{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6TJ6BXB62QUOJXNRBP2SILC56L","short_pith_number":"pith:6TJ6BXB6","canonical_record":{"source":{"id":"1404.3638","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-04-14T16:07:11Z","cross_cats_sorted":[],"title_canon_sha256":"772d4d68f8626b094ee7e21e3ff1532db4c71199ded25f2afe1c65bc1ea09add","abstract_canon_sha256":"e284b849c80319dbc37d3fb506ee2a2cd7ed33e6c38bceb9b30bdc938bb8d624"},"schema_version":"1.0"},"canonical_sha256":"f4d3e0dc3ed428e4ddb10bf5242c5df2e8a01c1f246b0f32a5b69a380f176912","source":{"kind":"arxiv","id":"1404.3638","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3638","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3638v2","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3638","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"pith_short_12","alias_value":"6TJ6BXB62QUO","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6TJ6BXB62QUOJXNR","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6TJ6BXB6","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6TJ6BXB62QUOJXNRBP2SILC56L","target":"record","payload":{"canonical_record":{"source":{"id":"1404.3638","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-04-14T16:07:11Z","cross_cats_sorted":[],"title_canon_sha256":"772d4d68f8626b094ee7e21e3ff1532db4c71199ded25f2afe1c65bc1ea09add","abstract_canon_sha256":"e284b849c80319dbc37d3fb506ee2a2cd7ed33e6c38bceb9b30bdc938bb8d624"},"schema_version":"1.0"},"canonical_sha256":"f4d3e0dc3ed428e4ddb10bf5242c5df2e8a01c1f246b0f32a5b69a380f176912","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:54.333410Z","signature_b64":"dxb6DmkFM9h7eCTRlijkxYPGThClUbSWP2NS6tRu5snWPDDR5p/+srg5HroagncjaURJ0UqDSw+MI1vJUhZyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4d3e0dc3ed428e4ddb10bf5242c5df2e8a01c1f246b0f32a5b69a380f176912","last_reissued_at":"2026-05-18T01:38:54.332888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:54.332888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.3638","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j+rvxW8efS0xWSkn60aCCHf5uSA69vhc/F7DxqO5HR2TAhbY0ymKw6e8S58W+7CfJzVTdlvEmJ9DDkWWAYofAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:10:33.431371Z"},"content_sha256":"e2b746cee1a8f2081926d78c598da4f2b483a2934598c3efc5ddf9d168e89ba6","schema_version":"1.0","event_id":"sha256:e2b746cee1a8f2081926d78c598da4f2b483a2934598c3efc5ddf9d168e89ba6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6TJ6BXB62QUOJXNRBP2SILC56L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate MMSE Estimator for Linear Dynamic Systems with Gaussian Mixture Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"Fabrice Labeau, Leila Pishdad","submitted_at":"2014-04-14T16:07:11Z","abstract_excerpt":"In this work we propose an approximate Minimum Mean-Square Error (MMSE) filter for linear dynamic systems with Gaussian Mixture noise. The proposed estimator tracks each component of the Gaussian Mixture (GM) posterior with an individual filter and minimizes the trace of the covariance matrix of the bank of filters, as opposed to minimizing the MSE of individual filters in the commonly used Gaussian sum filter (GSF). Hence, the spread of means in the proposed method is smaller than that of GSF which makes it more robust to removing components. Consequently, lower complexity reduction schemes c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3638","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iE5bfVku3vRkBjX5aLdRtkJ5swp9gs3FxlR7UBmyGBNSDCHhKLaxvGKwe7kG1hSSrSDHgHk7IdyfjNdsduHHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:10:33.432038Z"},"content_sha256":"f37fdf95ff628315638c61fa468c765116da7076b3c9ac78a2b60ad2cef19675","schema_version":"1.0","event_id":"sha256:f37fdf95ff628315638c61fa468c765116da7076b3c9ac78a2b60ad2cef19675"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6TJ6BXB62QUOJXNRBP2SILC56L/bundle.json","state_url":"https://pith.science/pith/6TJ6BXB62QUOJXNRBP2SILC56L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