https://github.com/konimarti/kalman
Adaptive Kalman filter in Golang
https://github.com/konimarti/kalman
filtering golang kalman prediction sensor sensor-fusion
Last synced: 5 months ago
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Adaptive Kalman filter in Golang
- Host: GitHub
- URL: https://github.com/konimarti/kalman
- Owner: konimarti
- License: mit
- Created: 2019-01-30T10:25:54.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2022-03-25T21:50:34.000Z (over 4 years ago)
- Last Synced: 2025-10-07T10:01:12.699Z (9 months ago)
- Topics: filtering, golang, kalman, prediction, sensor, sensor-fusion
- Language: Go
- Homepage:
- Size: 96.7 KB
- Stars: 94
- Watchers: 3
- Forks: 25
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Adaptive Kalman filtering in Golang
[](https://github.com/konimarti/kalman/blob/master/LICENSE)
[](https://godoc.org/github.com/konimarti/kalman)
[](https://goreportcard.com/report/github.com/konimarti/kalman)
```go get github.com/konimarti/kalman```
* Adaptive Kalman filtering with Rapid Ongoing Stochastic covariance Estimation (ROSE)
* A helpful introduction to how Kalman filters work, can be found [here](https://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures/).
* Kalman filters are based on a state-space representation of linear, time-invariant systems:
The next state is defined as
```math
x(t+1) = A_d * x(t) + B_d * u(t)
```
where A_d is the discretized prediction matrix and B_d the control matrix.
x(t) is the current state and u(t) the external input. The response (measurement) of the system is y(t):
```math
y(t) = C * x(t) + D * u(t)
```
## Using the standard Kalman filter
```go
// create filter
filter := kalman.NewFilter(
lti.Discrete{
Ad, // prediction matrix (n x n)
Bd, // control matrix (n x k)
C, // measurement matrix (l x n)
D, // measurement matrix (l x k)
},
kalman.Noise{
Q, // process model covariance matrix (n x n)
R, // measurement errors (l x l)
},
)
// create context
ctx := kalman.Context{
X, // initial state (n x 1)
P, // initial process covariance (n x n)
}
// get measurement (l x 1) and control (k x 1) vectors
..
// apply filter
filteredMeasurement := filter.Apply(&ctx, measurement, control)
}
```
### Results with standard Kalman filter
See example [here](example/car/car.go).
### Results with Rapid Ongoing Stochasic covariance Estimation (ROSE) filter
See example [here](example/rose/rose.go).
### Math behind the Kalman filter
* Calculation of the Kalman gain and the correction of the state vector ~x(k) and covariance matrix ~P(k):
```math
^y(k) = C * ^x(k) + D * u(k)
dy(k) = y(k) - ^y(k)
K(k) = ^P(k) * C^T * ( C * ^P(k) * C^T + R(k) )^(-1)
~x(k) = ^x(k) + K(k) * dy(k)
~P(k) = ( I - K(k) * C) * ^P(k)
```
* Then the next step is predicted for the state ^x(k+1) and the covariance ^P(k+1):
```math
^x(k+1) = Ad * ~x(k) + Bd * u(k)
^P(k+1) = Ad * ~P(k) * Ad^T + Gd * Q(k) * Gd^T
```
## Credits
This software package has been developed for and is in production at [Kalkfabrik Netstal](http://www.kfn.ch/en).