diff --git a/test/Project.toml b/test/Project.toml
index 686826f..d7556c9 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,9 +1,14 @@
 [deps]
 AbstractMCMC = "80f14c24-f653-4e6a-9b94-39d6b0f70001"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+DynamicIterators = "6c76993d-992e-5bf1-9e63-34920a5a5a38"
+GaussianDistributions = "43dcc890-d446-5863-8d1a-14597580bb8d"
+HypothesisTests = "09f84164-cd44-5f33-b23f-e6b0d136a0d5"
+Kalman = "d59c0ba6-2ef2-5409-8dc5-1fd9a2b46832"
 Libtask = "6f1fad26-d15e-5dc8-ae53-837a1d7b8c9f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Random123 = "74087812-796a-5b5d-8853-05524746bad3"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 SSMProblems = "26aad666-b158-4e64-9d35-0e672562fa48"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
diff --git a/test/linear-gaussian.jl b/test/linear-gaussian.jl
new file mode 100644
index 0000000..9872f1f
--- /dev/null
+++ b/test/linear-gaussian.jl
@@ -0,0 +1,111 @@
+"""
+Unit tests for the validity of the SMC algorithms included in this package.
+
+We test each SMC algorithm on a one-dimensional linear Gaussian state space model for which
+an analytic filtering distribution can be computed using the Kalman filter provided by the
+`Kalman.jl` package.
+
+The validity of the algorithm is tested by comparing the final estimated filtering
+distribution ground truth using a one-sided Kolmogorov-Smirnov test.
+"""
+
+using DynamicIterators
+using GaussianDistributions
+using HypothesisTests
+using Kalman
+
+function test_algorithm(rng, algorithm, model, N_SAMPLES, Xf)
+    chains = sample(rng, model, algorithm, N_SAMPLES; progress=false)
+    particles = hcat([chain.trajectory.model.X for chain in chains]...)
+    final_particles = particles[:, end]
+
+    test = ExactOneSampleKSTest(final_particles, Normal(Xf.x[end].μ, sqrt(Xf.x[end].Σ)))
+    return pvalue(test)
+end
+
+@testset "linear-gaussian.jl" begin
+    T = 3
+    N_PARTICLES = 100
+    N_SAMPLES = 50
+
+    # Model dynamics
+    a = 0.5
+    b = 0.2
+    q = 0.1
+    E = LinearEvolution(a, Gaussian(b, q))
+
+    H = 1.0
+    R = 0.1
+    Obs = LinearObservationModel(H, R)
+
+    x0 = 0.0
+    P0 = 1.0
+    G0 = Gaussian(x0, P0)
+
+    M = LinearStateSpaceModel(E, Obs)
+    O = LinearObservation(E, H, R)
+
+    # Simulate from model
+    rng = StableRNG(1234)
+    initial = rand(rng, StateObs(G0, M.obs))
+    trajectory = trace(DynamicIterators.Sampled(M, rng), 1 => initial, endtime(T))
+    y_pairs = collect(t => y for (t, (x, y)) in pairs(trajectory))
+    ys = [y for (t, (x, y)) in pairs(trajectory)]
+
+    # Ground truth smoothing
+    Xf, ll = kalmanfilter(M, 1 => G0, y_pairs)
+
+    # Define AdvancedPS model
+    mutable struct LinearGaussianParams
+        a::Float64
+        b::Float64
+        q::Float64
+        h::Float64
+        r::Float64
+        x0::Float64
+        p0::Float64
+    end
+
+    mutable struct LinearGaussianModel <: SSMProblems.AbstractStateSpaceModel
+        X::Vector{Float64}
+        observations::Vector{Float64}
+        θ::LinearGaussianParams
+        function LinearGaussianModel(y::Vector{Float64}, θ::LinearGaussianParams)
+            return new(Vector{Float64}(), y, θ)
+        end
+    end
+
+    function SSMProblems.transition!!(rng::AbstractRNG, model::LinearGaussianModel)
+        return rand(rng, Normal(model.θ.x0, model.θ.p0))
+    end
+    function SSMProblems.transition!!(
+        rng::AbstractRNG, model::LinearGaussianModel, state, step
+    )
+        return rand(rng, Normal(model.θ.a * state + model.θ.b, model.θ.q))
+    end
+    function SSMProblems.transition_logdensity(
+        model::LinearGaussianModel, prev_state, current_state, step
+    )
+        return logpdf(Normal(model.θ.a * prev_state + model.θ.b, model.θ.q), current_state)
+    end
+    function SSMProblems.emission_logdensity(model::LinearGaussianModel, state, step)
+        return logpdf(Normal(model.θ.h * state, model.θ.r), model.observations[step])
+    end
+
+    AdvancedPS.isdone(::LinearGaussianModel, step) = step > T
+
+    params = LinearGaussianParams(a, b, q, H, R, x0, P0)
+    model = LinearGaussianModel(ys, params)
+
+    @testset "PGAS" begin
+        pgas = AdvancedPS.PGAS(N_PARTICLES)
+        p = test_algorithm(rng, pgas, model, N_SAMPLES, Xf)
+        @test p > 0.05
+    end
+
+    @testset "PG" begin
+        pg = AdvancedPS.PG(N_PARTICLES)
+        p = test_algorithm(rng, pg, model, N_SAMPLES, Xf)
+        @test p > 0.05
+    end
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index b2c0990..03dd253 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -3,6 +3,7 @@ using AbstractMCMC
 using Distributions
 using Libtask
 using Random
+using StableRNGs
 using Test
 using SSMProblems
 
@@ -22,4 +23,7 @@ using SSMProblems
     @testset "PG-AS" begin
         include("pgas.jl")
     end
+    @testset "Linear Gaussian SSM tests" begin
+        include("linear-gaussian.jl")
+    end
 end