# Questions tagged [kalman-filters]

The Kalman filter is a mathematical method using noisy measurements observed over time to produce values that tend to be closer to the true values of the measurements and their associated calculated values.

409 questions
Filter by
Sorted by
Tagged with
235 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 \...
996 views

### Velocity estimation knowing acceleration and displacement from measurements using Kalman filter

I am having a hard time in trying to use a Kalman filter to obtain velocity from acceleration and position measurements. I think the main reason is that I am not familiar with Kalman filters (I had ...
140 views

### Correct Kalman Filter for Gaussian State Space Model

I am trying to follow a paper where they say they apply the Kalman filter, but don't give the forumulation for the Kalman filter! Moreover I have looked at two references Wikipeadia and Durbin and ...
419 views

### Extended kalman filter for accelerometer data on shaking table

I am using an accelerometer to record the motion of a shake table (a rocking table) which moves forward and backward in one direction. The signal is very noisy and decided to use Extended Kalman ...
402 views

### Kalman Filter: continuous state space, discrete observations

This is just an idea. How can we model the kalman filter to get the state representation in continuous space when the observations to the system are actually from the discrete space. The discrete ...
557 views

### Extended Kalman Filter - how do I get transition functions

I am measuring position and velocity, both have some noise in them. Velocity is defined as derivative of position. The system is apparently non-linear so I need to use EKF. Model: \begin{align} X&...
300 views

### Estimate process error for Kalman filter on financial data

I'd like to apply a Kalman filter, using Octave, to financial data but due to the nature of the data it will be difficult to impossible to specific the process error in advance of applying the filter. ...
1 vote
97 views

### What is the value of $0.01\log_{10}$?

I have posted this question in math.stackexchange.com, [can be found here], which I originally thought it is a math question. I now believe this would fit more to the Signal Processing community. For ...
1 vote
224 views

### Intuition for $\mathbf{P} = \mathbf{0}$ in steady-state when $\mathbf{Q} = \mathbf{0}$ (Kalman filter)

Consider the following discrete-time system: \begin{equation} \mathbf{x}(k+1) = \mathbf{A}_d \mathbf{x}(k) + \mathbf{B}_d \mathbf{u}(k) \end{equation} \begin{equation} y(k) = \mathbf{C}_d \mathbf{x}(k)...
1 vote
1k views

### What is the difference between Kalman filter algorithm and stationary Kalman filter algorithm?

I want to compute the stationary Kalman filter algorithm but I haven't found any information about that algorithm ( not even the pseudo code ) so, I wonder what is the difference between the Kalman ...
1 vote
124 views

### Can the Kalman filter estimate a factor of the model? Product of two state variables

I've written down a discrete state-space model for a simple pendulum, with the state variables angle, angular velocity and angular acceleration. This can be easily plugged into a simple Kalman filter ...
1 vote
2k views

### Kalman filter with multiple sensors

I have been reading more about EKF and I am a bit confused on how you handle predictions with multiple sensors. Ex, I have IMU, GPS, Odom and Stereo Camera. Each can be used to predict location, how ...
1 vote
128 views

### The Stability of the RLS Algorithm for Equalization

I am reading in the litterature that LMS is more stable than RLS. But RLS is far more faster in convergence. So my concern is how to be sure that my RLS algorithm will be stable when I am doing ... 1 vote
637 views

### Getting Vario (m/s) from a bmp180

I am building a variometer as a hobbie, this could be a duplicate from an existing question: How to use Kalman filter for altitude prediction based on barometer data? . Details follow: I have a ...
1 vote
1k views

### Discrete Kalman filter for a continuous system

The question is related to the implementation of a discrete kalman filter given a description of the system model in continuous time. I will give an example. Suppose we have a mass, spring and damper ...
1 vote
348 views

