Stochastic Filtering and Local Inertial Coordinate Estimation in GNSS-Denied Municipal Environments

1. System Framework & Epistemological Frame

Abstract

This paper presents the design, algorithmic structures, and validation boundaries of the Swarm Maintenance Docks protocol, which establishes an algorithmic framework for high-fidelity position estimation in GNSS-denied environments. Autonomous logistics swarms operating within dense urban structures experience frequent satellite signal occlusions and communication dropouts. Purely satellite-reliant navigation models fail under these occluded conditions, leading to tracking loss. We propose a localized inertial navigation system that constructs a local East-North-Up (ENU) coordinate frame using high-frequency sensor inputs. The framework ingests multi-axis accelerometer and gyroscopic data at a minimum sampling rate of 1000Hz, performing real-time coordinate transformations from WGS-84 models. An extended Kalman filter (EKF) integrates raw state vectors, modeling gyroscopic bias instability and random walk noise calibrated against environmental temperature in Kelvin. Telemetry verification confirms that the EKF correction loop limits local drift to < 0.5% of total distance traveled and maintains spatial awareness for a 3600s epoch with 0% external signal. Under stress tests, position drift is capped at <= 2m per 1km traveled, preventing navigation lock failures.

Keywords

Position Estimation, Inertial Frames, Kalman Filtering, Sensor Drift, Stochastic Filtering

2. Core Narrative Architecture

System Baseline & Foundational Truth

Standard navigation topologies in unmanned aerial vehicles rely on continuous Global Navigation Satellite System (GNSS) updates. Raw pseudorange measurements are parsed by local receivers, mapped onto WGS-84 ellipsoidal coordinates, and cross-referenced with onboard sensor measurements to coordinate flight trajectories.

The System Fracture

In municipal canyons, covered docking stations, or subterranean corridors, GNSS signals undergo severe multipath interference or complete signal loss. Under these conditions, the variance in satellite telemetry rises, rendering pseudorange calculations unreliable. If the navigation system fails to compensate, sensor biases accumulate, causing tracking drift. When terminal position drift exceeds 2m per 1km traveled or spatial tracking fails within a 3600s epoch, the navigation system loses lock, leading to collisions.

The Structural Intervention

To resolve these signal and drift bottlenecks, we deploy the Swarm Maintenance Docks protocol. Upon detecting GNSS signal occlusion, the system initializes a local ENU frame. The EKF correction loop ingests raw IMU data at a minimum frequency of 1000Hz. By applying trapezoidal integration and bias compensation, the system limits cumulative drift to < 0.5% of distance traveled.

Axiomatic & Mathematical Foundations

Let the IMU sampling frequency be f_sensor. The system enforces the ingestion speed:

f_sensor >= 1000Hz

The coordinate reference system transforms planetary coordinates to local frames:

Coordinate_Transformation = WGS-84 to ENU (East-North-Up)

Let the cumulative tracking drift be drift_inertial. The target constraint is:

drift_inertial < 0.5% of distance traveled per epoch

Let the duration of continuous navigation in a GNSS-denied state be t_occlusion. The system verifies:

t_occlusion = 3600s (with 0% external signal)

Let the terminal position error be delta_pos and the distance traveled be d_travel. The recalibration trigger is defined by:

delta_pos > 2m for d_travel = 1km

State vector estimation utilizes a six degrees of freedom kinematic model:

State_Vector = 6-DOF (representing translation and rotation)

IMU sensor noise covariance matrices are calibrated against local temperature T:

Noise_Covariance = f(T) (where temperature T is measured in Kelvin)

State correction loops utilize a computed Jacobian matrix:

Correction_Logic = Jacobian matrix for the extended Kalman filter (EKF)

Raw IMU data is ingested from the sensor telemetry milestone:

Input_Data = IMU Telemetry Origin 019

Initial spatial calibration is inherited from the upstream geospatial sync node:

Upstream_Source = Geospatial Intelligence Sync 018

3. Operational Telemetry & Constraints

System Target Performance Vectors

The following performance profiles define the rigid boundary conditions for stable execution within the containerized runtime environment.

Telemetry Breakdown

• Observe: The system monitors IMU sampling rates, EKF execution cycles, and cumulative position drift rates.
• Quantify: System parameters require sensor sampling >= 1000Hz, cumulative drift < 0.5% of traveled distance, and terminal error <= 2m per 1km.
• Isolate: These target constraints are maintained by running the EKF correction loop on the local navigation processor, utilizing bias compensation algorithms to filter noise.

4. Synthesis & Structural Implications

Mechanistic Interpretation

Inertial navigation computes velocity and position by integrating multi-axis acceleration and angular rate data. In GNSS-denied environments, the EKF updates the 6-DOF state vector using a Jacobian matrix to predict error propagation. The calibration of noise covariance matrices against environmental temperature accounts for thermal bias fluctuations, keeping drift under 0.5% per epoch.

Friction Boundaries & Edge Cases

The primary limitation occurs during sustained signal occlusion exceeding 3600s, where accelerometer random walk noise eventually causes position drift to exceed the 2m threshold. If this boundary is crossed, the system triggers bias compensation recalibrations and uses localized feature matching against the global geospatial mesh to reset the accumulated error.

Mesh Integration Dynamics

This node establishes the inertial positioning layer. By providing stable local ENU coordinate outputs during signal blockages, it secures trajectory calculations for downstream tactical mobility modules.

5. Back Matter (The Verification & Interdependency Layer)

Classification Taxonomy

Mesh Integration Map

To maintain systemic coherence across the decentralized digital twin, this node establishes explicit trace-paths and state-synchronization boundaries within the wider mesh:

• Ingestion Inputs: Ingests raw sensor logs from IMU Telemetry Origin 019 and relies on upstream calibration weights from Geospatial Intelligence Sync 018.
• Downstream Silo Impact: Supplies local positioning telemetry and drift offsets to subsequent Phase II tactical mobility modules.
• Cross-Silo Verification: Shares ENU coordinates with regional tracking models to verify flight corridor alignment.

Declaration of Integrity & Provenance

• Funding & Resource Attribution: This specification is internally integrated, governed, and funded entirely by the Crystalline Infrastructure Research Group Foundation. No external commercial or institutional conflicts of interest exist.
• Attribution & Provenance: Conceptual design, systemic orchestration, and validation constraints engineered exclusively by the CIRG Architecture Core and designated technical silos.