## 1 Introduction  
Current control systems integrating communication, calculation, and control into different levels of factory operations and information processing have become the trend of modern military, commercial, and industrial systems [1, 2], one of which is the robust nonlinear uncertain heat exchange control system. In such systems, sensors are employed to increase the accuracy of processing options. The values of physical variables such as temperature are usually picked up by sensors. Sensor transducers and electronics are subject to various random noise mechanisms that may affect the signal [3]. The systems accept the measured value from sensors and control based on the measurement and control law; the control performance of which can be reduced due to the presence of random noise. Wireless communication for data exchange between different sensors, actuators and other components is playing an increasingly important role in recent control systems. Ideally, data exchange through wireless communication should be accurate, timely, and reliable so as not to decrease the control performance. However, any communication system inevitably introduces random communication delays, and the performance degradation caused by such communication faults should be minimized [4, 5]. Based on the above, both sensor noise and time delay are interference terms that need to be considered for the performance of a control system, where an approximation to the real value of the signal that has the reduced effect of measurements with noise and time delay is a feasible choice. In recent years, methods for estimation from values with noise or uncertainties have emerged [6, 7, 8, 9]. These methods can reduce the influence of noise or can act as an estimator to avoid the installation of real sensors, one of which is the particle filter (PF). The particle filter can estimate states, variance, and other parameters based on the measurement values with noise [10; 11; 12]. From the law of large numbers, the estimated value of the particle filter can be infinitely approximated to the real value when the number of particles is large enough. The particle filter approach has the potential to ease the influence of random noise and time delay and has been successfully applied to some noise attenuation problems [13] and time delay effect mitigation issues [14]. In recent systems, such as that of uncertain heat exchange process, to model the underlying dynamics of a physical system accurately, nonlinearity and non-Gaussianity are often considered. Furthermore, known as a Monte Carlo technique, the particle filter has proven to be capable of analytically handling intractable probability distribution functions (pdfs) in nonlinear and non-Gaussian problems [15; 16; 17; 18; 19; 20]. The essence of the particle filter is representing the posterior distribution of states (or other parameters) by a set of random particles with associated weights, which enables it to deal with functions with any distribution. As a Bayesian approach, the target of state estimation is first to predict the state probability distribution function forward from one observation time to the next using the process model (prediction stage). Then, the update operation uses the latest observation to modify the prediction pdf [21] (update stage). Over the last few decades, the particle filter has become a research topic in positioning, tracking, and navigation [22; 23], econometrics [24], fault detection [25], and other applications. In this paper, a particle filter algorithm is incorporated into a robust nonlinear uncertain heat exchange control system to suppress the control performance degradation caused by random noise, especially large sensor noise, generated on sensors and time delay in wireless communication links. The particle filter is utilized for further state estimation observation prediction, where the objective is to obtain the approximation of a real signal with reduced noise and time delay effects, namely, the nearly real value of the system states and output.