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Consider a sensor for which we are designing a Kalman filter for improved accuracy or sensor fusion. Let us restrict this discussion to the goal using the filter to improve the accuracy of the aposteriori state estimate and avoid addressing sensor fusion. Further, let us assume the state and output to be identical and one-dimensional for simplicity.

The designer of the Kalman filter assumes the knowledge of the system dynamics and output channels including apriori knowledge of the variance (or squared standard deviation or squared intensity) of the Gaussian white noise appearing in the process dynamics and observations. While the well known methods to determine the noise variances are as follows,

  1. the standard industry approach to determine the noise intensity is by tuning the value in the Kalman gain computation to improve closed-loop performance,
  2. the auto-correlation least squares method which uses closed-loop data,

it is not clear in the literature if there are any algorithms which use open-loop data for determining the noise covariance.

How is the intensity of the Gaussian white noise model of a sensor determined experimentally using open-loop data?

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  • \$\begingroup\$ If it's a model (as in white noise model) then surely you know it. \$\endgroup\$
    – Andy aka
    Mar 19 at 9:26
  • \$\begingroup\$ @Andyaka I mean how do we calculate the parameter (intensity) of the model. For instance, the transition dynamics too have parameters which we determine experimentally (mass for instance). \$\endgroup\$
    – kbakshi314
    Mar 19 at 9:31
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I would think using an FFT or Spectral Density Analyzer is the most common way to measure noise to determine the amplitude and see if it is Gaussian or filtered Gaussian (Brown or Pink or White noise for example) or if there is a DC component...

The filtering to obtain maximum SNR ought to be matched to pass the spectral density of the signal and inversely matched or attenuated to spectral distribution of noise to obtain the ideal S/N ratio.

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