### Should I pass Kalman Filter absolute or offset-from-mean sensor values?

I'm using Kalman filters to segment the loudness of an acoustic signal from surrounding noise. The problem I've encountered is that muffled or faulty microphones measuring 'silence' (-70dB, -69dB, -...
1 vote
3k views

### Using Kalman Filter to fuse two sensor readings of the same type

I have always used Kalman Filter to smooth a signal comes from one sensor only. I would like to know if Kalman Filter could be used to fuse data coming from two different sensors that provide the ...
1 vote
945 views

### Apply Kalman filter to remove process noise, given zero measurement error

I have a recording, corrupted by environment noise. The measurement noise is zero. How can I use Kalman filter to remove environment noise? I tried this Matlab code here but if the measurement error ...
1 vote
1k views

### Kalman filter, defining the measurement model

I would like to implement a Kalman filter to estimate the velocity and position of an object. I have an accelerometer, therefore the acceleration is known. The approach is same as: Kalman filter for ...
1 vote
2k views

Hi everybody. I'm very new in Kalman filter. Today I try to design Kalman filter to get estimated postion, velocity and acceleration from measurement position (by linear encoder). I don't use optimal ...
1 vote
89 views

### How to generate ground truth in constant velocity Kalman simulation?

I'm trying to simulate a particle going from (-3,0) to (3,0) with a constant velocity and some noise (e.g. the particle is a quadcopter trying to fly at constant velocity, but may be pushed by gusts ...
1 vote
34 views

### Finite Difference Estimation for error propagation

For a complex system where symbolic computation of the jacobian is challenging, is estimating the jacobian via finite difference a viable option? To be explicit I'm mostly interested in playing around ...
1 vote
114 views

### IMU state estimation Covariance updating

EKF filter normally has a predict + update step, I am curious - how do you evolve the covariance of the state without one of the steps? In essence I want to evolve the state of an object using an IMU ...
1 vote
177 views

### EKF: IMU vs State Transition Model

Suppose you have an object you're interested in estimating the state of, ex position. Suppose you don't have a state transition model but you do have an IMU. Can the IMU be used to simulate a state ...
1 vote
82 views

### How does sampling jitter affect state estimation?

Suppose I have some process which is governed by: $$\vec{x_{k+1}} = A\vec{x_k} + B\vec{u_k} + w_k$$ where $u_k$ is the input, and $w_k$ is process disturbance. This process is continuous time in ...
1 vote
73 views

### Does a gyroscope get impacted by gravity?

When processing IMU data, does the gyroscope get impacted by gravity? Linear accelerometers need to have gravity compensation but nothing is said of IMU.
1 vote
260 views

### Kalman filter continues to update position even though speed is zero

Background I set up a conventional Kalman filter that makes use of smartphone GPS only (no inertial sensors). That is, it uses the position, doppler speed, and course, in order to create positions ...
1 vote
86 views

### Is Kalman Filter for LTV systems applicable on Hybrid systems?

As all of us know Kalman Filter is designed for LTV (Linear Time Variant) systems. But nobody in the literature applies that on Hybrid systems. In my opinion Linear Hybrid systems are a subset of ...
1 vote
131 views

### What is the name for a constant-heading Kalman filter model for vehicle tracking?

When applying Kalman filtering to estimate the position of a car, there are several different vehicle dynamics models that you could use. One of the simplest is "constant velocity" or CV, ...
1 vote
56 views

### Can a Kalman Filter Be Applied Using Measurement-Space Dependent Sensors?

I'm currently attempting to apply a Kalman filter to track the angular position, velocity, and acceleration of a bike wheel, and I'm having a lot of trouble, so I want to check if I'm even applying ...
1 vote
82 views

### Why is the concept of a "state covariance matrix" necessary in estimation?

I'm currently taking a course in optimal estimation (and it's still very early in the course). Much of our work is based around the idea of a measurement model $y=Hx + v$ This model assumes our ...
1 vote
103 views

