Kolloquium Satellitennavigation, TUM

Transcription

1 Selected Software Receiver Specific Processing Techniques: and Maximum-Likelihood Nico Falk, Tobias Hartmann, Thomas Pany, Bernhard Riedl Place: TU München, Raum BV 269 Date&Time: July 25 th, :15 18: Page 1 Page 2

2 SX-NSR Navigation Software Receiver The SX-NSR is a multi-frequency, multi-sensor software receiver combining advanced signal-processing algorithms with a highbandwidth RF front-end. All signal acquisition, tracking and positioning tasks are performed in software. The corresponding RF front-end provides 15 MHz bandwidth access. Download at Page 3 SX-NSR Key Components Signal Processing Software Windows Personal Computer 2GB RAM, SSSE3 capable processor Ultra high sensitivity, ~2 channels per CPU core RF Front-End 4 RF bands simultaneously Parallel use of two frontends for 8 bands GPS L1, L2P(Y), L2C, L5 Galileo E1, E5a, E5b, E5a+b, E6 SBAS L1 GLONASS G1, G2 15 MHz bandwidth 1 x High-speed USB2. Interfaces to various navigation sensors 2.48 or 4.96 MHz sample rate External power supply Page 4 Signal conditioning and pre-processing GNSS baseband processing (acquisition and tracking) for all civil GNSS signals plus GPS L2P(Y) Sensor data synchronization and processing Position computation with RAIM Standard interfaces

3 NavPort-4 features 4 RF bands simultaneously Four bands out of L1/E1, L2, L5/E5a, E5b, E6, G1, G2 Galileo AltBOC processing by coherent combination of E5a+E5b 15 MHz bandwidth each High interference robustness (IP1dB of -1 dbm) Dynamic gain range of about 4 db, software controllable Sample rate of 2.48 or 4.96 MHz with 2 bit Selectable 1 MHz reference clock Tunable internal TCXO External reference clock input Flexible data stream Transmitted to PC via a single USB 2. interface Select / deselect each RF band GNSS signals coupled with additional sensor data (external IMU, internal barometer, WiFi, external NMEA source, trigger, ), +/-2 µs sync accuracy for IMU data for high dynamics applications Integrated in a weather resistant housing Designed for rough environments Page 5 Trigger input, PPS output NavPort-4, Frontend Sync Inter frontend link Synchronizes two NavPort-4 devices by Synchronized sample rate Trigger for starting the digital data stream Hardware Connections: Reference Clock interconnection Inter frontend link Synchronization performance Synchronization bias accuracy guarantee of 475 ps Further improvement: frequency bias between master and slave is measured with an accuracy of <7 ps for bias correction NP-4 Master Bias stability observations during runtime, data provided via API inter-frontend link Ref Clk Out Ref Clk In NP-4 Slave Page 6

4 SX-NSR Key Features Page 7 Operational features: Real-time or post-processing mode Configuration settings via GUI, XML, or TCP/IP Low-level receiver parameters Multi-correlator Flexible reference signals (PRN codes, modulations schemes, ) IF sampling data recorder for post-mission mode Quick fix : acquire and track degraded GNSS signals Assisted data input, e.g. SP3(c) files Standard input and output (RINEX, NMEA, ASCII logs ) Software optimized for multi-core CPUs and GPUs 2-3 % average CPU load on a 7, Intel i7 26, 3.4 GHz PC for a SIS GPS L1/L2P/L2C/L5, Giove E1,E5a/b (July 211) Baseband processing: Fully configurable DLL, FLL, PLL Carrier aiding, smoothing Multipath mitigation with multicorrelator and waveform User configurable (non)coherent integration time for acquisition Key facts: 19 dbhz acquisition sensitivity 1 dbhz tracking sensitivity TTFF < 2 s in hot-start mode <.5 m CEP Single Point Positioning Galileo E5a+b (ideal signal reception) Code / Carrier accuracy: < 2cm / < 1 mm SX-NSR Acquisition High performance acquisition engine Acquisition Result displayed in real-time E.g. GPS C/A config: 16 ms coherent x 2 noncoherent ~ 17 dbhz correlators on a nvidia GTX48 graphics card, CPU only gives several 1. correlators 17 dbhz GPS C/A indoor signal Page 8

