FR3007232A1 - METHOD FOR DETECTION AND / OR AUTOMATIC CORRECTION OF ERRORS IN A MULTIPLEXED DATA STREAM - Google Patents

Abstract

The present invention relates to a method for automatically detecting and / or correcting errors in a multiplexed data stream. The data stream includes a plurality of interleaved data channels arranged cyclically in frames, each data channel having an assigned slot within each frame, in which there is a sample of data presumably belonging to the channel. The flow includes ordinary data samples and glitches, which causes the subsequent regular data samples to be shifted with respect to the intervals. Glitches are identified using a Viterbi algorithm. As states, associated with each sample of data, the algorithm uses the possible offsets (i.e., one interval offset, two intervals, etc.) caused by glitches received up to the same time. associated data sample. Permitted transitions between states include a first transition, representing a reception of an ordinary data sample, and a second transition, representing a reception of a glitch.

Description

Field of the Invention [0001] The present invention generally relates to the detection and / or automatic correction of errors in a multiplexed data stream, i.e. a sequence of samples. of data belonging to a plurality of interleaved channels. Technical Problem [0002] In a data stream containing data samples belonging to cyclically interleaved channels, any additional data sample that may be introduced into the data stream disrupts the periodicity of the interleaving. In the following, the number of intertwined channels will be called Ni ,. A sequence of Nc data samples in the data stream will be called a frame. Ideally, each channel is thus allocated the same interval within each frame, making demultiplexing or deinterleaving a relatively easy task. Samples of additional data, regardless of their source, result not only in outliers (called "glitchs") in the data stream but also in cyclical permutations of the downstream channels of the additional data samples, i.e. say a discrepancy or offset of the data samples that follow the additional data samples relative to the intervals in which they should actually be. An object of the present invention is to provide a method of automatic detection or detection and correction (deletion) of such additional data samples.

General Description of the Invention [0005] A method for detecting and / or automatically correcting errors in a multiplexed data stream is proposed. The method includes obtaining (for example, via a physical communication channel or from a memory) a multiplexed data stream containing data samples, the data stream comprising a plurality of data elements. interleaved data channels arranged cyclically in frames, each data channel having an assigned slot within each frame, in which there is a sample of data presumably belonging to the channel. The data samples transported by the data stream include ordinary data samples (each of which can be assigned to one of the interleaved channels) and additional data samples (glitches that can not be assigned to one any of the interleaved channels), which causes a shift of subsequent ordinary data samples with respect to the intervals. According to the present invention, the additional data samples are identified by the execution of a Viterbi algorithm. As so-called "hidden" states, associated with each data sample, the Viterbi algorithm uses the possible offsets (i.e., one interval offset, two intervals, etc.) caused. by additional data samples received up to the associated data sample. Allowed transitions between states include a first transition (i.e., a transition of a first type), representing a reception of an ordinary data sample and, therefore, an offset constancy, and a second transition (i.e., a transition of a second type), representing a reception of an additional data sample and, therefore, an offset increase of one unit (an interval). As will be seen, the glitch detection and / or suppression method exploits precisely the sequential nature of the corruption mechanism (cyclic permutation of the data channels inside the frames, ie say mismatch between the data channels and their assigned intervals respectively due to the presence of glitches) in order to retrieve the ordinary data samples that are actually present in the corrupted data stream and restore the correct channel order. Process embodiments have proven very effective in simulation experiments, in which initial data streams were artificially corrupted: 99.1% to 99.9% of the corrected data accurately matched the original uncorrupted data.

An interesting advantage of the method is that it does not require interpolation or extrapolation of data and therefore does not modify the informative content of the data stream. This aspect can be particularly useful in correcting scientific measurements. [0007] Preferably, the method comprises a step in which a corrected multiplexed data stream, which differs from the multiplexed data stream in that it does not contain the identified additional data samples, is produced (and, for example, displayed and / or stored in a computer memory). It is inherent in the Viterbi algorithm that each authorized transition has a weight (or length or cost) associated therewith. According to a preferred embodiment of the method according to the present invention, the weight associated with a first transition (corresponding to the assumption "ordinary data sample received") from a first state to a second state is defined to depend on the difference between the data sample associated with the second state and a presumed direct predicted data sample in the same data channel as the data sample associated with the second state. In addition, the weight associated with a second transition (corresponding to the "additional received data sample" assumption) from a first state to a second state depends on the difference between one or more of the subsequent sample data samples. data associated with the second state and a presumed direct predecessor data sample in the same data channel as the one or more subsequent data samples. The higher the difference, the stronger will be the weight of the corresponding transition. This embodiment of the method thus exploits the fact that local derivatives of data from the same data channel are small, whereas inter-local derivatives of data between two distinct data channels are comparatively high. Consequently, in the absence of a glitch, a transition of the first type will obtain a low weight while a transition of the second type will obtain a stronger weight. Similarly, in