# Questions tagged [state-space]

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### Is a Kalman filter suitable to filter projected points positions, given Euler angles of the capturing device?

My system is the following. I use the camera of a mobile device to track an object. From this tracking, I get four 3D points that I project on the screen, to get four 2D points. These 8 values are ...
9k views

### How do I find a system's impulse response from its state-space repersentation using the state transition matrix?

Suppose we have a linear represented in the standard state space notation: $$\dot{x}(t)=Ax(t)+Bu(t)$$ $$y(t) = Cx(t) + Du(t)$$ In order to get its impulse response, it is possible to take its ...
182 views

### Estimating the input to a system from a system state using EKF [closed]

[ Cross-posted from: https://math.stackexchange.com/questions/164169/estimating-the-input-to-a-system-from-a-system-state ] I have a system for which I have obtained a non-linear time-varying state-...
11k 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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### 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 $u(t)$ ...
222 views

### Can a state space model have changing state size over time?

I have worked with state space models in relation to Kalman estimation. Here I have always seen state space models with fixed state size over time, i.e. the state transition matrix is square. Let us ...
185 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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### 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 ...
175 views

### How to combine a perfect signal with a limited dynamic range with a poor one with high dynamic range?

I have two sensors that measure speed $v(t)$ of a moving vehicle. The first sensor produces a signal $f(t)$ which is a very accurate estimation of speed. However, it only works for slow to moderate ...
281 views

### State space system identification

Suppose I have a real (physical) dynamical system with some sensors and actuators, and I also have an idealized state-space model of this same system. How, in general, can I adjust the model to match ...
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 ...
189 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. ...
249 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 ...
312 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 ...
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 ...
81 views

### Linearized system and State Space

I want to ask about this scheme: $u_0$ should be something as input in specific point given by the initial conditions and $y_0$ output. Block State Spase represented linearized system by A, B, C, D ...
328 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 ...
475 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 $T(s)$, ...
891 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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### 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 ...
127 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 ...
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### 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 ...
663 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 ...
230 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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### 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): ...
814 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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### 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 ...
60 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 ...
285 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 ...
223 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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### 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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### 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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### 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 ...
156 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 ...
56 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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### 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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### 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: $x(t+1) = Ax + w$ $y(t) = Cx(t) + v$ ...
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### 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 ...