Kalman filter implementation in the J Language

kalmanfilter.ijs

NB. Port of https://scipy-cookbook.readthedocs.io/items/KalmanFiltering.html

require 'stats/distribs/normal'   
n =: 50 			NB. number of steps to compute
x =: _0.37227		NB. real value

z =: (x , 0.1) rnorm n	NB. readings (normal distribution)
Q =: 1e_5			NB. process variance
R =: 0.1^2			NB. estimate of variance

NB. function to compute gain from previous P value
Kk =: ((Q + {:) % (R + (Q + {:)))

NB. error estimate
P =: ($:@(, ((1 - Kk)*(Q + {:)) ) ` [ @. (n&=@#)) 1

NB. Kalman gain (i.e. how much readings are weighted)
K =: (Q + (0,P)) % ((Q + (0,P)) + R)

NB. estimate of x
xhat =: ($:@(, ({: + ({&K@# * ({&z@# - {:)))) ` [ @.(n&=@#)) 0

NB. plot that sucker
pd 'reset'
pd 'type line'
pd xhat
pd (n $ x)
pd 'type dot'
pd 'pensize 2'
pd z
pd 'show'