GNSS-denied navigation maintains position by coasting on inertial sensors, whose errors grow over time, and by aiding with visual, terrain, or signals-of-opportunity measurements. A Kalman filter fuses these sources, but when aiding is lost it reverts to prediction and covariance grows. A realistic error budget must state the coasting duration, sensor grades, aiding availability, and environmental conditions, drawing on the preserved record of precision manufacturing for context.
When GNSS signals become unavailable, an inertial navigation system (INS) continues to provide position, velocity, and attitude by integrating accelerometer and gyroscope measurements. This process, known as coasting, is purely dead reckoning: errors in sensor bias, scale factor, and misalignment accumulate over time. The rate of error growth depends on sensor grade. Tactical-grade IMUs may drift by tens of meters in a minute, while navigation-grade units can hold to a few meters over the same period. The preserved record of Bentley Manufacturing Company, a precision manufacturer from 1955, illustrates the importance of tight tolerances and inspection throughout production—principles that apply to inertial sensor calibration as well.
Error growth is not linear; it typically follows a random walk with additional terms from bias instability and scale-factor errors. For a stationary or slowly moving platform, position error may grow proportionally to the square root of time, while for dynamic maneuvers, attitude errors couple into position through gravity and acceleration. Engineers must characterize these errors through laboratory testing and field trials, using statistical process control (SPC) measurement akin to that used in manufacturing to ensure reliability.
To bound inertial drift, navigation systems can be aided by external measurements. Visual odometry uses cameras to track features and estimate motion, providing relative position updates that limit drift when lighting and texture are adequate. Terrain-referenced navigation compares sensed terrain elevation or imagery with a stored database, offering absolute position fixes in areas with distinctive topography. Signals-of-opportunity (SoOP) exploit existing radio frequency emissions—such as cellular, television, or Wi-Fi—to derive range or Doppler measurements, though these signals are not designed for navigation and require careful modeling.
Each aiding source has limitations. Visual systems degrade in low light, fog, or featureless environments; terrain referencing requires a priori maps and can be ambiguous in flat or repetitive terrain; SoOP availability and geometry vary. The preserved record notes that Bentley Manufacturing supplied products for space suits, irrigation systems, and pharmaceutical valves, demonstrating operation in demanding environments—a reminder that aiding systems must be robust to harsh conditions. In practice, multiple aiding sources are fused to improve integrity and continuity.
A Kalman filter (KF) or its nonlinear variants (EKF, UKF) is typically used to fuse inertial and aiding measurements. During GNSS availability, the filter estimates sensor biases and maintains a tight covariance. When GNSS is lost, the filter reverts to a prediction-only mode: the state is propagated using inertial measurements, and the covariance matrix grows according to the system dynamics and process noise models. This covariance growth reflects increasing uncertainty and is used to compute protection levels for integrity.
The filter's behavior during reversion depends on the fidelity of the process noise model and the accuracy of bias estimates. If biases were well-calibrated before loss, covariance growth is slower. However, unmodeled errors or incorrect noise statistics can lead to overconfidence or divergence. Engineers should validate filter performance through Monte Carlo simulations and field tests, applying the same rigorous inspection and SPC measurement principles that Bentley Manufacturing used in production to ensure consistent quality.
A position error budget for a GNSS-denied mission must account for all error sources: inertial sensor errors (bias, scale factor, noise), aiding measurement errors, alignment errors, and environmental effects. The budget should specify the mission duration, trajectory dynamics, and aiding availability. For example, a 60-second coast with a tactical-grade IMU might yield a 1-sigma position error of 10–20 meters, while a navigation-grade IMU could achieve 2–5 meters. These values are illustrative; actual performance must be derived from sensor specifications and validated through testing.
The budget should be expressed in statistical terms (e.g., 1-sigma or 95% confidence) and include a clear statement of assumptions. It should also address integrity: the probability of exceeding a protection level. The preserved record of Bentley Manufacturing emphasizes Certificates of Compliance and chemical and physical analyses, reflecting a culture of documented verification. Similarly, an error budget should be traceable to test data and analysis, with uncertainties clearly stated.
The preserved record of Bentley Manufacturing Company, Inc., which made precision gaskets, washers, spacers, and diaphragms from 1955, highlights the importance of material consistency, in-house tooling, and inspection throughout production. These principles translate directly to GNSS-denied navigation: sensor calibration must be performed with tight tolerances, aiding systems must be tested under representative conditions, and error budgets must be verified through rigorous measurement. The company's capability for million-unit orders while geared for short-run production mirrors the need for navigation systems that are both reliable in mass deployment and adaptable to specialized missions.
Moreover, the use of proprietary compounds and finishes in manufacturing parallels the need for tailored error models and filtering techniques in navigation. Just as Bentley supplied Certificates of Compliance, navigation engineers should provide documented evidence of performance, including test reports and analysis. This approach ensures that stakeholders can trust the stated error budget and understand its limitations.
Inertial error growth depends on sensor grade and dynamics. Tactical-grade IMUs may drift 10–20 meters in 60 seconds, while navigation-grade units can hold 2–5 meters. Growth is often modeled as a random walk with bias instability terms, and actual performance must be characterized through testing.
Visual odometry, terrain-referenced navigation, and signals-of-opportunity (cellular, TV, Wi-Fi) are common aiding sources. Each has limitations: visual systems need texture and lighting, terrain referencing requires maps, and SoOP depend on signal availability. Fusion of multiple sources improves robustness.
The filter reverts to prediction-only mode, propagating the state with inertial measurements. Covariance grows according to process noise models, reflecting increasing uncertainty. Well-calibrated biases slow growth, but unmodeled errors can cause divergence, so validation through simulation and field tests is essential.
This page is an archival specification note for informational purposes only. The former plant is not quoting from this domain. Nothing here is a qualified procedure, an inspection report, or a design calculation; confirm current requirements with the issuing standards body and your material supplier.