
54 views

How to check that the state observer works appropriately?

I have implemented a discrete state observer for a given dynamic system in continuous time domain in following form $$\bar{\mathbf{x}}(k) = \mathbf{A}_d\cdot\hat{\mathbf{x}}(k-1) + \mathbf{B}_d\cdot \...
Steve's user avatar
  • 397
2 votes
0 answers
82 views

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)): <...
SoftSail's user avatar
4 votes
1 answer
749 views

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 ...
user1477107's user avatar
0 votes
1 answer
64 views

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: \begin{equation} x_n = \sum_{k=1}^{K} \underbrace{(a_k e^{j\phi_k})}_{c_k} {\underbrace{e^{\{(- \...
Neuling's user avatar
  • 103
1 vote
3 answers
3k views

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 $u_{1}$ and $u_{2}$ are inputs and $y_{1}$ and $y_{2}$ are the outputs of the system I tried to place ...
user1477107's user avatar
2 votes
2 answers
73 views

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 ...
Sm1's user avatar
  • 291
1 vote
1 answer
317 views

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 ...
PidTuner's user avatar
0 votes
1 answer
25 views

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 ...
dmedine's user avatar
  • 163
1 vote
0 answers
657 views

Recursive Least Square For Filtering

I just started doing research on Recursive Least Square for filtering noises such as sensors and dc motors noises. The only thing I've seen on the internet was Theoretical information about RLS but ...
tosbağa's user avatar
2 votes
0 answers
48 views

State space representation using a given nilppotent matrix

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,...
havakok's user avatar
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0 votes
1 answer
132 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 ...
Ali Baradaran Birjandi's user avatar
1 vote
0 answers
190 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 $$ \...
eball's user avatar
  • 131
0 votes
1 answer
377 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 ...
Chen Huang's user avatar
4 votes
2 answers
769 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 $T(s)$, ...
Yiftah's user avatar
  • 154
2 votes
1 answer
101 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)...
OldSchool's user avatar
  • 123
2 votes
1 answer
133 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): ...
Danijel's user avatar
  • 492
1 vote
0 answers
176 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# ?...
ClBr's user avatar
  • 11
0 votes
1 answer
53 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 ...
ModCon's user avatar
  • 103
1 vote
1 answer
447 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 ...
Aditya TB's user avatar
  • 129
4 votes
1 answer
309 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 ...
chronosynclastic's user avatar
7 votes
1 answer
935 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 ...
Knut Inge's user avatar
  • 3,434
1 vote
4 answers
297 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 ...
João Pedro's user avatar
1 vote
1 answer
89 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 ...
Roxell's user avatar
  • 25
2 votes
1 answer
142 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. ...
Creator's user avatar
  • 88
4 votes
2 answers
1k 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} ...
ABK's user avatar
  • 171
3 votes
0 answers
551 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:...
the_src_dude's user avatar
1 vote
2 answers
95 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 ...
Engineer's user avatar
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