Numeric.Estimator.KalmanFilter

This module implements the Extended Kalman Filter estimation algorithm.

Documentation

data KalmanFilter state var

All variants of Kalman Filter, at their core, maintain the parameters of a multi-variate normal distribution.

Since different Kalman Filter variants share this filter type, you can mix and match algorithms within the same filter. For example, you could use a conventional Kalman filter for any linear measurements, and a Sigma-Point Kalman Filter for a non-linear process model.

Constructors

KalmanFilter

Fields

• kalmanState :: state var

  mean

• kalmanCovariance :: state (state var)

  covariance

Instances

GaussianFilter KalmanFilter

Methods

mapStatistics :: (state var -> state' var') -> (state (state var) -> state' (state' var')) -> KalmanFilter state var -> KalmanFilter state' var'

type Var (KalmanFilter state var)

type Var (KalmanFilter state var) = var

type State (KalmanFilter state var)

type State (KalmanFilter state var) = state

data KalmanInnovation obs var

Kalman filter estimators can report the innovation of each observation, as well as the covariance of the innovation.

Constructors

KalmanInnovation

Fields

• kalmanInnovation :: obs var
• kalmanInnovationCovariance :: obs (obs var)

newtype EKFProcess state var

A process model in an Extended Kalman Filter transforms a state vector to a new state vector, but is wrapped in reverse-mode automatic differentiation.

Constructors

EKFProcess (forall s. Reifies s Tape => state (Reverse s var) -> state (Reverse s var))

Instances

(Additive state, Traversable state, Distributive state, Num var) => Process (EKFProcess state var)

Methods

process :: EKFProcess state var -> State (EKFProcess state var) (State (EKFProcess state var) (Var (EKFProcess state var))) -> Filter (EKFProcess state var) (State (EKFProcess state var)) (Var (EKFProcess state var)) -> Filter (EKFProcess state var) (State (EKFProcess state var)) (Var (EKFProcess state var))

Estimator (EKFProcess state var)

Associated Types

type Filter (EKFProcess state var) :: (* -> *) -> * -> *

type Var (EKFProcess state var)

type Var (EKFProcess state var) = var

type State (EKFProcess state var)

type State (EKFProcess state var) = state

type Filter (EKFProcess state var)

type Filter (EKFProcess state var) = KalmanFilter

newtype EKFMeasurement state var

A measurement model in an Extended Kalman Filter uses the state vector to predict what value a sensor should return, while wrapped in reverse-mode automatic differentiation.

Constructors

EKFMeasurement (forall s. Reifies s Tape => state (Reverse s var) -> Reverse s var)

Instances

(Additive state, Distributive state, Traversable state, Fractional var) => Measure (EKFMeasurement state var)

Associated Types

type MeasureQuality (EKFMeasurement state var) (obs :: * -> *) :: *

type MeasureObservable (EKFMeasurement state var) (obs :: * -> *) :: Constraint

Methods

measure :: MeasureObservable (EKFMeasurement state var) obs => obs (Var (EKFMeasurement state var), EKFMeasurement state var) -> obs (obs (Var (EKFMeasurement state var))) -> Filter (EKFMeasurement state var) (State (EKFMeasurement state var)) (Var (EKFMeasurement state var)) -> (MeasureQuality (EKFMeasurement state var) obs, Filter (EKFMeasurement state var) (State (EKFMeasurement state var)) (Var (EKFMeasurement state var)))

Estimator (EKFMeasurement state var)

Associated Types

type Filter (EKFMeasurement state var) :: (* -> *) -> * -> *

type Var (EKFMeasurement state var)

type Var (EKFMeasurement state var) = var

type State (EKFMeasurement state var)

type State (EKFMeasurement state var) = state

type Filter (EKFMeasurement state var)

type Filter (EKFMeasurement state var) = KalmanFilter

type MeasureQuality (EKFMeasurement state var) obs

type MeasureQuality (EKFMeasurement state var) obs = KalmanInnovation obs var

type MeasureObservable (EKFMeasurement state var) obs

type MeasureObservable (EKFMeasurement state var) obs = (Additive obs, Traversable obs)