Questions tagged [kalman-filter]

For questions about Kalman filter.

Filter by
Sorted by
Tagged with
1 vote
1 answer
19 views

How to perform a matrix rotation of an information matrix

Within the Information Filter, the "inverse" of the Kalman Filter, resides the Information Matrix $Y$, which is itself the inverse of a covariance matrix, $P$, such that $Y=P^{-1}$. Now, as ...
user avatar
0 votes
0 answers
13 views

How can I calculate new latitude, longitude and height using initial coordinates, roll, pitch yaw and distance?

I have initial GPS coordinates of an object. I have an IMU and an odometer which are able to give me roll, pitch, yaw and distance. How can I use this data to calculate the new GPS coordinates? I ...
user avatar
  • 1
0 votes
0 answers
5 views

Is the state estimation error covariance matrix of the Kalman filter positive definite?

I'm reading through some papers about Kalman filter, and it seemed that the state estimation error covariance matrix is positive definite, but by definition PK|K=(I-KH)PK|K-1, I don't understand why ...
user avatar
0 votes
0 answers
51 views

Observability of non linear system using lie derivative

I want to design an EKF for a project, and i want to check the observability, in order to decide the sensor layout. I do not know about lie derivatives and lie algebra, but i with some research i ...
user avatar
0 votes
0 answers
6 views

What’s the autocovariance between two states in the kalman filter?

So I’m trying to work out the auto covariance of subsequent states in a Kalman filter (assuming HMM gaussian). I’ve found a paper which defines it (see Autocovariance) - link to paper: https://...
user avatar
0 votes
0 answers
14 views

Kalman Filter Time Varying Parameter

I have a simple doubt regarding time varying coefficients Kalman Filter. Lets consider Hamilton's notation for the state equation and transition equation, respectively: $$\xi_t = F_t \xi_{t-1} + v_t $$...
user avatar
  • 83
0 votes
0 answers
19 views

Are Kalman Filter innovations and state errors independent?

I have questions about the Kalman Filter. I know that the Kalman Filter residual is independent with the state error, which are defined as: Kalman Filter residual : $r_k=z_k - H_k x ̂_k^+ $ state ...
user avatar
0 votes
0 answers
10 views

Infinite Standard Deviation with Kalman Filter

I'm using a Kalman Filter code on Matlab that produces the results of Stock and Watson 1991 with some macroeconomic variables, GDP and a soft indicator to forecast the economy of a country (everything ...
user avatar
  • 21
1 vote
0 answers
48 views

Model is observable, but why doesn't the EKF implementation converge to correct values?

I have a vector field (unable to provide the details, unfortunately) $$\frac{dx}{dt} = f(x,u)$$ and measurements $$y = g(x,u)$$ Linearizing around any $\bar{x}$ and $\bar{u}$, I verified that the ...
user avatar
  • 151
0 votes
0 answers
23 views

Extended Kalman Filter: Measurement equation and Covariance Matrix

i am trying to implement an EKF for orbit determination of a spacecraft. The state which i am interested to estimate is $x = [r_{SC}\, v_{SC}\, \Delta Cd\, \Delta Cs\, b, d]$, where $\Delta Cd\,,\...
user avatar
2 votes
1 answer
33 views

Does the Bayes-Filter perform a convolution in the prediction step?

I am watching the (fantastic) SLAM lectures of Claus Brenner, where he introduces the Bayes-Filter (Kalman-Filter, Particle-Filter, Histogram-Filter). He says, that the prediction step involves the ...
user avatar
0 votes
0 answers
22 views

State error propagation of ODE with uncertain parameters

I have an idea on how to integrate uncertainty of the parameters of an ODE in the state error propagation. But I am unsure if my idea is correct. I have a non-linear ODE of the form: $$ \frac{d}{dt} \...
user avatar
0 votes
0 answers
18 views

Chained Kalman Filters

I have read the term “chaining Kalman filters” and I wanted to know precisely what the chained form of a Kalman filter is. I’ve seen also the term dual Kalman filter framed as a different concept ...
user avatar
  • 145
0 votes
0 answers
21 views

Is it possible to use a chunk of observations instead of one observation in Recursive Least Squares (RLS) at once?