the presence of a glitch, a transition of the first type will get a heavy weight while a transition of the second type will get a lower weight. The execution of the Viterbi algorithm comprises the construction of a plurality of paths through the states, each path of the plurality of paths corresponding to a specific sequence of transitions of the first and second types, each path of the plurality of paths having associated therewith a cumulative weight (or length or cost) corresponding to the sum of the weights associated with the first and second transitions constituting the path, and searching for a path of least weight among the plurality of paths. Since one is interested in finding the path with the lowest cumulative weight, at each crossing of two paths, the path with the highest cumulative weight is rejected. Each path of the plurality of paths preferably has associated therewith a sequence of presumed ordinary data samples. The corrected flow of multiplexed data then corresponds to the sequence of data samples associated with the minimum weight path found. According to a preferred embodiment of the method according to the invention, before the execution of the Viterbi algorithm, frames capable of containing at least one additional data sample are identified. The weights associated with the first and second transitions from a first state to a second state may in this case be modified (re-weighted) depending on whether the data sample associated with the second state belongs to a frame identified as likely to contain minus an additional sample of data. A preferred aspect of the present invention relates to a computer program comprising instructions that can be implemented by a processor, which, when executed by a processor, cause the processor to execute a method such as that described here. . Another preferred aspect of the present invention relates to a computing device comprising a processor and a non-volatile memory preferably containing in memory processor-operable instructions which, when executed by the processor, cause the processor to execute a method as described herein. Brief Description of the Drawings [0012] Preferred embodiments of the present invention are hereinafter described, by way of example, with reference to the accompanying drawings in which: Figure 1 is a schematic illustration of a flow of multiplexed data containing an additional data sample which causes subsequent samples to be shifted with respect to their assigned ranges. Figures 2 to 4 are schematic illustrations of the lattice construction using the Viterbi algorithm in a According to a preferred embodiment of the present invention, Figure 5 illustrates the performance of the method according to the present invention. Description of Preferred Embodiments 1. Introduction to MADRAS [0013] In the following, preferred embodiments of the present invention will be illustrated by the example of glitch detection and correction in data from MADRAS, which is a microwave imager embedded on the MEGHA-TROPIQUES satellite. It should be noted, however, that the method according to the present invention can be used for other purposes. The scientific data acquired by MADRAS consist of several hundred acquisitions (or scans) recorded in N, = 11 channels. A set of contiguous sweeps composes a multichannel image. A given 11-channel scan results from the reordering of a single data stream. Each cycle of Nlc data samples corresponds to one pixel of the image and is called a frame. The data stream thus contains a cyclic sequence of 11 ° NF measurements that are sequentially and periodically assigned to the 11 channels, where NF is the number of frames. Due to a malfunction in the communication chain between two electronic devices, this data flow is corrupted. The most frequent mechanism of corruption is such that additional data samples (glitchs) are concatenated to the measurements due to the occurrence of parasitic pulse signals (in the context of MADRAS, this anomaly is called "anomaly of type 1 "). As a result, the data collected contains most of the scientific measurements, but the multiple and random data insertions result in - the presence of additional data samples (glitches) in the data stream, - cyclic permutations of the data. channels after recombination of the data stream due to these additional data. A schematic view of the phenomenon is illustrated in FIG. 1, where for brevity only four channels have been considered (i.e., 15 Nc = 4 in FIG. 1) and the flow of Data 10 is divided into three successive frames 12. Each data channel has its allocated slot within each frame. In Figure 1, the numbers 1 to 4 refer to the data samples belonging to the different data channels. When a glitch (called G) appears in the reserved time slot for channel 3, then this interval receives an outlier (which can not be assigned to any of the data channels), the subsequent interval reserved for channel 2 receives the sample of data belonging to channel 3, the next reserved slot for channel 1 receives the sample of data belonging to channel 2, and the offset (discordance between channels and slots) is propagated to the next frame. The algorithm described below is designed to detect and remove these glitches for each scan individually. Once all the glitches have been removed from a scan, the data contains only the measurements that are recoverable, each data sample being located in its dedicated interval on all the frames. The corrected data is therefore scientifically exploitable. [0018] A second mechanism of frequent corruption (called "type 3 anomaly") is characterized by the observation of erratic values during several frames at the beginning of the scan followed by a single constant value in all the channels for the rest of the time. scanning. If a Type 3 anomaly is detected, the entire scan must be rejected. Type 3 anomalies and other less common types of anomalies will no longer be addressed in this document. According to the present invention, the Viterbi algorithm is used for the detection and suppression of glitches in the multichannel signal. The Viterbi algorithm is used to find the path with minimal cumulative weight through an appropriate lattice. For the application of the Viterbi algorithm, a lattice and the distances (weights) associated with all the branches of this lattice are defined. A trellis is an oriented graph whose nodes are organized in vertical slices (at the same discrete time increment) and each node is connected to at least one node at the previous time increment and at least one node at the level of the next time increment. Given a specific cost function, the solution given by the algorithm is the optimal path through the trellis, that is, the path that has the lowest cost among all of the possible paths at the time. through the lattice from the first moment to the last moment. In the proposed application, the solution path indicates the glitch locations, thus allowing their correction. 