Questions tagged [state-space]

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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 ...
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2 votes
2 answers
174 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-...
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2 votes
1 answer
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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 ...
1 vote
1 answer
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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 ...
1 vote
0 answers
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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 ...
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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)...
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1 vote
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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 ...
2 votes
2 answers
88 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 ...
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9 votes
2 answers
778 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 ...
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3 votes
1 answer
60 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 ...
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1 vote
1 answer
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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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How to choose appropriate discretization method for the state estimator?

Let's say I have following open loop state estimator of a dynamic system in the continuous time domain $$ \begin{bmatrix} \frac{\mathrm{d}\hat{\psi}_{r_\alpha}}{\mathrm{d}t} \\ \frac{\mathrm{d}\hat{\...
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1 answer
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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 \...
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2 votes
0 answers
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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)): <...
4 votes
1 answer
280 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 ...
0 votes
1 answer
57 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^{\{(- \...
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1 vote
1 answer
619 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 u1 and u2 are inputs and y1 and y2 are the outputs of the system I tried to place state variables on the ...
2 votes
2 answers
57 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 ...
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1 vote
1 answer
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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 ...
0 votes
1 answer
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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 ...
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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 ...
2 votes
0 answers
39 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,...
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1 answer
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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 ...
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1 vote
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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 $$ \...
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-1 votes
1 answer
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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 ...
4 votes
2 answers
628 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 $T(s)$, ...
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2 votes
1 answer
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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)...
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2 votes
1 answer
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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): ...
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1 vote
0 answers
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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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1 answer
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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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1 vote
1 answer
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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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4 votes
1 answer
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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 ...
7 votes
1 answer
418 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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1 vote
3 answers
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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 ...
1 vote
1 answer
63 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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2 votes
1 answer
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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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4 votes
2 answers
838 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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3 votes
0 answers
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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:...
1 vote
2 answers
79 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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2 votes
0 answers
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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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0 votes
1 answer
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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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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
0 answers
69 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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1 answer
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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 ...
4 votes
1 answer
423 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 ...
3 votes
1 answer
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 ...
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7 votes
3 answers
564 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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0 answers
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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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0 votes
1 answer
424 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
1 answer
478 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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