Questions tagged [state-space]

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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:...
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0answers
2k views

Difference between state space and transfer function model response (in Simulink)

Why I get a different response from the same system (e.g. three phase inverter with LC filter) in state space form and in transfer function (Laplace) form when using the same PI controller values ($...
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0answers
145 views

What is right and full Frobenius canonical form?

I'm having a trouble here. I'm supposed to learn Frobenius canonical representation form for finding statespace matrices, but I found many different forms. Let's suppose we have a system with this ...
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0answers
36 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,...
2
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1answer
289 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} ...
2
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0answers
558 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 ...
2
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0answers
59 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 ...
2
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0answers
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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0answers
51 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 ...
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0answers
34 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 $$ \...
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0answers
28 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# ?...
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0answers
68 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 ...
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0answers
31 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,...
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0answers
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: ...
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0answers
70 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 ...
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0answers
80 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 $\textbf{x}$ ...
0
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1answer
36 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 ...
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0answers
29 views

Kalman Filter - combining data from sensors with different measurement rates, does one have a good source where i can get more information about it?

someone already wrote a question about the topic, and thats exactly what i am looking for but i need a source to get more information and to cite from in my work i combine 2 kalman-filter for ...
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0answers
12 views

Very stiff state space matrices after linearizing my Simscape model

I want to simulate and build a furuta pendulum from scratch as a project. Currently I´m having some difficulties with the simulation of my model in Simscape and I can´t figure out what´s wrong with it....
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1answer
91 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 ...
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0answers
40 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 ...
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209 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 ...
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2answers
189 views

How to find derivative of 2-D elliptical Gaussian function with different standard deviations along $x$ and $y$ directions?

I am trying to find the 2-D derivative of an elongated Gaussian density. The Gaussian has standard deviations $\sigma_x$ and $\sigma_y$. How can I get the scale-normalized 2-D Gaussian derivative in ...