International Journal of Aerospace Engineering

Volume 2017 (2017), Article ID 4378640, 12 pages

https://doi.org/10.1155/2017/4378640

## Mars Atmospheric Entry Integrated Navigation with Partial Intermittent Measurements

^{1}School of Electrical and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 45002, China^{2}School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

Correspondence should be addressed to Tai-shan Lou

Received 12 June 2017; Accepted 13 August 2017; Published 24 September 2017

Academic Editor: Christopher J. Damaren

Copyright © 2017 Tai-shan Lou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Signal degradation suffered by the vehicle is a combination brownout and blackout during Mars atmospheric entry. The communications brownout means that signal fades and blackout means that the signal is lost completely. The communications brownout and blackout periods are analyzed and predicted with an altitude and velocity profiles. In the brownout period, the range measurements between the vehicle and the orbiters are modeled as intermittent measurements with the radio signal arrival probabilities, which are distributed as a Rayleigh distribution of the electron number density around the entry vehicle. A new integrated navigation strategy during the Mars atmospheric entry phase is proposed to consider the probabilities of the radio measurements in the communications brownout and blackout periods under the IMU/beacon scenario based on the information filter with intermittent measurements. Numerical navigation simulations are designed to show the performance of the proposed navigation strategy under the integrated navigation scenario.

#### 1. Introduction

On 5 August 2012, the Mars Science Laboratory’s (MSL) Curiosity rover successfully landed on Mars after suffering the Seven Minutes of Terror, in which the MSL entry, descent, and landing (EDL) system brings the velocity of the vehicle from about 5.9 km/s to 0.75 m/s. Especially, during Mars entry phase, the vehicle experienced the most rugged aerodynamic environment, which includes high temperature and pressure, peak heating (peak temperatures of up to 2090°C), and peak deceleration (out at 15g), and the signal between the vehicle and the orbiters can fade or suffer from total loss to make the ultrahigh frequency (UHF) relay links from the MSL to the orbiters suffer a period of about 70 s of degradation [1, 2]. The Mercury, Gemini, and Apollo spacecraft entering the Earth’s atmosphere and the Mars Pathfinder entering Mars’ atmosphere all endured communications blackouts, and the lasting time is from 30 seconds to several minutes [3]. During communications blackout period, it is difficult to perform real-time communication between the vehicle and the orbiter to provide the range measurements in time for the navigation system. So, it is necessary to predict trends or likelihood of the signal degradation and design appropriate navigation technology and strategy.

The communications blackout is caused by reflecting or absorbing the electromagnetic at some frequencies by the sheath of ionized atmospheric gases around the spacecraft when the spacecraft enters into a planetary atmosphere with a hypersonic velocity. Whether or not the communications blackout occurs depends on the electron number density (END), the critical electron number density (CEND) at the link frequency, such as UHF. If the electron number density exceeds the corresponding critical electron number density, the communications blackout may happen under some frequencies. In order to analyze and forecast any possible blackout problem, two aerothermodynamic analysis programs, which include the Jet Propulsion Laboratory (JPL) Normal Shock and Chemical Equilibrium Program (also called the Horton program) [4] and the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) program [5], have been used in Mars entry vehicles as they fly through Mars atmospheric environment [6]. The JPL Horton program was developed in the 1960s [4] and then used to predict any possible communications blackout problem [2, 6]. These tools output the velocity of the shock layer and the electron number density at the stagnation point by using the composition, pressure, temperature, and density of the Mars atmosphere [6]. Morabito analyses the communications blackout problem of the Mars Pathfinder at X-band based on the wake-region electron density estimates produced by the JPL Horton program and the LAURA program and compares the predicted results of the two programs [6]. Morabito and Edquist predicted the communications blackout at UHF for different MSL entry cases by using the above two tools [3]. After the MSL successfully landed on Mars, Morabito and Edquist analyzed the UHF communications brownout and blackout experienced by the MSL during Mars atmospheric entry, which coincided with the predicted signal degradation from preflight analyses in literature [3]. Schratz et al. discussed the performance of the MSL telecommunications for UHF during the EDL phase and analyzed the signal strength and the plasma blackout during Mars entry [7].

Future Mars explorations need the capability of pinpoint landing on the preselected high scientifically valuable regions to meet the scientists’ requirements. It is difficult to achieve this target if the only available measurement sensor is the on-board default inertial measurement unit (IMU) to provide measurement information for the navigation, guidance, and control system during Mars atmospheric entry phase [8, 9]. An innovative integrated navigation scheme during Mars atmospheric entry was proposed, which is adding the range measurements between the vehicle and the surface beacons or orbiters by using the UHF radio communication [10, 11]. The key technology of the above navigation scheme is that the UHF radio communication is not blocked by the plasma sheath around the vehicle. National Aeronautics and Space Administration (NASA) develops an advanced Mars Network’s Electra UHF transceiver, which is a prototype, embedded, real-time navigation system and can provide radio communication information between the vehicle and an orbiter or a surface beacon [10, 12]. Levesque and de Lafontaine researched four integrated navigation scenarios and their observability based on radio ranging by using the unscented Kalman filter during the Mars atmospheric entry [11]. Li et al. did a lot of works based on a six-dimension dynamic model by using radio communication under the IMU/beacon integrated navigation schemes [9, 13, 14]. Yu et al. primarily analyzed the optimization of the Mars entry navigation beacon configuration based on the system observability by using radiometric measurements [15, 16]. Lou et al. considered the uncertain model parameters and the measurement biases by using consider Kalman filter (also called Schmidt-Kalman filter) [17–19] and analyzed the sensitivity of the parameter uncertainties based on the robust desensitized extended Kalman filter [20] under the radio beacon navigation schemes during Mars atmospheric entry.

