Kalman Filter Roll Angle Correction for Spinning Projectiles
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Solution Overview
Problem
Inertial navigation systems for spinning guided projectiles face challenges in maintaining accurate roll angle calculations due to high roll rates and low-cost MEMS gyro scale factor errors, leading to significant navigation errors that accumulate quickly, especially in ballistic flight environments where initial roll angle knowledge is unknown or poorly defined.
Innovation Solution
An inertial measurement system that initializes the Kalman filter with a roll angle error uncertainty representing an unknown roll angle, using pseudo-measurements from stored expected flight data to correct roll angle errors, allowing immediate navigation solution convergence without a separate upfinding process, and enabling operation from launch without relying on initial roll angle knowledge.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If low-cost MEMS gyroscopes are used, then cost is reduced, but roll angle measurement precision deteriorates due to scale factor errors of several thousand ppm
Solution Approach 1:
The patent implements a feedback mechanism where the Kalman filter continuously estimates roll angle error based on the difference between expected and actual measurements, then applies this error estimate as a correction to the roll angle. This closed-loop feedback compensates for the scale factor errors in low-cost MEMS gyroscopes, enabling the use of inexpensive sensors while maintaining acceptable measurement precision.
Solution Approach 2:
The patent introduces an intermediary computational process (the Kalman filter with pseudo-measurements) that mediates between the imperfect raw gyro measurements and the required accurate roll angle. This intermediary system processes the low-precision measurements through error estimation and correction algorithms, transforming them into reliable navigation data without requiring high-precision hardware.
2Measurement precision
If traditional upfinding process is used to determine initial roll angle, then roll angle accuracy is improved, but device complexity and software complexity increase
Solution Approach 1:
The patent extracts and removes the separate upfinding process from the navigation system initialization sequence. Instead of implementing a complex dedicated upfinding algorithm to determine initial roll angle, the system takes out this requirement and handles it through the standard Kalman filter initialization with pseudo-measurements, significantly reducing software complexity while maintaining accuracy.
Solution Approach 2:
The patent merges the roll angle initialization function into the standard Kalman filter startup process. By combining what was previously a separate upfinding operation with the existing filter initialization routine, the system eliminates redundant code and simplifies the overall software architecture while achieving the same roll angle determination goal.
3Adaptability or versatility
If roll angle error uncertainty is initialized to represent unknown roll angle, then adaptability is improved, but convergence time increases
Solution Approach 1:
The patent performs preliminary action by pre-computing expected measurements and storing them as pseudo-measurements before the Kalman filter begins operation. This preparatory work enables the filter to immediately start correcting roll angle errors using the difference between expected and actual measurements, significantly reducing convergence time while maintaining adaptability to unknown initial roll angles.
Solution Approach 2:
The patent ensures continuity of useful action by having the Kalman filter operate continuously from startup without requiring a separate upfinding phase. The filter continuously estimates and corrects roll angle error using pseudo-measurements throughout flight, maintaining uninterrupted error correction and achieving rapid convergence while adapting to unknown initial conditions.
4Device complexity
If Kalman filter operates without pseudo-measurements, then device complexity is reduced, but navigation error growth increases
Solution Approach 1:
The patent implements a self-service mechanism where the navigation system generates its own correction data through pseudo-measurements derived from expected flight dynamics. Rather than requiring external aiding sensors or complex initialization procedures, the system serves itself by computing expected measurements from stored data and using these to continuously correct its own navigation errors, maintaining reliability without increasing hardware complexity.
Data Source
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AI summary
An inertial measurement system for a spinning projectile comprising: a first, roll gyro with an axis 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; operate a Kalman filter that receives a plurality of measurement inputs including at least the roll angle, pitch angle and yaw angle and that outputs at least a roll angle error; initialise the Kalman filter with a roll angle error uncertainty representative of a substantially unknown roll angle; generate at least one pseudo-measurement from stored expected flight data, the or each pseudo-measurement corresponding to an expected measurement input of the Kalman filter; provide said pseudo-measurements) to the corresponding measurement input of the Kalman filter; and apply the roll angle error from the Kalman filter as a correction to the roll angle; wherein the Kalman filter is arranged to calculate the roll angle error as a function of the pseudo-measurement(s). This process allows navigation approach in which integrated navigation is initialised immediately after power-up, even though the roll angle is unknown or only known to a very coarse degree. The navigation Kalman filter configured with this pseudo-measurement update process allows reliable and rapid convergence to an accurate navigation solution without the need for a discrete upfinding process as it is not reliant on any knowledge of the initial roll angle.