5 SX-NSR Tracking Performance Various configurable tracking methods for all civil GNSS signals plus GPS L2P(Y); accuracy near theoretical limit, e.g.: Galileo OS on E1 Galileo_E1_dump_PRN2.dumplog Galileo AltBOC on E5a+b Galileo_E5ab_dump_PRN2.dumplog.5 Code minus carrier [m] GPS time - t = s [s] Code minus carrier [m] GPS time - t = s [s] Page 9 Signal Analysis Multi-Correlator Example Compute correlation function on a code phase(=delay), Doppler grid Multipath Line-of-sight./. = prompt Correlator/channel NCO Doppler Delay Offsets with respect to channel NCO (~ line-of-sight signal) Page 1

6 SX-NSR Framework Architecture Measurement Sensors GNSS antenna IMU Barometer WiFi IMU & magnetic RF-Signal Sync field RS-232 DIO I2C Sensor Control L1 A Split L2 ter Datastream USB E5/L5 D Merger IF E6 (IF + Sensor Data) NavPort Frontend File Input USB IF Datastream Merger (IF + WiFi Data) Signal manipulation or injection API 1 Baseband (Acquisition and Tracking) API 2 Baseband (Acquisition and Tracking) API 2 Sample Provider Sensor API 5 Acquisition API 2 (Baseband) Typical Configurations: L1 / L2 / E5a / L5 / E6 L1 / E5b / G1 / G2 Internal NSR functions and/or user supplied Tracking Receiver Processing API 2 (Baseband) API 4 Assistance (External Navigation Utility API Data) (Positioning) (write Text to Screen, get/set API 3 config options, access to internal data structures, Data Transfer Gateway for direct connection PVT between all user supplied DLLs Solution SX-NSR API 6 Rinex, NMEA, various dump logs NavPort interface, Framework architecture, API interfaces Page 11 Difference Correlator Page 12

7 Difference Correlator Principle Page 13 Goal: Typical rover/reference station setup up, but reference data already used in signal processing to avoid cycle slips in degraded environments and to use carrier phase observations for decimeter accurate positioning. Batch Processing (Zero Difference) Transparent receiver measurements required Measurement covariance partly unclear if DLL/FLL/PLL tracking used New method wanted Batch processing: Each RINEX obs. record based on a certain batch of the GNSS signal Timely uncorrelated measurements (from the receiver side, not physical) Based on JPL patent, discussed at IGS AC workshop 28 Small or no overlap between batches Sync. epoch Carrier NCO Unwrap (V)DLL/(V)FLL tracking Prompt I/Q, NCO e.g. 5 Hz Ringbuffer + Polynomial evaluation Carrier phase continuation Phase discrimintor RINEX carrier phase RINEX epoch sync. e.g. 1 Hz Batch extractor I/Q batches, e.g. 1 Hz Bit/symbol wipe-off Polynomial fit Cycle slip check Page 14 Navigation data bits/symbols The whole discussion is demonstrated with the prompt correlator for phase tracking, but can be extended to code tracking with early/late correlators

8 Cycle Slips in Batch Processing Standard carrier phase tracking is a high rate process, e.g. 5 Hz A single incorrect discriminator value can cause a cycle slip Values noisy due to short integration time (e.g. 2 ms) Phase discriminator non-compatible with longer filter time Basically no redundancy at single-channel level Even for static measurements, a standard PLL operates with 5 15 Hz, due to clock jitter No slip Slip?.2.15 GPS C/A PRN 12 NCO+disc. polyfit.6.4 GPS C/A PRN 27 NCO+disc. polyfit.1.2 Carrier phase [cyc] Carrier phase [cyc] Page Time before RINEX epoch [s] Time before RINEX epoch [s] Single Differences I Conventional receiver single difference observation: ( t ), ( t ), ( t ) ϕ = ϕ ϕ k k k rov k k ref k φ k,rov φ k,ref φ k Rover carrier phase to satellite k [rad] Reference carrier phase to satellite k [rad] Single difference carrier phase [rad] exp a(t) P k,rov Correlator/carrier phase relation: φ k,nco 1 { ϕ ( )} = ( ) exp ϕ ( ) Amplitude function (not relevant here) { } ( ) k, rov k, NCO k, rov i t a t i t P t Rover carrier phase to satellite k [rad] based on NCO reading while using internal FLL tracking Rover prompt correlator (complex valued) capturing the difference of the internal FLL tracking to the true received signal Page 16