Morabito et al. [2] pointed that the UHF radio signals fade or break off in the communications brownout and blackout periods for the MSL during Mars atmospheric entry. This signal degradation makes the two-way range measurements for the navigation system cannot reach (or at a certain probability) the MSL. Li and Peng primarily analyzed the effect of the communications blackout under the radio beacons/IMU integrated navigation and pointed that as the communications blackout occurs, the navigation errors will gradually increase [9]. Wang and Xia compared the performance of the unscented Kalman filter under the surface beacons/IMU integrated navigation and the orbiters/IMU integrated navigation when the communications blackout happens [21]. The above researches considered that the vehicle does not receive any radio signal in the communications brownout period during Mars atmospheric entry and the probabilities of the arrival of the range measurements are not analyzed [2]. Adding the potential range measurements, which arrives at a certain probability, into the navigation system undoubtedly improves the navigation accuracy in the communications brownout period.

Recently, the intermittent measurements, which are also called missing measurements and modeled by a Bernoulli distributed sequence [22–24], were introduced into a series of filtering algorithms to deal with these intermittent data phenomena, such as the Kalman filtering [24, 25], unscented Kalman filter [25, 26], and robust filtering [23, 27]. These filters are committed to obtain the optimal estimates when the arrival of the measurement is not in time; in other words, the measurement is lost at a certain probability. This filtering problem with intermittent measurements has motivated researcher’s interest, because these missing measurement phenomena are more popular in practical applications, such as the navigation of a moving vehicle [28], and networked control systems [29]. Subsequently, the intermittent measurement problem with different loss probabilities, which means that the measurement loss might be partial, has been investigated, and some solutions are proposed [30, 31].

The aim of this paper is to develop an integrated navigation scenario with the probabilities of the radio measurements in the communications brownout and blackout periods during the Mars atmospheric entry phase by using the information filter with intermittent measurements (IFIM). The communications brownout and blackout periods are analyzed and predicted with an altitude and velocity profiles during Mars atmospheric entry. The signal arrival probabilities of the UHF radio signals are modeled as the Rayleigh distribution of the electron number density around the entry vehicle. The range measurements between the vehicle and the orbiters are described as a Bernoulli distributed sequence with different probabilities in the communications brownout period. Then, the IFIM algorithm is derived and designed for the navigation filter. The numerical navigation simulations are designed to show the performance of the proposed navigation strategy.

This paper is organized as follows: firstly, the Mars entry dynamic model and measurement model based on the IMU and three orbiters are introduced; secondly, the communications brownout and blackout phenomena are predicted by an aerodynamical tool during Mars atmospheric entry; thirdly, the information filter with intermittent measurements is derived; and lastly, the results of the navigation simulation are discussed.

#### 2. Dynamics of the Navigation System

##### 2.1. Dynamic Equations for Mars Entry

During Mars atmospheric entry, the dynamic model of the vehicle is modeled as six state equations of a six-dimensional state, which includes the altitude (radial distance from the center of the vehicle mass to the Mars center), radial velocity , flight path angle (FPA) , longitude , latitude , and azimuth angle (a clockwise rotation angle starting at due north), in the Mars-centered Mars-fixed coordinate system. Some assumptions are that the planet is nonrotating, its atmosphere is stationary and quiet, and winds in the atmosphere and the centripetal and Coriolis effects are neglected [17, 32]. Then, the six entry dynamic equations of the vehicle are described by [11, 17, 19, 32] where is the bank angle, is the simplified gravitational acceleration, and is the Mars gravitational constant (). and are, respectively, the aerodynamic drag and lift accelerations given as follows: where and are, respectively, the vehicle drag coefficient and lift coefficient, is the reference surface area of vehicle, is the mass of the vehicle. represents the Mars atmospheric density with an exponential model is given by [18, 33] where is the nominal reference density on the Mars surface, denotes the nominal reference radial position , and denotes the constant scale height . For convenience’s sake in this work, the lift-to-drag ratio is defined by , and the ballistic coefficient is defined as .

##### 2.2. Measurement Models

To improve the navigation accuracy based on the IMU information, a potential integrated navigation scenario with both IMU and UHF radio communication is proposed to support pinpoint landing accuracy for future Mars missions. The IMU provides three components of acceleration for the navigation system. The UHF radio provides communication between the entry vehicle and the orbiting satellites or surface beacons (e.g., a preset fixed beacon or a previous Mars lander) and measures the distance between the vehicle and an orbiter or a surface beacon for the navigation system [12, 18, 19, 34]. At present, there are only three available Mars orbiters to provide radio communications, which are Mars Reconnaissance Orbiter (MRO), Mars Odyssey (MO), and Mars Express (MEX), and no surface radio beacons are preset on Mars. In this work, three orbiting radio satellites are considered to provide the two-way range measurements by using the UHF radio communications. The diagram of the three orbiter navigation scenarios and the position of the UHF antenna, the stagnation point and the wake-region, which need to estimate the electron number density, is shown in Figure 1.