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The parameters and of this model can be estimated from observations of sensor outputs when the inputs are known, the process called calibration.

The purpose of calibration is sensor compensation, which is essentially inverting the input‐output of Equation 3.1 to obtain

(3.3)

the sensor inputs compensated for scale factor, misalignment, and bias errors.

This result can be generalized for a cluster of gyroscopes or accelerometers, the effects of individual biases,scale factors, and input axis misalignments can be modeled by an equation of the form

(3.4)

where is the Moore–Penrose pseudoinverse of the corresponding , which can be determined by calibration.