Scalar Kalman Filter Calculator
Filter ordered scalar measurements with a constant-state random-walk process model.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Apply process uncertainty before every measurement, including the first, with fixed known measurement variance.
Ppred=P+Q; gain=Ppred/(Ppred+R); x←x+gain(z−x); P←(1−gain)Ppred
Worked example
Prior mean0/variance1, Q0,R1 and measurements1,2,3 give final mean1.5 and variance0.25.
Assumptions and input details
Scalar identity observation/transition model, independent zero-mean Gaussian noises. No smoothing, dynamic velocity, learned noise parameters or model-validity guarantee.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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