2. Type anomaly detection and correction [0020] As indicated above, given a specific cost function, the solution given by the Viterbi algorithm is optimal in the sense that the solution path has the highest cost. weak among all the possible paths through the lattice from a start instant (time 0) to a terminal instant. The application of the Viterbi algorithm to a specific problem therefore requires the design of a lattice and the specification of a suitable metric for its branches. A possible implementation of the Viterbi algorithm for glitch detection and suppression is given below. Further details can be found in the computer pseudocodes at the end of this description. In the following, x (n) denotes the data sample received at the discrete instant n. x (n) can be a regular data sample or an additional data sample (glitch). The set of all sequentially received samples x (n) (measures and glitches) represents the data flow. 2.1. Design of the trellis [0021] As states of the Viterbi algorithm, the possible offsets (i.e., one interval shift, two intervals, etc.) caused by samples of the Viterbi algorithm are used. additional data received up to the associated data sample. The lattice contains NS (? .. Ne) nodes per instant n (i.e. arrival of a sample) which are designated ck; n, with k = 0, NS - 1 for the sake of convenience. The node Ck; n corresponds to the state value in which k (modulo NS-1) glitchs were detected and deleted along the path reaching it (i.e. from the n samples received up to the). Each node ck; n is connected to the nodes ck-1; ri-1 and Ck; n-1, associated with the previous instant, and to the nodes cku, ÷, and ck + 1; n + 1, associated at the next moment. The lattice is "circular" in the sense that the node is connected to the node cNs_I; n-1, and the node cNs_iu is connected to the node + 1. The vertices connecting the 20 nodes are called branches. The branch connecting the nodes ck; n and Ck; n-1 is denoted by v ° k; n, and the branch connecting the nodes Ck; n and ck-tn-i is denoted by v1k; n- Note that the vlku branch , corresponds to the hypothesis "x (n) is a glitch" for the state k, while the branch v ° k; n corresponds to the hypothesis "x (n) is not a glitch" for the state k. 2.2. Viterbi Algorithm Each branch vc) ku, and vlk; n has a weight do (k; n) and a weight di (k; n) assigned to it. A possible definition of the weights do (k; n) and di (k; n) is described in the following subsection. In summary, the Viterbi algorithm removes at all times n all but one of the branches reaching the same Cree * state, so that each state cn: k can be reached by only a single path through the trellis. At time n-1, at each node has been assigned the cumulative weight D (k; n-1) of the branches of the unique path reaching it. ## EQU1 ## denotes the sequence of presumably valid samples encountered on the unique path reaching node ckm_i. In the following, we will use the notation: = [ek (2), xk (nk) l, where nk is the number of likely valid samples received on the path reaching the Ckm-1 node. Note that nk = n-k since k glitchs were detected in state k. If at the node Ck; n, the sum of D (k; n-1) and do (k; n) is smaller than the sum of D (k-1; n1) and di (k; n ), that is, if the hypothesis "x (n) is not a glitch" leads to a smaller cumulative weight D (k; n) than the hypothesis "x (n) is a glitch ": o The branch vlk; n is removed from the lattice and the branch v ° k; n is preserved. o Sample x (n) is accepted as a valid measure (regular data sample) by state ckm. The sequence of all the samples that have been accepted along the unique path reaching the node Ck; n is thus obtained by [2] k; n = x (n)], where [. ,.] is the concatenation operator. In the opposite case, if at the node ckrn, the sum of D (k; n-1) and do (k; n) is greater than the sum of D (k-1; n-1) and of di (k; n), that is, if the hypothesis "x (n) is not a glitch" leads to a higher cumulative weight D (k; n) than the hypothesis "x ( n) is a glitch ": o The branch v ° k; ,, is removed from the lattice and the branch vik; ,, is preserved. o The sample x (n) is not accepted as a valid measure (ordinary data sample) by the state Ck; n. The resulting sequence of valid measurements [2] k; n on the path up to the node Ck; n is thus the same as the sequence of valid measurements reaching the node ck_im -1I1 reik-1; n-1. After receiving the last sample of data x (N), the path through the lattice with the lowest cumulative weight D (k; N) is chosen.

Designated by k = arg min (D (k; N)), the corrected data flow is given by the sequence [x] k; 2.3. Branch Metric [0028] The metric assigned to the trellis branches is based on local derivatives of a sample of data x (n) with past and future received data samples. 1) The weight assigned to the branch v ° k; n connecting the nodes ck; r1 and Ck; n-1 is given by the square root of the absolute value of the difference between x (n) and the last valid data sample that is assumed to belong to the same data channel as x (n) that the ckm state has received, namely ek (nk-N1, + 1). As a result: do (k, n) =. \ 11x (n) - xk (nk - +1) (Equation 1) 2) The weight di (k; n) assigned to the branches vikm connecting the nodes Ck; n and Ck-1; n-1 ^ k = 0, ..., Ne-1 is constructed as an average of a subset of the differences between the last valid data samples 2k (nk-Nc + 1 ) on the paths that reach the states Ck; nk = 0, ..., Ne-1, and a Nfuture number of future samples x (n + 1), x (n + 2), x (n + N 1 The subset of differences is given by future / - the smallest 1 truturen differences associated with each state.In the case of MADRAS, the choice Nfuture = 10 proved to be advantageous wp Ar_cl (Equation 2) di (k, n) = 1: h (k, n), where (Equation 3) N, k-0 2 Nfid '"/ 2 h (k, n) = E Csk n (i), with Nfuture i = 1 iNfuture 1 = output (i) x (n + j) - Sc (n - +1 lj = (Equation 4) The coefficient WD1 is a normalization factor In this example: WD1 = It should be noted that the weights di (k, n) do not depend on k, that is, ie, they are identical for all the branches v1, [0029] This choice of the weights can be motivated according to the observation that the data in each data channel, considered individually, exhibit a correct behavior in the sense that their local derivative remains within certain limits (which depend on the type of data).

