Purpose – A full-order multi-objective anti-disturbance robust filter for SINS/GPS navigation systems with multiple disturbances is designed. Generally, the unmodeled dynamics, the external environmental disturbance and the inertial apparatus random drift may exist simultaneously in an integrated navigation system, which can be classified into three type of disturbances, that is, the Gaussian noise, the norm bounded noise and the time correlated noise. In most classical studies, the disturbances in integrated navigation systems are classified as Gaussian noises or norm bounded noises, where the Kalman filtering or robust filtering can be employed, respectively. While it is not true actually, such assumptions may lead to conservative results. The paper aims to discuss these issues. Design/methodology/approach – The Gaussian noises, the norm bounded noises and the time correlated noises in the integrated navigation system are considered simultaneously in this contribution. As a result, the time correlated noises are augmented as a part of system state of the integrated navigation system error model, the relative integrated navigation problem can be transformed into a full-order multi-objective robust filter design problem for systems with Gaussian noises and norm bounded disturbances. Certainly, the errors of the time correlated noises are estimated and compensated for high precision navigation purpose. Sufficient conditions for the existence of the proposed filter are presented in terms of linear matrix inequalities (LMIs) such that the system stability is guaranteed and the disturbance attenuation performance is achieved. Findings – Simulations for SINS/GPS integrated navigation system given show that the proposed full-order multi-objective anti-disturbance filter, has stronger robustness and better precision when multiple disturbances exist, that is, the present algorithm not only can suppression the effect of white noises and norm bounded disturbance but also can estimate and compensate the modeled disturbance. Originality/value – The proposed algorithm has stronger anti-disturbance ability for integrated navigation with multiple disturbances. In fact, there exist multiple disturbances in integrated navigation system, so the proposed scheme has important significance in applications.