Abstract: The performance of high-precision inertial navigation modules faces significant error challenges caused by temperature drift across the entire temperature range. The traditional step-by-step calibration method (independent temperature testing followed by motion calibration) cannot effectively separate and couple the multidimensional errors of temperature and dynamic motion. The dual axis temperature control turntable integrates high-precision dual axis motion functions with an integrated temperature control environment to construct a dynamic temperature composite calibration benchmark system, achieving integrated, efficient, and high-precision calibration and modeling of the navigation module (core IMU)'s full temperature domain error parameters. This report provides a detailed explanation of its system composition, calibration process, core technologies, and value.

1、   System Overview: From Devices to Solutions

The dual axis temperature control turntable is not simply a "turntable heating box", but an integrated temperature control motion reference system designed specifically for inertial device calibration.

Core components:

High precision dual axis turntable: provides precise angular position, angular velocity, and angular acceleration excitation around the inner and outer axes (usually corresponding to pitch and azimuth axes). Its key indicators include extremely low shaft system error (orthogonality error, end jump, radial jump), high-resolution encoder feedback, and excellent rate stability, ensuring the known and accurate input excitation.

Integrated temperature control cabin: directly integrated into the working chamber of the turntable, with fast lifting and high stability temperature control capabilities (such as temperature change rate of ± 5 ℃/min or above, stability of ± 0.5 ℃). The cabin design ensures minimal impact on the mechanical and electrical performance of the turntable.

Synchronous control system: The core lies in achieving precise timing synchronization and coordinated control of temperature cycling (T-t curve) and motion sequence (θ/ω - t curve), which is the key to achieving coupled excitation.

The core problem solved is that traditional methods place IMU in a temperature chamber for static temperature testing, which can only obtain the relationship between zero bias and other parameters and temperature, while dynamic parameters such as scale factor and installation error still need to be calibrated separately with a turntable at room temperature. This method ignores the variation of dynamic parameters with temperature and cannot characterize the complex effects coupled with motion during temperature changes, such as transient errors caused by thermal deformation. The dual axis temperature control turntable realizes the free combination of two modes: "precise movement at the set temperature" and "temperature change control during movement", thus fully stimulating all error sources.

2、   Systematic calibration testing process

The calibration process of the dual axis temperature control turntable is a multi-stage, multi-mode system engineering aimed at maximizing the observability of parameters.

Phase 1: Static multi position calibration across the entire temperature range

Objective: To establish a preliminary mapping relationship between the main zero bias of sensors and temperature, and evaluate the impact of temperature gradient on the installation base.

Method: Set the temperature control chamber to run according to the predetermined program (such as changing from -40 ℃ to+70 ℃ at a rate of 1 ℃/min). During the temperature change process, the turntable is not stationary, but executes a slow multi position flipping sequence (for example, pointing in six directions: east, north, sky, west, south, and earth at fixed temperature intervals). Collect data in stable segments at each location.

Output: Obtain the initial curves of accelerometer and gyroscope zero bias with temperature variation, and observe the consistency of temperature sensing under different postures, providing a basis for accurate modeling in the future.

Phase 2: Dynamic accuracy calibration of characteristic temperature points

Purpose: Accurately calibrate all motion related error parameters at key temperature points (usually including low temperature limit, normal temperature, high temperature limit, and characteristic inflection point temperature).

Method: Stabilize the temperature control chamber at a certain characteristic temperature point (such as -40 ℃), and after sufficient thermal soaking, perform a complete dynamic testing sequence:

Speed test: Rotate around each axis at a series of positive and negative precise speeds (such as ± 1 °/s, ± 10 °/s, ± 50 °/s, ± 100 °/s, ± 200 °/s), calibrate the scaling factor and nonlinearity.

Position calibration: Perform multi position static testing (such as the 24 position method or a more optimized custom position set), using gravity vectors and Earth rotation rate vectors as references, to accurately calibrate zero bias, installation misalignment angle, g-sensitive error (for gyroscopes), etc.

Output: Obtain a complete error parameter matrix (including zero bias, scale factor, installation error, second-order nonlinear coefficients, etc.) at discrete temperature points.

Phase 3: Temperature motion coupling excitation test

Purpose: To actively stimulate and identify transient errors coupled with motion states during rapid temperature changes, such as quasi-static angular displacement caused by thermoelastic deformation.

Method: This is an advanced testing mode unique to the dual axis temperature control turntable. For example, control the turntable to rotate continuously at a constant rate (such as 10 °/s), while instructing the temperature control cabin to perform temperature cycling at a higher temperature rise and drop rate (such as ± 5 ℃/min). By analyzing the phase and amplitude relationship between IMU output and known motion input and temperature changes, the parameters of the thermal hysteresis effect model that cannot be separated by static methods can be identified.

3、   Key technology: Temperature motion coupling modeling and parameter identification

Based on the data collected by the dual axis temperature control turntable, the error modeling has been upgraded from the traditional independent models of "temperature related" or "motion related" to a unified "temperature motion" coupled field model.

Coupling error model:

For any error parameter P (such as gyroscope X-axis zero bias); B_gx）， Its model is extended to:

P = f(T, dT/dt,ω,f)

among which, T  For temperature, dT/dt  For the rate of temperature change (used to characterize dynamic thermal effects), ω  For angular velocity input, f  To input force. In practical applications, the method of sub item modeling and synthesis is often used.

Parameter calculation method:

Segmented two-step method: First, use dynamic calibration data to calculate the complete error parameters of each characteristic temperature point, and then use these parameter values as observation values to fit their polynomial or exponential relationship with temperature T (and dT/dt).

Global optimal estimation method: A large-scale overdetermined equation system is constructed by combining a global coupled model containing all coefficients to be identified with test data from all stages (static temperature variation, fixed-point dynamics, coupled excitation). Weighted least squares or batch Kalman filtering is used for one-time global optimization solution. This method theoretically has the highest accuracy and can optimally allocate the weights of data in each stage, but it requires extremely high accuracy and data quality for the model.

4、   Summary of Application Advantages and Value

Calibration accuracy leap: By providing synchronized and traceable temperature and motion benchmarks, the problem of error coupling is fundamentally solved, and the calibrated compensation model is closer to the real working environment, which can improve the full temperature domain accuracy of the navigation module by an order of magnitude.

Calibration efficiency revolution: Integrating traditional processes such as temperature cycling testing, static multi position calibration, and dynamic rate calibration that require several weeks and multiple devices into one device for automated completion, the time can be shortened to several days.

Revealing deep mechanisms: The unique coupling excitation testing capability helps R&D personnel to gain a deeper understanding of the mechanisms behind device level (such as g-sensitivity coefficient temperature drift in MEMS gyroscopes) and system level (lever arm changes caused by PCB thermal bending) errors, guiding forward design improvements.

Improving reliability: By applying stress tests covering the entire temperature range and dynamic range before leaving the factory and completing precise compensation, potential defects are exposed in advance, significantly enhancing the long-term reliability and stability of navigation products under complex working conditions.

Conclusion: The dual axis temperature controlled turntable represents the advanced direction of current inertial navigation module calibration technology. It seamlessly integrates temperature controlled environments with high-precision motion benchmarks, not only as a testing device, but also as a complete solution for "error excitation, measurement, and modeling". Through its systematic application process, a high fidelity temperature motion coupling error model can be established, which is an indispensable key tool for achieving high performance and reliability of high-end inertial navigation systems.