PINE LIBRARY
Aggiornato KalmanEngineLib
KalmanEngineLib
A Pine Script v6 library that provides a reusable engine for multi-state Kalman filtering, symmetric covariance packing, sequential scalar measurement updates, Mahalanobis gating, adaptive noise estimation, online coupling estimation, multi-scale trajectory storage, covariance-derived confidence bands, and k-step covariance propagation.
What it does
Implements a generic N-state Kalman filter where the posterior covariance P is stored as a packed upper triangle (n*(n+1)/2 elements), saving ~47% memory vs a full matrix.new<float>(n,n) at n=14.
Supports block-diagonal transition matrices via separate sub-blocks (3×3 kinematics, 6×6 z-score dynamics, 5×5 Mahalanobis, 3×5 cross-coupling Γ_lag) instead of a single n×n F matrix.
Provides a sequential scalar measurement update in Joseph form for numerical stability; calling it once per observation is equivalent to a batch update but avoids allocating an m×n H matrix.
Core components
UDTs: KalmanState_N, TransitionConfig, TrajectoryStore, ConceptConfig — callers own all persistent state; library functions are stateless transforms.
Triangle primitives: f_tri_idx, f_tri_get, f_tri_set, f_tri_new, f_tri_diag, f_tri_add_outer_product for packed symmetric matrix arithmetic.
Prediction: f_predict_block, f_predict_identity, f_P_predict_diag, f_P_predict_cross.
Update: f_sequential_update returning [innovation, S] for external diagnostics.
Gating: f_mahalanobis_3d (analytic 3×3 inverse with Ledoit-Wolf shrinkage and diagonal fallback near singularity), f_nis_test, f_gating_gain_mod.
Adaptive noise: f_adaptive_Q_scalar (windowed MLE), f_adaptive_R_scalar (innovation z-score ratchet).
Coupling: f_gamma_lag_update (scalar 1-D Kalman β-tracker for Γ_lag elements).
Trajectory: f_traj_init, f_traj_update, f_traj_xcorr — circular buffers at Δ={3,5,7} bar skips with Pearson cross-correlation for lag calibration.
Bands and projection: f_covariance_band_width, f_confidence_envelope, f_k_step_cov_propagation, f_z_spread.
Derived outputs: KMEMA (adaptive EMA modulated by innovation shock, TE confidence, velocity), online OLS beta update, execution-score helpers.
Architecture notes
All functions are stateless transforms operating on UDTs passed by the caller; no var declarations inside library functions.
Element budget: ~3,600 for the core engine; ~1,800 for TrajectoryStore at depth=100, n_feat=6. Total ~22K elements under Pine's 100K limit.
Self-healing: f_state_sanitize resets na or overflow entries in x and P diagonals to caller-supplied defaults.
Usage pattern
Declare a var KalmanState_N state = f_init_regression(n, P0, Q0, R0) in the indicator.
Each bar: call f_predict_block → f_P_predict_diag/f_P_predict_cross → one or more f_sequential_update per scalar observation → optional f_mahalanobis_3d/f_adaptive_Q_scalar/f_adaptive_R_scalar → read outputs via f_z_spread, f_confidence_envelope, f_k_step_cov_propagation.
Scope
General-purpose Kalman infrastructure; no market-specific logic, no signals, no thresholds embedded. Intended as a dependency for indicators and strategies that need rigorous multi-state filtering with adaptive noise and regime-aware gating.
License
Mozilla Public License 2.0.
A Pine Script v6 library that provides a reusable engine for multi-state Kalman filtering, symmetric covariance packing, sequential scalar measurement updates, Mahalanobis gating, adaptive noise estimation, online coupling estimation, multi-scale trajectory storage, covariance-derived confidence bands, and k-step covariance propagation.
What it does
Implements a generic N-state Kalman filter where the posterior covariance P is stored as a packed upper triangle (n*(n+1)/2 elements), saving ~47% memory vs a full matrix.new<float>(n,n) at n=14.
Supports block-diagonal transition matrices via separate sub-blocks (3×3 kinematics, 6×6 z-score dynamics, 5×5 Mahalanobis, 3×5 cross-coupling Γ_lag) instead of a single n×n F matrix.
Provides a sequential scalar measurement update in Joseph form for numerical stability; calling it once per observation is equivalent to a batch update but avoids allocating an m×n H matrix.
Core components
UDTs: KalmanState_N, TransitionConfig, TrajectoryStore, ConceptConfig — callers own all persistent state; library functions are stateless transforms.
Triangle primitives: f_tri_idx, f_tri_get, f_tri_set, f_tri_new, f_tri_diag, f_tri_add_outer_product for packed symmetric matrix arithmetic.
Prediction: f_predict_block, f_predict_identity, f_P_predict_diag, f_P_predict_cross.
Update: f_sequential_update returning [innovation, S] for external diagnostics.
Gating: f_mahalanobis_3d (analytic 3×3 inverse with Ledoit-Wolf shrinkage and diagonal fallback near singularity), f_nis_test, f_gating_gain_mod.
