// multi-utility computation suite · offline · instant · precise
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│ computation suite │
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math.kalman-filter Calculator
Implements one step of the Kalman filter update — computing the Kalman gain and updating the state estimate and uncertainty from a new measurement. The Kalman filter is the optimal linear estimator under Gaussian noise — the algorithm behind GPS, autopilots, and inertial navigation.
Inputs
X Est
Reference formula or conversion factor shown for context.
P Est
The square of standard deviation. Less intuitive than SD (units are squared), but used in many statistical formulas.
Z Meas
Reference formula or conversion factor shown for context.
R Meas
The square of standard deviation. Less intuitive than SD (units are squared), but used in many statistical formulas.
Results
updated estimate
The value at the specified point or condition.
Kalman gain K
The improvement or increase over the baseline.
updated variance P
Standard deviation squared — average squared deviation from the mean. Essential for ANOVA, regression, and many statistical tests, though the squared units make it less intuitive directly.
innovation (z-x)
The value at the specified point or condition.
K=0 means ignore measurement, K=1 trust fully
Arithmetic average — sum divided by count. Simple and familiar, but pulled by outliers. If your data contains extreme values, the median may be more representative.
filter type
The classification or type assigned based on the inputs.