The weight do (k, n) basically corresponds to the local derivative at the sample x (n) if this sample and the previous one are not glitches. As a result, do (k, n) will be small in the sense that it will not be greater than a normal variation in a given data channel in the absence of a glitch. The branches v1 are weighted on the assumption that x (n) is a glitch. If this assumption is correct, the data after x (n) are shifted to a position within the frame relative to data before x (n). With correction for the applied offset, it can again be expected that the data channels will behave correctly in the above sense. The calculation of di (k, n) is based on the computation of quantities 5k, n (i) corresponding to local derivatives for a number of data channels (Equation 4), where it is assumed that x (n) itself even must be rejected as a glitch. The quantities Esk, r, (1) are sorted in ascending order and only the lower half of these is used to calculate the quantity h (k, n) (Equation 3), which represents a quantity that can be considered as an average local derivative (where the average is taken on the data channels presenting the most correct behavior only). Taking the average only on the lowest quantities Ôk, n (i) reduces the risk that the quantity h (k, n) is denatured due to a large natural variation in a data channel or due to a glitch occurring shortly after x (n) in the data stream. di (k, n) is finally obtained (Equation 2) by calculating the average of the quantities h (k, n), k = 0, ..., Na-1, on the possible states (the different hypotheses for the number of glitches that occurred at this stage). The pseudocode algorithms 1 and 2 at the end of the description implement the Viterbi algorithm described in sections 2.1. to 2.3. Figures 2 to 4 illustrate how the above Viterbi algorithm operates on a data stream with four slots per frame. For illustrative purposes, the branch metric is simplified compared to the example above. The weights of the branches are indicated in the table below: The branches viim, (corresponding to the hypothesis "x (n) is a glitch"), receive o the weight 1 if the sample x (n) is actually a glitch and o the weight 3 if the sample x (n) is actually an ordinary data sample. Branches v ° k; (corresponding to the hypothesis "x (n) is not a glitch") receive o the weight 0 if the sample x (n) is an ordinary data sample and the corresponding state is the correct state, o the weight 2 if the sample x (n) is an ordinary data sample but the corresponding state is erroneous, and o the weight 3 if the sample x (n) is actually a glitch. It should be noted that the metric used here is artificial because in a real-life situation, one would not have prior knowledge of the dynamics of each data channel. At time n = 0, an entire frame was received. Figure 2 illustrates the lattice after receipt of the data sample (ordinary) at time n = 1. The weight of each individual branch is indicated above the respective branch. Cumulative weights are shown above the lattice nodes. The weight of the branch y ° 0.1 is determined by glitch steps glitch i glitch -> i glitch 0 (in the correct state) 2 (in the wrong state) 3 i glitch -> (i + 1 ) ',' d5 glitch 3 1 ---------- 13 the comparison of the data sample x (n = 1) with its predicted predecessor in the same data channel. Since the end node of the branch v ° 0.1 is col, no glitch is considered to have occurred at this stage and the data sample x (n = 1) is therefore compared to the sample of data Nc (in this case 4) time intervals forward, that is to say with x (n = -3). Since x (n = 1) and x (n = -3) actually belong to the same data channel, the do weight (0.1), calculated using Equation 1 above, will be comparatively small. In the case illustrated, this fact is reflected by the fact that the branch vc) 0.1 receives the weight 0, according to the table above. The weight of the v11.1 branch is determined using Equation 2 above. The assumption here is that x (n = 1) is a glitch, but since x (n = 1) is not a glitch, the di (1,1) weight will be comparatively strong. In the case illustrated, this fact is reflected by the fact that the v11.1 branch receives the weight 3. [0034] FIG. 3 illustrates the lattice after receiving the (additional) data sample at the instant n = 2. The weight of the branch v 0.2 is determined by comparing the data sample x (n = 2) with its predicted predecessor in the same data channel. Since the end node of the branch v ° 0.2 is co; 2, no glitch is considered to have occurred at this stage and the data sample x (n = 2) is therefore compared to the data sample four time intervals forward, that is to say at x (n = -2). Since x (n = 2) is actually a gine, the weight do (0,2) will be comparatively strong. In the case illustrated, this fact is reflected by the fact that the branch v (10.2 receives the weight 3. The weight of all the branches v1k, 2 (k = 0, 1, 2, ...) is determined at The hypothesis is that x (n = 2) is a glitch and since this is indeed the case, the weights di (k, 2) will be comparatively small. branches v11,2 and Y12,2 receive the weight 1. The weight of the branch v 1,2 is determined by means of equation 1, ie by the comparison of the data sample x (n = 2) to its presumed predecessor in the same data channel Since the end node is c1,2, a glitch is considered to have occurred at this point, the data sample x (n = 2) is then compared to the data sample I ^ 10 + 1 (here: 5) time intervals forward, ie to x (n = -3). Since x (n = 2) is actually a glitch, the do weight (1,2) will be comparatively strong (weight 3). now to be reached by two different paths. The Viterbi algorithm thus eliminates the path with the highest cumulative weight. Figure 4 illustrates the lattice after receipt of the data sample (ordinary) at time n = 3. The weight of the v 0.3 branch is determined by comparing the data sample x (n = 3) with its predicted predecessor in the same data channel. Since the end node of the branch y ° 0.3 is co; 3, no glitch is considered to have occurred at this