As a developer I always found these maths-first approaches to Kalman filters impenetrable (I guess that betrays my lack of knowledge, I dare cast no aspersions on the quality of these explanations!). However, if like me, it helps with the learning curve to implement it first, here's a 1-dimensional version simplified from my blog:
function transpose(a) { return a } // 1x1 matrix eg a single value.
function invert(a) { return 1/a }
const qExternalNoiseVariance = 0.1
const rMeasurementNoiseVariance = 0.1
const fStateTransition = 1
let pStateError = 1
let xCurrentState = rawDataArray[0]
for (const zMeasurement in rawDataArray) {
const xPredicted = fStateTransition * xCurrentState
const pPredicted = fStateTransition * pStateError * transpose(fStateTransition) + qExternalNoiseVariance
const kKalmanGain = pPredicted * invert(pPredicted + rMeasurementNoiseVariance)
pStateError = pPredicted - kKalmanGain * pPredicted
xCurrentState = xPredicted + kKalmanGain * (zMeasurement - xPredicted) // Output!
}