Sample Complexity of Kalman Filtering for Unknown Systems

by   Anastasios Tsiamis, et al.
University of Pennsylvania

In this paper, we consider the task of designing a Kalman Filter (KF) for an unknown and partially observed autonomous linear time invariant system driven by process and sensor noise. To do so, we propose studying the following two step process: first, using system identification tools rooted in subspace methods, we obtain coarse finite-data estimates of the state-space parameters and Kalman gain describing the autonomous system; and second, we use these approximate parameters to design a filter which produces estimates of the system state. We show that when the system identification step produces sufficiently accurate estimates, or when the underlying true KF is sufficiently robust, that a Certainty Equivalent (CE) KF, i.e., one designed using the estimated parameters directly, enjoys provable sub-optimality guarantees. We further show that when these conditions fail, and in particular, when the CE KF is marginally stable (i.e., has eigenvalues very close to the unit circle), that imposing additional robustness constraints on the filter leads to similar sub-optimality guarantees. We further show that with high probability, both the CE and robust filters have mean prediction error bounded by Õ(1/√(N)), where N is the number of data points collected in the system identification step. To the best of our knowledge, these are the first end-to-end sample complexity bounds for the Kalman Filtering of an unknown system.


page 1

page 2

page 3

page 4


Online Learning of the Kalman Filter with Logarithmic Regret

In this paper, we consider the problem of predicting observations genera...

Learning the Kalman Filter with Fine-Grained Sample Complexity

We develop the first end-to-end sample complexity of model-free policy g...

Finite Sample Analysis of Stochastic System Identification

In this paper, we analyze the finite sample complexity of stochastic sys...

SLIP: Learning to Predict in Unknown Dynamical Systems with Long-Term Memory

We present an efficient and practical (polynomial time) algorithm for on...

Efficient learning of hidden state LTI state space models of unknown order

The aim of this paper is to address two related estimation problems aris...

UltimateKalman: Flexible Kalman Filtering and Smoothing Using Orthogonal Transformations

UltimateKalman is a flexible linear Kalman filter and smoother implement...

Adaptive Visual Servo Control for Autonomous Robots

This paper focuses on an adaptive and fault-tolerant vision-guided robot...

Please sign up or login with your details

Forgot password? Click here to reset