Questions tagged [dynamic-system]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
12 votes
6 answers
7k views

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 ...
Ole-M's user avatar
  • 221
8 votes
2 answers
4k views

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 ...
mhirano's user avatar
  • 93
6 votes
1 answer
829 views

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 ...
SuperCodeBrah's user avatar
5 votes
3 answers
785 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 ...
MisterFilter's user avatar
5 votes
2 answers
394 views

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 ...
Jim's user avatar
  • 265
5 votes
2 answers
2k views

Unscented Kalman Filter Equations for Constant Turn Rate and Velocity Process Model

I am learning about Unscented Kalman Filters in Udacity's Self-Driving Car Nanodegree. The UKF is designed to track an object moving under the assumptions of constant turn rate $\ddot\psi$ and ...
farhanhubble's user avatar
5 votes
3 answers
308 views

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 ...
Marcus's user avatar
  • 49
3 votes
1 answer
121 views

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 ...
Lanny's user avatar
  • 33
3 votes
1 answer
650 views

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 ...
Mark Lumar's user avatar
2 votes
1 answer
83 views

Simulation of the discrete linear Kalman filter

I have been working on a Scilab simulation of the discrete Kalman filter which is used as a state observer of the linear dynamic system. The Scilab script for the discrete Kalman filter is as follows <...
Steve's user avatar
  • 395
2 votes
2 answers
113 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 ...
L92MD14's user avatar
  • 21
2 votes
1 answer
1k views

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 ...
LM2357's user avatar
  • 103
1 vote
3 answers
212 views

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&...
Hugo Christ's user avatar
1 vote
1 answer
29 views

How does the state estimate selection work?

I have been solving following problem. I have two open loop state estimators used for estimation of the unmeasurable states of a given linear dynamic system. The first estimator provides estimate $\...
Steve's user avatar
  • 395
1 vote
1 answer
248 views

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 ...
andykl's user avatar
  • 13
1 vote
0 answers
352 views

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-...
axel's user avatar
  • 53
0 votes
1 answer
268 views

How to set initial values of the elements in the covariance matrices in the Kalman filter?

Let's say I would like to use the discrete version of the Kalman filter in a role of a state observer of a linear dynamic system. The observed continuous time domain dynamic system can be described ...
Steve's user avatar
  • 395
0 votes
1 answer
27 views

The least time needed to measure a change of a system and Nyquist rate

We have a system $A$, and I measure that system's state, $s(t)$ using a very accurate probing tool that captures zero noise. The state can be whatever signal, like the voltage, current, etc. Assume ...
rando's user avatar
  • 121
0 votes
1 answer
37 views

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 $...
user47808's user avatar
0 votes
1 answer
363 views

Time invariance and linearity of recursive system

I am confused about the definition of linearity and time invariance of recursive system Given $$y[n] = y[n-1] - y[n-2] - x[n]$$ To test time invariance, we shift the input $x[n]$ for shifting and ...
Morcus's user avatar
  • 141
-1 votes
1 answer
102 views

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^{...
havakok's user avatar
  • 672