9 Single Differences II Definition of single difference correlator: ( ) exp{ ϕ ( )} ( ) { ( )},, exp ϕ, ( ) = P k t k i k NCO t k P k rov t k i k ref t k d t k sent d P Broadcast navigation data bit (if any) Single difference correlator Page 17 Discussion Aiding of signal processing with reference station data Difference is a linear operation A phase discriminator/pll is nonlinear Preserves spectral separation of multipath and line-of-sight signal Common mode errors (mostly) eliminated (sat. clk./dyn., atmosphere) Batch processing can be applied to difference correlator Dedicated filters can be applied (see next slides) Complex argument of filtered single difference correlator is added to φ k,ref to obtain the conventional rover carrier phase Reference station data in RINEX/RTCM format 1 Hz; interpolation to e.g. 5 Hz Double Differences Definition of double difference correlator: t k (, ) ( ) ( ) P t t = P t P t k, l k l k k l l Other satellite epoch in [s] when a correlator value for the satellite k is available P Double difference correlator l Reference satellite index k Other satellite index Discussion Receiver clock error eliminated from correlator Extraction of double difference carrier phase straight forward, but conversion to undifferenced carrier phase values requires rec. clk. assumptions, e.g. Receiver clock =. Receiver clock derived from strongest rover code measurement Page 18

10 Implementation, Correlator Filter Piggyback principle: Reference RINEX obs. file (V)DLL/ DLL/FLL Prompt I/Q, NCO Ringbuffer tracking e.g. 5 Hz (V)FLL Carrier NCO Reference correlator reconstuction Internal tracking compensation ( ) exp{ ϕ ( )} ( ) exp{ ϕ ( )} ( ),,, = P k t k i k NCO t k P k rov t k i k ref t k d t k sent I/Q batches, e.g. 5 Hz, duration = 1 s Correlator single/double difference Q k ( t) = F { P k ( t )} = Q k ( t ) exp{ i η k ( t )} Diff. correlator values FFT Adaptive Doppler filter RINEX epoch sync. e.g. 1 Hz Batch extractor I/Q batches, e.g. 5 Hz, duration = 1 s Bit/symbol wipe-off Diff. correlator values Line-of-sight Doppler detection LOS Doppler Diff. correlator values Phase discrimintor k ϕ k k ( t) = η ( t) + ϕ ( t), rov, ref exp k { iϕ k ( t )} P k ( t ), NCO k, rov Navigation data bits/symbols Carrier NCO Unwrapping Polynomial evaluation Undifferencing & carrier phase continuation Single diff. carrier phase Polynomial fit Cycle slip check RINEX carrier phase Page 19 Filter Option: Adaptive Doppler Filter Adaptive Doppler Filter Assumption: line-of-sight signal dominates frequency spectrum DD Spectrum 12 x PSD of double diff corr. Filtered spectrum Freq. [Hz] Double difference correlator spectrum: T coh = 3 s, urban canyon one satellite heavily attenuated, ref. PRN 26, C/N = 45 dbhz, other PRN 11 C/N = dbhz Page 2

11 Filter Option: Cost Minimization Fit a model based on certain cost function: E.g. minimize carrier phase residuals during batch interval ϕ, f, a µ ( ( { ( ) { ( )}} )) 2 µ µ µ ˆ ϕ, fˆ, aˆ = arg min 1 cos arg P t exp i 2π ft + 2π at + ϕ φ f a P Carrier phase offset [rad] Doppler frequency [Hz] Acceleration [Hz/s] Zero, single or double difference correlator or maximize signal energy (ML estimator) Page 21 Maximum Batch Length Batch length ~ coherent integration time Typical constraints eliminated (data bit, receiver clock, ) Need to model the carrier phase during batch interval Linear carrier phase model (phase + Doppler) Use case Typical user dynamics Fit better than 5 mm Fit better than λ/2 Walking pedestrian 5 m/s 2.45 s.195 s Pedestrian with MEMS IMU aiding.5 m/s 2.14 s.62 s Static (baseline length = 5 m) 1 µm/s 2 1 s 436 s Page 22