stage and the data sample x (n = 3) is therefore compared to the data sample four time intervals forward, that is to say at x (n = -1). Since a glitch has occurred in the meantime at n = 2, there is an unaccounted channel mismatch and the do weight (0.3) will be comparatively high but less than the weight that would be obtained by comparing a glitch to an ordinary data sample (weight 2). The weight of all branches vlk, 3 (k = 0, 1, 2, ...) is determined using equation 2 above. The hypothesis is that x (n = 3) is a glitch, but since x (n = 3) is not actually a glitch, the weights d1 (k, 3) will be comparatively strong. The branches v11,3, v12,3 and v13,3 thus receive the weight 3. The weight of the branch v 1,3 is determined by means of the equation by the comparison of the sample of data x (n = 3) to its predicted predecessor in the same data channel. Since the end node of the branch v ° P, 3 is ci; 3, a glitch is considered to have occurred at this stage. The sample of data x (n = 3) is therefore compared with the data sample N1,4-1 forward time intervals, that is to say at x (n = -2). Since x (n = -2) and x (n = 3) actually belong to the same data channel, the weight do (1,3) will be comparatively small (weight 0). The weight of the branch% / 02.3 is also determined by equation 1 by comparison of the data sample x (n = 3) with its predicted predecessor in the same data channel. Since the end node of the v2.3 branch is c2.3, two glitches are considered to have occurred at this stage. The sample of data x (n = 3) is therefore compared to the sample of data N0 + 2 (here: 6) time intervals forward, ie to x (n = -3 ). Since x (n = -3) and x (n = 3) do not actually belong to the same data channel, the weight d0 (2,3) will be comparatively strong (weight 2). Each of the nodes ci, 3 and C2,3 could now be reached by two different paths. The Viterbi algorithm always removes the path with the highest cumulative weight. While the lattice is constructed, the algorithm retains a trace of the sequences [2] k; n of potentially valid data samples. At the moment n = 2: o [210: 2 = [x (n = 1), x (nz - 2)], o [2] 1, 2 = [x (n = 1)], 10 0 0 [] 2; 2 = [(empty sequence). At time n = 3: o [113 = [x (n = 1), x (n = 2), x (n = 3)], obtained as a concatenation of e10; 2, x (n = 3) )], o [1; 3 = [x (n = 1), x (n = 3)], obtained as the concatenation of [[-] 1; 2, 15 x (n = 3)], o [ 2] 2; 3 = [x (n = 1)], obtained by resuming the sequence of the previous node on the path: [212; 3 = [211; 2 oo re} 3; 3 = [(empty sequence) , obtained by resuming the sequence of the previous node on the path: []] 3; 3 = P12; 2. When the last sample x (N) has been received, the Viterbi algorithm selects the node ck, N, k = 0, 1, ..., Ns, on which the path with the most cumulative weight low happens. Assume that Ckmin, N is this node, the corrected data stream can be produced as [2] kmin, N. For example, if x (n = 3) was the last sample received, the sequence [.i.] 1.3 = [x (n = 1), x (n = 3) would be found as a corrected data stream. )]. 3. Detection of corrupted frames [0038] This section describes an algorithm that allows the detection of frames that potentially contain type 1 anomalies. Similar to the algorithm described in the previous section 2, it uses a metric based on local derivatives to decide if a frame is corrupted or not. However, the metric is built together for all channels in a frame, which adds robustness against false alarms in areas of the scan where the N0 channels take values that are very close to each other. It is designed to work frame by frame and can therefore only be used to detect whether a frame contains a glitch or not and can not solve the problem of whether an individual sample is a glitch or not. 3.1. Metric and Detection Criterion Let m be the index of frames and denote by xr ,,) the samples in this frame, i = 1, ..., N0. The algorithm is based on the following dual metric: 1) Intra-channel differences (between samples of the same data channel i): ô. (i) = - 4:21 Nc Dm 1 = Sm 2 2) inter-channel differences (between channel i and channel samples (i + d;) modulo Nc, where di = 1, ..., N0-1 ): ôn, (i, d,) = x, (,! / ++: '- 1) where [.] = mod (., Nc) 7', '(d,) = Nc Eig,' (1 , d,) 12 [0040] The principle underlying this metric resides in the following observations: o If the frame m and the frame m + 1 do not contain glitches, then the intra-channel differences 6.7 (I ) correspond to the local derivatives of the measurements that are transmitted in channel i, and the inter-channel differences (5.0, d,) to the difference of the measurements transmitted in the interval i to the interval i + di. The sum of intra-channel differences will be small compared to the sum of inter-channel differences. o If the frame m or the frame m + 1 contains ng glitchs, then the intra-channel differences Sm (r) correspond either to the difference of the measurements transmitted in the interval i and the measurements that should have been transmitted in the interval j = i + n9, or unlike the measurements transmitted in the channel i and the value of the glitch. In both cases, the sum of the intra-channel differences will be high. Conversely, the inter-channel differences c5m (i, d,) that satisfy the condition di = ng correspond to the local derivatives of the measurements that must be transmitted in the channel i. Their sum will therefore be small. As a result, glits in a frame m * are considered detected if the following criterion is satisfied: D ',.> Min T', '(d,) The number of glitches in the frame m * can be estimated by : ng (m *)> arg min Tm. (d,) d 3.2. Algorithm for the Detection of Corrupted Frames The algorithm (pseudocode algorithms 3 to 5 at the end of the present description) loops through frames m of a scan. If for the frame m *, the criterion De> minT .. (d,) is satisfied and that consequently glitches are detected: 1) The frame m * is detected as being corrupted and the index of the frame is placed in memory. 