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Kalman Filter for 1D State-Space Model

Medium · time_series · Quant Researcher interview question · kalman_filter, state_space, recursive_estimation, signal_extraction, time_series

Financial signals like true mid-price or alpha are latent and must be inferred from noisy market data. The Kalman filter provides an optimal recursive solution for estimating such signals from linear Gaussian state-space models. It is widely used in quantitative trading for tasks ranging from fair-value estimation to regime tracking. Task Implement the function kalman_filter_1d(observations, a, h, Q, R, x0, P0) to compute filtered state estimates for a 1D linear Gaussian state-space model. The