Recursive Least Squares (RLS) by its structure reestimates coefficients iteratively utilizing one new observation in each iteration. Is it possible to use $n$ new observations in one iteration to ...
user avatar
1 vote
0 answers
22 views

Variance convergence in Kalman Filtering when applying motion and measurements updates?

I'm developing a visualization interface for Kalman Filters in 1D. I have an initial variance $variance\_init$ and constant motion and measurement variances. When I apply consecutive motion-...
user avatar
0 votes
0 answers
30 views

Vectorization of the Extended Kalman Filter Gain Equations

I was trying to vectorize the extended Kalman Filter equations, I got the Kalman gain equation vectorized and got it working for a very niche case (where only 1 measurement is available). Originally: $...
user avatar
1 vote
0 answers
33 views

Kalman Filter with measurement delays (Out of Sequence Measurement Problem)

I have an understanding of how the Kalman Filter (as well as some of its nonlinear extensions like EKF and UKF) works as a linear estimator for a task such as tracking an object. With real world ...
user avatar
  • 145
0 votes
0 answers
11 views

Extracting Covariance matrix from Expected value

I am studying multivariate Kalman Filter and came across the following explanation for $𝔼[(𝐱−𝜇)(𝐱−𝜇)^𝖳]$: $\ 𝐏 = 𝔼[(𝐅𝐱−𝜇)(𝐅𝐱−𝜇)^𝖳]$ $\ = \mathbf{𝐅} 𝔼[(𝐱−𝜇)(𝐱−𝜇)^𝖳]𝐅^𝖳$ ...
user avatar
  • 131
1 vote
0 answers
25 views

Incredibly low standard errors

I am currently estimating the parameters of an interest rate model by means of a maximum likelihood estimation in combination with the iterated extended Kalman filter, and I obtain incredibly low ...
user avatar
  • 11
0 votes
0 answers
23 views

What are the equations of the matrix state for the Extended Kalman Filter?

I unfortunately I don't know very wall the system theory and in particular the Kalman Filter, so I would like to ask you a question. I have GPS data and IMU data. GPS data gives me latitude, longitude,...
user avatar
0 votes
1 answer
24 views

Meaning of left multiplying a matrix A with another B and then right multiply the result with a transposed B?

I am currently in the process of learning Kalman Filters and facing the following Equations: $$\vec x_k = F\vec x_{k-1} + B\vec u_k$$ $$P_k = FP_{k-1}F^T + Q$$ $\vec x_k$: state vector. $P_k$: ...
user avatar
0 votes
1 answer
24 views

What dynamic model is used for the prediction step when designing a Kalman filter to compute absolute orientation from a 9dof sensor?

(first: if you think this should be moved to another StackExchange where it would fit better, just let me know!). I think that I understand relatively well the concepts behind Kalman filters, and that ...
user avatar
  • 121
4 votes
1 answer
114 views

Whiteness hypothesis in Kalman filtering

In Kalman filter mathematical treatment I have always read that a foundamental hypothesis is represented by the whiteness of the process noise. I have tried to do again the mathematical steps in the ...
user avatar
0 votes
0 answers
36 views

Calculate kalman filter

I have covariation matrix of every measure $$\Sigma _{m}: $$ [[8, 0, 0, 0], [0, 8, 0, 0], [0, 0, 4, 0], [0, 0, 0, 4]] covariation matrix of current state $$ \...
user avatar
0 votes
1 answer
46 views

When should I use a kalman filter, if the observability function is known?

Assume that we have a nonlinear dynamical model, e.g called transition function $$\hat x = f(x, u)$$ And $y = x$ as our observability function. According to Mathworks Kalman filters are used to ...
user avatar
  • 2,531
0 votes
1 answer
34 views

How to fuse inertial and optical tracking data with an error-state kalman filter, and provide pose estimations for both update types?

