Due to the inherent characteristics of the flight mission of a space launch vehicle (SLV), which is required to fly over very large distances and have very high fault tolerances, in general, SLV tracking systems (TSs) comprise multiple heterogeneous sensors such as radars, GPS, INS, and electrooptical targeting systems installed over widespread areas. To track an SLV without interruption and to hand over the measurement coverage between TSs properly, the mission control system (MCS) transfers slaving data to each TS through mission networks. When serious network delays occur, however, the slaving data from the MCS can lead to the failure of the TS. To address this problem, in this paper, we propose multiple model-based synchronization (MMS) approaches, which take advantage of the multiple motion models of an SLV. Cubic spline extrapolation, prediction through an

The range safety system (RSS) [

In the past several decades, considerable research has been undertaken in the field of launch vehicle tracking based on multiple dynamic models; researchers have shown interest in various applications such as the tracking of reentry vehicles, short-range projectiles, and sounding rockets [

In this paper, multiple model-based synchronization (MMS) approaches are proposed to synchronize the time delayed slaving data of the RSS. The proposed approaches can be expressed via two distinct multiple models, a nonlinear model and a linear model. The nonlinear model considers comprehensive factors such as thrust, gravity, drag coefficient, Mach number, and air density [

The remainder of the paper is organized as follows. Section

The transmission of slaving data from the MCS to multiple TSs facilitates seamless tracking of the SLV in a sparsely located multiple TS environment. If a data transmission delay problem occurs, it can cause an SLV tracking failure. As depicted in Figure

Illustration of problem statement for delayed slaving data in RSS.

Let us assume a synchronized slaving state vector to be an unknown function of the delayed slaving state vector whose values are known only until time

We approximate

When the state estimation covariance for a time invariant system converges under suitable conditions to a steady-state value, explicit expressions of the steady-state covariance and filter gain can be obtained. The resulting steady-state filters for noisy kinematic models are known as

The motion of the SLV is simply depicted as a discretized Wiener process acceleration model [

Singer [

Nonzero mean acceleration PDF in the PFP model (a) along

From (

Finally, complete recursion of the IMM with mode matched KF for the SLV tracking is summarized as follows:

Model-conditioned reinitialization (for

predicted mode probability:

mixing weight:

mixing estimate and covariance:

Model-conditioned filtering (for

predicted estimate and covariance:

measurement residual:

residual covariance:

filter gain:

update of state and covariance:

Mode probability update (for

mode likelihood:

mode probability:

Combination (for

For a nonlinear ballistic model, the state vector for the propelled mode is denoted as

Normalized drag coefficient [

The measurement matrix

An IMM algorithm for nonlinear dynamics with different sizes of the mode state vector is summarized as follows [

Model-conditioned reinitialization (for

predicted mode probability:

mixing weight:

unbiased mixing estimate and covariance:

Model-conditioned filtering (for

predicted estimate and covariance:

measurement residual:

residual covariance:

filter gain:

update of state and covariance:

Mode probability update (for

mode likelihood:

mode probability:

Combination (for

To demonstrate the performance of the proposed synchronization approaches for delayed slaving data, we simulated the SLV tracking problem based on the nominal flight trajectory of the Korea Space Launch Vehicle-I (KSLV-I). In the simulation, the radar measurement noise intensities of (

Synchronization errors at PFP and CFP.

In this paper, we investigated the time synchronization approaches of delayed slaving data in the RSS for SLV tracking. One of the most important roles of the RSS is to distribute slaving data to each TS for continuous tracking of the SLV. If there is a critical network delay resulting in time delayed slaving data being sent to each TS, the MCS will not receive accurate SLV tracking data. This problem can give rise to significant difficulties for the SLV mission progress and analysis. To overcome this problem, we proposed MMS approaches which take advantage of the multiple motion models of an SLV. The linear IMM-based synchronization approach was developed using Singer’s model with ternary uniform mixtures and the nonlinear IMM-based synchronization approach was derived from a nonlinear ballistic model with a drag coefficient. For verification of the proposed algorithms, SLV tracking simulations using KSLV-I and the radar measurement data generated from nominal trajectory were conducted. To demonstrate the superiority of time synchronization performance in these simulations, we compared the proposed algorithm with benchmark approaches for absolute error between the nominal trajectory data and the synchronized slaving data; the simulation results demonstrated that the proposed MMS approaches performed competitively.

The authors declare that there are no competing interests regarding the publication of this paper.