基于Matlab卡尔曼滤波的IMU和GPS组合导航数据融合（源码+数据）.rar

function [retval, s, errorb, tau] = allan_overlap(data,tau,name,verbose) % ALLAN_OVERLAP Compute the overlapping Allan deviation for a set of % time-domain frequency data % [RETVAL, S, ERRORB, TAU] = ALLAN_OVERLAP(DATA,TAU,NAME,VERBOSE) % % Inputs: % DATA should be a struct and have the following fields: % DATA.freq or DATA.phase % A vector of fractional frequency measurements (df/f) in % DATA.freq *or* phase offset data (seconds) in DATA.phase % If phase data is not present, it will be generated by % integrating the fractional frequency data. % If both fields are present, then DATA.phase will be used. % % DATA.rate or DATA.time % The sampling rate in Hertz (DATA.rate) or a vector of % timestamps for each measurement in seconds (DATA.time). % DATA.rate is used if both fields are present. % If DATA.rate == 0, then the timestamps are used. % % TAU is an array of tau values for computing Allan deviation. % TAU values must be divisible by 1/DATA.rate (data points cannot be % grouped in fractional quantities!). Invalid values are ignored. % NAME is an optional label that is added to the plot titles. % VERBOSE sets the level of status messages: % 0 = silent & no data plots; 1 = status messages; 2 = all messages % % Outputs: % RETVAL is the array of overlapping Allan deviation values at each TAU. % S is an optional output of other statistical measures of the data (mean, std, etc). % ERRORB is an optional output containing the error estimates for a 1-sigma % confidence interval. Error bars are plotted as vertical lines at each point. % TAU is an optional output containing the array of tau values used in the % calculation (which may be a truncated subset of the input or default values). % % Example: % % To compute the overlapping Allan deviation for the data in the variable "lt": % >> lt % lt = % freq: [1x86400 double] % rate: 0.5 % % Use: % % >> ado = allan_overlap(lt,[2 10 100],'lt data',1); % % The Allan deviation will be computed and plotted at tau = 2,10,100 seconds. % 1-sigma confidence intervals will be indicated by vertical lines. % You can also use the default settings, which are usually a good starting point: % % >> ado = allan_overlap(lt); % % % Notes: % This function calculates the overlapping Allan deviation (ADEV), *not* the % standard ADEV. Use "allan.m" for standard ADEV. % The calculation is performed using phase data. If only frequency data is % provided, phase data is generated by integrating the frequency data. % However, the timestamp-based calculation is performed using frequency % data. Phase data is differentiated to generate frequency data if necessary. % No pre-processing of the data is performed, except to remove any % initial offset in the time record. % For rate-based data, ADEV is computed only for tau values greater than the % minimum time between samples and less than the half the total time. For % time-stamped data, only tau values greater than the maximum gap between % samples and less than half the total time are used. % The calculation for fixed sample rate data is *much* faster than for % time-stamp data. You may wish to run the rate-based calculation first, % then compare with time-stamp-based. Often the differences are insignificant. % The error bars at each point are calculated using the 1-sigma intervals % based on the size of the data set. This is usually an overestimate for % overlapping ADEV; a more accurate (and usually smaller uncertainty) % value can be determined from chi-squared statistics, but that is not % implemented in this version. % You can choose between loglog and semilog plotting of results by % commenting in/out the appropriate line. Search for "#PLOTLOG". % This function has been validated using the test data from NBS Monograph % 140, the 1000-point test data set given by Riley [1], and the example data % given in IEEE standard 1139-1999, Annex C. % The author welcomes other validation results, see contact info below. % %#ok<*AGROW> versionstr = 'allan_overlap v2.24'; % defaults if nargin < 4, verbose = 2; end if nargin < 3, name=''; end if nargin < 2 || isempty(tau), tau=2.^(-10:10); end if isfield(data,'rate') && isempty(data.rate), data.rate=0; end % v2.1 % Formatting for plots FontName = 'Arial'; FontSize = 14; plotlinewidth=2; % if verbose >= 1, fprintf(1,'allan_overlap: %s\n\n',versionstr); end %% Data consistency checks v2.1 if ~(isfield(data,'phase') || isfield(data,'freq')) error('Either ''phase'' or ''freq'' must be present in DATA. See help file for details. [con0]'); end if isfield(data,'time') if isfield(data,'phase') && (length(data.phase) ~= length(data.time)) if isfield(data,'freq') && (length(data.freq) ~= length(data.time)) error('The time and freq vectors are not the same length. See help for details. [con2]'); else error('The time and phase vectors are not the same length. See help for details. [con1]'); end end if isfield(data,'phase') && (any(isnan(data.phase)) || any(isinf(data.phase))) error('The phase vector contains invalid elements (NaN/Inf). [con3]'); end if isfield(data,'freq') && (any(isnan(data.freq)) || any(isinf(data.freq))) error('The freq vector contains invalid elements (NaN/Inf). [con4]'); end if isfield(data,'time') && (any(isnan(data.time)) || any(isinf(data.time))) error('The time vector contains invalid elements (NaN/Inf). [con5]'); end end % sort tau vector tau=sort(tau); %% Basic statistical tests on the data set if ~isfield(data,'freq') if isfield(data,'rate') && data.rate ~= 0 data.freq=diff(data.phase).*data.rate; elseif isfield(data,'time') data.freq=diff(data.phase)./diff(data.time); end if verbose >= 1, fprintf(1,'allan_overlap: Fractional frequency data generated from phase data (M=%g).\n',length(data.freq)); end end if size(data.freq,2) > size(data.freq,1), data.freq=data.freq'; end % ensure columns s.numpoints=length(data.freq); s.max=max(data.freq); s.min=min(data.freq); s.mean=mean(data.freq); s.median=median(data.freq); if isfield(data,'time') if size(data.time,2) > size(data.time,1), data.time=data.time'; end % ensure columns s.linear=polyfit(data.time(1:length(data.freq)),data.freq,1); elseif isfield(data,'rate') && data.rate ~= 0; s.linear=polyfit((1/data.rate:1/data.rate:length(data.freq)/data.rate)',data.freq,1); else error('Either "time" or "rate" must be present in DATA. Type "help allan_overlap" for details. [err1]'); end s.std=std(data.freq); if verbose >= 2 fprintf(1,'allan_overlap: fractional frequency data statistics:\n'); disp(s); end % scale to median for plotting medianfreq=data.freq-s.median; sm=[]; sme=[]; % Screen for outliers using 5x Median Absolute Deviation (MAD) criteria MAD = median(abs(medianfreq)/0.6745); if verbose >= 1 && any(abs(medianfreq) > 5*MAD) odl = (abs(medianfreq) > 5*MAD); outliers = data.freq(odl); fprintf(1, 'allan_overlap: OUTLIERS: There appear to be %d outliers in the frequency data.\n', length(outliers)); % idl = (abs(medianfreq) < 5*MAD); % data.freq = data.freq(idl); s.outliers = length(outliers); else s.outliers = 0; end %%%% % There are four cases, freq or phase data, using timestamps or rate: %% Fixed Sample Rate Data % If there is a regular interval between measurements, calculation is much % easier/faster if isfield(data,'rate') && data.rate > 0 % if data rate was given if verbose >= 1 fprintf(1, 'allan_overlap: regular data '); if isfield(data,'freq') fprintf(1, '(%g freq data points @ %g Hz)\n',length(data.freq),data.rate); elseif isfield(data,'phase') fprintf(1, '(%g phase data points @ %g Hz)\n',length(dat