diff --git a/src/Accelerators.jl b/src/Accelerators.jl
index fea306743..78ce9021b 100644
--- a/src/Accelerators.jl
+++ b/src/Accelerators.jl
@@ -63,32 +63,3 @@ function update_state!(
     ## push "v" state to EKP object
     push!(ekp.u, DataContainer(v, data_are_columns = true))
 end
-
-
-"""
-State update method for UKI with no acceleration.
-The Accelerator framework has not yet been integrated with UKI process;
-UKI tracks its own states, so this method is empty.
-"""
-function update_state!(
-    ekp::EnsembleKalmanProcess{FT, IT, P, LRS, DefaultAccelerator},
-    u::MA,
-) where {FT <: AbstractFloat, IT <: Int, P <: Unscented, LRS <: LearningRateScheduler, MA <: AbstractMatrix{FT}}
-
-end
-
-"""
-Placeholder state update method for UKI with Nesterov Accelerator.
-The Accelerator framework has not yet been integrated with UKI process, so this
-method throws an error.
-"""
-function update_state!(
-    ekp::EnsembleKalmanProcess{FT, IT, P, LRS, NesterovAccelerator{FT}},
-    u::MA,
-) where {FT <: AbstractFloat, IT <: Int, P <: Unscented, LRS <: LearningRateScheduler, MA <: AbstractMatrix{FT}}
-    throw(
-        ArgumentError(
-            "option `accelerator = NesterovAccelerator` is not implemented for UKI, please use `DefaultAccelerator`",
-        ),
-    )
-end
diff --git a/src/EnsembleKalmanProcess.jl b/src/EnsembleKalmanProcess.jl
index 803cf62f0..f5d1506da 100644
--- a/src/EnsembleKalmanProcess.jl
+++ b/src/EnsembleKalmanProcess.jl
@@ -696,11 +696,13 @@ include("SparseEnsembleKalmanInversion.jl")
 export Sampler
 include("EnsembleKalmanSampler.jl")
 
+# struct Accelerator
+# [Must go before Unscented include]
+include("Accelerators.jl")
+
+
 # struct Unscented
 export Unscented
 export Gaussian_2d
 export construct_initial_ensemble, construct_mean, construct_cov
 include("UnscentedKalmanInversion.jl")
-
-# struct Accelerator
-include("Accelerators.jl")
diff --git a/src/UnscentedKalmanInversion.jl b/src/UnscentedKalmanInversion.jl
index 99483822d..25b51d012 100644
--- a/src/UnscentedKalmanInversion.jl
+++ b/src/UnscentedKalmanInversion.jl
@@ -226,8 +226,12 @@ function EnsembleKalmanProcess(
     process::Unscented{FT, IT};
     kwargs...,
 ) where {FT <: AbstractFloat, IT <: Int}
+
+    u_mean = process.u_mean[end]
+    uu_cov = process.uu_cov[end]
+
     # use the distribution stored in process to generate initial ensemble
-    init_params = update_ensemble_prediction!(process, 0.0)
+    init_params = update_ensemble_prediction!(process, u_mean, uu_cov, 0.0)
 
     return EnsembleKalmanProcess(init_params, obs_mean, obs_noise_cov, process; kwargs...)
 end
@@ -235,10 +239,10 @@ end
 function FailureHandler(process::Unscented, method::IgnoreFailures)
     function failsafe_update(uki, u, g, failed_ens)
         #perform analysis on the model runs
-        update_ensemble_analysis!(uki, u, g)
+        u_mean, uu_cov = update_ensemble_analysis!(uki, u, g)
         #perform new prediction output to model parameters u_p
-        u = update_ensemble_prediction!(uki.process, uki.Δt[end])
-        return u
+        u_p = update_ensemble_prediction!(uki.process, u_mean, uu_cov, uki.Δt[end])
+        return u_p, u_mean, uu_cov
     end
     return FailureHandler{Unscented, IgnoreFailures}(failsafe_update)
 end
@@ -290,19 +294,19 @@ function FailureHandler(process::Unscented, method::SampleSuccGauss)
 
         ########### Save results
         push!(uki.process.obs_pred, g_mean) # N_ens x N_data
-        push!(uki.process.u_mean, u_mean) # N_ens x N_params
-        push!(uki.process.uu_cov, uu_cov) # N_ens x N_data
 
         push!(uki.g, DataContainer(g, data_are_columns = true))
 
         compute_error!(uki)
+
+        return u_mean, uu_cov
     end
     function failsafe_update(uki, u, g, failed_ens)
         #perform analysis on the model runs
-        succ_gauss_analysis!(uki, u, g, failed_ens)
+        u_mean, uu_cov = succ_gauss_analysis!(uki, u, g, failed_ens)
         #perform new prediction output to model parameters u_p
-        u = update_ensemble_prediction!(uki.process, uki.Δt[end])
-        return u
+        u = update_ensemble_prediction!(uki.process, u_mean, uu_cov, uki.Δt[end])
+        return u, u_mean, uu_cov
     end
     return FailureHandler{Unscented, SampleSuccGauss}(failsafe_update)
 end
@@ -355,6 +359,47 @@ function construct_sigma_ensemble(
     return x
 end
 
