Adaptive Kalman filtering in Golang

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.

• Kalman filters are based on a state-space representation of linear, time-invariant systems:

x(t+1) = Ad  x(t) + Bd  u(t)

y(t)  = C  x(t) + D  u(t)

Using the standard Kalman filter

// 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.

Results with Rapid Ongoing Stochasic covariance Estimation (ROSE) filter

See example here.

Math behind the Kalman filter

• Calculation of the Kalman gain and the correction of the state vector ~x(k) and covariance matrix ~P(k):

^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):

^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.