Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [dynamic-system]

16 questions
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Kalman Filter - Implementation, Parameters and Tuning

First of all, this is the first time I try to make a Kalman filter. I earlier posted the follwoing question Filter out noise and variations from speed values on StackOverflow which describes the background for this post. This is a typical sample of…
Ole-M
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Kalman Filter State Covariance Matrix for Non Constant Process Noise Matrix in PyKalman

I'm experimenting with the pykalman Python library to learn about Kalman Filters. In the code below, I'm generating a random walk where each step is the last step multiplied by 1 plus some noise: 1 + std_dev. In the first block, the covariance…
SuperCodeBrah
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How Are Unmeasured Properties (Velocity and Covariance of Velocity) Handled with a Kalman Filter?

I'm trying to understand how I can update a Kalman filter with a state variable for position and velocity when I only measure position. I have a covariance matrix of the position measurements. But what does the overall covariance matrix of the…
Jim
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How to Improve the Kalman Filter for Tracking the Periodic Motion of a Car?

I have a quite typical Kalman filter to design. I really read a lot of articles about the design of this filter but the performances of my filter are still quite bad. Here is my situation. I have a small car that does periodic constant motion. This…
Marcus
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How to Reduce Phase Lag Caused by Kalman Filter

Background I have been developing a system using a moving robot with a distance sensor against another robot. I want to control these robots by estimating relative velocity and acceleration derived from the distance sensor. So I'd like to estimate…
mhirano
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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 want to calculate the state $\boldsymbol{x}$ for a…
MisterFilter
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Improving Velocity Estimation Using Multiple Sensors in a Dynamic System

I have a sensor reduction model which gives me a velocity estimate of a suspension system(velocity 1) . This suspension system estimate velocity is used to calculate another velocity(velocity 2) via a transfer function/plant model. Can I use…
Lanny
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Alternatives to offline Kalman filtering

Recently I got into vehicle models and filtering in general and immediately faced with the following question. I have the recorded GPS data from car driving on a highway. However, there is a substantial level of noise present, so I decided to filter…
Mark Lumar
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Check whether a system has memory or not

My question is whether the systems below are memoryless or not: $1.) \ y(t)=K$ where $K$ is a constant $2.) \ y(t) = x(t_0) $ where $t_0$ is a constant So, from the definition I have been using so far (A system is memoryless if its output at a given…
user35508
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Linear approximation of a system described by a logarithm - how?

The system described by a logarithm of any base, let's call it $y(t) = \ln(t)$, is non-linear. Is it possible, by any means (transforms, operators etc.), and for small values of $t$ (for example, $t>0$ and $t\leq 0.5$), to obtain a linear…
Hugo Christ
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Time-Invariant (non)autonomous Systems

Regarding potential distinctions between autonomous, non-autonomous, time-invariant and time-varying systems, I have found out opinions supporting that: autonomous systems are time-invariant and non-autonomous are time-varying, (A treatise on…
axel
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Kalman Filter - Order of Update Step?

I have seen some literature where the covariance is updated first, like $(P_k)^{-1} = (P_k^-)^{-1} + H^T R^{-1} H$, where $P^-$ is the a priori estimate of the state covariance $P$. Then, the updated covariance is used to calculate the Kalman gain…
andykl
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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}…
Steve
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Calculating the output of a pole eigen signal in a difference equation

Let an IAR system be defined by the following difference equation: $$y[n]-\frac{1}{4} y[n-2]=x[n]+3x[n-1]$$ and an input signal $x[n]=(-0.5)^n$. The transfer function is defined as $H^z(z)=\frac{1+3z^{-1}}{1-0.25 z^{-2}}$. The value $z=-0.5$ is a…
havakok
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What does it mean for a dynamical system to be well-behaved?

I have recently stumbled across a paper about learning arbitrary dynamical systems in a spiking neural network. The paper assumes an underlying dynamical system of the form $\dot{x}=f(x)+c(t)$ where $c$ is just a random input and $f$ can be a…
user47808
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