+"""
+State update method for UKI with no acceleration. Here it simply saves it.
+"""
+function update_state!(
+    uki::EnsembleKalmanProcess{FT, IT, P, LRS, DefaultAccelerator},
+    u_tuple::TT,
+) where {FT <: AbstractFloat, IT <: Int, P <: Unscented, LRS <: LearningRateScheduler, TT <: Tuple}
+
+    (u, u_mean, uu_cov) = u_tuple
+
+    ## push  state to UKI object
+    push!(uki.u, DataContainer(u, data_are_columns = true))
+    push!(uki.process.u_mean, u_mean) # N_ens x N_params 
+    push!(uki.process.uu_cov, uu_cov) # N_ens x N_data
+end
+
+"""
+State update method for UKI with Nesterov Accelerator.
+Performs identical update as with other methods, but requires reconstruction of mean and covariance of the accelerated positions prior to saving.
+"""
+function update_state!(
+    uki::EnsembleKalmanProcess{FT, IT, P, LRS, NesterovAccelerator{FT}},
+    u_tuple::TT,
+) where {FT <: AbstractFloat, IT <: Int, P <: Unscented, LRS <: LearningRateScheduler, TT <: Tuple}
+
+    (u, u_mean, uu_cov) = u_tuple
+
+    #identical update stage as before
+    ## update "v" state:
+    k = get_N_iterations(uki) + 2
+    v = u .+ (1 - uki.accelerator.r / k) * (u .- uki.accelerator.u_prev)
+
+    ## update "u" state: 
+    uki.accelerator.u_prev = u
+
+    ## push "v" state to UKI object
+    push!(uki.u, DataContainer(v, data_are_columns = true))
+    push!(uki.process.u_mean, construct_mean(uki, v)) # N_ens x N_params 
+    push!(uki.process.uu_cov, construct_cov(uki, v)) # N_ens x N_data
+
+end
 
 """
     construct_mean(
@@ -550,7 +595,12 @@ end
 
 UKI prediction step : generate sigma points.
 """
-function update_ensemble_prediction!(process::Unscented, Δt::FT) where {FT <: AbstractFloat}
+function update_ensemble_prediction!(
+    process::Unscented,
+    u_mean::AV,
+    uu_cov::AM,
+    Δt::FT,
+) where {FT <: AbstractFloat, AV <: AbstractVector, AM <: AbstractMatrix}
 
     process.iter += 1
     # update evolution covariance matrix
@@ -558,14 +608,14 @@ function update_ensemble_prediction!(process::Unscented, Δt::FT) where {FT <: A
         process.Σ_ω = (2 - process.α_reg^2) * process.uu_cov[end]
     end
 
-    u_mean = process.u_mean[end]
-    uu_cov = process.uu_cov[end]
+    #    u_mean = process.u_mean[end]
+    #    uu_cov = process.uu_cov[end]
 
     α_reg = process.α_reg
     r = process.r
     Σ_ω = process.Σ_ω
 
-    N_par = length(process.u_mean[1])
+    N_par = length(u_mean[1])
     ############# Prediction step:
 
     u_p_mean = α_reg * u_mean + (1 - α_reg) * r
@@ -621,12 +671,11 @@ function update_ensemble_analysis!(
 
     ########### Save results
     push!(uki.process.obs_pred, g_mean) # N_ens x N_data
-    push!(uki.process.u_mean, u_mean) # N_ens x N_params
-    push!(uki.process.uu_cov, uu_cov) # N_ens x N_data
 
     push!(uki.g, DataContainer(g, data_are_columns = true))
 
     compute_error!(uki)
+    return u_mean, uu_cov
 end
 
 """
@@ -675,16 +724,14 @@ function update_ensemble!(
         @info "$(length(failed_ens)) particle failure(s) detected. Handler used: $(nameof(typeof(fh).parameters[2]))."
     end
 
-    u_p = fh.failsafe_update(uki, u_p_old, g_in, failed_ens)
+    u_p, u_mean, uu_cov = fh.failsafe_update(uki, u_p_old, g_in, failed_ens)
 
-    push!(uki.u, DataContainer(u_p, data_are_columns = true))
 
     if uki.verbose
-        cov_new = get_u_cov_final(uki)
-        @info "Covariance-weighted error: $(get_error(uki)[end])\nCovariance trace: $(tr(cov_new))\nCovariance trace ratio (current/previous): $(tr(cov_new)/tr(cov_init))"
+        @info "Covariance-weighted error: $(get_error(uki)[end])\nCovariance trace: $(tr(uu_cov))\nCovariance trace ratio (current/previous): $(tr(uu_cov)/tr(cov_init))"
     end
 