12 Sensitivity/Cycle Slips Timely adjacent batches of carrier phase estimates are concatenated allowing an integer (ambiguity) offset Phase estimate must be precise, otherwise cycle slip Std. dev. of phase < 3 (rule-of-thumb) var coh 2 ϕ = + + σ ω 2 ftcohc / N 2 TcohC / N 2 f T φ f T coh 2 ω Carrier phase of a difference correlator [rad] Factor (=1 for double difference, =2 for single difference) Coherent integration time [s] σ Doppler accuracy [rad 2 /s 2 ] Phase std. dev. [rad] T coh =.2 s single T coh = 1 s double Threshold Page C/N [dbhz] Results Prototype implementation with SX-NSR API for GPS L1/L2 Post processing of recorded rover signals Reference station data read via RINEX3 (gpstk) Page 24

13 Pedestrian Walk (Zero Difference) Pedestrian walk in the urban canyons of a Bavarian village (Schönau), 4 times along the same path, GPS L1 C/A Parameter Code/Doppler tracking scheme Carrier tracking scheme Integration time Overlap Carrier phase estimation Max./Min Doppler Doppler grid points Max./Min. acceleration Acceleration grid points Value VDLL/VFLL aided by a dead reckoning trajectory Undifferenced 25 ms 2 ms Cost function +/- 25 Hz 81 +/- 16 Hz/s 41 Data processed by TTC (super smoothed) Page 25 Canopy Test I Static user in a forest, GPS L1 C/A, L2CM Baseline length ~ 1.7 km Parameter Value Code/Doppler tracking scheme VDLL/VFLL (fixed position) Carrier tracking scheme Double difference Integration time 5 s Overlap.5 s Carrier phase estimation Cost function Max./Min Doppler +/- 5 Hz Doppler grid points 81 Max./Min. acceleration +/- Hz/s Page 26 Acceleration grid points -

14 Canopy Test II Carrier PR [m] L2CM L1C/A Carrier PR [m] L1C/A Time [s] Double difference carrier phase PRN5/PRN7 linear trend (.27 m/s) removed Time [s] Double difference carrier phase PRN5/PRN28 linear trend (.27 m/s) removed Signal travels ~ 1 m through the forest Page 27 Indoor Test Double difference carrier phase GPS PRN 25&12 received through the ceiling DD Carrier PR [m] L1 L2 Slowly developing cycle slip on L2 ok GPS PRN 12&29 double difference wide lane after removing all geometry ( /-.3) Time [s] Reference network with.5 cm accuracy Page 28

15 Maximum Likelihood Multipath Estimation Page 29 Multipath Requirements and Conditions The new strategy shall: Provide precise carrier phase pseudoranges Later used by RTK or by attitude software Provide precise code pseudoranges (they constrain the ambiguities) Be substantially better than a narrow correlator Be universal Requirements: Environment similar to state-of-art RTK applications (free line-of-sight, maybe some canopy effects) Internal tracking provides good Doppler estimate and maintains Doppler and code lock, PLL tracking or stable FLL Strategy: Use multiple correlators to detect and mitigate multipath Page 3

16 Block Diagram Piggyback principle: + Robust + Fallback to standard tracking possible + Easy initialization Page 31 Fit this model to the correlator values C b = M m= Correlator Model b b { ϕ } b ( τ τ c c ) ( ω ω, ) a exp i T f R T rec sinc m m coh s m coh m Page 32 <C b > b m M a m φ m T coh f s R x,y c c rec b τ m τ b ω m ω b Sample rate [Hz] Expected value for the correlator with index b Index, counts the different complex valued correlators Index, counts the received signals (line-of-sight and multipath signals) Number of signals Estimated parameter: real valued signal amplitude of signal m Estimated parameter: carrier phase at the mid point of the integration interval [rad] Coherent integration time [s] Correlation function of signal x with signal y Received GNSS signal at baseband Internal reference signal used for correlator b Estimated parameter: code phase of signal m [s] Correlator code phase offset of correlator b [s] Estimated parameter: Doppler of signal m [rad/s] Correlator Doppler offset of correlator b [rad/s] Doppler losses can be neglected