Adaptive noise: f_adaptive_Q_scalar (windowed MLE), f_adaptive_R_scalar (innovation z-score ratchet).
Coupling: f_gamma_lag_update (scalar 1-D Kalman β-tracker for Γ_lag elements).
Trajectory: f_traj_init, f_traj_update, f_traj_xcorr — circular buffers at Δ={3,5,7} bar skips with Pearson cross-correlation for lag calibration.
Bands and projection: f_covariance_band_width, f_confidence_envelope, f_k_step_cov_propagation, f_z_spread.
Derived outputs: KMEMA (adaptive EMA modulated by innovation shock, TE confidence, velocity), online OLS beta update, execution-score helpers.
Architecture notes
All functions are stateless transforms operating on UDTs passed by the caller; no var declarations inside library functions.
Element budget: ~3,600 for the core engine; ~1,800 for TrajectoryStore at depth=100, n_feat=6. Total ~22K elements under Pine's 100K limit.
Self-healing: f_state_sanitize resets na or overflow entries in x and P diagonals to caller-supplied defaults.
Usage pattern
Declare a var KalmanState_N state = f_init_regression(n, P0, Q0, R0) in the indicator.
Each bar: call f_predict_block → f_P_predict_diag/f_P_predict_cross → one or more f_sequential_update per scalar observation → optional f_mahalanobis_3d/f_adaptive_Q_scalar/f_adaptive_R_scalar → read outputs via f_z_spread, f_confidence_envelope, f_k_step_cov_propagation.
Scope
General-purpose Kalman infrastructure; no market-specific logic, no signals, no thresholds embedded. Intended as a dependency for indicators and strategies that need rigorous multi-state filtering with adaptive noise and regime-aware gating.
License
Mozilla Public License 2.0.
Note di rilascio
v2Note di rilascio
v3Note di rilascio
v4Added:
f_kalman1d_init(P0, Q, R)
Initialize 1D Kalman filter
Parameters:
P0 (float): Initial estimate variance
Q (float): Process noise variance
R (float): Measurement noise variance
Returns: Initialized KalmanState1D
method update(s, z)
Update 1D Kalman filter with new measurement
Namespace types: KalmanState1D
Parameters:
s (KalmanState1D): KalmanState1D to update (mutated in-place)
z (float): New measurement
Returns: Updated state (same reference as input)
KalmanState1D
Simple 1D Kalman filter for scalar smoothing (ergonomic wrapper over N-dim API)
Fields:
x (series float)
P (series float)
Q (series float)
R (series float)
Note di rilascio
v5Added:
f_sep_pair5(mu_a, sigma_a, mu_b, sigma_b, use_f4, use_f5, var_floor)
Parameters:
mu_a (array<float>)
sigma_a (matrix<float>)
mu_b (array<float>)
sigma_b (matrix<float>)
use_f4 (bool)
use_f5 (bool)
var_floor (float)
Note di rilascio
v6Added:
method update_value(s, z, Q, R)
Namespace types: KalmanState1D
Parameters:
s (KalmanState1D)
z (float)
Q (float)
R (float)
f_inverse_covariance3_diag(sigma, active_dims, variance_floor, determinant_floor)
Parameters:
sigma (matrix<float>)
active_dims (array<bool>)
variance_floor (float)
determinant_floor (float)
Note di rilascio
v7Added:
f_sequential_update_metric(x, P_tri, z, H_row, R, n, use_lorentzian, bandwidth, max_r_multiplier)
Parameters:
x (array<float>)
P_tri (array<float>)
z (float)
H_row (array<float>)
R (float)
n (int)
use_lorentzian (bool)
bandwidth (float)
max_r_multiplier (float)
Libreria Pine
Nello spirito di TradingView, l'autore ha pubblicato questo codice Pine come libreria open source affinché altri programmatori della nostra community possano riutilizzarlo. Complimenti all'autore! È possibile utilizzare questa libreria privatamente o in altre pubblicazioni open source, ma il riutilizzo di questo codice nelle pubblicazioni è soggetto al Regolamento.
Declinazione di responsabilità
Le informazioni e le pubblicazioni non sono intese come, e non costituiscono, consulenza o raccomandazioni finanziarie, di investimento, di trading o di altro tipo fornite o approvate da TradingView. Per ulteriori informazioni, consultare i Termini di utilizzo.
Libreria Pine
Nello spirito di TradingView, l'autore ha pubblicato questo codice Pine come libreria open source affinché altri programmatori della nostra community possano riutilizzarlo. Complimenti all'autore! È possibile utilizzare questa libreria privatamente o in altre pubblicazioni open source, ma il riutilizzo di questo codice nelle pubblicazioni è soggetto al Regolamento.
Declinazione di responsabilità
Le informazioni e le pubblicazioni non sono intese come, e non costituiscono, consulenza o raccomandazioni finanziarie, di investimento, di trading o di altro tipo fornite o approvate da TradingView. Per ulteriori informazioni, consultare i Termini di utilizzo.