GNSS Aided Navigation and Tracking -- James L. Farrell, VIGIL, Inc.

Better performance guaranteed -- now it has been verified with TEST DATA
Performance is half of the good news; the other half is simplicity. Ease and clarity of implementation readily follow from exploiting modern capabilities:

* Processing of inertial instrument outputs can be direct, in ways that werenot feasible with yesteryear's computing and sensing limitations

* Updating can be simplified by exploiting short term propagation traits.

NOTE THAT the short-term characterization, applicable to updating algorithms, does not limit inertial sensor data processing. Usage of accelerometer and gyro outputs in algorithms presented here -- much easier than conventional approaches -- can provide state-of-the-art performance in all situations.

Estimation algorithm simplifications, in contrast, apply under a restrictive condition of frequent updates -- which is applicable to a large majority of operations.

Following is a listing of considerations of interest to potential users with varying priorities.

HANDLING OF GNSS DATA

FOR THOSE HAVING ONLY INTERMITTENT AND AMBIGUOUS CARRIER PHASE DATA Optional separation of position from dynamics estimator enables operation with

* carrier phases remaining ambiguous at all times for every SV

* prompt recovery from track loss, with just one credible 1-sec phase change

* rigorous integrity test for that credibility of the change over 1 second The main benefit is a giant improvement in robustness; here is the top row of Table 5.1, obtained from real flight data:

-359.71 818.26 -245.14 -174.79 -38.63 -0.01

Sequential changes in across-SV phase differences are simply compared to their anticipated values, based on velocity estimates combined with 1-sec changes in SV locations. Chapter 5 provides all terms and their derivations. The last column is a residual, from an algebraic sum within 1 cm in 1 sec. Every row of the table exhibits that behavior and, in a severely vibrating DC3 for almost an hour with turns and speed changes, the resisuals support cm/s RMS velocity.

FOR THOSE WHO MUST CONTEND WITH UNSATISFACTORY USER CLOCK PERFORMANCE Subtraction of simultaneous measurements across SV's has long been known to

* cancel user clock errors -- but also --

* introduce correlations between measurement errors An original approach by this author accounts for the resulting correlations.

FOR THOSE WHO MUST ACHIEVE INTEROPERABILITY WITH DATA FROM MIXED CONSTELLATIONS Usage of across-SV difference in sequential phase changes, already described, is a major step toward interoperability; it is immaterial whether those changes occurred in one satellite constellation or another. Follow through with position updating according to prescribed procedures.

INTEGRITY

FOR THOSE REQUIRING COMPATIBILITY BETWEEN MATRIX FACTORIZATION AND ESTIMATION Complete derivations originating with this author are provided in Chapter 6.

FOR THOSE NEEDING TO TEST INTEGRITY OF SPARSE GNSS DATA Chapter 6 shows rigorous equivalence between

* widely accepted QR factorization used in parity testing for integrity, and

* normalized residual testing, for each individual difference observation without any requirement for favorable geometry -- or even any requirement to have enough satellites for an instantaneous solution.

Methodology applies to sequential carrier phase and pseudorange differences, both in tandem.

INERTIAL DATA

FOR THOSE WITH ACCESS TO RAW GYRO AND ACCELEROMETER DATA A single one-page diagram shows the full "raw-data-to-final-output" evolution Wander azimuth by the simplest possible method is succinctly provided Complete task lists define incrementing of attitude, velocity, and position.

All tasks are fully defined with complete formulations

FOR THOSE WISHING A SIMPLIFIED UNDERSTANDING OF INS ERROR PROPAGATION

* Intuitive illustration is provided for the Schuler period

* Straightforward characterizations are presented to cover frequent updating

* An inituitive position/velocity/acceleration model is related to a basic inertial position/velocity/verticality model -- followed by relation to a basic velocity/verticality/drift model -- for insight.

FOR THOSE REQUIRING DETAILED CHARACTERIZATION OF INERTIAL INSTRUMENT ERRORS

* "Good-news/Bad-news" -- Conventional concepts have fundamental limitations -- but the algorithms can still be made to work unfailingly

* Gyro scale factor and cross-axis errors VIOLATE conventional formulations -- but can be adaptively taken into account

* Full clarification for the role of coning and sculling - WITHOUT the usual complications involved in preprocessing the inertial sensor outputs.

ESTIMATION

FOR THOSE WANTING A SYSTEMATIC RATIONALE FOR SETTING PROCESS NOISE LEVELS Simple expressions separately relate accelerometer noise, accelerometer bias, gyro noise, and gyro bias to chosen data-averaging durations.

FOR THOSE REQUIRING JUSTIFICATION OF MODEL CHARACTERIZATIONS

* Formulations, algorithms, and performance defined with and without IMU

* "Swiss army knife" estimator with omission or retention of various states -- opportunity to tailor usage for application-dependent conditions

FOR THOSE INVOLVED IN TRACKING OF MULTIPLE REMOTE OBJECTS

* Double differencing of GNSS pseudoranges applied to the case wherein all objects can be moving. All states are then relative -- which precisely characterizes the information needed for that scenario

* Potential markedly superior to all "position-reporting" schemes - and WHY

* For observations of nonparticipants, experience is drawn from real-world operations involving radar and optical sensors

* Suitable suboptimal (alpha-beta and alpha-beta-gamma) estimators provided

* Underlying commonality fully exploited, and yet :

* traits strikingly unique to specific operations (bistatic/multistatic operation, orbit determination, reentry vehicles, projectiles, littoral environments, supporting functions) fully represented in algorithms

PRACTICALITY ISSUES

FOR THOSE WHO MUST OBTAIN SYNCHRONOUS DATA FROM ASYNCHRONOUS SOURCES Straightforward computational realignment with minimal latency, validated by results shown using real inertial measurement data

FOR THOSE WHO WANT RESULTS TO SUPPORT ALL ANALYTICAL METHODS AND ALGORITHMS Presentation of extensive van test and flight test data, generated with usage of algorithms presented in the book