I am searching for an error-state kalman filter that is able to fuse inertial and optical tracking data but provides pose estimates for both optical and inertial updates. Currently I am using the ...
user avatar
1 vote
0 answers
29 views

Is it possible to apply a Kalman filter to a 2D thermal problem?

I have a transient thermal problem: I've created a 2D geometry with two different materials, I've put in an internal source, I've mashed it and solved the PDE. After a t time I can see how the ...
user avatar
0 votes
0 answers
25 views

Interest rate modelling: Iterated extended kalman filter with Maximum Likelihood

I recently started to deepen my knowledge about interest rates' modelling, and I am trying to estimate a two-factor Ornstein–Uhlenbeck process using Euro area OIS rates by means of an Iterated ...
user avatar
  • 11
2 votes
0 answers
64 views

Does * mean transpose in some scientific reports?

I'm reading this report about Square Root Kalman Filter and I'm stuck at the line $$S_k^- = qr\left \{\left [ \sqrt{W_1^{(c)}} \left ( \chi^*_{1:2L,k|k-1} - \hat x_k^- \right ) \sqrt{R_v} \right ] ...
user avatar
  • 2,531
1 vote
0 answers
59 views

Using Unscented Transformation with Quaternions (Unscented Kalman Filter)

I have a standard UKF with quaternions. Lets suppose that in the state vector I have mixed coordinates of elements from the "normal" vector-space (v) and not (quaternion q representing ...
user avatar
0 votes
0 answers
44 views

Kalman Filter with Non-Constant Acceleration

I want to model my state space using the following model: $$ a_{t} = a_{0} e^{-\alpha t} + \sqrt{2 \alpha \sigma^2} \int_{0}^{t} e^{-\alpha(t-s)} d W_{s} $$ $$ v_{t} = v_{0} + \int_{0}^{t} a_{s} ds ...
user avatar
  • 1,015
1 vote
0 answers
58 views

Derivation of the Kalman filter prediction step

I've been working through Murphy's Machine Learning A Probabilistic Perspective and have had a slight issue with the section on the Kalman Filter. As a setup we're assuming a linear-Gaussian state ...
user avatar
  • 1,805
1 vote
0 answers
38 views

Kalman Filter using Batch Time Series

I have a non-linear problem that I have solved using EKF. However, the solution requires that the time series is input 1 sample at a time and that is not possible. I want to model the KF in such a way ...
user avatar
  • 11
1 vote
0 answers
41 views

Using parameter estimation for training a neural network

Assume that we have 4 layers in a neural network. $$z_1 = L_1(x, W_1)$$ $$z_2 = L_2(z_1, W_2)$$ $$z_3 = L_3(z_2, W_3)$$ $$y = L_1(z_3, W_4)$$ Where $x$ is the vector input, $y$ is the vector output ...
user avatar
  • 2,531
1 vote
1 answer
88 views

Circular data problem for Kalman filter

I've been trying to implement a Kalman filter to get estimates of current heading (angle) of a vehicle by performing a sensor data fusion (GPS + IMU). The GPS sensor provides heading information $\...
user avatar
  • 11
1 vote
0 answers
30 views

Is this "predictor" equivalent to the typical Kalman filter?

In "Introduction to Stochastic Control" by K. Astrom, page 228 Theorem 4.1, he introduces a state estimator for the discrete-time system: $$ \begin{aligned} x(t+1)&=\Phi x(t)+v(t)\\ y(t)&...
user avatar
0 votes
0 answers
96 views

How do you convert the covariance matrix of a 3D rotation error-state to the covariance matrix of the corresponding quaternion?

I'd like to convert the covariance matrix of an error-state Kalman Filter that uses Euler angles to the corresponding covariance matrix of a quaternion state. I basically use this for standard INS-...
user avatar
  • 11
1 vote
1 answer
50 views

Unscented Kalman Filter weightings

I'm trying to understand the weightings used in the Unscented Transform, as part of the Unscented Kalman Filter. The transformation uses weightings in the calculations of the mean and covariance. By ...
user avatar
  • 13
0 votes
1 answer
33 views

Why we use the expectation conditional on signal one period before as the estimation of state variable in Kalman filter?

