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---

layout: document

theme: voltage

title: Autonomous Systems Specification

client: Apex Robotics Lab

document-id: SPEC-2026-09

lang: en

---

## 2. Deterministic State Estimation

Core control loop executes deterministic state estimation over 200 Hz boundary:

$$V(x) = \frac{1}{2} x^T P x + \int_0^t \gamma \|u(\tau)\|^2 d\tau$$

Where $P \succ 0$ satisfies continuous-time Riccati bounds:

$$A^T P + P A - P B R^{-1} B^T P + Q = 0$$

> "Deterministic convergence guaranteed within 14 ms for perturbations."

### Milestone Deliverables

| :--- | ---: | :--- | ---: |

| EKF Estimator | < 2.4 ms | Hard Real-Time | 99.99% |

Issues (0)ChangesTemplateUTF-8 · LF · Markdown

FOLIO / APEX ROBOTICS§ 2.4 STATE ESTIMATION & BOUNDSSPEC-2026-09

2. Deterministic State Estimation

The core trajectory planner executes deterministic state estimation over a 200 Hz boundary. System stability is proven through the Lyapunov function $P \succ 0$ :

V(x) = \frac{1}{2} x^T P x + \int_0^t \gamma \|u(\tau)\|^2 d\tau

(2.1)

Where the algebraic Riccati matrix satisfies positive definiteness for all disturbances bounded by $\Omega \subset \mathbb{R}^n$ :

A^T P + P A - P B R^{-1} B^T P + Q = 0

(2.2)

"Deterministic convergence is mathematically guaranteed within 14 ms for all initial state perturbations bounded by the stability envelope."

// MILESTONE DELIVERABLES & LATENCY BUDGET

Module	Latency	Determinism	Target SLA
State Estimator	< 2.4 ms	Hard Real-Time	99.99%
Trajectory QP	< 8.1 ms	Bounded Loop	99.95%
CAN Bus Link	< 0.8 ms	Deterministic	99.99%

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