1. Biological and statistical complexity are features common to most ecological data that hinder our ability to extract meaningful patterns using conventional tools. Recent work on implementing modern statistical methods for analysis of such ecological data has focused primarily on population dynamics but other types of data, such as animal movement pathways obtained from satellite telemetry, can also benefit from the application of modern statistical tools. 2. We develop a robust hierarchical state-space approach for analysis of multiple satellite telemetry pathways obtained via the Argos system. State-space models are time-series methods that allow unobserved states and biological parameters to be estimated from data observed with error. We show that the approach can reveal important patterns in complex, noisy data where conventional methods cannot. 3. Using the largest Atlantic satellite telemetry data set for critically endangered leatherback turtles, we show that the diel pattern in travel rates of these turtles changes over different phases of their migratory cycle. While foraging in northern waters the turtles show similar travel rates during day and night, but on their southward migration to tropical waters travel rates are markedly faster during the day. These patterns are generally consistent with diving data, and may be related to changes in foraging behaviour. Interestingly, individuals that migrate southward to breed generally show higher daytime travel rates than individuals that migrate southward in a non-breeding year. 4. Our approach is extremely flexible and can be applied to many ecological analyses that use complex, sequential data.