-    return u_p
+    return u_p, u_mean, uu_cov
 end
 
 """
diff --git a/test/EnsembleKalmanProcess/runtests.jl b/test/EnsembleKalmanProcess/runtests.jl
index 519db3961..28af52be0 100644
--- a/test/EnsembleKalmanProcess/runtests.jl
+++ b/test/EnsembleKalmanProcess/runtests.jl
@@ -81,8 +81,9 @@ end
 
 @testset "Accelerators" begin
     # Get an inverse problem
-    y_obs, G, Γy, _ = inv_problems[end - 1] # additive noise inv problem
+    y_obs, G, Γy, _ = inv_problems[end - 2] # additive noise inv problem (deterministic map)
     rng = Random.MersenneTwister(rng_seed)
+    N_ens = 5
     initial_ensemble = EKP.construct_initial_ensemble(rng, prior, N_ens)
 
     # build accelerated and non-accelerated processes
@@ -104,36 +105,48 @@ end
     @test typeof(eksobj_noacc_specified.accelerator) <: DefaultAccelerator
 
     ## test NesterovAccelerators satisfy desired ICs
-    @test ekiobj.accelerator.r == 3.0
+    @test ekiobj.accelerator.r ≈ 3.0
     @test ekiobj.accelerator.u_prev == initial_ensemble
-    @test eksobj.accelerator.r == 3.0
+    @test eksobj.accelerator.r ≈ 3.0
     @test eksobj.accelerator.u_prev == initial_ensemble
 
     ## test method convergence
     # Note: this test only requires that the final ensemble is an improvement on the initial ensemble,
     # NOT that the accelerated processes are more effective than the default, as this is not guaranteed.
     # Specific cost values are printed to give an idea of acceleration.
-    processes = [Inversion(), Sampler(prior), TransformInversion(inv(Γy))]
-    T_end = 1 # (this could fail a test if N_iters is not enough to reach T_end)
+    processes = [Inversion(), TransformInversion(inv(Γy)), Unscented(prior; impose_prior = true), Sampler(prior)]
+
     for process in processes
         accelerators = [DefaultAccelerator(), NesterovAccelerator()]
-        N_iters = [30, 30, 30]
+        N_iters = [5, 5, 5, 5]
         init_means = []
         final_means = []
-
+        scheduler = DefaultScheduler(0.1)# DataMisfitController()
         for (accelerator, N_iter) in zip(accelerators, N_iters)
-            println("Accelerator: ", nameof(typeof(accelerator)), " Process: ", nameof(typeof(process)))
+            process_copy = deepcopy(process)
+            scheduler_copy = deepcopy(scheduler)
+            println("Accelerator: ", nameof(typeof(accelerator)), " Process: ", nameof(typeof(process_copy)))
             if !(nameof(typeof(process)) == Symbol(Unscented))
                 ekpobj = EKP.EnsembleKalmanProcess(
                     initial_ensemble,
                     y_obs,
                     Γy,
-                    process,
+                    process_copy,
+                    rng = copy(rng),
+                    scheduler = scheduler_copy,
+                    accelerator = accelerator,
+                    verbose = true,
+                )
+            else
+                ekpobj = EKP.EnsembleKalmanProcess(
+                    y_obs,
+                    Γy,
+                    process_copy,
                     rng = copy(rng),
+                    scheduler = scheduler_copy,
                     accelerator = accelerator,
                 )
             end
-
             ## test get_accelerator function in EKP
             @test ekpobj.accelerator == get_accelerator(ekpobj)
 
@@ -155,7 +168,7 @@ end
                 norm(inv_sqrt_Γy * (y_obs .- G(transform_unconstrained_to_constrained(prior, final_means[end]))))
             @info "Convergence:" cost_initial cost_final
 
-            if typeof(process) <: Inversion
+            if typeof(process_copy) <: Inversion
                 u_star = transform_constrained_to_unconstrained(prior, ϕ_star)
                 @test norm(
                     inv_sqrt_Γy * (y_obs .- G(transform_unconstrained_to_constrained(prior, final_means[end]))),
@@ -165,15 +178,7 @@ end
         end
 
     end
-    ## test that error is thrown when applying acceleration to UKI
-    ukiobj = EKP.EnsembleKalmanProcess(
-        y_obs,
-        Γy,
-        Unscented(prior; impose_prior = true),
-        rng = copy(rng),
-        accelerator = NesterovAccelerator(),
-    )
-    @test_throws ArgumentError EKP.update_ensemble!(ukiobj, zeros(length(y_obs), 5))
+
 end