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Performance tips

Use of StaticArrays.jl is recommended for optimal performance when the state dimension is small, e.g., less than about 10-15 for Kalman filters and less than about 100 for particle filters. In the section Parameter optimization we demonstrate one workflow that makes use of StaticArrays everywhere it is needed for an UnscentedKalmanFilter in order to get a completely allocation free filter. The following arrays must be static for this to hold

  • The initial state distribution (the vector and matrix passed to d0 = MvNormal(μ, Σ) for Kalman filters). If you are performing parameter optimization with gradients derived using ForwardDiff.jl, these must further have the correct element type. How to achieve this is demonstrated in the liked example above.
  • Inputs u measured outputs y.
  • In case of Kalman filters, the dynamic model matrices A, B, C, D and the covariance matrices R1, R2.
  • The dynamics functions for UnscentedKalmanFilter and particle filters must further return static arrays when passed static arrays as inputs.

Analysis using JET

All flavors of Kalman filters are analyzed for potential runtime dispatch using JET.jl. This analysis is performed in the tests and generally requires a completely static filter using static arrays internally. See the tests for an example of how to set a filter up this way.

High performance Distributions

When using LowLevelParticleFilters, a number of methods related to distributions are defined for static arrays, making logpdf etc. faster. We also provide a new kind of distribution: TupleProduct <: MultivariateDistribution that behaves similarly to the Product distribution. The TupleProduct however stores the individual distributions in a tuple, has compile-time known length and supports Mixed <: ValueSupport, meaning that it can be a product of both Continuous and Discrete dimensions, something not supported by the standard Product. Example

using BenchmarkTools, LowLevelParticleFilters, Distributions, StaticArrays
dt = TupleProduct((Normal(0,2), Normal(0,2), Binomial())) # Mixed value support

A small benchmark

sv = @SVector randn(2)
d = Distributions.Product([Normal(0,2), Normal(0,2)])
dt = TupleProduct((Normal(0,2), Normal(0,2)))
dm = MvNormal(2, 2)
@btime logpdf($d,$(Vector(sv)))  # 19.536 ns (0 allocations: 0 bytes)
@btime logpdf($dt,$(Vector(sv))) # 13.742 ns (0 allocations: 0 bytes)
@btime logpdf($dm,$(Vector(sv))) # 11.392 ns (0 allocations: 0 bytes)
@btime logpdf($d,$sv)  # 13.964 ns (0 allocations: 0 bytes)
@btime logpdf($dt,$sv) # 12.817 ns (0 allocations: 0 bytes)
@btime logpdf($dm,$sv) # 8.383  ns (0 allocations: 0 bytes)

Without loading LowLevelParticleFilters, the timing for the native distributions are the following

@btime logpdf($d,$sv)  # 18.040 ns (0 allocations: 0 bytes)
@btime logpdf($dm,$sv) # 9.938  ns (0 allocations: 0 bytes)