2) The frame m * is deleted from the data. Specifically, the frame m * (which is presumed to contain at least one glitch) is rejected, and the frame m * + 1 takes its place, i.e., is now at position m * for the rest of the algorithm for detecting corrupted frames. The channels of all frames m * + 1, m * + 2, ... are permutated circularly by ng (m *). As a result, x # (1L and x '(' L 5 contain measurements from the same data channel and the order of the channels has been restored.) 4) The algorithm continues with the next frame of the data stream. weighted Viterbi combined with detection of corrupted frames [0043] In this section, the Viterbi algorithm described in section 2 is generalized to allow the use of prior information on a specific sample x (n). The generalization is motivated by the fact that, in many cases, most of the samples in a scan are actually valid measurements, if, for example, sample sequences are known to be valid measurements (or, conversely, glitch), this information can be used to improve the performance of the Viterbi algorithm. [0044] The prior information places the algorithm in the form of a factor y (n) which acts as a multiplier for the Viterbi algorithm. s di (k, n) given by equation 2. Instead of di (k, n), then c71 (k, n) is used which is defined as: jn) = Y (n) - d 1 (k, n) [0045] Consequently, the factor y (n) influences the decision according to which the branches v ° k; n or the branches vlk; n must be suppressed at time n. O Case y (n) = co The choice Y (n) c ° is made if the sample x (n) is known to be a valid measure (a sample of ordinary data). Based on this earlier information, the Viterbi algorithm is forced to remove the vik; n branches of the lattice (for all k's) and accept the x (n) sample as a valid measure. o Case 1 <7 (n) <This choice is made if the sample x (n) is most likely a valid measure (a sample of ordinary data). The branches vlk; n are penalized by their increase in terms of weight. As a result, the probability that x (n) is accepted as a valid sample is increased (compared to the algorithm that uses dl (k, n) instead of j1 (k, n)). o Case 7 (n) = ° This choice is made if it is known that the sample x (n) is a glitch. The fact that the vlk; n branches will receive zero weight causes the Viterbi algorithm to remove the vOk: n branches of the trellis. The sample x (n) is detected as a glitch and is not accepted as a valid sample by any state ck; n, regardless of the value of k. o Case ° <Y (n) <1 This choice is made if it is very likely that the sample x (n) is a glitch. The weight of branches vlk; n is decreased compared to the algorithm that uses di (k, n). As a result, the probability that x (n) is accepted as a valid sample is decreased. The weighted Viterbi algorithm is detailed in the pseudocode algorithms 6 and 7 at the end of the description. It is coupled here to a corrupted frame detection algorithm, for example, the algorithm detailed in section 3.2. (pseudocode algorithms 3 to 5) with Mweight = infinite (Go). The pseudocode algorithm 6 accordingly assigns a weight y (n) = 'I to all the samples in frames which are detected as corrupted and the weight y (n) = co to all the samples in frames which are not not detected as corrupted. The branches vlk; n are therefore removed from the lattice of the pseudocode algorithms 6 and 7 for all the samples in frames that are not detected as being corrupted by pseudocode algorithms for detecting corrupted frames 3 to 5. As a result, the processing cost of the Viterbi algorithm is reduced for scans that are only weakly corrupted. In addition, the probability of false alarm (ie the detection of a non-existent glitch and the deletion of a valid measurement) is decreased, especially in areas where all channels have a very similar dynamic . Figure 5 illustrates the performance of the algorithm for detecting and removing glitchs according to pseudocode algorithms 6 and 7 on a set of synthetic data. Graph 14 illustrates the original data. Each moment (x axis) corresponds to a frame. The original data was artificially corrupted by the insertion of glitches (graph 16), resulting in a cyclical permutation of the data channels after each glitch. The corrupted data in graph 16 was then introduced into the glitch detection and removal method. The result of the correction is shown as graph 18. As can be seen, the correction works well: glitches are effectively removed from the corrected data stream. It should be noted that the correction is only applied to frames 37 to 485, in which all channels of the MADRAS instrument contain measurements. Although specific embodiments have been described in detail, those skilled in the art will be able to observe that various modifications and variations to these details could be developed in light of the overall conclusions of the invention. Accordingly, the particular arrangements described are intended to be merely illustrative and not limiting as to the scope of the present invention to which the full scope of the appended claims and any equivalents thereof should be attributed.

Algorithm 1 Viterbi Algorithm Part 1: Initialization -Entry CorruptedScan: matrix [11 x Nf] matrix [11x Nf] t> corrupted scan - frames 37-485 -R r> corrected scan - frames 37-485 CorrectedScan: cweight:> cumulative distance of the corrected scan path %% iNITIALIZATION N, 4-11; NOT.

