A Trailing Suction Hopper Dredger (TSHD) is a ship that excavates sediments from the sea bottom while sailing. In situ material is excavated with a special tool called the Drag-Head, then it is hydraulically transported through a pipe to the hopper where it is temporarily stored. After the dredging is completed the collected material is transported and discharged at a specified location. The efficiency of this process is highly dependent on the detailed knowledge of the excavated soil. The optimization of dredging operations is of vital importance for future improvement in efficiency, accuracy and from the viewpoint of labor saving. The automated onboard systems that have been developed to optimize the dredging performance require knowledge of several uncertain soil-dependent parameters. These cannot be directly measured but have to be estimated online from the available measurements. Such estimation is a challenging task due to lack of sufficient sensors, severe nonlinearities in models, and time-varying nature of the parameters of interest. In this thesis we focus on two of the most important TSHD-related models. These are: I. Drag-Head Model - describing the excavation process, II. Hopper Model - describing the sedimentation process occurring inside the hopper. They contain several uncertain soil-dependent parameters that need to be estimated. These are: I. horizontal cutting force coefficient kch (Drag-Head Model ), II. ratio kvh between the horizontal and vertical cutting forces (Drag-Head Model ), III. in situ permeability ksi (Drag-Head Model ), IV. average grain diameter dm (Hopper Model ). Both processes, together with the corresponding estimation problems, are discussed in detail in Chapter 2. The highly uncertain and time-varying nature of the soil-dependent parameters and the nonlinear dynamics of the models used to describe dredging process make the estimation a challenging task. The algorithms that are capable of tackling these type of problems are Nonlinear Bayesian Filters (NBF). In Chapter 3 we review several types of NBF, namely: I. parametric filters based on the Taylor series expansion (EKF, IEKF), II. parametric filters based on statistical approximations (UKF, GHF, CDF), III. parametric filters based on Gaussian Sum approximations (GSF), IV. nonparametric filters based on the importance sampling (BPF), V. nonparametric filters based on the mean-field control-oriented approach (FPF). In Chapter 4 we investigate the applicability of these nonlinear filters to the estimation problems that originate from the Drag-Head Model. The problems are: the Cutting Estimation Problem and the Cutting and Jetting Estimation Problem. The Cutting Estimation Problem applies for any cutting excavation tool whereas the Cutting and Jetting Estimation Problem is applicable only for tools equipped with cutting and jetting components. The former problem considers estimation of the ratio kvh between cutting forces and the horizontal cutting force coefficient kch, the latter problem deals with the estimation of the horizontal cutting force coefficient kch and the in situ permeability ksi. To solve the aforementioned estimation problems one needs to handle time-varying delay in the measurement of incoming density ?i, which is discussed separately. It is concluded that among the tested methods the best solution to the Cutting Estimation Problem is provided by the CDF and, in case of large uncertainty in the initial states, by the GSF. To solve the Cutting and Jetting Estimation Problem it is crucial to exploit the correlation between the horizontal cutting force coefficient kch and the in situ permeability ksi. This is done by a cascaded filter, which uses the PF to obtain an estimate of ksi, which will be further filtered by a Steady State Identification (SSI) filter, and finally by the BF to produce a final estimate of kch. In Chapter 5 we develop a novel class of nonlinear particle filters: the Saturated Particle Filter (SPF) that is used to solve the Hopper Estimation Problem. The SPF is a general method designed for Saturated Stochastic Dynamical Systems (SSDS), which are severely nonlinear systems often used in modeling real-life problems. They are characterized by a constrained probability distribution exhibiting singularity on the boundary of the saturation region. Such singularities make it difficult to estimate the states or the parameters of SSDSs by standard nonlinear filters. Our new method exploits the specific structure of the SSDS in order to design an importance sampling distribution that accounts for the most recent measurements in the prediction step of the filtering algorithm. Chapter 6 deals with the asymptotic properties of the SPF. We establish the conditions under which the SPF converges to the optimal theoretical filter. The convergence of our method is closely related to the appropriate resampling scheme. This led to the development of the improved Saturated Particle Filter (iSPF) which combines the importance sampling of the SPF with a novel resampling algorithm. In Chapter 7 the iSPF together with other nonparametric methods from Chapter 3 are used to estimate the average grain diameter dm, which solves the Hopper Estimation Problem. Because the sedimentation process is naturally divided into three regimes, to find the most efficient filtering method we considered each mode separately. We conclude that: I. for the No-Overflow loading phase the best estimate of dm is obtained by the FPF, II. for the Overflow loading phases with weak erosion, the recommended filtering method is the Reduced-Order PF, III. for the Overflow loading phases with strong erosion, the best estimation performance is achieved by the Reduced-Order PF when the excavated soil is fine and the Hybrid SPF when the excavated soil is coarse. The final solution to the Hopper Estimation Problem is obtained by integrating the filters designed for separate modes into a global estimator. Chapter 8 concludes the thesis.