LinearGaussianStateSpaceModel distribution and 1D time series

Is there a way to create a LinearGaussianStateSpaceModel for a 1D time series using the function tfd.JointDistributionSequential?

The model I want to create is as follow:

z0 = 0
z[t] = z[t-1] + epsilon[t], with epsilon[t] ~ N(0, state_std)
y[t] = z[t] + eta[t], with eta[t] ~ N(0, obs_std)

For example in JAGS I can write:

# State equation
z0 <- 0
state.precision <- 1 / (state_std * state_std)
obs.precision <- 1 / (obs_std * obs_std)

z[1] ~ dnorm(z0, state.precision)
for(t in 2:T) {
    z[t] ~ dnorm(z[t-1], state.precision)
}

# Observation equation
for(t in 1:T)  {
    y[t] ~ dnorm(z[t], obs.precision)
}

Thanks in advance !

Start by reading the LinearGaussianStateSpaceModel and tfd.JointDistributionSequential entry points mentioned in the issue, then compare their expected inputs with the supplied JAGS state and observation equations. No repository file or test is named; done would be a documented, working construction for the requested 1D time series, with its behavior verified against the stated model.