### 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 ...
1 vote
1k views

### Implementing a 1-D Kalman Filter Regression, Missing the smoothing action (getting the opposite)

I am implementing the 1D Kalman Filter in Python on a fundamentally noisy set of measurement data, and I should be observing a large amount of smoothing...but, instead, my Kalman Filter is doing the ...
1 vote
2k 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: $x(t+1) = Ax + w$ $y(t) = Cx(t) + v$ ...
1 vote
1k views

### Relation between Kalman filter and Sequential linear MMSE estimation

Are the results of applying Kalman filter and recursive linear MMSE estimation process the same ?
1 vote
74 views

### Gyroscope Error Propagation: Why not use Euler Angles?

Looking at the EKF formulation for Gyroscopes in more depth I'm wondering, why can't we use Euler Angles in the Error State EKF framework for error and covariance propagation instead of Quaternions? ...
1 vote
245 views

### Kalman Filter - Comparing the Static Kalman gain and the Dynamic/Recursively updating Kalman Gain

I studied Kalman filters some time ago, and recently came to realize I do not understand some parts on them. Specifically related to the difference between using a static Kalman-gain, found by ...
1 vote
60 views

### What are the Kalman filter capabilities for the state estimation in presence of the uncertainties in the system input?

I have a question regarding the capabilities of the discrete Kalman filter for estimation of the unmeasurable state variables of a dynamic system. In the time being I have been using a discrete ...
1 vote
72 views

### What's the best way of modeling 3d target motion with only 2d angle observations?

A maneuvering target is flying in 3d cartesian space, but a sensor (passive infrared or mic array, etc.) can only observe it in polar coordinate with 2d orientations (azimuth, elevation). For ...
1 vote
180 views

### Kalman filtering with dynamic covariance/variance

What is the appropriate way to implement KF if your sensor confidence is time and observation dependent? Ex, you asses the quality of camera tracking by the percentage of features correctly matched by ...
1 vote
659 views

### If there are state variables in the Kalman filter that aren't being measured, is their output just rubbish?

I've been learning about the Kalman filter on this website: https://www.kalmanfilter.net/multiExamples.html As you can see there is a numerical example regarding a car that is traveling in a 2 ...
1 vote
537 views

### How to initialize observation Matrix in Kalman Filter when there is no clear relationship between measurement and state?

I am try to use Linear Kalman to do time series prediction. I understand that I have to define a model process matrix which indicate how system state evolve, and a measurement matrix H which convert ...
1 vote
1k views

### Kalman filtering for position using GPS,accelerometer and speed sensors

I am working on tracking a vehicle under tunnel when GPS is lost. Whenever the vehicle in on the road, the GPS works fine and gives good accuracy but when the vehicle is under tunnel, the GPS is lost ...
1 vote
65 views

### Tracking movement of audio speaker driver using images

I have a speaker emitting low-frequency sinusoidal wave and I have physically marked a curved edge on the speaker driver as shown in red in the image below, which I would like to track: I detect the ...
1 vote
699 views

### Reduce Jitter in Live Kalman Filter

I have a stream of data over time that I have fed into a Kalman filter. This data represents the vertical displacement in time of a vehicle's rearwheel as it travels over a bump in the road. The ...
1 vote
501 views

### why does DFE feedback filter matters?

I recently came across an article on the inventor of adaptative equalizer Robert Lucky, In this article : An Oral History by Robert Lucky (http://www.ieeeghn.org/wiki/index.php/Oral-History:...
1 vote
278 views

### Fuse two sources of linear acceleration with a Kalman filter

How would I fuse two different sources of linear acceleration with a Kalman filter (perhaps linear acceleration readings from an IMU and from a dedicated accelerometer)? My state is defined by ...
1 vote
345 views

### Kalman Filter Process Noise - Model Where It Vanished

I am trying to use the Kalman filter (the scalar version) to estimate the steady state of a set measurements which is a random process. I have used a constant dynamic model as the state equation,  ...
1 vote
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 ...