PINE LIBRARY

Kalman Filter

Kalman Filter

Joint-state Linear / EKF / UKF steps for CV and CA price filters. Helpers private; consumer owns buffers and noise inputs.

Exported functions

initFilter() — initialize state mean and diagonal covariance from the first measurement
linearStep() — one linear joint-state KF predict/update (level observation)
ekfStep() — one extended KF step with velocity damping
ukfStep() — one unscented KF step with the same nonlinearity (falls back to EKF if Cholesky fails)

Matrix helpers, Jacobian, and sigma-point utilities stay private inside the library.

Usage

The consumer owns var state/covariance buffers and workspace arrays, then calls a step each bar:

[code]
//version=6
indicator("Example", overlay = true)
import igor_sinkovec/kalman_filter/1 as kf

var float[] x = array.new_float(3, na)
var float[] P = array.new_float(9, 0.0)
var float[] xpred = array.new_float(3, 0.0)
var float[] Ppred = array.new_float(9, 0.0)
var float[] F = array.new_float(9, 0.0)
var float[] Ft = array.new_float(9, 0.0)
var float[] tmp = array.new_float(9, 0.0)
var float[] K = array.new_float(3, 0.0)

int n = 2
if barstate.isfirst or na(array.get(x, 0))
kf.initFilter(x, P, n, close)

float filtered = kf.linearStep(x, P, n, close, 0.01, 0.001, 0.0, 3.0, xpred, Ppred, F, Ft, tmp, K)
plot(filtered)
[/code]

Important notes

Consumers wire observation noise, process-noise diagonals, and UKF (α, β, κ) themselves.
Buffers use a fixed 3×3 row-major layout (9 covariance slots) even when n = 2.

Licence

© igor_sinkovec — Mozilla Public License 2.0.

Library "kalman_filter"

initFilter(x, P, n, z)
Initialize joint-state mean and covariance (level = z, other components 0; diagonal P = 1).
Parameters:
x (array<float>): State vector buffer (length >= 3)
P (array<float>): Covariance buffer (9 elements, row-major 3x3 layout)
n (int): State dimension: 2 (CV) or 3 (CA)
z (float): Initial measurement (level)
Returns: Initial level z

linearStep(x, P, n, z, q0, q1, q2, R, xpred, Ppred, F, Ft, tmp, K)
One linear joint-state Kalman predict/update step (level observation).
Parameters:
x (array<float>): State vector (in/out)
P (array<float>): Covariance (in/out)
n (int): State dimension: 2 or 3
z (float): Measurement
q0 (float): Process noise (level)
q1 (float): Process noise (velocity)
q2 (float): Process noise (acceleration; used when n = 3)
R (float): Measurement noise
xpred (array<float>): Workspace: predicted state
Ppred (array<float>): Workspace: predicted covariance
F (array<float>): Workspace: transition matrix
Ft (array<float>): Workspace: F transpose
tmp (array<float>): Workspace: matrix multiply temp
K (array<float>): Workspace: Kalman gain
Returns: Filtered level

ekfStep(x, P, n, z, dmp, q0, q1, q2, R, xpred, Ppred, F, Ft, tmp, K)
One extended Kalman step with velocity damping nonlinearity.
Parameters:
x (array<float>): State vector (in/out)
P (array<float>): Covariance (in/out)
n (int): State dimension: 2 or 3
z (float): Measurement
dmp (float): Velocity damping coefficient
q0 (float): Process noise (level)
q1 (float): Process noise (velocity)
q2 (float): Process noise (acceleration; used when n = 3)
R (float): Measurement noise
xpred (array<float>): Workspace: predicted state
Ppred (array<float>): Workspace: predicted covariance
F (array<float>): Workspace: Jacobian / transition
Ft (array<float>): Workspace: F transpose
tmp (array<float>): Workspace: matrix multiply temp
K (array<float>): Workspace: Kalman gain
Returns: Filtered level

ukfStep(x, P, n, z, dmp, q0, q1, q2, R, alpha, beta, kappa, xpred, Ppred, F, Ft, tmp, tmp2, Lchol, xi, yi, K, Ysig)
One unscented Kalman step with the same velocity damping as ekfStep; falls back to EKF on Cholesky failure.
Parameters:
x (array<float>): State vector (in/out)
P (array<float>): Covariance (in/out)
n (int): State dimension: 2 or 3
z (float): Measurement
dmp (float): Velocity damping coefficient
q0 (float): Process noise (level)
q1 (float): Process noise (velocity)
q2 (float): Process noise (acceleration; used when n = 3)
R (float): Measurement noise
alpha (float): UKF alpha
beta (float): UKF beta
kappa (float): UKF kappa
xpred (array<float>): Workspace: predicted state
Ppred (array<float>): Workspace: predicted covariance
F (array<float>): Workspace: unused except EKF fallback
Ft (array<float>): Workspace: unused except EKF fallback
tmp (array<float>): Workspace: unused except EKF fallback
tmp2 (array<float>): Workspace: scaled covariance for Cholesky
Lchol (array<float>): Workspace: Cholesky factor
xi (array<float>): Workspace: sigma point state
yi (array<float>): Workspace: transformed sigma point
K (array<float>): Workspace: Kalman gain / cross-cov accumulator
Ysig (array<float>): Workspace: stored sigma rows (21 floats)
Returns: Filtered level

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