Consider a simple state space model $$x_{t+1}=Ax_t+C\omega_t\\ y_t=Gx_t+v_t $$ Besides the orthogonal assumption for $w_{t+1}$ and $v_t$, we assume that $w_{t+1}\sim N(0,I)$ and $v_t\sim N(0,R)$. We ...
user avatar
  • 1
0 votes
0 answers
32 views

Can I use g-h Filter (Alpha-Beta filter) for control system to model things like cruise control

I'm working on a problem to simulate(& implement) a cruise control like system on an indoor bicycle trainer and I've been told to look at g-h filter but I'm having issues w/ the formula and/or ...
user avatar
  • 101
2 votes
1 answer
68 views

Kalman Filter with Missing Measurement: UB and LB on error covariance matrix

I consider 2 linear Kalman filters (KF) that follow periodic cycles as shown here: KF(1) : Receive 1 measurement at time $k$, No measurements at time $k+1$, Receive 1 measurement at time $k+2$, No ...
user avatar
  • 21
0 votes
0 answers
21 views

Are there different ways to make the Kalman filter differentiate data?

I have a kalman filter that estimate 3D position I have in my state position, speed and acceleration. I only have speed readings so I use it as a measurement update and for the acceleration I get it ...
user avatar
  • 1
0 votes
1 answer
54 views

Can the transition function for Kalman Filter be a random normal distributed variable?

One simple question about Kalman Filters. It's told that you need a model of the system to estimate the next measurement, e.g state. The model is called a transition function. $$\dot x = f(x, u)$$ ...
user avatar
  • 2,531
1 vote
0 answers
23 views

Kalman gain derivation, how to prove that minimization problem is convex?

I follow www.kalmanfilter.net to try derivation kalman filter my self. I've notice that the cost function is SSEs which clearly convex. but look at "Differentiate the trace of Pn,n with respect ...
user avatar
  • 111
0 votes
0 answers
26 views

Quantitative comparison Kalman filter VS Least squares

I've been asked to give a quantitative confirmation of the Kalman filter that I develop. My obvious first idea was to compare the residuals. $$ \chi = {\lvert\lvert C \hat x - y \rvert\rvert}_2^2 $$ ...
user avatar
  • 11
1 vote
1 answer
59 views

Calculating Marginal Probability of the product of two Gaussian PDFs

The problem I am interested in is as follows: Let $$ P(x_k|x_{k-1}) \sim\mathcal{N}(F x_{k-1}, Q)\\ P(x_{k-1}|z^{k-1}) \sim \mathcal{N}(\mu, R) $$ I would like to calculate $$ P(x_k|z^{k-1})=\int_{x_{...
user avatar
  • 357
0 votes
0 answers
79 views

Why does covariance $P$ matrix become non positive definite in Unscented Kalman Filter?

I'm doing Unscented Kalman Filter in MATLAB code and I have followed this tutorial how to create one. First I initilize the $\hat x$ vector and covariance $P$ matrix first. In MATLAB code, I just set ...
user avatar
  • 2,531
0 votes
1 answer
57 views

Bias in process noise covariance matrix

Assume I have the following gyroscope model in the continuous time: $ \begin{bmatrix} \dot{\theta} \\ \dot{\omega_{bias}} \end{bmatrix} = \begin{bmatrix}0 & 1 \\ 0 & 0\end{bmatrix} \begin{...
user avatar
  • 29
0 votes
1 answer
29 views

Is it possible to generate multi-step forecasts with the Kalman Filter (KF)? [closed]

I wanted to double check with the community but I think I already have the answer to this question. Can the KF (or its variants such as the ensemble KF) produce meaningful multi-step forecasts? My ...
user avatar
1 vote
0 answers
47 views

Mixing Least squares and Kalman fitler

I'm not sure it is the right department. I try my chance I am wondering if there is a way to make a hybrid formulation of a least-square problem and a Kalman filter. Let me explain what I mean: The (...
user avatar
  • 11

1
2 3 4 5
8