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#!/usr/bin/awk -f
### kalman.awk
# kalman csv experiemnt
BEGIN {
OMFT = "%.18"
sign = "[+-]?"
decimal = "[0-9]+[.]?[0-9]*"
fraction = "[.][0-9]*"
exponent = "([Ee]" sign "[0-9]+)?"
number = "^" sign "(" decimal "|" fraction ")" exponent "$"
}
NR == 1 {
header_nf = NF
for (n=1; n<=NF; n++) {
($n !~ number) ? header[n] = "d" $n : header[n] = "col_" n
}
}
NF != 0 {
print ORS NR ":" OFS $0 ORS
if (NF > max_nf)
max_nf = NF
### iterate over columns
for (n=1; n<=max_nf; n++) {
if ($n ~ number) {
count[n] = ($n ~ number) + (last[n] ~ number) + (last2[n] ~ number)
diff[n] = $n - last[n]
diff2[n] = 0.5*($n - 2.0*last[n] + last2[n])
sum[n] = $n + last[n] + last2[n]
(count[n]) ? mean[n] = sum[n]/count[n] : mean[n] = sum[n]
delta[n] = $n - mean[n]
delta2[n] = delta[n]*delta[n]
sum_delta[n] = delta[n] + delta_last[n] + delta_last2[n]
sum_delta2[n] = delta2[n] + delta2_last[n] + delta2_last2[n]
(count[n] > 1) ? var[n] = sum_delta2[n]/(count[n] - 1) : var[n] = 0
if (count[n]) {
meas_err[n] = sqrt(var[n]/count[n])
}
### error covariance
for (m=1; m<=max_nf; m++) {
count[m,n]++
sum_xy[m,n] += 1
delta_xy[m,n] = delta[m]*delta[n]
(count[m,n] > 1) ? meas_cov[m,n] = delta[m]*delta[n]/(count[m,n] - 1) : meas_cov[m,n] = 0
est_err_last_cov[m,n] = 1
print meas_cov[m,n], est_err_last_cov[m,n]
}
### kalman gain
if (count[n] <= 1) {
KG[n] = 1
est_err[n] = sqrt(diff[n]*diff[n]) + 2.0*sqrt(diff2[n]*diff2[n])
est_err_last[n] = sqrt(diff[n]*diff[n]) + 2.0*sqrt(diff2[n]*diff2[n])
}
else
KG[n] = est_err_last[n]/(est_err_last[n] + meas_err[n])
### update estimate and estimated error
est[n] = est_last[n] + KG[n]*($n - est_last[n])
est_err[n] = (1.0 - KG[n])*est_err_last[n]
### visual check
printf "meas: " OFS OFMT OFS OFMT OFS OFMT, $n, meas_err[n], count[n]
printf "d1: " OFS OFMT, diff[n]
printf "d2: " OFS OFMT, diff2[n]
printf "est: " OFS OFMT OFS OFMT OFS OFMT, est[n], est_err[n], KG[n]
### update previously remembered values
last2[n] = last[n]
last[n] = $n
diff_last2[n] = diff_last[n]
diff_last[n] = diff[n]
delta_last2[n] = delta_last[n]
delta_last[n] = delta[n]
delta2_last2[n] = delta2_last[n]
delta2_last[n] = delta2[n]
est_last[n] = est[n]
est_error_last[n] = est_error[n]
printf ORS
}
}
}
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