How can I estimate a NAIRU in R using Kalman filter?

Question

I'm trying to estimate a NAIRU from Brazil using a Kalman filter in R. For this, I'm gonna use this two equations:

1. A Phillips Curve, so that the inflation is equal to his expectation, plus the difference in the unemployment and the NAIRU and plus three control variables. This equation will be the measurement equation of the state space model

2. Another equation modelling the NAIRU as a random walk. This equation will be de transition equation and the NAIRU will be the unobserved variable of the state space model

The equations will be something like this:

The two equatios of the state space model

I already have a data frame in R with all of those variables (except the NAIRU, obviously, because it is the variable that I want to estimate). My data frame with my variables is called "base" and those are my columns:

"date" "inflacao" "expec" "desem" "commo_ener" "cambio" "import"

Where "date" is the date of each observation, "inflacao" is the current inflation, "expec" is the inflation expectation for the period, "desem" is the unemployment for the period and the last three variables are the controls

This was one of my tentatives:

install.packages(c("KFAS", "ggplot2"))
library(KFAS)
library(ggplot2)

# Define the equations of the Phillips Curve model
modelo_CP <- SSModel(
  Z = matrix(c(1, -1, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0), nrow = 2, byrow = TRUE),
  H = diag(c(0.2, 0.1)),
  T = diag(c(1, 0.95, 1)),
  a1 = c(0, 0, 4),
  P1 = diag(c(1, 1, 1))
)

# Estime os parâmetros do modelo usando o filtro de Kalman
resultado_CP <- fitSSM(modelo_CP, y = as.matrix(base[, c("inflacao", "desem", "commo_ener", "cambio", "import")]))

# Estimate model parameters using Kalman filter
NAIRU_estimada_CP <- resultado_CP$state[, "state.1"]

# Create a data frame with NAIRU estimates and the unemployment variable
data_plot_CP <- data.frame(
  Date = base$date,
  NAIRU = NAIRU_estimada_CP,
  Desemprego = base$desem
)

# Create a plot with ggplot2 to visualize time series
ggplot(data_plot_CP, aes(x = Date)) +
  geom_line(aes(y = NAIRU, color = "NAIRU"), size = 1) +
  geom_line(aes(y = Desemprego, color = "Desemprego"), size = 1) +
  labs(y = "Valor", color = "Legenda") +
  scale_color_manual(values = c("NAIRU" = "blue", "Desemprego" = "red")) +
  theme_minimal()

I think I need to use the SSMregression() function, but I'm not understanding how to implement in my context