1. Overview of Cross-Axis Sensitivity
Cross-axis sensitivity (CAS) is a measurement of the undesirable interaction of orthogonal sensing axes of an inertial measurement unit (IMU). The effect of an acceleration or a rotation about one axis is that a sensor which is perfectly orthogonal would generate zero output along the other axes. Practically, a small percentage of the input is represented on the non-intended axes, as a percentage of the primary-axis sensitivity. . In tri-axial accelerator, this coupling is described by six terms (Sxy,Sxz,Syx,Syz,SzxSzy).
2. Primary Sources of CAS
- Mechanical mis-alignment- The- MEMS proof mass or springs not orthogonal in their ideal orientation during fabrication.
- Package-to- die orientation error Rotation of the silicon die with respect to the IC package, and extending into the PCB mounting.
- Circuit crosstalk Circuit coupling between analog front-end circuits or digital read-out routes.
- Fabrication errors – Inaccuracies in etching, non-uniform stress or asymmetrical distribution of mass which change non-sensing direction stiffness.
- System-level mis-placement System-level CAS on top of the device-level value PCB layout or module integration which does not maintain orthogonality.
3. Why CAS Matters
- Error Propagation – Error propagation occurs in navigation algorithms where small terms cross axis are accumulated with time resulting in drift in velocity and position estimates.
- Complexity of Calibration – CAS needs to be defined and be countered in factory calibration; high values add time and money to that process.
- Performance Limits – CAS has been used in high-performance applications (such as aerospace, robotics, seismic monitoring) with error budget requirements of CAS of 0.1percent.
- Temperature Sensitivity – CAS is sensitive to temperature. See our guide on IMU temperature compensation for more details due to a change in mechanical properties and alignment, and is also an additional drift component that needs to be monitored.
4. Cross-axis Sensitivity Measurement.
- Static Test – Then subject the sensor to known 1 0 /s acceleration (or 0 0 /s rotation) along a single axis with the sensor firmly clamped. Note down the results on the orthogonal axes. \[ CAS_{xy} = \frac{V_y (\text{input } x)}{V_x (\text{input } x)} \times 100\% \]
- Dynamic Test – This is done by sweeping frequency and amplitude using a rate table or shaker to acquire frequency-dependent CAS.
- Temperature Sweep – Repeat the experiment with the static test with different temperatures to purchase CAS -v-temperature curves.
The largest of the six terms is generally reported as CAS specifications of the device.
5. Mitigation Strategies
| Level | Technique | Effect |
|---|---|---|
| Design | Symmetric proof-mass and spring design; geometries of decoupled suspension used to minimize the mechanical coupling. | Lowers intrinsic CAS (often <0.5%). |
| Design | Optimize die-to-package orientation during assembly; employ alignment marks and automated flip-chip bonding. | Reduces package-level CAS. |
| Fabrication | Tight control of etching and deposition tolerances; stress-relief anneals. | Reduces coupling that is caused by asymmetry. |
| Circuit | Separate analog front-ends with shielding; differential routing to suppress crosstalk. | Cuts electrical CAS. |
| System Integration | Accurate layout of PCB with the orthogonal mounting holes; with the calibration fixtures that makes the module in line with the board reference frame. | Limits system-level CAS. |
| Calibration & Compensation | Perform multi axis calibration (6 degree of freedom) to estimate Full CAS matrix, perform real time matrix inversion in firmware. | Eliminates low level CAS from output data. |
| Temperature Compensation | Model CAS drift versus temperature and update compensation coefficients on-the-fly. | Keeps CAS stable across operating range. |
6. IMU Manufacturers Practical Design Checklist
- Specify Target CAS – Specify a maximum possible CAS (e.g. less than or equal to 0.2 per cent for consumer grade, less than or equal to 0.05 per cent for industrial).
- Prototype Characterization – Test CAS on test silicon on the above methods of testing; repeat mechanical design until stable.
- Package Alignment Control – Implement Automated die-to-package alignment validation (X-ray and optical inspection).
- PCB & Module Layout Review – Verify orthogonal mounting tolerances (< 0.1°) and isolate analog routing.
- Factory Calibration – Attach a six axis calibration operation that retrieves the complete CAS matrix and loads it in non-volatile memory.
- Temperature Test Matrix – Experiments Verify CAS over entire operating temperature; produce tables of compensation.
- Documentation – The CAS specifications (individual terms and max) should be published in the datasheet along with recommended calibration procedures.
7. Concluding Remarks
Cross-axis sensitivity is one of the unavoidable flaws of IMUs based on MEMS, due to both mechanical and electrical, as well as system-level cause. Although it cannot be completely avoided, mechanical design, assembly, circuit isolation, and extensive calibration can be used to minimize CAS to values that are acceptable in most applications. It can be used to make IMUs that can predictively perform at their intended effectiveness with low post-processing overheads by modeling CAS as a first-order error term, and incurring it as a cost against the error budget of the sensor.