211Tc CONST: #channels; # states of the Viterbi algorithm WD1 + - CONST: branch measurement multiplier FUTUR 4- 10 CONST: # future samples in the branch metric do (1: N.) <- 0; di (1: N.) 4- 0 lattice branch distances distances_cum (1: N.) 4- oc; distances_curn (1) 4- 1 t> cumulative distance for each state iast_index (1: N.) 4- N. r> index of the last valid sample received for i = 1 -> Nc do r> place the scan in the vector format and initialize the output data for j = 1 -> Nf do data ((] - 1) - Nf CorruptedScan (i, j) CorrectedScan (i, j) 0 end for end for sarnplereceived (1: (Ni - N, ), 1: N.) 4- 0 initialize state path vectors for k - = 1 N. do for n = 1 -> N, do sample_received (n, k) 4- scan (n) end for end for dd (1: FUTURE) 4- 0; pre_k 4- 0; disto 4- 0; dist]. 0; sid 4- 0; cweight 0 oldsample_received (1: (Nf - N,), 1: N.) 4- 0> working variables and buffer memories olddistancescurn (1: N.) 4- 0 oid_last_index (1: N.) 4- 0 following the algorithm 2 30072 32 22 Algorithm 2 Viterbi Algorithm Part 2: Loop main ... continued from algorithm 1 9/0% --- MAIN: SHAPING ON SAMPLE - 910% for n = Ne-F1-NeNf- FUTU R do for k = 1 -> N do> calculate the branch metric of the sample lon n for each state k do (k) abs (data (n) - sample received (k, lastindes (k) - N 1)) 4` dd (1: FUTURE) abs (data (n + 1: n FUTUR) - sample_received (k, last_index (k) - + 1)) i dd 4- sort (dd)> sort in ascending order di (k) for j = 1 FUTU R / 2 do di (k) = di (k ) + T / VD1 - dd (j) / FUTUR end for end for old_distances_curn 4- distances curn old_lastindez 4- last_index old_sample_received sample received for k = 1- * N do> update state vectors pre_k k - 1 If k = = 0 then pre k N end If dist_ old_distances_curra (k) do (k) D branch distance kk distl old_distances_cum (pre_k) mean (di 1 t> branch distance k-1 k if dist '<disto then> sample considered as a glitch distances_curn (k) 4- disti sample received (:, k) old_sample_received (:, pre k) fast index (k) 4- old lastindez (pre_k) else> sample considered valid distart.ces_cum (k) fast index (k) fast inde-c (k) + 1 sample_received (last_index (k), k) 4- data (n) end If end for end for cre% DECISION sid index_of_rnin (distances curn) `Yo% t> path with the lowest cumulative distance cweight 4- di stances_curn (sid) D corresponding cumulative distance for i = 1 -4- ./V. do for j = 1 Nf do C orrectedScan (i, j) samplereceived ((j - 1) - N f i, sid) p place the corrected scan in an end for matrix format end for OUTPUT C orr ectedS can; cweight Algorithm 3 Recursive Prototype - Corrupted Scan Input - frames 37 to 485 D weight to be assigned to samples in non-CorruptedScan frames: matrix [11 x N 1] Mweight: CON ST corrupted-Output D tags for frames uncorrupted Fvalid: vector [1 x Nf] Grnetric: vector [1 x 11 - N1] D weight for each sample in CorruptedScan %% - INITIALIZATION CONST: #channels; # states of the Viterbi DCONST algorithm: maximum order of rotation of DCONST channels: corrupted frame neighborhood to be tagged CONST: maximum number of iterations Nc 4- 11 unspecified assumed frame index D beacons for non-corrupted frames NG 4- - 1 weight for each sample DD 3 MITER 1- 30 Nr ÷ - Nf for n = 1 -> Nf do NGindex (n) n Fvalid (n) + - 1 for i 1 -> Nc do Grnetric ((n - 1), N1 + i) +> 1 end for end for% of, RECURRING: DETECTION AND REMOVAL OF CORRUPTED FRAMES RUN t- 1; ITER 0 data r4- CorruptedScan while RUN-1 do ITER ITER + 1 4- DetectRemove (see Algorithm 5) end while %% --BALIZE CORRUPT FRAMES AND ATTRACT WEIGHTS TO VITERBI% ° / 0 4- Your Goose ight ( see Algorithm 6) Fvalid OUTPUT; Gmetric Algorithm 4 Recursive "Prototype" Algorithm: DetectRemove DetectRemove Part% Tc, - DETECTION OF CORRUPT FRAMES iG <-1 TabG (1) <- 0; PerrnG (1) 4-- 0 for n = 1 N, - - 3 do do 4-0 for i = 1 -> Nc do do 4- do + abs (data_r (iin) - data_rei, n end for do 4- (do) i` 64 (1 Na) 4- 0; dp (1: Na) <- 0; data_c (1: Ne) <- data_r (1: Nein) for 1 -> Na do tmp F datac (1 data_c (1 - 1) data_c (2: Ne); data_c (Ne) trng for = 1 -> N, do di (j) t di (j) abs (data_c (i, n) - data_r (i, ## EQU1 ## ) = (dp (jW end for index_of_min (di); idp <- indexof_min (dp) if do> di (idi) AND TabC (iG) <n then iG 4- iG +1; TabG (iG) i- n + 1 PermG (iG) t idp end if end for iC iG -1; for i = 1 -> iG do TabG (iG) - (- TabG (iG + 1); PermG (iG) 4- Perrne (ie -I- 1) end for %% DELETE CORRUPTED FRAMES if iG> 0 then lor 1 -> iG do old_data_r data_r data r (1 PerrnG (i), TagG (i): 4- old_data_r (Ne - PerrnG (i) -1- 1: Ne, TagG (i): data_r (PerniG (i) + 1: NeiTagG (i): Ne) + - old_data_r (1: Ne - PermG (i), TagG (i): Nr) end for old_data_r <- data_r old_NGindex NGindex for i = 1-> iC do %% initialize counters for this recursion. Loop on the frames: Detection P. calculate the distance calculate the distance i> The frame n + 1 presents a problem - 9'0 ° / 0 new glitchs found r> correct the order of the channels> delete the corrupted frames data r ( :, Taga (i) - i + 1: Nr - i) aid_data_r (:, TagG (i) + 1: Ni-) NGindex (TagG (i) - i + 1: Ni- - old NGindex (TagG (i) 1-1: Ni.) End for Ni- 4-- Ni. - e else> no new glitches found RUN 4- end if if ITER> = MITER then RUN 4-0 end il 3007232 - 25 Algorithm 5 Algorithm «Prototype Recursive: TagWeight Part TagWeight ° / 0% - SCAN CORRUPT FRAMES for n = 1 Nf do valid .4- 0 for k = 1 -> Air do if NGindex (k) n then .vadid 1 end if end for if vaiid == 0 then it max (1, n - DD); i2 rain (Nf, ra DD - 1) i2) 0 end If end for cyce, - ATTRIBUTE WEIGHTS FOR VITERBI ALGORITHM for n = 1 N1 do for i 1 - + Nc do if Fvalid (n) == 0 then Gmetric ((n - 1) - Nf i) 4-1 Cinetric ((n - 1) - Nf i) 4- Mweight end if end for end to t> mark the corrupted frame e and its neighbors t> tag valid samples Algorithm 6 Weighted Viterbi Algorithm Part 1: Initialization Input CorruptedScan: matrix [11 x Nf] Grnetric: vector [1 x 11 - N1] -Range CorrectedScart: matrix [11 x Nf] cweight: > corrupted scan - 37-485 frames of the branch metric for each sample in CorruptedScan corrected scan - frames 37 to 485 cumulative scan path distance corrected %% INITIALIZATION 910% <- 11; N. 4- 2.71r> CONST: #channels; # states of the Viterbi algorithm PV_Di N / Tr> CONST: branch measurement multiplier FUTUR -4-10> CONST: # future samples in the branch metric do (1: Na) 4- 0; cd1 (1: Na) 4- 0 lattice branch distances distances cum (1: N.) 4- oo; distances_curra (1) 4- 1 cumulative distance for each state last_index (1: Na) 4- N. r 'index of the last valid sample received for i = 1 -> Nc do r' place the scan in the vector format and initialize the output data for j = 1 Nf do data ((j - 1) - Nf 0 4-- CorruptedScan (i, j) CorrectedScan (i, j) 0 end for end for sample_received (1: - N.) , 1: Na) 4- 0 r 'initialize state path vectors for k = 1 -> Na do for n = 1 -> N. do sampie_received (n, k) scan (n) end for end for for n = 1 -> ./\Ç-N1 do r search for weights 00 If Grnetric (n) then Plum (n) 4- 1 else Plum (n) 4- G end if end for dd (1: FUTURE) 0 ; pre_k 4- 0; distortion 4- 0; dist1 0; sid 0; cweight 4- 0 old_sarnple_received (1: (N1 - Nc), 1: Ne) 4- 0 old_distances_cum (1: N5) 4- 0 oldictst_index (1: Na) 4- 0 ... following algorithm 7> variables Algorithm 7 Algorithm of Viterbi Weighted Viterbi Part 2: Main Boude Following the algorithm 6%. PRINCIPAL: SHAPING ON SAMPLES - ° h.