17 Correlator Model II Correlator covariance (scales with IF sample variance): ( ) Q = cov C, C = f T a R τ τ cov<c b,c b > a, b c rec a,b τ a,b a b a b s coh m a b crec, crec Covariance matrix Index, counts the different complex valued correlators Internal reference signal used for correlator a or b (real valued) Correlator code phase offset of correlator a or b [s] Line-of-Sight and Multipath parameters: ( a τ a τ ) q = M T Maximum Likelihood (=LSQ) principle: ( ) 1 Q ( ) qˆ = argmin C Cq C Cq q Page 33 Example with Bit-True Simulation I Signalspectrum Correlation function R c, cp R' c, cp Power Spectrum Magnitude (db) Correlation function Frequency x Code phase [chip] GPS C/A, 15 MHz bandwidth, 45 dbhz line-of-sight, 35 dbhz multipath, 2-bit, 1 x 2 ms coherent integration time, delay = 76 m Page 34 pure MATLAB

18 Example with Bit-True Simulation II Correlator fit x 15 3 Model Measured Corr function Code offset [samples] Page 35 GPS C/A, 15 MHz bandwidth, 45 dbhz line-of-sight, 35 dbhz multipath, 2-bit, 1 x 2 ms coherent integration time, delay = 76 m pure MATLAB Least Squares Challenges I Unknown number of multipath signals Start with multipath signals fit chi-squared test on the correlator residuals if incompatible increase number of multipath signals by 1 Maximum likelihood search strategy Detect local peaks to identify coarse multipath delay does not work Full grid search over all code phases required Amplitude and phase can be determined analytically High processing demands Use longer integration intervals Data wipe-off Provide models for correlation function and derivatives plus efficient interpolation Work with a low number of multipath signals (, 1, 2 ) Separate C code for each case Page 36

19 Least Squares Challenges II Line-of-sight and multipath parameters highly correlated (especially for similar delays), normal matrix nearly singular Identify correlations and numerical instabilities Be conservative and provide plausibility checks Fallback to a lower number of multipath signals or fallback to standard tracking Tuning parameters Coherent integration time and RINEX obs. rate Corrections from several coherent integrations fitted and added as correction to standard DLL/PLL ranges Number of LSQ iterations Detection thresholds Correlator positions Page 37 Testing the SX-NSR Implementation Parameter Modulation scheme Bandwidth (dual sided) Sample rate Quantization Line-of-sight range rate / CN Multipath1 range rate / CN Multipath2 range rate / CN Coherent integration time Time interval for RINEX correction Correlator spacing in multiplies of the inverse sample rate Chi-squared thresholds for line-of-sight, multipath 1, multipath 2, Grid bin extension of tracking error and multipath Remark Value CBOC E1C 13 MHz 2.48 MHz (4.96 MHz native) 2 bit 1 m/s, 5 dbhz 1.2 m/s, 44 dbhz - 1 ms 2 ms -12, -8, -3, -2, -1,, 1, 2, 3, 8 25, 5, 2, 4 / -6, -4, -2,, 2, 4, 6 [* 1/49.14 MHz] Maximum number of iterations: 4 Page 38

20 CBOC Single Multipath Best Fit Correlator value 12 x Stars observations Red only LOS Green LOS + 1 MP Q Correlator offset [chip] Page 39 CBOC Single Multipath 5 Code error Code error.5 Carrier error Carrier error Code error [m] -5-1 Black narrow Red MP estimating Carrier error [m] Time [s] Time [s] Multipath delay rate =.2 m/s, starting at t = s with zero delay Page 4 preliminary

21 CBOC Two Multipaths 1 x 15 Correlator Values measured M=3 M=2 1 x Carrier error Carrier error Narrow M max =2 5 imag. M=1 real Carrier error [m] M max = Time [s] M Number of assumed propagation paths Page 41 Implementation Page 42 preliminary

22 Sumary and Outlook Impressive carrier stability Uses SX-NSR API Maximum Likelihood Multipath Estimation Real-time implemenation in core SX-NSR Site monitoring, measurement analysis, R&D applications, indoor,... Everything tested in real environments using large data sets! Page 43