It can be life-saving to monitor the respiratory rate (RR) even for healthy people in real-time. It is reported that the infected people with coronavirus disease 2019 (COVID-19), generally develop mild respiratory symptoms in the early stage. It will be more important to continuously monitor the RR of people in nursing homes and houses with a non-contact method. Conventional, contact-based, methods are not suitable for long-term health monitoring especially in-home care services. The potentials of wireless radio signals for health care applications, such as fall detection, etc., are examined in literature. In this paper, we focus on a device-free real-time RR monitoring system using wireless signals. In our recent study, we proposed a non-contact RR monitoring system with a batch processing (delayed) estimation method. In this paper, for real-time monitoring, we modify the standard joint unscented Kalman filter (JUKF) method for this new and time-critical problem. Due to the nonlinear structure of the RR estimation problem with respect to the measurements, a novel modification is proposed to transform measurement errors into parameter errors by using the hyperbolic tangent function. It is shown in the experiments conducted with the real measurements taken using healthy volunteers that the proposed modified joint unscented Kalman filter (ModJUKF) method achieves the highest accuracy according to the windowing-based methods in the timevarying RR scenario. It is also shown that the ModJUKF not only reduces the computational complexity approximately 8.54% but also improves the accuracy 36.7% with respect to the standard JUKF method. INDEX TERMS Unscented Kalman filter, joint unscented Kalman filter, respiratory rate tracking, devicefree, vital signs, health monitoring, radio signals.