% for 71 - = Nc 4- 1 Nc -N1 - FUTUR do for k = 1 -> N, do r> calculate the branch metric of sample n for transitions k - k do (k) 4- abs (data (n) - sample_received (k, last_index ( k) - No + 1)) to end for if Prune == 0 then for k = 1 -> N. d calculate the branch metric of sample n for transitions k-1 dd (1: FUTURE) 4- abs (data (n + 1: n + FUTUR)) - sarnple received (k, last_index (k) - N + 1)) to dd sort (dd) D sort in ascending order d1 (k) 4-- 0 for j = 1 FUTUR / 2 do di (k) dl (k) WD1 - dd (j) IFUTUR end for end for old distances_cum distances_curn old_last index 4- last_index old_sample_received sample_received for k = 1- * N, do> update the state vectors pre k 4-- k - 1 if k == 0 then pre_k N end if disto old_distances_curn (k) do (k) D branch distance kk disti dd distances_cum (pre_k) Grnetric (n) - mea D branch distance k-1 -ek If disti <disto then> sample considered to be a glitch distances_curn (k) dist 'sample_received (:, k) old sarnple_received (:, pre_k) last_index (k) 4- aldjast_index ( pre k) else> sample considered to be valid distances_curn (k) disto last_index (k) 4- last_index (k) + 1 sarriple_received (last irudex (k), k) 4- da end if end for else I> branches k -1 - k do not exist for k = 1 -> N. do distances_cum (k) 4-- distances cum (k) do (k) Last index (k) weights index (k) + 1 sarnple received (dast_index ( k), k) 4- data (n) end for end if end for 94% - DECISION ° / 0% sid = index of_min (distances cang) D path with the lowest cumulative distance ctoeight = distances_cum (sid) D distance corresponding cumulative for i = 1 -> N, do for j = 1 -> Nf do Corrected Scan (i, j) samplereceived ((j - 1) - Nfsid) r> set the corrected scan in mn end for matrix format end for OUTPUT CorrectedScdn; cweight

Claims (5)

REVENDICATIONS1. A method for automatically detecting and / or correcting errors in a multiplexed data stream, comprising: obtaining a multiplexed data stream containing data samples, said data stream comprising a plurality of interleaved data channels cyclically arranged in frames, each data channel having an assigned slot within each frame, in which a sample of data, presumably belonging to said channel, is located, said data samples comprising ordinary data samples and samples of additional data, said additional data samples causing a shift of subsequent ordinary data samples from the intervals, and identification of said additional data samples by execution of a Viterbi algorithm, having as states associated with each sample data, possible offsets caused by additional data samples received up to the associated data sample and in which allowed transitions between states comprise a first transition, representing a reception of an ordinary data sample and, therefore, an offset constancy, and a second transition, representing a reception of an additional data sample and, therefore, an incremental shift of one unit. The method of claim 1, comprising generating a corrected multiplexed data stream that differs from the multiplexed data stream in that it does not contain said identified additional data samples. 3. The method of claim 1 or 2, wherein each allowed transition has a weight associated therewith, the weight associated with a first transition from a first state to a second dependent state. 4. 15 5. A difference between the data sample associated with said second state and a direct predecessor data sample assumed in the same data channel as said data sample associated with said second state, and the associated weight. at a second transition from a first state to a second state depending on a difference between at least one data sample subsequent to said data sample associated with said second state and a predicted direct data sample in the same data channel as said at least one subsequent data sample. The method of claim 3, wherein said executing said Viterbi algorithm comprises constructing a plurality of paths through said states, each of said plurality of paths corresponding to a specific sequence of first and second transitions, each of said paths of said plurality of paths having associated therewith a cumulative weight corresponding to the sum of the weights associated with the first and second path transitions, and searching for a path of least weight among said plurality of paths. The method of claim 4 when dependent on claim 2, wherein each of said paths of said plurality of paths has associated therewith a sequence of presumed ordinary data samples, and wherein said corrected multiplexed data stream corresponds to the sequence of data samples associated with the minimum weight path found. The method of any one of the preceding claims, wherein prior to performing said Viterbi algorithm, frames capable of containing at least one additional data sample are identified. The method according to claim 6, when dependent on claim 3, wherein the weights associated with said first and second transitions from a first state to a second state are changed according to whether the data sample associated with said second state is or not to a frame identified as being capable of containing at least one additional data sample. A computer program comprising processor operable instructions, which, when executed by a processor, causes said processor to execute a method according to any one of claims 1 to 7. 9. A device computer system comprising a processor and a non-volatile memory preferably containing in memory processor-operable instructions, which, when executed by said processor, cause said processor to execute a method according to any one of the claims 1 to 7.