Auxiliary particle filter

<p>In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, the auxiliary particle filter (APF) is a <a href="/facts/Particle_filter/192bI79g">particle filter</a> algorithm introduced by Michael K. Pitt and Neil Shephard in 1999 to improve upon the <a href="/facts/Sequential_importance_resampling/192bI79g">sequential importance resampling</a> (SIR) method, a technique in <a href="/facts/Bayesian_filtering/vzBrW5U4">Bayesian filtering</a> that uses random samples (or "particles") to track underlying patterns in noisy data. SIR can falter when observations come from <a href="/facts/Heavy-tailed_distribution/BHLSHPku">heavy-tailed distributions</a>—where extreme values are more common than in typical models—leading to poor performance. The APF enhances this by using an auxiliary variable (an extra step to focus on likely samples) to guide the sampling process, making it more effective for complex <a href="/facts/State-space_model/Jf4EanCP">state-space models</a> (systems tracking hidden patterns over time). 
</p><p>For example, in tracking a stock price with sudden jumps, APF adapts to erratic changes better than SIR. This method is widely used in <a href="/facts/Time_series/fSXPR817">time series</a> analysis and <a href="/facts/Signal_processing/Npaja6zb">signal processing</a>.
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Auxiliary particle filter open-in-new

Auxiliary particle filter