# Tagged Questions

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.

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### (Unscented) Kalman Filter with variable state dimensions

i have to estimate a process which changes over time, not with respect to the system-evolution or the measurement-function, but regarding the number of objects that have to be estimated. So every ...
2answers
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### Smoothing data by using Kalman filter

I would like to ask about smoothing data by using Kalman filter. Due to quantization, I have data that is not smooth. How can I smooth this data by using Kalman Filter. For your information, the data ...
1answer
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### More on: Kalman filter for position and velocity

Thanks to everyone who posted comments/answers to my query yesterday (Implementing a Kalman filter for position, velocity, acceleration ). I've been looking at what was recommended, and in particular ...
1answer
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### Implementing a Kalman filter for position, velocity, acceleration

I've used Kalman filters for various things in the past, but I'm now interested in using one to track position, speed and acceleration in the context of tracking position for smartphone apps. It ...
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### 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 ...
1answer
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### information filter instead of kalman filter approach

I read many sources about kalman filter, yet no about the other approach to filtering, where canonical parametrization instead of moments parametrization is used. So I would like to learn on examples ...
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### Sequential processing of uncorrelated measurements in Kalman Filter

I'm starting to brush up on the Kalman Filtering I learned a couple decades ago. From what I remember, if you have a measurement vector $$z=H x + v$$ and the $n$ components of the measurement ...
1answer
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### Is Kalman smoother symmetric in time?

Suppose my model is reversible in time (e.g. GPS + accelerometers for a vehicle), so that I can run Kalman filter forwards or backwards. Kalman filter, of course, cannot be symmetric, because it is ...
1answer
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### How to combine a perfect signal with a limited dynamic range with a poor one with high dynamic range?

I have two sensors that measure speed $v(t)$ of a moving vehicle. The first sensor produces a signal $f(t)$ which is a very accurate estimation of speed. However, it only works for slow to moderate ...
2answers
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### Can Kalman Filter be used to track Randomly Moving Target?

i want to track random moving object with a camera using kalman filter...i have the following questions... Randomly moving target means $Corelation(t) = E[ x(T)x(T+t) ]$ is very low...where $x(T)$ ...
1answer
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### estimation of the position of the magnetic source

I have a flying robot with magnetic coil as a sensor. An output from the coil is measured every second in different position. I know the position of the coil and its angles. I need to estimate the ...
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### Optimal inference for nonlinear state space models

When considering a linear-Gaussian state space model, it is often referred that, optimal inference is tractable which is very rare in state space models. When considering a nonlinear state space ...
1answer
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### Doubt on Weighted Least Square Estimation

This is a page from the book linear algebra,geodesy and gps by Gilbert Strang.... the page explains about the justification of the inverse of the of the co variance matrix of measurement vector $b$ ...
2answers
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### Least Square Error Estimation doubt when can we write $(A^TA)^{ -1} = A^{-1}(A^T)^{-1}$?

I am new to linear algebra and have this simple question... in least sqaure estimation...the best estimation of the equation $Ax = b$ is $x_{Estimated} = A (A^t A )^{-1} A^t b$...the projection of $b$ ...
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### Good book or reference to learn Kalman Filter

I am totally new to the Kalman filter. I've had some basic courses on conditional probability and linear algebra. Can someone suggest a good book or any resource on the web which can help me can ...
2answers
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### Estimating velocity from known position and acceleration

I am stuck at modeling a system model, i.e. getting my state vector and input vector. My guess is that position and velocity are state vector and acceleration is input vector. My 2nd guess is that all ...
1answer
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### Kalman filter in practice

I have read the description of the Kalman filter, but I am not clear on how it comes together in practice. It appears to be primarily targeted at mechanical or electrical systems since it wants linear ...
2answers
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### When to use EKF and when Kalman Filter?

I'm learning Kalman Filter for a week now. I just discovered that EKF (extended Kalman Filter) might be more appropriate for my case. Le't suppose I'm applying KF/EKF for variometer (the device that ...
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### Estimating the input to a system from a system state using EKF

[ Cross-posted from: http://math.stackexchange.com/questions/164169/estimating-the-input-to-a-system-from-a-system-state ] I have a system for which I have obtained a non-linear time-varying ...
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### 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: Questions: ...
1answer
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### Role of Kalman filter in nonlinear dynamics

I am quite interested to know the significance of using kalman filter,unscented kalman filter and extended kalman filter in chaos synchronization when infact the very basics of chaos ...
2answers
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### Kalman filter - implementation and deciding parameters

First of all, this is the first time I try to make a Kalman filter. I earlier posted this thread on stackoverflow which describes the background for this post. This is a typical sample of values I'm ...
1answer
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### Filtering difference of correlated measurements

I have an application with two separated GPS receivers giving live positions and I'm deriving a heading/displacement from the vector between them. Each set of position measurements is noisy and has ...
0answers
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### Statistical properties of the Kalman estimates under Gaussian noise

For a linear state-space model with independent Gaussian state and output noises and perfect guess for initial state, do Kalman estimates have the following properties:  E(\hat{x}_{k|k} - x_k) = 0 ...
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### Optimal measurement model for Kalman in Augmented Reality

I am developing an augmented reality SDK that uses Kalman for tracking a planar marker. My state is composed of 3D position, a quaternion, velocity and angular velocity. ...
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### What is the relationship between Kalman filter and polynomial regression?

What is the relationship, if any, between Kalman filtering and (repeated, if necessary) least squares polynomial regression?
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### How to understand Kalman gain intuitively?

The Kalman filter algorithm works as follows Initialize $\hat{\textbf{x}}_{0|0}$ and $\textbf{P}_{0|0}$. At each iteration $k=1,\dots,n$ Predict Predicted (a priori) state estimate ...
2answers
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### Different state-space representations for Auto-Regression and Kalman filter

I see that there are different ways to write an AR model into a state-space representation, so that we can apply Kalman filter to estimate the signal. See Example 1, 2 and 3 here. I wonder what ...
4answers
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### Intuitive explanation of tracking with Kalman filters

I would much appreciate an intuitive explanation for (visual) tracking with Kalman filters. what I know: Prediction step: Dynamic system state Xt: target ...
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### 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. ...
1answer
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### How to derive the stationary Kalman filter predictor?

In its chapter on Kalman filters, my DSP book states, seemingly out of the blue, that the stationary Kalman filter for a system \begin{cases} x(t+1) &= Ax(t) + w(t) \\ y(t) &= Cx(t) + v(t) ...
2answers
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### Is a Kalman filter suitable to filter projected points positions, given Euler angles of the capturing device?

My system is the following. I use the camera of a mobile device to track an object. From this tracking, I get four 3D points that I project on the screen, to get four 2D points. These 8 values are ...
2answers
388 views

### Should the input of a Kalman filter always be a signal and its derivative?

I always see the Kalman filter used with such input data. For example, the inputs are commonly a position and the correspondent velocity: $$(x, \dfrac{dx}{dt})$$ In my case, I only have 2D ...
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