Projectile IMU Roll Angle Correction Using Euler-Kalman Filtering
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Solution Overview
Problem
Inertial navigation systems for projectiles face challenges in maintaining accurate roll angle calculations due to high roll rates and scale factor errors in low-cost MEMS gyroscopes, leading to significant navigation errors, especially during the initial phase of flight.
Innovation Solution
An inertial measurement system that includes a roll gyro, a second gyro, and a third gyro to define a 3D coordinate system, with a controller that computes attitude and calculates roll angle errors using an Euler angle filter, providing inputs to a Kalman filter for roll rate scale factor correction, which models errors as functions of roll rate and wind variables, allowing for real-time adjustments and crosswind compensation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If low-cost MEMS gyroscopes are used, then device cost is reduced, but measurement precision deteriorates due to scale factor errors of several thousand ppm
Solution Approach 1:
The system implements feedback by continuously monitoring pitch and yaw angles during flight and using a Kalman filter to generate corrections for roll angle errors. The measured pitch and yaw angles are fed back into the navigation algorithm to detect deviations from expected values, which then trigger corrective actions to compensate for the gyroscope scale factor errors, enabling the use of low-cost MEMS sensors while maintaining acceptable navigation accuracy.
Solution Approach 2:
The invention introduces pitch and yaw angle measurements as intermediary variables to indirectly detect and correct roll angle errors. Instead of directly measuring roll angle with high-precision sensors, the system uses pitch and yaw angle deviations as mediators to infer roll errors caused by scale factor inaccuracies, then applies corrections through the Kalman filter to compensate for the low-cost gyro limitations.
2Reliability
If roll rate is increased to stabilize the projectile, then navigation reliability improves, but roll angle error accumulates faster due to scale factor errors
Solution Approach 1:
The system uses feedback to continuously monitor pitch and yaw angle deviations that result from roll angle errors during high roll rate flight. The Kalman filter processes these feedback signals to generate real-time corrections, allowing the system to maintain reliable high roll rate stabilization while compensating for the accelerated accumulation of roll angle errors through continuous error detection and correction based on pitch and yaw measurements.
3Measurement precision
If Kalman filtering is used to correct inertial sensor errors, then measurement precision improves, but device complexity increases
Solution Approach 1:
The invention simplifies the Kalman filter implementation by using pitch and yaw angle measurements as intermediary variables to indirectly observe roll angle errors. This approach reduces the complexity of directly measuring and correcting roll angles with multiple high-precision sensors, instead using the available pitch and yaw data as mediators to infer and correct roll errors, thereby maintaining navigation accuracy while reducing system complexity.
4Measurement precision
If external aiding sensors are added to correct inertial errors, then measurement precision improves, but device complexity and cost increase
Solution Approach 1:
The system implements multi-functionality by using pitch and yaw angle measurements for multiple purposes: they serve both as navigation parameters for determining projectile orientation and as error detection signals for correcting roll angle inaccuracies. This universal use of existing sensors eliminates the need for additional dedicated correction sensors, maintaining high navigation accuracy while avoiding the complexity and cost of external aiding sensors.
Data Source
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AI summary
An inertial measurement system for a spinning projectile comprising: a first, roll gyro to be oriented substantially parallel to the spin axis of the projectile; a second gyro and a third gyro with axes arranged with respect to the roll gyro such that they define a three dimensional coordinate system; a controller, arranged to: compute a current projectile attitude from the outputs of the first, second and third gyros, the computed attitude comprising a roll angle, a pitch angle and a yaw angle; calculate a roll angle error based on the difference between the computed pitch and yaw angles and expected pitch and yaw angles; provide the roll angle error as an input to a Kalman filter that outputs a roll angle correction and a roll rate scale factor correction; and apply the calculated roll angle correction and roll rate scale factor correction to the output of the roll gyro; wherein the Kalman filter models roll angle error as a function of roll rate and one or more wind variables. The system provides improved calibration of the roll axis rate gyro scale factor, e.g. of an IMU fitted to a rolling projectile. A separate process (an Euler angle filter) is used to calculate an estimate of the roll angle error without the use of the Kalman filter and is then provided as an input to the Kalman filter which can then operate in a stable manner. The filter can be configured to estimate and correct for crosswind effects which would otherwise significantly degrade performance.