# 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.

411 questions
Filter by
Sorted by
Tagged with
1 vote
16 views

### Can the Kalman Filter process covariance be estimated from measurements?

I'm looking for the simplest possible method for estimating the process noise covariance $\mathbf{Q}$ and measurement noise covariance $\mathbf{R}$ for a Kalman Filter. This is assuming a time-...
1 vote
10 views

### When is the Kalman Filter state (un)observable?

In Rudolf Kalman's seminal paper, the problem of filtering is defined as below (p. 2): We are given signal $x_1(t)$ and noise $x_2(t)$. Only the sum $y(t) = > x_1(t) + x_2(t)$ can be observed. ...
1 vote
63 views

### Which filter is suitable for reducing noise in feature detection?

I have a feature detection algorithm that is called FAST - Feature Accelerated Segmented Test. It's a very fast algorithm for finding feature points, e.g "corners" inside an image. Here is ...
61 views

### How to define Q matrix (covariance matrix for process noise) in EKF

I am implementing an Extended Kalman Filter (EKF). I have developed the model for my system and I know must find the Q matrix. I have searched all over the web and noone explains how to define this ...
1 vote
34 views

### Is it possible to reformulate a Kalman Filter as a Gaussian Markov Random Field?

The generic formulation of a KF uses a set of transitition equations, while the GMRF is typically specified through its mean and precision. However, a simple KF involves Gaussianity and Markov ...
33 views

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? ...
100 views

### Confusion on Error State Kalman Filter reset

I have been reading about kalman filters for IMU and I am confused on the error state formulation. Reading this paper, starting on page 63 and going onto 64 the paper addresses the reset of the error ...
101 views

1 vote
90 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 ...
100 views

### Kalman filter in data fusion

I am very new to Kalman filter. I am doing a project using one sensor the track the sensor's position. I developed 2 methods to solve the position, one in better accuracy and one is less accurate. I ...
52 views

### How to simulate the synthetic data for 2 pole low pass filter for Kalman application?

I was trying to simulate data for a 2 pole low pass filter inorder to solve with kalman filter to estimate the true states. With the below code I was unable to generate true states that look like sin ...
228 views

### Forward problem of Kalman filter causing NaN values during recursion?

\begin{eqnarray} X_k &=& F X_{k-1}+ \omega_k \nonumber \\ Z_k &=& H X_k + \nu_k \end{eqnarray} The first equation is state exploration equation and second one measurement ...
55 views

### Advice for Kalman filter for position with velocity input

I am currently building a Kalman filter to add positions derived from high-sample rate velocity data (from an IMU) to lower-sample rate GNSS data. Normally, I understand you would use acceleration ...
19 views

### UKF vs random sampling/monte carlo error propagation

What are the pros/cons of propagating uncertainty of a system via random sampling the distribution of the current state and refitting a gaussian on the prediction vs using UKF?
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 ...
124 views

### Understanding an adaptative single neuron PID controller

I only know the "vanilla" use of a Kalman filter and I am currently trying to understand an article available here (the algorithm is presented in the 6 first pages) : Adaptive Single Neuron ...
1 vote
254 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 ...
78 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 <...
175 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 ...
1 vote
62 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 ...
374 views

### Getting position data from 9-axis IMU

I want to track the movement of a person in a 2D plane using a 9-axis IMU. The size of the plane in which the movement is not bigger than 6 by 6 meter. The IMU is mounted on the head of the person and ...
1 vote
139 views

### Sensor Fusion of Two Same Type of Data

I have an object moving with sinusoidal motion. I estimate the position of the object using lidar and camera separately. Then I want to fuse these two estimation data in the optimal way. For example I ...
459 views

### Kalman Filter on Sensor Fusion

Assume I have 2 sensors capable of measuring distance to an object of known distance. If I apply a Kalman filter to these 2 sensors, I would have 2 correction and prediction equations. If I have 2 ...
1 vote
130 views

### Initial Process Covariance in 1-D Kalman Filter

Having a bit of confusion about what the initial process covariance (P) should be. Assume a 1-D tracking problem where I am measuring the distance/position of a static object. Would P not just be ...
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 ...
120 views

### Approaches to work around differing signal lengths when using Kalman filter

I have a set of vector valued signals $\boldsymbol{y}_{1:T}$ where each $\boldsymbol{y}_k \in \mathbb{R}^{v_k}$. Each signal is potentially of different dimensionality. I'd like to apply filtering and ...
622 views

### Why does sequential update of Kalman Filter work when you have multiple sensors?

If you are using a kalman filter with multiple sensing sensors there are two ways to fuse them. One way is doing a single observation step where you include all the sensors in a single vector and a ...
1 vote
115 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
144 views

### Derivation of the process noise covariance matrix for non linear system in UKF

I have a continuous (in time) non-linear system in the form $\dot{x}=f(x(t)) + Bu(t) + w(t)$ which I would like to track with a UKF. $w(t)$ represent white noise (in particular, the acceleration and ...
108 views

### Using kalman filter in R for sine wave frequency estimation

I'm pretty new to Kalman filtering techniques, and have a problem that I'm trying to solve. Imagine in a lake I have a splash generator that sends out sine waves across the lake. At various places ...
469 views

### Unscented Kalman Filter for Parameter Estimation (Tracking) of Amplitude Frequency and Phase of a Multi Component Harmonic Signal

I'm trying to implement an Unscented Kalman Filter that tracks the amplitude, frequency, and phase of a multi-component oscillatory signal. Below is an attempt using the ...
70 views

### Wiener filter for vector-valued signal

I'm trying to understand the derivation of a Wiener filter for a vector-valued signal, found in the paper "Kalman filtering in non-Gaussian model errors: a new perspective," IEEE Signal ...
1 vote
229 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
96 views

### Time fusion Kalman filter

Suppose I have a set of estimators, $$\{S^1, S^2, S^3, S^4,\ldots,S^n\}$$ that output at each timestep $t$ a measurement representing an estimate of the true signal $y$, however the output of each ...
75 views

### Example for implementing the unscented kalman filter

Currently, I'm learning about the UKF and in order to understand it in a good way, I programmed it, however in order to see it working I need a problem to solve which I can't now find. Can you please ...
1 vote
181 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
51 views

### Single Kalman Filter: Resistance based on measurment of current and Voltage [closed]

Given measurement of voltage and current, which contain gaussian noise with known variance and a constant unknown offset $a_0$, I have attempted to estimate the resistance $R=\frac{V}{I}$. The ...
124 views

### Interpreting sensor noise data

Introduction :I am trying to create an EKF for an autonomous vehicle, and i need to model the error of the sensors. (I am a mechanical engineer so my knowledge on electric signals is limited). The ...
164 views

### Simulink delay block doesn't recognize vectors as intial conditions

I am trying to implement the kalman filter on simulink, for which I need the delay block to compute the new estimate based on the previous one. My state vector is three dimensional, and for some ...
1 vote
### In particle filter: what is the meaning of $\pi_n(x_n|x_{1:n-1})$?
In the survey article of particle filter A Tutorial on Particle Filtering and Smoothing: Fifteen years later, the equation (39) are  \begin{aligned} \pi_{n}\left(x_{n} \mid x_{1: n-1}\right) &=p\...