# Questions tagged [kalman-filter]

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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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://...
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### 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: $$\xi_t = F_t \xi_{t-1} + v_t$$...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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{...