6TJ6BXB62QUOJXNRBP2SILC56L/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-12T03:10:33Z","links":{"resolver":"https://pith.science/pith/6TJ6BXB62QUOJXNRBP2SILC56L","bundle":"https://pith.science/pith/6TJ6BXB62QUOJXNRBP2SILC56L/bundle.json","state":"https://pith.science/pith/6TJ6BXB62QUOJXNRBP2SILC56L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6TJ6BXB62QUOJXNRBP2SILC56L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6TJ6BXB62QUOJXNRBP2SILC56L","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e284b849c80319dbc37d3fb506ee2a2cd7ed33e6c38bceb9b30bdc938bb8d624","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-04-14T16:07:11Z","title_canon_sha256":"772d4d68f8626b094ee7e21e3ff1532db4c71199ded25f2afe1c65bc1ea09add"},"schema_version":"1.0","source":{"id":"1404.3638","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3638","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3638v2","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3638","created_at":"2026-05-18T01:38:54Z"},{"alias_kind":"pith_short_12","alias_value":"6TJ6BXB62QUO","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6TJ6BXB62QUOJXNR","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6TJ6BXB6","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:f37fdf95ff628315638c61fa468c765116da7076b3c9ac78a2b60ad2cef19675","target":"graph","created_at":"2026-05-18T01:38:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this work we propose an approximate Minimum Mean-Square Error (MMSE) filter for linear dynamic systems with Gaussian Mixture noise. The proposed estimator tracks each component of the Gaussian Mixture (GM) posterior with an individual filter and minimizes the trace of the covariance matrix of the bank of filters, as opposed to minimizing the MSE of individual filters in the commonly used Gaussian sum filter (GSF). Hence, the spread of means in the proposed method is smaller than that of GSF which makes it more robust to removing components. Consequently, lower complexity reduction schemes c","authors_text":"Fabrice Labeau, Leila Pishdad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-04-14T16:07:11Z","title":"Approximate MMSE Estimator for Linear Dynamic Systems with Gaussian Mixture Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3638","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e2b746cee1a8f2081926d78c598da4f2b483a2934598c3efc5ddf9d168e89ba6","target":"record","created_at":"2026-05-18T01:38:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e284b849c80319dbc37d3fb506ee2a2cd7ed33e6c38bceb9b30bdc938bb8d624","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2014-04-14T16:07:11Z","title_canon_sha256":"772d4d68f8626b094ee7e21e3ff1532db4c71199ded25f2afe1c65bc1ea09add"},"schema_version":"1.0","source":{"id":"1404.3638","kind":"arxiv","version":2}},"canonical_sha256":"f4d3e0dc3ed428e4ddb10bf5242c5df2e8a01c1f246b0f32a5b69a380f176912","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4d3e0dc3ed428e4ddb10bf5242c5df2e8a01c1f246b0f32a5b69a380f176912","first_computed_at":"2026-05-18T01:38:54.332888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:54.332888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dxb6DmkFM9h7eCTRlijkxYPGThClUbSWP2NS6tRu5snWPDDR5p/+srg5HroagncjaURJ0UqDSw+MI1vJUhZyBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:54.333410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.3638","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2b746cee1a8f2081926d78c598da4f2b483a2934598c3efc5ddf9d168e89ba6","sha256:f37fdf95ff628315638c61fa468c765116da7076b3c9ac78a2b60ad2cef19675"],"state_sha256":"17033722bfaa5f74f31ff5a54158ea57173172093995b908cbd7270eb1026353"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+5o0Kgp0N2Ik419Y1yz8o9MeRWuqyIPHA3Tz/veAMRCeOHpY3icn8qnNXOADGoc31SHHZ2SV+kR0uDEcDFyOCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:10:33.436678Z","bundle_sha256":"369e6b512ceb36176b57683d17867bee17077aad2795edc87bc0dd1549919df1"}}