fintech-algorithms

Extended Kalman Filter

Install and import

bash
npm install fintech-algorithms
ts
import { runFilter } from "fintech-algorithms/statistical-time-series/state-and-regime-models/extended-kalman-filter";

Signature

runFilter(observations, config)

Worked example

executed Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

Input

observations
[
  0.1740564489,
  0.7180957323,
  0.0365723689,
  -0.3580227464,
  0.3553945738,
  0.4323328535
]

Showing 6 of 160 elements.

config
{
  "a": 0.9,
  "b": 0.22,
  "c": 0.04,
  "q": 0.06,
  "r": 0.49,
  "initial_mean": 0,
  "initial_variance": 1.5
}

Call

runFilter(observations, config)

Returns

array of 160 objects

[
  {
    "index": 0,
    "transition_jacobian": 1.12,
    "measurement_jacobian": 1,
    "predicted_mean": 0,
    "predicted_variance": 1.9416000000000002,
    "predicted_observation": 0,
    "innovation": 0.1740564489,
    "innovation_variance": 2.4316000000000004,
    "kalman_gain": 0.7984865931896693,
    "filtered_mean": 0.13898174090485277,
    "filtered_variance": 0.391258430662938
  },
  {
    "index": 1,
    "transition_jacobian": 1.1178786662536586,
    "measurement_jacobian": 1.0124448968753026,
    "predicted_mean": 0.15556121094128242,
    "predicted_variance": 0.5489371591527625,
    "predicted_observation": 0.15652918255526316,
    "innovation": 0.5615665497447369,
    "innovation_variance": 1.0526851087201852,
    "kalman_gain": 0.5279533460534298,
    "filtered_mean": 0.452042149910696,
    "filtered_variance": 0.25551725369409706
  },
  {
    "index": 2,
    "transition_jacobian": 1.0979025313193456,
    "measurement_jacobian": 1.040234775932769,
    "predicted_mean": 0.5029346991596126,
    "predicted_variance": 0.36799793432466277,
    "predicted_observation": 0.5130524316243634,
    "innovation": -0.47648006272436344,
    "innovation_variance": 0.8882062919307445,
    "kalman_gain": 0.4309857431023305,
    "filtered_mean": 0.2975785852529078,
    "filtered_variance": 0.20301476071185573
  }
]

Showing 3 of 160 elements.

Diagrams

Extended Kalman Filter — diagnostic scorecard
Extended Kalman Filter — failure boundary
Extended Kalman Filter — family handoff
Extended Kalman Filter — scenario comparison
Extended Kalman Filter — state update
Extended Kalman Filter — uncertainty ledger

Calculation flow

Extended Kalman Filter Causal Update Flow 
flowchart LR
    A["Filtered state at t-1"] --> B["Predict state at t"]
    B --> C["Read observation available at t"]
    C --> D["Compute evidence or innovation"]
    D --> E["Normalize or gain-weight update"]
    E --> F["Filtered state at t"]
    F --> G["Publish diagnostics"]
    F --> A

How it works

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References