# 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 ...
8k 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 ...
179 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-...
2k 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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### 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 ...
203 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 ...
6k 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 ...
169 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 ...
186 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. ...
257 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 ...
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 ...
273 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 ...
617 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., ...
102 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 ...
236 views

### State-Space Representation of Forward and Backward Filters

In , the author shows an efficient way of implementing the forward and backward filter using matrices. One can also implement this using filtfilt command in ...
598 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 ...
73 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 ...
123 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:...
2k views

734 views

### The two types of stability and “Why exponential”

When I was learning about LTI systems, I noticed that LTI system is said to be BIBO stable if and only if its square sum of impulse response is finite. This expression is found on many textbook of ...
155 views

### Doubt in state space representation

$y$ is scalar observations and so C will be a 1x2 matrix. I want to represent the following model as a state space representation so as to estimate the hidden states from the noisy observations $y$ ...
1k views

### 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: $x(t+1) = Ax + w$ $y(t) = Cx(t) + v$ ...
664 views

### Does the system matrix being singular tell us anything about the system?

If we have a linear system, represented in State Space and the A matrix is singular (det(A) == 0), can we expect any special properties from the system?
42 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 ...
66 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 ...
29 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,...
8 views

### State Space model of a differential eqn. for use in Least Squares

The code in this page solves the Least Squares problem for the following dynamic model: $\dot{y}=ay+bu$ where $a$ and $b$ are constants, $u$ is an input. The code is as follow: ...
62 views

### Identifiability for Time Invariant State Space Models

Kevin Murphy's Kalman Filter toolbox (for Matlab) contains an example where it's the fact that the state space system in not identifiable causes problems. I include the example in it's entirety but ...
77 views

### Simulating a state space model

I want to simulate data from the following model: $\textbf{z}_k=\textbf{H}\textbf{x}_k+\textbf{v}_k$ $\textbf{v}_k \sim N(\textbf{0},\textbf{R})$ $\textbf{H}$ does not change over time $\textbf{x}$ ...
314 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 ...
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 ...