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Signal Processing

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  • $\begingroup$ Thanks for your answer! I tried the constant jerk model (4-state Kalman filter) and obtained less phase-lag acceleration estimation, but also introduced much larger error. I edit the question to share the trial. Can we somehow reduce phase lag while maintaining error level? $\endgroup$ Commented Mar 23, 2020 at 8:25
  • $\begingroup$ Just some thoughts... The simulated acceleration is periodic, so really you would need an infinite order polynomial to truly capture the process dynamics. The process noise captures this model mismatch, so increasing Q essentially gives the model more flexibility, but will increase the estimate noise. Decreasing Q increases lag. An excellent discussion on this topic which directly addresses tradeoffs in model order, selection of Q, and the resulting filter lag and performance can be found in Ch. 5 of Fundamentals of Kalman Filtering by Paul Zarchan. Highly recommend. $\endgroup$ Commented Mar 23, 2020 at 15:34