Discrete Kalman Process Noise Covariance Derivation from Inertial Bench Test Metrics
Bench Allan variance parameters convert to discrete Kalman process noise matrices by integrating state transition matrices over the sampling interval.
Sampling Frequency
Rate Specification
Temporal resolution parameters define the number of data points collected from a continuous signal over a specific unit of time. The chosen sampling frequency determines the ability of a digital system to capture the high-frequency components of an analog input. It is expressed in hertz and represents the reciprocal of the time interval between successive measurements.
Nyquist Limit
Nyquist limits dictate that the frequency must be at least twice the highest frequency present in the signal to prevent aliasing. When the sampling frequency falls below this threshold, high-frequency signals appear as low-frequency artifacts that cannot be removed by digital filtering. This phenomenon distorts the data and invalidates the results.
Hardware Capability
Hardware capabilities constrain the maximum rate at which a system can operate. High-speed analog-to-digital converters allow for a high sampling frequency, but they also generate larger volumes of data that must be stored or transmitted. The choice of rate involves a balance between the bandwidth of the phenomenon being measured and the memory limits of the processor.
Designers often employ anti-aliasing filters before the converter to remove frequencies that exceed half the sampling rate.
Power Consumption
Power consumption is directly linked to the speed of data acquisition. A higher sampling frequency requires more frequent sensor activation and more intensive processing, which drains battery life in remote deployments. Reducing the rate extends the operational life of the device.