Augmenting Extended Kalman Filters with Dynamic Temperature Derivative State Models
Augmenting Extended Kalman Filters with dynamic temperature derivative states eliminates dynamic thermal bias drift during rapid ramp conditions.
Finite Impulse Response Differentiator
Mathematical Operator
Digital filter architectures designed to calculate the time derivative of a sampled signal utilize a finite number of weighted past input values. In high-speed sensor applications, the finite impulse response differentiator provides a bounded, stable calculation of rate-of-change data from discrete position or pressure measurements. The algorithm operates by convolving incoming data with a set of symmetric coefficient values.
Phase Integrity
Linear phase response represents the primary metrological advantage of this filter class because it preserves the alignment of different frequency components in the time domain. This characteristic prevents signal distortion and ensures that the calculated derivative remains synchronized with the physical event. The constant group delay allows the system to adjust for the latency through a simple temporal offset.
Noise Amplification
High-frequency sensor noise is inherently amplified by the differentiating process because the gain of the operator increases linearly with frequency. To mitigate this effect, the coefficient design includes a low-pass filter to attenuate signals above the frequency band of interest. Calibration engineers verify this attenuation across the entire measurement bandwidth to confirm that high-frequency electronic noise does not swamp the desired physical measurement.
Performance Boundary
Truncating the filter coefficients to a finite length introduces a trade-off between the flatness of the frequency response and the computational delay. A longer filter yields a more accurate derivative but increases the processing time and memory storage required by the microprocessor.